Marek P Kobylański

Agnieszka Tercjak

Hynd Remita

Xiajiao Yuan

Onur Cavdar

Junkal Gutierrez

Adriana Zaleska-Medynska

A PEDOT-Pt-TiO 2 hybrid material synthesized by the casting method for photocatalytic hydrogen generation

Keywords: Hybrid nanomaterials, Titanium dioxide nanotube arrays, Radiolysis, The casting method, Hydrogen-photogeneration catalysis

This study describes the synthesis and characterization of a hybrid material consisting of titanium dioxide nanotube arrays (TiO 2 NTs) modified by platinum nanoparticles (Pt-TiO 2 NTs) via radiolysis and a conductive poly(3,4-ethylenedioxythiophene) (PEDOT) layer, for the first time. The NTs were fabricated by a two-step anodic oxidation process and exhibited different morphologies using electrolyte solutions with different water contents (2-10 vol%).

The polymer layer of poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) (PEDOT: PSS) was coated on the Pt-TiO 2 scaffold using the casting method. The PEDOT: PSS-PT-TiO 2 NTs exhibited stability in the photocatalytic process after additional calcination; the nanotubes with lengths of ~3 µm exhibited the highest photocatalytic activity (~4.5x10 -3 µmol•cm -2 of H 2 ). Additionally, the samples obtained from electrolyte solutions containing 5 and 10 vol% water exhibited nanostructures with the highest catalytic activity.

Introduction

Composites containing semiconductors and polymers have been extensively investigated in the last 10 years due to their unique properties. Polymeric materials enhance the optical, conductive, and photocatalytic properties of nanotubes [START_REF] Abdelnasser | Enhanced photocatalytic performance of poly(3,4-ethylenedioxythiophene)-coated TiO 2 nanotube electrodes[END_REF][START_REF] Yang | In-situ fabrication of diketopyrrolopyrrole-carbazole-based conjugated polymer/TiO 2 heterojunction for enhanced visible light photocatalysis[END_REF], forming materials with high surface areas, good conductivity [START_REF] Wang | A Scalable route to prepare core-shell structured ZnO@PEDOT nanowires and PEDOT nanotubes and their properties as electrode materials[END_REF][START_REF] Szkoda | Electrodes consisting of PEDOT modified by Prussian Blue analogues deposited onto titania nanotubestheir highly improved capacitance[END_REF], and biocompatibility [START_REF] Huang | Modulating cell-uptake behavior of Au-based nanomaterials via quantitative biomolecule modification[END_REF]. TiO 2 nanotubes (TiO 2 NTs) are nanotubular structures that are commonly modified by polymeric materials [START_REF] Abbas | Recent advances in the use of TiO 2 nanotube powder in biological, environmental, and energy applications[END_REF]. They have been utilized in medicine [START_REF] Torres | PAMAM-grafted TiO 2 nanotubes as novel versatile materials for drug delivery applications[END_REF], water and air treatment [START_REF] Wu | Selective removal of perfluorooctanoic acid using molecularly imprinted polymer-modified TiO 2 nanotube arrays[END_REF], electronic devices [START_REF] Sidhu | Solution processed TiO 2 nanotubular core with polypyrrole conducting polymer shell structures for supercapacitor energy storage devices[END_REF][START_REF] Jia | Photoelectrochemical properties of polypyrrole/TiO 2 nanotube arrays nanocomposite under visible light[END_REF], lithiumion batteries [START_REF] Plylahan | Enhanced electrochemical performance of Lithium-ion batteries by conformal coating of polymer electrolyte[END_REF][START_REF] Kyeremateng | Electrodeposited copolymer electrolyte into nanostructured titania electrodes for 3D Li-ion microbatteries[END_REF][START_REF] Plylahan | Highly conformal electrodeposition of copolymer electrolytes into titania nanotubes for 3D Liion batteries[END_REF], sensors [START_REF] Wang | CO gas sensitivity and its oxidation over TiO2 modified by PANI under UV irradiation at room temperature[END_REF][START_REF] Victorious | Integrating TiO 2 annoparticles within a catecholic polymeric network enhances the photoelectrochemical response of biosensors[END_REF], and solar cells [START_REF] Ma | Fabrication of polymer/TiO 2nanotube-based hybrid structures using a solvent-vapor-assisted coating method[END_REF][START_REF] Baran | Preparation and characterization of poly (3-hexylthiophene) sensitized Ag doped TiO 2 nanotubes and its carrier density under solar light illumination[END_REF][START_REF] Imaz | anodic ordered titania nanostructures and in-situ electropolymerized poly-3-methylthiophene films for hybrid photovoltaic solar cells[END_REF].

Numerous investigations have focused on using nanoparticles to enhance the properties of polymers [START_REF] Bustamante-Torres | Polymeric Composite of Magnetite Iron Oxide Nanoparticles and Their Application in Biomedicine: A Review[END_REF][START_REF] Garavand | A comprehensive review on the nanocomposites loaded with chitosan nanoparticles for food packaging[END_REF][START_REF] Moya Betancourt | Effect of and polymeric-modified magnetic nanoparticles on the drug ion transfer across liquid/liquid interfaces[END_REF][START_REF] Yuan | Modified Polypyrrole Nanostructures with Nanoparticles (Pt, Ni) as Photocatalysts for H2 Generation[END_REF][START_REF] Yuan | Remita Highly promoted photocatalytic hydrogen generation by multiple electron transfer pathways[END_REF]. However, the ability of polymers to intensify the features of nanomaterial scaffolds using a semiconductor still requires investigation. Hence, this study aimed to synthesize and analyze the properties of a polymer-modified inorganic nanomaterial.

Synthesizing nanoparticles using a polymer-material-embedded matrix is a major challenge.

Moreover, the synthetic strategy used to fabricate NT-polymers hybrid materials determine the morphology and properties of the new material. Thus, the matrix, its morphology, and potential applications should be considered while selecting the modification route [START_REF] Abdelnasser | Enhanced photocatalytic performance of poly(3,4-ethylenedioxythiophene)-coated TiO 2 nanotube electrodes[END_REF].

Hierarchical TiO 2 NTs obtained via anodic oxidation are used as scaffolds for polymeric materials [START_REF] Imaz | anodic ordered titania nanostructures and in-situ electropolymerized poly-3-methylthiophene films for hybrid photovoltaic solar cells[END_REF][START_REF] Kowalski | Polypyrrole self-organized nanopore arrays formed by controlled electropolymerization in TiO 2 nanotube template[END_REF][START_REF] Cai | Immobilization of Pt nanoparticles via rapid and reusable electropolymerization of dopamine on TiO 2 nanotube arrays for reversible SERS substrates and nonenzymatic glucose sensors[END_REF][START_REF] Plylahan | High energy and power density TiO 2 nanotube electrodes for single and complete lithium-ion batteries[END_REF]. Electropolymerization is commonly used to synthesize hybrid materials composed of TiO 2 NTs and polymers [START_REF] Kyeremateng | Electrodeposited copolymer electrolyte into nanostructured titania electrodes for 3D Li-ion microbatteries[END_REF][START_REF] Plylahan | Highly conformal electrodeposition of copolymer electrolytes into titania nanotubes for 3D Liion batteries[END_REF][START_REF] Kowalski | Polypyrrole self-organized nanopore arrays formed by controlled electropolymerization in TiO 2 nanotube template[END_REF][START_REF] Cai | Immobilization of Pt nanoparticles via rapid and reusable electropolymerization of dopamine on TiO 2 nanotube arrays for reversible SERS substrates and nonenzymatic glucose sensors[END_REF][START_REF] Plylahan | High energy and power density TiO 2 nanotube electrodes for single and complete lithium-ion batteries[END_REF][START_REF] Ambade | Polythiophene infiltrated TiO 2 nanotubes as high-performance supercapacitor electrodes[END_REF][START_REF] Kyeremateng | Electropolymerization of copolymer electrolyte into titania nanotube electrodes for high-performance 3D microbatteries[END_REF][START_REF] Duan | Sulfonated poly(phenylene oxide)/Ti 3+ /TiO 2 nanotube arrays membrane/electrode with high performances for lithium ion battery[END_REF]; This synthetic route enables the fabrication of conductive polymer layers using monomers coupled to an electrode surface.

The growth rate and thickness of the polymer layer can be controlled by the current density, applied voltage, and charge values [START_REF] Ambade | Controlled growth of polythiophene nanofibers in TiO 2 nanotube arrays for supercapacitor applications[END_REF]. However, the practicability of this method is limited due to scaling-up difficulties [START_REF] Abdelnasser | Enhanced photocatalytic performance of poly(3,4-ethylenedioxythiophene)-coated TiO 2 nanotube electrodes[END_REF]. Hybrid materials containing polymer-modified TiO 2 NTs are also fabricated via casting, spin-coating and dip-coating [START_REF] Abdelnasser | Enhanced photocatalytic performance of poly(3,4-ethylenedioxythiophene)-coated TiO 2 nanotube electrodes[END_REF][START_REF] Ma | Fabrication of polymer/TiO 2nanotube-based hybrid structures using a solvent-vapor-assisted coating method[END_REF][START_REF] Baran | Preparation and characterization of poly (3-hexylthiophene) sensitized Ag doped TiO 2 nanotubes and its carrier density under solar light illumination[END_REF]; these methods utilize matrix and polymer solutions, making them easily retriable. Surprisingly, very few studies have utilized these methods to synthesize hybrid materials.

Therefore, this study aimed to fabricate and characterize photoactive hybrid materials containing TiO 2 NTs and a conductive polymer (PEDOT). Platinum particles were deposited on the surface of the TiO 2 NTs via radiolysis to improve the photocatalytic properties of the composites [START_REF] Nischk | Enhanced photocatalytic, electrochemical and photoelectrochemical properties of TiO 2 nanotubes arrays modified with Cu, AgCu and Bi nanoparticles obtained via radiolytic reduction[END_REF]. Additionally, the effects of the morphology and synthetic route of the TiO 2 -NT matrix on the hybrid material were analyzed to optimize the conditions for the fabrication of Pt-polymer-TiO 2 -NT hybrid materials for the model reaction of hydrogen photogeneration.

Material and Methods

TiO 2 NT fabrication

Titanium foil (Sigma Aldrich) was cut into pieces (3 cm x 2 cm), cleaned using ultrasound for 10 min in acetone, isopropanol, methanol, and deionized water, and subsequently dried in a stream of air. A cylindrical platinum mesh was used as the counter electrode. The process was carried out at room temperature for 60 min at 40 V using a solution of ammonium fluoride (0.09 M) in a mixture of ethylene glycol and deionized water (90-98 and 2-10% v/v, respectively) as the electrolyte. Anodic oxidation was carried out under 40 V at room temperature using a MANSON SDP 2603 power supply. After anodic oxidation, the NTs were completely removed from the surface using an ultrasonic bath, followed by another anodic oxidation. Subsequently, the samples were dried for 24 h at 80 °C and calcined at 450 °C for 1 h using a temperature gradient of 2 °C/min.

Radiodeposition of platinum particles on the NT surface

Platinum particles were deposited on the surface of the NTs via radiolysis. The determination of the amount of Pt precursor to be used to enable the photocatalytic application of the fabricated materials has been described in the Supporting Materials. After applying 150 µl of a 0.1 M solution of Pt(acac) (Sigma Aldrich) in isopropanol (Sigma Aldrich) on the TiO 2nanotube surface, the samples were placed in a Petri dish, and the platinum ions were reduced by γ-irradiation (2.5 kGy•h -1 ) under a nitrogen atmosphere. Radioreduction, using 60 Co as the source of γ radiation, was continued for 6 h. Radiolysis is a powerful technique to synthesize metal nanoparticles of controlled size, shape and structure in solutions and on supports [START_REF] Belloni | Radiation-induced synthesis of mono-and multimetallic clusters and nanocolloids New[END_REF][START_REF] Kowalska | Modification of titanium dioxide with platinum ions and clusters: Application in photocatalysis[END_REF] . The metal complexes are reduced by solvated electrons and radicals (here alcohol radicals) induced by solvent radiolysis.

Casting of the polymer layer

The samples were modified with the PEDOT: PSS layer, which was cast directly on the surface of the Pt-TiO 2 nanotubes. One drop of the PEDOT: PSS solution was applied on the surface of the matrix, and some samples were additionally heated at 350 °C for 1 h to remove the PSS. Furthermore, the most suitable method for polymer casting on the NT surface was determined (it has been described in the Supporting Materials).

Surface properties

Scanning electron microscope (SEM) images of the surface of analyzed hybrid materials were collected in a Hitachi S-4800 with an accelerating voltage of 5 kV.

X-ray diffraction (XRD) was performed on a Philips PW 1710 diffractometer. The Cu Kα Xray source was set to 40 kV and 100 mA and the hybrid materials were examined at room temperature in the angular range of 10° to 30°.

The elemental compositions of hybrid materials were analyzed by X-ray Photoelectron Spectroscopy (XPS, SPECS). The XPS was equipped with a Phoibos 150 1D-DLD energy analyzer with Al K monochromatic radiation (hν = 1486.7 eV).

The optical properties of the materials were analyzed using a UV 2600 spectrophotometer (Shimadzu) with a barium sulfate integrating sphere attachment as a reference sample. The spectra were recorded in the wavelength range of 300-700 nm.

To estimate the recombination rate of the reactive electron-hole pairs, luminescence spectra of the samples were recorded by an LS-50B luminescence spectrometer (Perkin Elmer) using an excitation wavelength of 300 nm.

Fourier transform infrared spectroscopy (FTIR) spectra were done using a Nicolet Nexus Spectra equipped with a Golden Gate single reflection diamond ATR accessory. The FTIR spectra of hybrid materials were taken with a 2 cm -1 resolution in a wavenumber range from 4000 to 400 cm -1 . A semiconductor characterization system (Keithley model 4200-SCS) was used to study the conductive properties of the hybrid materials. Two-point probe experiments were carried out applying current from X to Y V to verify the response of the investigated hybrid materials.

Photocatalytic hydrogen generation

Unmodified and modified TiO 2 nanotubes were placed in a Teflon reactor (equipped with quartz glass and a cooling system) with a reactor volume of 30 cm 3 . For hydrogen photogeneration, 20 mL of an aqueous solution containing 5 wt% methanol was used at a temperature of 20 °C. An Oriel 1000-W Xe lamp was used as the light source with an irradiation intensity of 100 mW/cm 2 . After placing the sample in the reactor, the reaction space was filled with the methanol solution. Subsequently, the system was purged with nitrogen for air removal and an equilibrium state was attained by constantly stirring the solution at 500 rpm for 30 min. Samples (200 µL) were collected each hour; The hydrogen content was determined by gas chromatography-thermal conductivity detector (GC-TCD) using a calibration curve. The preparation of the calibration curve has been described in the Supporting Materials.

Results

Morphology

Fig. 1 shows the synthesis and modification scheme of the TiO 2 NTs. The samples exhibited different NT morphology, controlled by the water content of the electrolyte used during anodic oxidation (in the range of 2-10% v/v) and the nanotube-layer modification steps. NT modification involved deposition of platinum nanoparticles by radiolysis, PEDOT: PSS layer casting, and the thermal decomposition of PSS. This process was used to analyze the influence of the matrix morphology and its modification on the properties of the hybrid material.

Scanning electron microscopy was used to analyze the surface structure of the synthesized material. As a multistep synthetic procedure was used, the morphology was analyzed after each modification step (Fig. 2). The synthesized NTs exhibited lengths in the range of 2.10-6.60 µm, consistent with previous reports of nanostructures obtained under similar conditions [START_REF] Nischk | Ordered TiO 2 nanotubes: The effect of preparation parameters on the photocatalytic activity in air purification process[END_REF]; the samples obtained using electrolyte solutions containing 5 and 10 vol% water exhibited comparable NT lengths (~3 µm). The synthesized NTs exhibited internal and external diameters in the range of 107-140 nm and 37-85 nm, respectively. Increasing the water content of the electrolyte solution during anodic oxidation increased the external and internal diameters, and the space between the individual nanotubes, thus, increasing the water content decreased the active surface of the hybrid material [35,[START_REF] Kozak | Electrochemically obtained TiO 2 /Cu x O y nanotube arrays presenting a photocatalytic response in processes of pollutants degradation and bacteria inactivation in aqueous phase[END_REF].

Additionally, the space between the nanotubes facilitated the deposition of polymeric material on the walls and deep penetration of the NTs into the scaffold. The diameter dimensions of the PEDOT-Pt-TiO 2 _5% sample could not be accurately defined because the polymer layer filled the spaces between the nanotubes forming a core-sheath structure. The structure did not exhibit any changes on annealing (to thermally degrade PSS from the polymer layer), and no significant differences were observed in the recorded photos after calcination at 350 °C.

Notably, the morphology of the Pt-TiO 2 _5% sample singularized after modification by the PEDOT: PSS layer; the polymer layer filled the spaces between the NTs, coating each nanotube. Its morphology remained unchanged after the thermal decomposition of PSS through calcination. The core-shell structure prevented the unequivocal determination of the NT diameter size for PEDOT:PSS-Pt-TiO 2 _5% and PEDOT-Pt-TiO 2 _5%.

Surface properties

XRD patterns were recorded for the Pt-TiO 2 samples fabricated using electrolytes containing different amounts of water (Fig. 3 XPS analysis was used to determine the elemental composition of the samples after platinum radioreduction (Table S2). Although oxygen, titanium, nitrogen, and carbon were detected on the surface of each sample, the presence of platinum could not be confirmed by the XPS analysis. This is possibly because XPS analyzes a small area of the sample. It is possible that platinum nanoparticles are deposided inside the sample [35, [39].

Subsequently, attenuated total reflectance-fourier transform infrared (ATR-FTIR) spectroscopy was used to characterize the samples further (Fig. S2-). Signals were observed in the range of 1250-1100 cm -1 due to the SO 3-group of PSS [START_REF] Pasha | Conductivity and dielectric properties of PEDOT-PSS doped DMSO nano composite thin films[END_REF]. The thermal degradation of PSS was confirmed by a lack of the SO 3-signals in the samples annealed at 350 °C (marked as PEDOT) and the presence of peaks attributed to C-O-C (1250 cm -1 ) and C=C bonds (1600 cm -1 ) [START_REF] Susanti | Effect of localized surface plasmon resonance from incorporated gold nanoparticles in PEDOT:PSS hole transport layer for hybrid solar cell applications[END_REF]. The unmodified nanotubes exhibited a signal at 500 cm -1 due to Ti [START_REF] Susanti | Effect of localized surface plasmon resonance from incorporated gold nanoparticles in PEDOT:PSS hole transport layer for hybrid solar cell applications[END_REF][START_REF] Niu | Fabrication and antibacterial properties of cefuroximeloaded TiO 2 nanotubes[END_REF].

Notably, all the samples exhibited similar spectra after the same modification step, regardless of the electrolyte composition (i.e., the morphology of the samples).

To confirm the presence of platinum in the NTs, conductivity tests were carried out before and after radiolysis (Fig. S1). The conductivity increased after modification by γ-irradiation; This was attributed to the deposition of platinum particles on the NTs [START_REF] Th | Electrical conductivity study of hydrogen spillover on TiO 2[END_REF].

Photocatalytic hydrogen generation

The model reaction of photocatalytic hydrogen generation was used to investigate the photocatalytic activity of the TiO 2 NTs modified by the conductive polymer; The results are summarized in Table 3. Materials containing PEDOT: PSS were unstable in aqueous phase; thus, they were not tested in the model reaction.

As shown in Fig. 4, the modification of the TiO 2 NTs with platinum and the conductive polymer increased their hydrogen-generation efficiency. PEDOT-Pt-TiO 2 _10%

exhibited the highest photocatalytic activity with 4.5x10 -3 µmol•cm -2 of photogenerated hydrogen after 4 h of irradiation. Similar hydrogen production (4.3x10 -3 µmol•cm -2 after 4 h of irradiation) was observed using the NTs fabricated in the electrolyte contained 5 vol% water.

The aforementioned photocatalysts exhibited similar NT-layer thickness values (of ~3 µm); Therefore, a TiO 2 -NT length of 3 µm is optimal for the hydrogen generation process.

Furthermore, the TiO 2 _2% sample, with the longest nanotubes (~6 µm), exhibited the lowest hydrogen-photogeneration activity. Earlier reports indicate that the TiO 2 NTs obtained in electrolytes containing 2 vol% of water exhibit enhanced photocatalytic activity in the model reaction of pollutant photodecomposition [START_REF] Nischk | Enhanced photocatalytic, electrochemical and photoelectrochemical properties of TiO 2 nanotubes arrays modified with Cu, AgCu and Bi nanoparticles obtained via radiolytic reduction[END_REF][START_REF] Belloni | Radiation-induced synthesis of mono-and multimetallic clusters and nanocolloids New[END_REF][START_REF] Kowalska | Modification of titanium dioxide with platinum ions and clusters: Application in photocatalysis[END_REF][START_REF] Susanti | Effect of localized surface plasmon resonance from incorporated gold nanoparticles in PEDOT:PSS hole transport layer for hybrid solar cell applications[END_REF]. Additionally, they indicate that the TiO 2 -NT lengths exhibiting the highest photocatalytic activity for pollutant photodegradation in the water and gas phase cannot be effectively used for hydrogen photogeneration. This is consistent with the results of this study.

Very few publications describe the utilization of TiO 2 NTs for hydrogen photogeneration. The earliest publication describes a photocatalyst (TiO 2 NTs modified by Pt nanoparticles; with NTs exhibiting an inner diameter of 120 nm and length of 10 µm) with a higher hydrogenphotogeneration efficiency (25.0 μmol h -1 •cm -2 ) than that obtained in this study [START_REF] Sun | Synthesis and characterization of highly ordered TiO 2 nanotube arrays for hydrogen generation via water splitting[END_REF]. Another publication describes a hydrogen photogeneration process utilizing Pt-modified TiO 2 NTs obtained by an anodic oxidation process with a powder-form photocatalyst [START_REF] Antony | Efficient photocatalytic hydrogen generation by Pt modified TiO 2 nanotubes fabricated by rapid breakdown anodization[END_REF]; This process produces 30 mmol•g -1 •h -1 of photogenerated hydrogen, which is higher than the efficiency of the photocatalyst in the form of a thin NT film on a Ti plate. However, the separation and reuse of photocatalysts in the powder form from electrolytes is challenging. According to previous publications, nanotubes fabricated by the hydrothermal method exhibit a hydrogenphotogeneration efficiency of 0.27 µm•min -1 [START_REF] D'elia | Impact of three different TiO 2 morphologies on hydrogen evolution by methanol assisted water splitting: Nanoparticles, nanotubes and aerogels[END_REF] and 15.7 mmol•g -1 •h -1 [START_REF] Xu | Highly efficient CuO incorporated TiO 2 nanotube photocatalyst for hydrogen production from water[END_REF].

This study could not confirm an enhancement in the photocatalytic properties of Pt-TiO 2 on modification with a conductive polymer. Only the Pt-TiO 2 _10% sample exhibited an increase in hydrogen photogeneration after polymer-layer casting; for the remaining samples, hydrogen photogeneration decreased on modification with the polymeric material (Fig. 4).

Authorship Statement

Fig. 1 .

 1 Fig. 1. The manufacture of PEDOT-Pt-TiO 2 NTs (showing the intermediate stages).

Fig. 2 .

 2 Fig. 2. Morphology of TiO 2 NTs fabricated using electrolyte solutions containing different amounts of water (horizontal); their surfaces after each modification step (vertical).

  (a)); additionally, a PEDOT-Pt-TiO 2 _2% analysis was carried out after each modification step (Fig.3(b)). All the diffractograms exhibited signals characteristic to anatase at 2θ = 25 ° and titanium form (Ti foil) at 2θ = 40 ° [37]. The samples fabricated using electrolytes with different water contents exhibited similar results. The diffractogram of the NTs modified by PEDOT: PSS exhibited a wide signal in the range of 2θ = 15-35° due to the presence of PEDOT: PSS on the NT surface [38].

Fig. 3 .

 3 Fig. 3. XRD patterns for samples obtained: (a) Using electrolyte solutions containing different

Fig. 4 .

 4 Fig. 4. Photocatalytic activities of the hydrogen photogeneration reaction exhibited by the

Table 1 .

 1 Morphology of the TiO 2 NTs before and after each modification step

			Length	Inner diameter	External diameter
	Sample label	Preparation
			(µm)	(nm)	(nm)
	TiO 2 _2%	2-step anodization, calcination at 450 °C	6.50 ± 0.2	107 ± 10	37 ± 5
	TiO 2 _5%		3.10 ± 0.1	113 ± 12	71 ± 1
	TiO 2 _7%		2.10 ± 0.1	120 ± 8	78 ± 2
	TiO 2 _10%		3.15 ± 0.2	127 ± 7	79 ± 3
	Pt-TiO 2 _2%	2-step anodization, calcination at 450 °C, radioreduction of Pt 6.35 ± 0.2	106 ± 8	40 ± 4
	Pt-TiO2 5%		3.25 ± 0.1	108 ± 9	73 ± 2
	Pt-TiO 2 _7%		2.10 ± 0.1	119 ± 8	75 ± 3
	Pt-TiO 2 10%		3.30 ± 0.2	125 ± 5	81 ± 4
	PEDOT:PSS-Pt-TiO 2 _2% 2-step anodization, calcination at 450 °C, radioreduction of Pt,	6.60 ± 0.1	111 ± 13	71 ± 8
	PEDOT:PSS-Pt-TiO 2 _5%	PEDOT: PSS casting	3.00 ± 0.1	115 ± 8	75 ± 7
	PEDOT:PSS-Pt-TiO 2 _7%		2.15 ± 0.2	130 ± 10	65 ± 8
	PEDOT:PSS-Pt-TiO 2 _10%		3.20 ± 0.3	120 ± 8	73 ± 7
	PEDOT-Pt-TiO 2 _2%	2-step anodization, calcination at 450 °C, radioreduction of Pt,	6.20 ± 0.2	104 ± 8	63 ± 9
	PEDOT-Pt-TiO 2 _5%	PEDOT: PSS casting, calcination at 350 °C	3.20 ± 0.3	----	55 ± 7
	PEDOT-Pt-TiO 2 _7%		2.30 ± 0.2	147 ± 20	63 ± 9
	PEDOT-Pt-TiO 2 _10%		3.50 ± 0.3	140 ± 17	85 ± 11

Table 2 .

 2 Photocatalytic activities of the TiO 2 nanotubes and hybrid materials (PEDOT-Pt-TiO 2 ) in the model reaction of hydrogen photogeneration.

	Sample label	Amount of hydrogen after 4 h of irradiation
		(µmol•cm -2 )
	TiO 2 _2%	1.84 x 10 -4
	TiO 2 _5%	7.15 x 10 -4
	TiO 2 _7%	3.30 x 10 -4
	TiO 2 _10%	5.11 x 10 -5
	Pt-TiO 2 _2%	6.62 x 10 -4
	Pt-TiO 2 _5%	4.60 x 10 -3
	Pt-TiO 2 _7%	2.75 x 10 -3
	Pt-TiO 2 _10%	3.45 x 10 -3
	PEDOT:PSS-Pt-TiO 2 _2%	Sample unstable in aqueous solution
	PEDOT:PSS-Pt-TiO 2 _5%	Sample unstable in aqueous solution
	PEDOT:PSS-Pt-TiO 2 _7%	Sample unstable in aqueous solution
	PEDOT:PSS-Pt-TiO 2 _10%	Sample unstable in aqueous solution
	PEDOT -Pt-TiO 2 _2%	9.75 x 10 -5
	PEDOT -Pt-TiO 2 _5%	4.33 x 10 -3
	PEDOT -Pt-TiO 2 _7%	1.52 x 10 -3
	PEDOT -Pt-TiO 2 _10%	4.51 x10 -3

Acknowledgments

This research was funded by the Polish National Science Center, grant number 2017/27/N/ST8/00946.

Declaration of Competing Interest

The authors have no conflicts of interest to declare that are relevant to the content of this article.


Singh Gopal

Phartiyal
email: gphartiyal@ec.iitr.ac.in

Dharmendra Singh

Hussein Yahia

Improved Mapping of Flood Affected Villages in India: A Novel Three-Stage Approach Using PolSAR Polarization Signatures and Ensembled Dilated CNNs

Keywords: Fully polarimetric SAR, Polarization Signatures, Ensembled-Dilated-Convolutions

During floods, updated and accurate information on affected human settlements helps save lives and reduces time to rescue. Therefore, approaches that can provide reliable information during floods via the use of all-weather and real-time functional technology is highly needful. The study presented here attempts to efficiently and precisely map human settlements in the Indian sub-continent during floods via a three-stage approach which uses PolSAR data. However, the sagregation of human settlements in India even with PolSAR data is challenging because the built-up structures in the villages of rural India are closely packed and are randomly oriented w.r.t. each other. This condition either hinders their segregation or otherwise induces false alarms during extraction. More descriptive land cover characterization features and powerful feature classifiers may address this challenge. The study in this paper proposes a novel approach to efficiently detect and map flood affected villages which utilize polarization signatures from PolSAR imagery, ensemble-ofdilated-convolutions based CNNs, apriori knowledge, and image morphology. The approach broadly involves three stages; -first, built-up area extraction from a PolSAR image, -second, detection of villages in a built-up area image and, -third, identification and mapping of villages that are affected by the flood. In the first stage, an ensemble of varying dilated-convolutions based novel CNN classifier which directly utilizes PolSAR-2 polarization signatures (PSs) in window-mode as features are developed to extract built-up areas. The second stage provides a novel village detection filter based on apriori knowledge and image morphology to detect actual villages and mask out the false objects.

Finally, in the third stage, flood affected villages are mapped via a series of morphological operations based degree-of-intersection measure. Experiments are conducted on both; simulated and natural flooded area datasets. Experimental results show 81% detection accuracy and 100% mapping performance of the proposed approach which indicates its potential as an effective flood affected village mapping system.

Introduction

A significant 65% of the Indian population lives in towns and villages and floods are the most frequent, widespread, and damaging disasters for majority this population (Flood Affected Area Atlas of India -Satellite Based Study 2023;Jain and Singh 2023). During floods in Indian villages, monitoring and dissemination of rescue operations becomes both critical and challenging at the same time (Mukherjee 2023). Crucial due to the fact that a large proportion of population lives here and challenging because of resiource constraints in these regions for frequent update on the situation. A very good example of resource constraints on rural India compared to urban cities is the study done by researchers in (Young et al. 2022). The study highlights the difference in the social media resoiurce exploitation for information and rescue updates between major cities like Kochi and Tiruvananthpuram and other rural districts of Kerala.

Therefore, to address this crucial but challebging task, a rapid and reliable monitoring is key to minimize the loss of human lives and property in rural parts of India. An accurate and updated near-real-time information of flood affected rural areas can lead to an efficient disaster mitigation plans.

In terms of technologies for flood affected area monitoringin rural India, satellite imaging is one of the most helpful and reliable technology. This resource is geographicaly and socialy unconstrained i.e same fidelity to cities and villages . Especially, the synthetic aperture radar (SAR) imaging modality has proved to be a very effective and all-weather successful technology for monitoring flood affected areas and planning rescue operations (Martinis et a{Citation}l., 2015), [START_REF] Giustarini | A Change Detection Approach to Flood Mapping in Urban Areas using TerraSAR-X[END_REF] [START_REF] Sharma | SAR for Disaster Management[END_REF].

In particular, the ability of satellite PolSAR imaging instruments to remotely sense the changes in polarization states which in-turn are introduced by the "interaction" of EM waves with earth surface objects (in this case, land covers).

For example, built-up structures usually show double bounce scattering response. It means that these built-up structures appear bright (high backscattering response) in the "HH" image.

Whereas, tall vegetation (e.g. forests) show volume scattering response (bright in in "HV" image), and smooth surfaces such as water show single bounce scattering response.

PolSAR imaging has also proved its popularity, significance and unique effectiveness in flood monitoring and mitigation also [START_REF] Pradhan | A New Semiautomated Detection Mapping of Flood Extent from TerraSAR-X Satellite Image Using Rule-Based Classification and Taguchi Optimization Techniques[END_REF] [START_REF] Schnebele | Real Time Estimation of the Calgary Floods Using Limited Remote Sensing Data[END_REF] [START_REF] Dasgupta | Optimized GLCM-based Texture Features for Improved SAR-based Flood Mapping[END_REF] [START_REF] Giustarini | A Change Detection Approach to Flood Mapping in Urban Areas using TerraSAR-X[END_REF] However, mapping human settlements during floods in India is difficult even with PolSAR imagery. The built-up structures (e.g.: Houses) in these human settlements (especially in villages of rural India), are closely packed and randomly oriented with respect to reach other.

Therefore, these villages show volume scattering response along with double bounce scattering response in a PolSAR image. The mixed scattering response from these villages hinders their segregation from tall vegetation in a PolSAR image [START_REF] Garg | Development of an Efficient Contextual Algorithm for Discrimination of Tall Vegetation and Urban for PALSAR Data[END_REF][START_REF] Mishra | Critical Analysis of Model-Based Incoherent Polarimetric Decomposition Methods and Investigation of Deorientation Effect[END_REF][START_REF] Phartiyal | An improved land cover classification using polarization signatures for PALSAR 2 data[END_REF]. Therefore, the detection and mapping of these villages during a flood event is challenging even with PolSAR imagery as there is high risk of false alarms and hence ineffective rescue operations. To address such challenges, raw PolSAR data has been transformed and represented in different bases and forms namely decompositions, factorizations, coherency, covariance etc. in various flood monitoring studies [START_REF] Dasgupta | Optimized GLCM-based Texture Features for Improved SAR-based Flood Mapping[END_REF][START_REF] Dumitru | Data analytics for rapid mapping: Case study of a flooding event in Germany and the tsunami in Japan using very high resolution SAR images[END_REF][START_REF] Manavalan | Landuse / Landcover based Flood Area Assessment using L-and C-band SAR Data of Coastal Region of Andhra Pradesh, India[END_REF][START_REF] Silvana | Adaptive SAR Image Processing Techniques to Support Flood Monitoring from Earth Observation Data[END_REF]. The current study proposes the utilization of PolSAR polarization signatures (PSs) features for the detection and mapping of villages that are affected by flood.

Polarization signature (PS) is a two-dimensional or 2D representation depicting backscatter response from any target at a particular polarization state. Polarization signature or PSs are introduced in [START_REF] Kennaugh | Effects of type of polarization on echo characteristics[END_REF] and has been depicted graphically by many researchers in different perspectives [START_REF] Bielecka | SAR Images Analysis based on Polarimetric Signatures[END_REF][START_REF] Van Zyl | Imaging radar polarization signatures: Theory and observation[END_REF]. PSs have been proved useful for characterization of land covers [START_REF] Jafari | A New Method for Land Cover Characterization and Classification of Polarimetric SAR Data Using Polarimetric Signatures[END_REF] [START_REF] Phartiyal | An improved land cover classification using polarization signatures for PALSAR 2 data[END_REF]. A comparison of PSs-based features and decomposition-based features for land cover characterization is presented in [START_REF] Phartiyal | An improved land cover classification using polarization signatures for PALSAR 2 data[END_REF]. Their study demonstrates the significance of the utilization of PSs over decomposition-based features for land cover characterization and classification in mixed land cover scenarios. This is motivating since a similar scenario is at hand here and therefore, the current study considers PSs as PolSAR features. Theoretical background on PSs is discussed under section 2.

A lack of studies that directly utilize the PSs is notable although normalized signature correlation mapper (NSCM), a correlation-based measure, and normalized Euclidean distance (NED), a distance-based measure, are the popular PSs-derived features used in various applications [START_REF] De Carvalho | Spectral Correlation Mapper (SCM): An Improvement on the Spectral Angle Mapper (SAM)[END_REF], [START_REF] Maurya | A Critical Analysis of Polarimetric Signatures on PALSAR 2 Data for Land Cover Classification[END_REF].. This is because of the fact that PSs are two dimensional features and a two-dimensional feature extractor would be more efficient to exploit it. As of today, convolutional deep neural networks (CNNs) are one of the most popular, efficient, and powerful image (two-dimensional) feature extractors. Their unique characteristic of "local connectivity" and "parameter sharing" makes them best tools to extract complex and localized features from images [START_REF] Lecun | Deep learning[END_REF]. Authors in [START_REF] Phartiyal | Improved Utilization of Polsar Polarization Signatures Using Convolutional-Deep Neural Nets for Land Cover Classification[END_REF] explored the significance of CNNs as PSs feature extractors and indicated to the potential of PSs and CNN based models in other applications. However, more detailed study is required to this end. Therefore, the current study extensively explores the utilization of CNNs as PS feature extractors in order to map flood affected human settlements with PolSAR imagery.

The currrent study also explores the [p;arization signature sub-space via dilated convolutions and aggregates the different convolutions to achieve better performance.

To summarize, this paper presents a novel approach to detect and map villages affected by a flood with the help of PolSAR PSs, CNNs, apriori knowledge and image morphology. The novel approach involves three stages. These are; This paper is divided into following sections. The fundamentals of the CNNs and the PSs are discussed in section 2. Section 3 provides detailed information on the materials used which involves study areas and datasets considered, and ancillary information collected for the study.

Section 4 discusses the three-stage approach development for mapping flood affected villages.

Qualitative and quantitative evaluation of the results is also in this section. At last, section 5 concludes the study.

Theoretical Background

Polarization Signatures

Polarization signature (PS) is a peculiar representation of backscattering behaviour of a target, or in the case of current study, a land cover. PSs are a two-dimensional in nature. In a polarization signature representation, the y-axis and the x-axis represent orientation angle and ellipticity angle respectively and the z-axis represent the received backscattered power coefficient ( o ). The tilt or orientation angle (ψ) spans from 90  o to 90 o whereas the ellipticity angle (χ) spans from 45  o to 45 o The signatures are computed using equation (1). The ellipticity angle represents to the polarization behaviour (i.e. elliptical, circular or linear polarization). On the other hand, the orientation or tilt angle represents to the polarization states (i.e. either horizontal polarization or vertical polarization (Jong-Sen [START_REF] Lee | Polarimetric Property Preservation in SAR Speckle Filtering[END_REF].

    1 1 4 π c o s 2 c o s 2 c o s 2 c o s 2 c o s 2 s in 2 c o s 2 s in 2 s in 2 s in 2 l l m m l l m m l l m m l m k                                                 Κ (1)
where σ represents backscattering coefficient, suffix m and l represent received and transmit combinations respectively. Given the polarization characteristics of the receiving antenna ,K i.e. the Kennaugh matrix, represents the received power [START_REF] Antenna Laboratory | Effects of Type of Polarization on Echo Characteristics[END_REF].

It is alternatively termed as the Stokes scattering operator or the Stokes scattering matrix.

Computation of the kennaugh parameters is done similar to [START_REF] Harold | The Kennaugh Matrix, in: Remote Sensing with Polarimetric Radar[END_REF]. Further, k is the propagation constant. Two variants of PSs are computed namely co-polarized polarization signatures and cross-polarized polarization signatures.

The co-polarized signature is calculated via a transmit and receive settings of . Figure 1 is the co-polarized PS of a sample of a land cover.

Figure 1 Land cover class sample co-polarized signature.

Convolutional Neural Networks

Convolutional neural networks have become a popular neural network type that utilizes the deep learning technology very well. Fundamental CNN models were proposed in (Ian [START_REF] Goodfellow | Deep learning[END_REF] [START_REF] Ciresan | Multi-column Deep Neural Networks for Image Classification[END_REF] [START_REF] Fukushima | Neocognitron: A Self-Organizing Neural Network Model for a Mechanism of Visual Pattern Recognition[END_REF]Miyake, 1982) (LeCun et al., 1998) [START_REF] Zhang | Image Processing of Human Corneal Endothelium Based on a Learning Network[END_REF] (2)

where,  indicates to the convolution operation and pool denotes to a spatial aggregation strategy. Weights of the links connecting the convolutional layer to the layer resides in the matrix whereas the vector b l is the bias term. A non-linear pointwise activation function g(.) is applied Subsequently. For the selection of dominant features, finally, a pooling layer is placed with a certain window.

If required, any number of convolutional and/or pooling layers queued in any order to constitute a feature extraction architecture that is hierarchical in nature. The last convolution or pooling layer features are reprojected to a one-dimensional feature. Further, this feature is input to a "fully connected" or alternatively termed as "dense" layer which can be perceived as a typical multi perceptron layer. At the end of a CNN network, the final layer is usually a dense layer with either a "linear" activation function (for "regression" scenarios) or a dense layer with a "SoftMax" activation function (for "classification" scenarios) layer. The node count at this layer matches the number of outputs desired.

The weights, and the biases, of the CNN represents the parameters of the model. These are learned iteratively and optimized jointly via objective (e.g. overall accuracy in case of classification) optimization over constraints such as "training" set.

Equivalently, models can be realized for 1D or 3D convolution application scenarios.

The aforementioned network in whole, still expresses a single differentiable score function from the 2D input on one end to class scores at the other. The property that 2D CNN architectures make the explicit assumption that the inputs are images. As explored and utilized in the case of PSs in this study which allows encoding certain properties into the architecture.

This in turn make the proceeding operations and functions more efficient. CNNs with deep learning have found their application in PolSAR data as well [START_REF] Zhu | Deep Learning in Remote Sensing: A Comprehensive Review and List of Resources[END_REF].

Materials and Methods

Study Area

For critical analysis, development and evaluation of the proposed three-stage approach, three sites are considered. The first study area is the "Roorkee" city which is situated near the "Rajaji" national park at the foothills of the great Himalayas. This study area spans from

Satellite Data

For the Roorkee and Haridwar study regions, raw single look complex SAR data acquired by the JAXA's PALSAR-2 L-band fully polarimetric SAR instrument onboard the ALOS-2 satellite on March 13, 2015 is considered. The raw "single look complex" PolSAR data is multilooked, speckle filtered, calibrated, and terrain corrected in that order to obtain backscattering ( o ) coefficients [START_REF] Phartiyal | Optimal Use of Polarimetric Signature on PALSAR-2 Data for Land Cover Classification[END_REF]. Speckle filtering with "Gamma MAP" polarimetric filter is performed analogous to [START_REF] Mishra | Critical Analysis of Model-Based Incoherent Polarimetric Decomposition Methods and Investigation of Deorientation Effect[END_REF] with a 3 3  window size. Calibration and terrain correction are performed in method similar to [START_REF] Phartiyal | Optimal Use of Polarimetric Signature on PALSAR-2 Data for Land Cover Classification[END_REF]. 1.

Second, the total number of villages (a common term opted here to represent all types of human settlements in the study region) in each study area are counted for validation of the proposed approach.

Approach, Results, and Discussion

This section discusses the development of the proposed novel approach to detect, identify, and map flood affected villages in a PolSAR image. The overall approach is divided into three stages.

In the first stage, design and development of a PSs based CNN model for extraction of built-up areas from PolSAR image is done. This stage is discussed in sections 4.1 and 4.2. Model performance evaluation and comparisons are also discussed in section 4.2.

In second stage, development of a novel methodology, for designing "village detection filters" based on apriori knowledge and image morphology, is discussed. These filters help in detection of villages in a 'built-up' class image extracted from classification image (stage-1) and also help suppress false alarms. Section 4.3.1 covers the development of this methodology.

Evaluation of the detection performance of this methodology is also covered in section 4.3.1.

Finally, in the third stage, development of methodology, for identification and mapping of villages that are affected by flood and masking out villages that are not, is discussed. This methodology exploits the phenomena of 'enclosed' that happens when a village is surrounded by water (flooded from all sides). Section 4.3.2 discusses the development of this methodology.

Evaluation of this methodology is discussed in section 4.3.2. The three methodologies, proposed in the three stages above, sum up to provide a novel 'flood affected village detection and mapping' approach. Flowchart shown in Figure 5 depicts the overall proposed approach.

Land Cover Polarization Signatures

Based to the discussion in section 2.1, both co-polarized signatures and cross-polarized signatures are computed from PolSAR data using equation (1). Co-polarized PS plots for considered land cover class (averaged over all class samples, refer to Table 1) are shown in Figure 6. Backscatter power response shown in Figure 6 is plotted for orientation angle  range (

Stage 1: PolSig-CNN Classification Model for Built-Up Area Extraction

PSs based features have been used for land cover characterization and classification in many studies. Classifiers in [START_REF] Phartiyal | Optimal Use of Polarimetric Signature on PALSAR-2 Data for Land Cover Classification[END_REF], [START_REF] Jafari | A New Method for Land Cover Characterization and Classification of Polarimetric SAR Data Using Polarimetric Signatures[END_REF] and [START_REF] Maurya | A Critical Analysis of Polarimetric Signatures on PALSAR 2 Data for Land Cover Classification[END_REF] model from here onwards in this paper and, its configuration is provided in Table 2. A twodimensional spatial window of PSs is used as input. The window-based approach, via averaging, helps suppresses the random volume scattering responses generated from closely packed built-up structures in built-up areas. This in turn improves the segregation of these built-up areas. A 3 * 3 window of neighbouring PSs is considered. This corresponds to a 5 4 * 1 1 1 (refer section 4.1) matrix/image as input to the PolSig-CNN model. This 5 4 * 1 1 1 input image has two channels i.e. Signature correlation mapper or SCM is a cross correlogram constructed by calculating the cross-correlation between two polarimetric signatures. The SCM obtained from the Pearson correlation coefficient and varies from -1 to 1. The SCM between two signatures p 1 and p 2 is given by equation (3).

-1-1 10, 9 1 3  , 11  C-1-2 10, 56  , 9 1 8  C-1-3 10, 33  ,18 3 7  ReLU, 0.1 C-2-1 10, 9 1 3  ,11  C-2-2 10, 33  ,11  C-2-3 10, 33  ,11  C-3-1 10, 9 1 3  ,11  C-3-2 10, 55  ,11  C-3-3 10, 55  ,11  C-4-1 15, 1 5 3 3  ,11  C-4-2 15, 55  ,11  C-4-3 15, 55  ,11  C-5-1 15, 1 5 3 3  ,11  C-5-2 15, 6 1 5  ,11  C-5-3 15, 6 1 5  ,
1 2 1 2 1 1 1 1 2 2 2 2 2 1 1 2 2 1 1 1 1 ( , ) m m m m m m m m p p p p S p p m p p m p p                                                        (3)
where m is the number of polarization states (Jafari et al., 2015)(de Carvalho and[START_REF] De Carvalho | Spectral Correlation Mapper (SCM): An Improvement on the Spectral Angle Mapper (SAM)[END_REF]. NSCM is obtained by normalizing the range of SCM between 0 and 1 using equation (4). N 0 .5 *( + 1 ) S S  (4) 21 Euclidean distance (ED) is the distance metric which provides a quantitative measure of the distance between vectors representing the two polarimetric signatures, and it reflects the dissimilarity between the polarimetric signatures (Gower, 1985) [START_REF] Jafari | A New Method for Land Cover Characterization and Classification of Polarimetric SAR Data Using Polarimetric Signatures[END_REF]. The Euclidean distance between two signatures p 1 and p 2 is given by equation ( 5).

2 1 2 1 2 1 ( , ) ( ) m D p p p p    ( 5
)
where m is the number of polarization states. Further, NED is the normalized version of ED. Both NSCM and NED have been utilized for land cover characterization [START_REF] Jafari | A New Method for Land Cover Characterization and Classification of Polarimetric SAR Data Using Polarimetric Signatures[END_REF] and for land cover classification [START_REF] Maurya | A Critical Analysis of Polarimetric Signatures on PALSAR 2 Data for Land Cover Classification[END_REF].

Detection and Mapping of Flood Affected Villages using Apriori Knowledge and Image

Morphology

This section presents post classification methodologies based on apriori knowledge and image morphology to map the villages affected by flood. Flood affected village maps are obtained using the built-up area image obtained in stage 1. This section covers stage 2 and stage 3 of the proposed approach. The methodology presented under stage 2 detects villages in the built-up area image from section 4.2. This methodology utilizes apriori knowledge and image morphology to build village detection filters. Binary morphological image processing is well suited in this case because of the type of outputs produced in stage 1 and the suitability of morphological operations to operate on this data [START_REF] Zou | Object-Based Classification of PolSAR Images Based on Spatial and Semantic Features[END_REF]. These filters detect villages in the built-up area image and significantly remove false alarms or misclassifications.

Development of this methodology is discussed under stage 2 in section 4.3.1.

Stage 3 presents a methodology which further identifies and maps villages that are affected by flood and mask out villages that are not affected by flood from the total villages detected in stage 2. This methodology also utilizes image morphology to map flood affected villages. Development of this methodology is discussed in section 4.3.2.

Stage 2: Village Detection

The focus of this stage is to detect villages in the built-up area image obtained in stage 1 (refer section 4.2). Here, at first, the built-up area image __ a binary image __ is cleaned before detection because the image might contain objects (built-up areas) that are close to each other and could be part of same village or, there might be objects with holes in them which is undesirable. These artefacts could lead to inaccurate detection of villages. Therefore, a series of morphological operations are utilized to clean the binary image. The objects or components which are close to each other, are merged together at first using a morphological image closing filter provided in equation ( 6).

I

. Figure 9(c) depicts the result of the hole filling operation.

Finally, an area limit is set to filter out objects that are not villages. The idea is that if any object is to be a village, it must have at least 5000 m 2 of ground area. The area limit is established based on apriori knowledge of the Indian rural human settlements. An area limit ( L A ) of 5000 m 2 (140 pixels approx. in case of PALSAR-2 image considered here) is set. Equation ( 9)

demonstrates the process of filtering objects based on its area.

f ille d f ilte r e d f ille d L L 1 i f ( ) A ( ) f o r 1, 2 , ..N 0 i f ( ) A K I k I K I O O k O          (9)
where, If the BBOR of a particular object pair is above a predefined threshold, then the corresponding object in the test image is counted a successful detection, otherwise not. The threshold is set to 0.5 based on experiment and is set identical for both Roorkee and Haridwar study areas for consistency purpose.

True positives (successfully detected villages), true negatives (villages missed), and false alarms or false positives (objects detected as villages in the test image but are actually not) are computed using equation ( 11) through ( 14).

m i     (11)
Where, m is the total number of objects (villages) in the reference image, and 1 if th re s h o ld lo g ic a l( ) 0 if th re s h o ld In figure 13(a-c), the flood affected villages are marked with yellow colour and the nonflooded villages are marked with red colour. It is evident from figure 13(a-c) that the methodology proposed in this section successfully identifies and maps villages that are completely affected by flood and masks out villages that are not affected by flood. Although, this methodology includes the step 'generation of artificial flood scenarios', however, in real flood situation, this step is skipped and flooded villages can be directly be mapped. The methodology is also evaluated on real flood scenario and results are highlighted in section 4.4.

x x x          (12)
Overall, two methodologies are proposed in section 4. In the second stage, a novel village detection methodology is developed. The methodology detects whether a particular object in the built-up area image, obtained from stage 1, is a village or not using a village detection filter. The detection filter is built on apriori knowledge on the minimum average size of rural human settlements in India and image morphology. The detection methodology also significantly removed false alarms and false negatives. A strong detection accuracy of 80% is achieved with this methodology. Qualitative results are also in agreement with the performance.

In the third and final stage, flood affected villages are identified and non-flooded villages are masked out using another image morphology-based methodology. This stage-3 mapping methodology computes a degree-of-intersection between successfully detected villages and flooded area masks and utilizes it for identification of flood affected villages. Experiments are conducted on simulated and real flood datasets and performance of the three-stage approach is

  __ first, design and development of PSs based novel CNN model for extraction of built-up areas from PolSAR image which contains the flooded region, __ second, development of methodology for design of village detection filters based on apriori knowledge and image morphology and, __ third, development of another methodology for identification, and mapping of flood affected villages using image morphology.

  landscape including multiple land covers. This study area is termed as 'Roorkee' study area in this paper. Figure2(a) shows a true colour Google Earth image of Roorkee. Another study area is the Haridwar city and its neighbouring region. This area extends from 2 km 2 of landscape again including multiple land covers such as the river Ganges.This second study area is termed as 'Haridwar' study area in this article. Figure3(a) shows a true colour Google Earth image of Haridwar. The third study area is considered for validation of the developed approach. This study area is Patna and neighbouring region which were affected during the 'Bihar 2016' floods.

  Four features namely HH, HV, VH, and VV are achieved. Intuitively, VH and HV are identical and therefore redundant, only HH, VH, and VV are considered further. Figure 2(b) shows a false colour image of the preprocessed Roorkee dataset and Figure 3(b) shows a false colour image of the pre-processed Haridwar dataset. In addition, for the Patna study area, PALSAR-2 PolSAR image acquired on September 3, 2016 is considered as validation data. Ground Truth Ground truth is collected on two counts. First, ground truth sample points are collected for classifier training and validation. Bare soil (BS), built-up, tall vegetation (TV), short vegetation (SV), and water are the five land cover classes considered. On the basis of visual inspection, ground truth class sample points are measured directly on the terrain. A total of 1200 data points are collected separately for two i.e. Roorkee, and Haridwar study areas. More details of the ground truth survey are shown in Table



  Built-up structure: Man-made structures.  Built-up area: A collection of built-up structures.  Village or town: Built-up area larger than a predefined size.  Object: A connected group of image pixels.  Detected villages: Villages that have been successfully detected  Flooded villages: Villages that are affected by flood These terminologies help to better understand the different stages of the study.

Figure 2 .

 2 Figure 2. (a): Imagery of the Roorkee collected from Google Earth with major land cover classes marked. (b): FCC of the pre-processed March 13, 2015 PolSAR data.

Figure 3 .

 3 Figure 3. (a): Imagery of the Haridwar collected from Google Earth with major land cover classes marked. (b): FCC of the pre-processed March 13, 2015 PolSAR data.

Figure 4 .

 4 Figure 4. Areas highlighted in white are villages in the (a) Roorkee and, (b) Haridwar study area.

  ellipticity angle  range ( 45   degree to 45   ) degree and a step size of 5  degree in each direction. This results in a 1 8 3 7  two-dimensional feature space. It is evident from figure 6 that PSs of considered land covers are different from each other.

Figure 5 .

 5 Figure 5.Flowchart of the proposed approach

  used PSs based distance/correlation one-dimensional features which do not consider the twodimensional neighbourhood during classification and therefore PSs remain under-utilized. A PSs based CNN classifier is introduced here which explores and extends to more effective utilization of PSs directly with CNNs in order to extract built-up areas from PolSAR images. In this stage, a CNN model is developed to directly utilize PSs as features for built-up area extraction from PolSAR imagery. The proposed CNN model is termed as 'PolSig-CNN'

  copol, and crosspol. Therefore, the overall size of the input to the PolSig-CNN is 5 4 * 1 1 1 * 2 . The PolSig-CNN used five convolutional layers and three parallel convolutions with different dilation rates. The parallel convolutions with varied dilation rates helps to extract localized polarization feature seb-spaces. This should improve classification performance. The output form these varied convolutions are finally concatenated before connecting to fully connected layers.The number of convolution filters and kernel sizes used in each layer are listed in Table2. ReLU activation function and Dropout fraction of 10% is used in each convolutional layer. The dropout regularization strategy is employed to reduce overfitting and achieve better generalization(Srivastava et al., 2014). Further, two Fully Connected (FC) layers, first with 50 nodes and second with 10 nodes are used. Both FC layers used the ReLU activation function and a Dropout fraction of 10% . Finally, a SoftMax classification layer with 5 output labels is used. The five output labels are; built-up (BU), water, bare soil (BS), tall vegetation (TV), and short vegetation (SV). A batch normalization process is carried out before the convolutions to speed up the training process and to reduce the network sensitivity. Overall, an eight layered PolSig-CNN classification model is realized as shown in Figure7.

Figure 8

 8 Figure 8(a) and figure 8(c) shows the classified image for Roorkee and Haridwar via the

Figure 8

 8 Figure8(e) and 8(g) shows classified images using the NSCM as features for Roorkee

Figure 8 .

 8 Figure 8. Roorkee classified image obtained using; (a). the PolSig-CNN classifier, (e). the NED classifier and, (i); the NSCM classifier. Areas classified as Built-up in Roorkee dataset using;

  image, I is the image on which the morphological closing operation is to be performed, S is the structuring element used in the closing operation, and  &  represents the morphological dilation and erosion operations respectively. The vicinity, within which two objects can be merged together is set via the size of the structuring element parameter.The vicinity is set based on an apriori knowledge of the approximate minimum distance between two villages and PolSAR image pixel resolution.The approximate minimum distance between two villages is set to 200 meters based on ground surveys, geographical metadata. Since, the ALOS PALSAR-2 PolSAR data considered in this study has 6-meter spatial resolution. Therefore, S is set as a disc of 15 pixels' diameter (100 meters) and two objects within this distance are merged as one. However, similar relationship can be modelled with other PolSAR imagery. Figure9(b) depicts the effects of closing operation. It can be observed from figure 9(b) that some objects are merged together. Next, the holes in the objects in the c lo s e d I image are to be filled. The holes are filled using equation (7).

  with holes obtained from equation (6), U is the union operator, and k X is obtained through iterative process governed by equation

  area limit and, N is the total number of objects in fille d I image.

Figure 9

 9 Figure 9(d) depicts output of the area-based filtering. It is observed from Figure 9(d) that many

Figure 9

 9 Figure 9 (a). Segment of image shown in figure 6(a). Corresponding segments of: (b). Image after the closing operation, (c) Image after the holes filling operation and, (d). image after the filtering operation

i 1 T

 1 ru e P o s itiv e (T P ) lo g ic a l(IO U th re s h o ld )

F

  a ls e N e g a tiv e ( T N ) T o ta l n u m b e r o f v illa g e s in r e f e r e n c e im a e P o s itiv e (F P ) T o ta l n u m b e r o f o b je c ts in t e s t im a g e T P   (14) True positives (TP), False negatives (FN), false positives (FP), and intersection over union (IoU) are computed for Roorkee and Haridwar study areas for PolSig-CNN, NED, and NSCM.

  figure 12(a), flood (highlighted in blue) has affected the whole study region whereas in the

  3. The stage-2 methodology detects villages and removes false alarms and misclassifications in a built-up area image. The stage-3 methodology maps flooded villages and masks out non-flooded villages. These two methodologies in combination with the PolSig-CNN classifier completes the novel 'flood affected village detection and mapping' approach.

Figure 11 Figure 12

 1112 Figure 11 Stage 3 methodology flowchart for flood affected village detection.

Figure 13

 13 Figure 13 Flood affected villages (in yellow) and non-flooded villages (in red) under; f(a) Food scenario 1. (b) Flood scenario 2. (c) Flood scenario 3. Colour scheme: yellow = villages affected by flood, red = non-flooded villages and, blue = flooded region.

Figure 14 (

 14 Figure 14(c) shows the FCC of the PALSAR-2 PolSAR data acquired over Patna region on

Figure 14

 14 Figure 14 Validation of the proposed approach. (a) India's state administrative boundaries illustration with Bihar highlighted in red, (b) Bihar's district administrative boundaries illustration with Patna highlighted in red and study area demarcated with yellow box, (c) False color composite (red = HH, green = HV, and blue = VV) PALSAR-2 PolSAR imagery of the validation study area, (d) Classification image using the PolSig-CNN classifier proposed in stage-1, (e) Villages extracted (DV image) using stage-2 methodology, and (f) Flood affected villages (highlighted in yellow) using stage-3 methodology.

  in the early stages but have quite matured now. For the sake of completeness, the building

	Imagine a CNN with L layers (including pooling, dropout, or loss), the state vector of the
	output of the	convolutional layer is denoted by , where	 lL  1, 2 , 3, ......		and	represents
	the input. Let's say the input is passed onto to a 1D, 2D or 3D convolutional layer based on
	application. The convolution also intakes a kernel size, filter count, stride and dilation strategy,
	and activation function. For the sake of reader's interest, a 2D convolution is elucidated here.
	The convolution plus pooling in the	layer is represented in equation (2).
		o	( ( ll p o o l g  o		1		W	ll  b	))
	blocks but not limited to of a conventional CNN are listed here. These are: a convolutional layer
	with kernel size, activation function, strides and dilation strategy settings, a pooling layer with
	strides and dilation strategy settings, a dropout layer with dropout fraction, a fully connected
	layer with node count and activation function, and a loss layer.

  Table 1 also lists the actual number of villages in the Roorkee and Haridwar study areas. Further, Figure 4 highlights the villages in the Roorkee and Haridwar study regions captured from Google Earth imagery. Any village in the rural parts of India consists of a minimum of 30 houses and is spread over a minimum area of 5000 m 2 . These physical dimensions help in detection of villages in a PolSAR image

It is important to note here that in this paper; different terminologies have been used at different stages to represent different versions of built-up areas. Basic terminologies are defined here.

Table 1

 1

	LC Class	Training	Roorkee	Testing	Training	Haridwar	Testing
	Bare Soil (BS)	201			39	201		39
	Tall Veg (TV)	201			39	201		39
	Short Veg (SV)	201			39	201		39
	Built-Up (BU)	201			39	201		39
	Water	201			39	201		39
	Total	1005			195	1005	195
	Total number of villages in Roorkee region	93
	Total number of villages in Haridwar region 60

Ground survey details. TV = Tall Vegetation, *BS =Bare SOIL, SV = Short Vegetation, BU= Built-Up.

  Architecture of the proposed PolSig-CNN model. 311 20 The developed PolSig-CNN model is trained on labelled samples collected via ground survey (refer Table 1). The choice of loss function during training is the "categorical cross entropy" function. The learning rate is set to 0.01 and the number of training epochs is set to 200. For network weight optimization, "Adam" optimizer is chosen. Model architecture and hyperparameters are set similar for Roorkee and Haridwar datasets for consistency purposes and are listed in Table 2.

	310
	Figure 7	11 
	Fully connected	Filters
	FC1	50
	FC2	10
	Output layer	5	SoftMax
		19

Table 3

 3

	summarizes the quantitative assessment of classification performance of the
	PolSig-CNN, NSCM, and NED classifiers for Roorkee and Haridwar datasets. The PolSig-CNN
	classifier performs land cover classification with good overall accuracies, i.e. 72% for Roorkee
	and 75.5% for Haridwar dataset. In contrast, the NED performed the classification with 62.5 %
	and 59.5% overall accuracy and, the NSCM performed the classification with 64% and 66%

overall accuracy for the Roorkee and Haridwar dataset respectively. Both NED and NSCM showed low kappa values (refer table 3) whereas the kappa for PolSig-CNN is satisfactory.

Furthermore, the PolSig-CNN classifier successfully segregates the built-up class. The built-up class is segregated with 83.7% user and 77.5% producer accuracies for Roorkee and 82.5% user and 82.5% producer accuracies for Haridwar which supports the visual interpretations.

Table 3

 3 Summary of the classification performance of classifiers for Roorkee and Haridwar datasets. OA = overall accuracy, UA = user accuracy, PA = producer accuracy

	Dataset/Study	Method	OA (%)	Kappa Class	UA (%)	PA (%)
	area
	Roorkee	PolSig-CNN	72.0	0.69	BS	65.91	72.5
					TV	84.21	80
					SV	56.00	70
					BU	83.78	77.5
					Water 77.42	60
		NSCM	64.0	0.57	BS	59.18	72.5
					TV	72.73	60.0
					SV	50.00	70.0
					BU	75.76	62.5
					Water 75.86	55.0
		NED	62.5	0.53	BS	57.45	69.2
					TV	70.59	60.0
					SV	48.21	67.5
					BU	78.13	62.5
					Water 73.33	55.0
	Haridwar	PolSig-CNN	75.5	0.72	BS	65.9	72.5
					TV	75.6	77.5
					SV	72.2	65.5
					BU	82.5	82.5
					Water 82.0	80.5
		NSCM	66.0	0.58	BS	65.9	72.5
					TV	72.9	67.5
					SV	48.1	65.0
					BU	75.8	55.0
					Water 77.7	70.0
		NED	59.5	0.52	BS	54.17	66.6
					TV	70.59	60.0
					SV	45.00	67.5
					BU	75.86	55.0
					Water 71.43	50.0

  Table 4 summarizes the quantities assessment of the DV images of the PolSig-CNN, NED, and NSCM classifiers. The PolSig-CNN successfully extracts 75 (out of 93) villages in the Roorkee study area and 47 (out of 60) villages in the Haridwar study area. Whereas, NED successfully extracts 26 villages in Roorkee and 20 villages in Haridwar and, NSCM successfully extracts 22 villages in Roorkee and 27 villages in Haridwar. The low detection rate in case of the NED and the NSCM resonates with their low classification accuracies for built-up class (refer table 2). The false alarms are also high for the NED and the NSCM. The low values of kappa for NED and NSCM (refer table 2) indicate to the high false alarms. The PolSig-CNN offers higher detection rate and low false alarms for both Roorkee and Haridwar study areas. Table 4 Summary of quantitative assessment of performance of PolSig-CNN, NED, and NSCM.Intuitively, the villages that are flooded must be completely enclosed by water and villages that are not completely flooded should not be enclosed by water. It means that any village that is completely flooded should appear as 'hole' in the 'water' class image and any village that is not completely affected by flood should not appear as a hole and may have presence of other class in the vicinity. Based on this interpretation, a criterion is set i.e. if an object in the DV image obtained from section 4.3.1 is a subset of an object in the water class image, then, that object in the DV image is a flooded village otherwise it is a non-flooded village. This criterion separates flooded villages from non-flooded villages.

	Dataset	Measures	NED NSCM PolSig-CNN
			Total number of villages in the study area	93	93	93
	ee	Roork	TP (Villages successfully mapped) FN (Villages missed) FP ( or False Alarms)	26 67 31	22 71 41	75 18 1
			IoU	0.22	0.16	0.98
			Total number of villages in the study area	60	60	60
	Harid war	TP (Villages successfully mapped) FN (Villages missed) FP (or False Alarms)	20 40 33	27 33 39	47 13 5
			IoU	0.21	0.22	0.92
	Stage 3: Mapping flood affected villages
	Since, any PolSAR image acquired to monitor a flood may include both, flooded and not flooded
	regions. Therefore, it is important here to identify flood affected villages and mask-out non-
	flooded villages since the result may impact the planning of a rescue operation. A separate
	(stage-3) methodology is proposed to achieve this task. The methodology presented in this
	section encompasses stage 3 of the overall approach.

(b, d, f, h, j and, l), it is evident that the PolSig-CNN is able to segregate the built-up class very efficiently.

Acknowledgements

Data: Authors would like to thank JAXA, Japan for providing the ALOS-2 PALSAR-2 dataset. Authors would like to thank IIRS, Dehradun, India for supporting this work. Authors would also like to thank all the lab members of MISTAL, IIT Roorkee for their support.

satisfactory. An average detection accuracy of approx. 80% and further, mapping accuracy of 100% is achieved over different study areas. In summary, the three-stage novel approach presented here successfully detects and maps flood affected villages with the help of a PolSAR image. The approach indicates potential to be tested at a real-time.

Data Availability Statement

lab, Availability of the data is subjected to be used exclusively uunder the affiliation of Prof.

Dharmendra Singh, ECE Department, IIT Roorkee. Collaborations are invited to use the data for impactful studies.

Word Count: 8562

Declaration of Interest Statement

The authors declare that authors have no conflit of interest.


Johana Leidy

Quintero-Rodríguez

Ignacio Enrique Zaldívar-Huerta

Yanhua Hong

Cristina Masoller

Min Won Lee

Permutation entropy analysis of the output of a laser diode under stimulated Brillouin scattering optical feedback

The chaotic output emitted by a diode laser with optical feedback has fascinated the community for decades. The external cavity delay time imparts a weak level of periodicity to the laser output (the so-called "time delay signature", TDS) that is a drawback for applications that require random optical signals. A lot of efforts have focused in suppressing the TDS either by post-processing the signal, or by using alternative ways to generate random optical signals. Here, we compare the signals generated by two optical feedback setups: in the first one, the stimulated Brillouin backscattered light from a standard optical fibre is re-injected into the laser (stimulated Brillouin scattering optical feedback, SBSOF); in the second one, the light transmitted through the fibre is re-injected into the laser (conventional optical feedback, COF). We analyse the permutation entropy, a well-known measure of complexity that captures order relations between values of a time series. We find that, on average, the signal generated by the SBSOF setup has slightly lower PE than the one generated by the COF setup, except when the sampling time of the intensity signal is an exact multiple of the delay; in that case, due to TDS, the entropy of the COF signal is lower than that of the SBSOF signal. We interpret the lower entropy value of the SBSOF signal as due to oscillations at the Brillouin frequency shift. Taken together, our results show that TDS suppression can have an undesirable side effect: a decrease of the entropy of the signal.

Introduction

Chaotic dynamics in laser diodes subject to optical feedback has been widely studied for decades [START_REF] Ohtsubo | Semiconductor Lasers: Stability, Instability and Chaos[END_REF]. The complexity of chaotic dynamics has been of great interest in many applications [START_REF] Sciamanna | Physics and applications of laser diode chaos[END_REF]. Complex dynamics have been exploited in reflectometry applications [START_REF] Xia | Simultaneous and precise fault locating in WDM-PON by the generation of optical wideband chaos[END_REF][START_REF] Zhang | Chaotic Brillouin optical correlation-domain analysis[END_REF], reservoir computing [START_REF] Larger | Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing[END_REF][START_REF] Brunner | Parallel photonic information processing at gigabyte per second data rates using transient states[END_REF], rogue wave studies [START_REF] Reinoso | Extreme intensity pulses in a semiconductor laser with a short external cavity[END_REF][START_REF] Lee | Demonstration of optical rogue waves using a laser diode emitting at 980 nm and a fiber Bragg grating[END_REF] and random number generation [START_REF] Uchida | Fast physical random bit generation with chaotic semiconductor lasers[END_REF][START_REF] Sakuraba | Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers[END_REF][START_REF] Kim | Massively parallel ultrafast random bit generation with a chip-scale laser[END_REF].

Chaotic dynamics in laser diodes subject to optical feedback exhibit a weak level of periodicity which arises from the round-trip delay time in the feedback cavity. This periodicity has been referred to as "time delay signature" (TDS) [START_REF] Rontani | Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback[END_REF] and is a drawback in applications that require fully random or chaotic optical signals. In Ref. [START_REF] Zhang | 640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser[END_REF] high speed random bit generation (640 Gbit/s) was demonstrated by choosing only 4-least significant bits of the 8-bit digitization of a chaotic signal generated by a monolithic integrated dual-mode amplified feedback laser; however, post-processing was needed to suppress TDS.

A lot of efforts have focused on suppressing TDS, not only by using signal post-processing, but also, hardware alternatives: different feedback configurations have been proposed that have different difficulties, limitations and challenges. Self-interference of chaotic signals has been shown to suppress TDS [START_REF] Wang | Generation of wideband chaos with suppressed time-delay signature by delayed self-interference[END_REF], but it requires two high-speed photodetectors. Brillouin backscattering of optical fibre was examined in Ref. [START_REF] Zhang | Suppression of Time Delay Signature Based on Brillouin Backscattering of Chaotic Laser[END_REF], where the chaotic light generated by an external cavity DFB laser was injected into an Er-doped fibre amplifier (EDFA). While significant reduction (but not complete suppression) of TDS was obtained, the setup has the drawbacks of using a rather high injection power (in the range 400-1500 mW) and rather expensive optical components (an EDFA and an optical isolator). TDS has also been shown to reduce significantly when using fibre Bragg grating (FBG) feedback, but it is not suppressed completely [START_REF] Li | Distributed Feedbacks for Time-Delay Signature Suppression of Chaos Generated From a Semiconductor Laser[END_REF][START_REF] Li | Chaotic Time-Delay Signature Suppression in a Semiconductor Laser With Frequency-Detuned Grating Feedback[END_REF][START_REF] Zhong | Polarization-resolved time-delay signatures of chaos induced by FBG-feedback in VCSEL[END_REF][START_REF] Li | Random bit generation at tunable rates using a chaotic semiconductor laser under distributed feedback[END_REF].

Stimulated Brillouin scattering (SBS) is a nonlinear optical process that is initiated by quantum noise [START_REF] Boyd | Noise initiation of stimulated Brillouin scattering[END_REF], and thus, it has potential for generating, all-optically, highly random signals. In Ref. [START_REF] Fu | Broadband optical chaos for stimulated Brillouin scattering suppression in power over fiber[END_REF] it was shown that broadband optical chaos generated from a single-mode semiconductor laser with optical injection increases the SBS threshold (as compared to that of the cw output from the free-running laser). In the setup in Ref. [START_REF] Fu | Broadband optical chaos for stimulated Brillouin scattering suppression in power over fiber[END_REF], SBS was not used to generate a chaotic signal; in contrast, we have recently proposed a new setup [START_REF] Correa-Mena | Investigation of the Dynamical Behavior of a High-Power Laser Diode Subject to Stimulated Brillouin Scattering Optical Feedback[END_REF] in which SBS backscattered light in the fibre is re-injected into the laser and generates a chaotic output in which TDS is completely absent. By using spectral and autocorrelation analysis, we showed that TDS is present in the chaotic signal generated by conventional optical feedback (COF), while it is removed in the signal generated by the SBSOF setup, without any need of signal post-processing.

An open question is whether the SBSOF signal is genuinely more random than the COF signal. To address this issue, here we analyse the permutation entropy (PE) of the signals generated by the two setups, COF and SBSOF. The PE is a well-known nonlinear measure of complexity that captures order relations between values of a time series [START_REF] Bandt | Permutation Entropy: A Natural Complexity Measure for Time Series[END_REF][START_REF] Zunino | Characterizing the Hyperchaotic Dynamics of a Semiconductor Laser Subject to Optical Feedback Via Permutation Entropy[END_REF][START_REF] Toomey | Mapping the dynamic complexity of a semiconductor laser with optical feedback using permutation entropy[END_REF][START_REF] Aragoneses | Unveiling Temporal Correlations Characteristic of a Phase Transition in the Output Intensity of a Fiber Laser[END_REF][START_REF] Chao | Permutation entropy analysis of chaotic semiconductor laser with chirped FBG feedback[END_REF]. We show that TDS suppression in the SBSOF setup can have an unwanted side effect: it can decrease the entropy of the signal.

Experimental setup and linear analysis

Figure 1 illustrates the experimental setups (they were described in detail in Ref. [START_REF] Correa-Mena | Investigation of the Dynamical Behavior of a High-Power Laser Diode Subject to Stimulated Brillouin Scattering Optical Feedback[END_REF]). A high-power multimode laser diode emitting at 1450 nm with a mode-spacing of 0.1 nm is used together with a standard 4 km-long optical fibre spool. The spectrum of the free-running laser diode is displayed in Fig. 1(c). The maximum free-running power of the laser diode is 𝑃 0 = 270 mW for a pump current of 1000 mA, but the power injected into the fibre is around 140 mW (21.5 dBm) because of the components losses. The light backscattered by SBS from the fibre is injected back into the laser diode as optical feedback forming a closed-loop in Fig. 1(b). In the COF setup, as seen in Fig. 1(a), only the light transmitted through the fibre is injected back into the laser diode. In both setups the time delay is around 21 µs. We note that the SBS threshold power for chaotic laser light in a fibre of 4 km is higher than 30 dBm [START_REF] Fu | Broadband optical chaos for stimulated Brillouin scattering suppression in power over fiber[END_REF]; therefore, with an injected power of 21.5 dBm, SBS is not present in the COF setup. In contrast, in the SBSOF setup, the SBS threshold power is 16 dBm; therefore, the injected power, 21.5 dBm, is higher than the SBS threshold. Rayleigh scattering also exists in the setup, but SBS is almost 12 dB greater than Rayleigh scattering [START_REF] Correa-Mena | Investigation of the Dynamical Behavior of a High-Power Laser Diode Subject to Stimulated Brillouin Scattering Optical Feedback[END_REF] and thus dominant in dynamics.

The dynamical behaviours in the time domain for both the setups appear complex, but very different as shown in Figs. 2(a with a sampling rate of 40 GS/ over a time window of 200 µs. But only a window of 10 µs is shown. Their mean amplitudes are measured as 0.84 V (𝑃 = 295 mW and 0.14 V RMS ) for COF and 0.78 V (𝑃 = 287 mW and 0.12 V RMS ) for SBS. For the COF setup, the dynamics look like noise. For the SBSOF setup, the signal manifests complex with a burst form which appears irregularly. Their fast dynamics are also shown in Figs. 2(c) and 2(d). In the SBSOF case, a fast oscillation can be observed. This is due to the Brillouin frequency shift (BFS) of 11.46 GHz as seen clearly in Fig. 2(f). This frequency matches to the theory at 1450 nm [START_REF] Correa-Mena | Investigation of the Dynamical Behavior of a High-Power Laser Diode Subject to Stimulated Brillouin Scattering Optical Feedback[END_REF]. The power spectrum for COF in Fig. 2(e) does not show such a peak for the BFS. The auto-correlation function (ACF) of the laser intensity in both the setups is presented in Fig. 3. In the COF case the ACF displays a distinct peak at 21.09 µs in Fig. 3(a). The peak corresponds to the time delay (𝜏 𝑒𝑥𝑡 = 21.09 µs) from the 4 km-long fibre. Another peak is also present at 42.18 µs (2𝜏 𝑒𝑥𝑡 ). On the other hand, the TDS vanishes in the SBSOF case as seen in Fig. 2(b). In the SBS setup, the round-trip time is 42.18 µs, but no peak is seen at this time-shift. Therefore, the TDS is suppressed in the SBSOF dynamics. However, the ACF for COF decays much faster than that for SBSOF as shown in the insets of the figure. The large oscillation seen in the inset of Fig. 3(b) is due to the peak at around 4 GHz. Such oscillation with the similar period as the SBSOF one can also be observed in the COF case, but decays much faster than in the SBSOF case. The background is noisy, but oscillation can be noiticed in the SBSOF case and its period corresponds to the BFS at 11.46 GHz. This is because of the strong presence of the BFS in the RF power spectrum shown in Fig. 2(f). Despite of the background oscillation, the TDS is completely suppressed. The TDS suppression is also confirmed by the external-cavity frequency measurement with RF power spectra available in the supplementary material [28].

As a form of distributed feedback, SBSOF can be considered similar to FBG feedback, but in the SBSOF setup, feedback comes from an infinitely large number of reflectors, while in the FBG setup, it comes from a finite number of reflectors. This may be the reason why SBSOF fully suppresses TDS, while in a FBG setup, TDS does not vanish completely [START_REF] Li | Distributed Feedbacks for Time-Delay Signature Suppression of Chaos Generated From a Semiconductor Laser[END_REF][START_REF] Li | Chaotic Time-Delay Signature Suppression in a Semiconductor Laser With Frequency-Detuned Grating Feedback[END_REF][START_REF] Zhong | Polarization-resolved time-delay signatures of chaos induced by FBG-feedback in VCSEL[END_REF][START_REF] Li | Random bit generation at tunable rates using a chaotic semiconductor laser under distributed feedback[END_REF].

Permutation entropy nonlinear analysis

The permutation entropy (PE) [START_REF] Bandt | Permutation Entropy: A Natural Complexity Measure for Time Series[END_REF] is a complexity measure that is calculated from the probabilities of symbols, known as ordinal patterns, that are defined by the temporal order relations of datapoints in the time series (see Ref. [START_REF] Zunino | Characterizing the Hyperchaotic Dynamics of a Semiconductor Laser Subject to Optical Feedback Via Permutation Entropy[END_REF] for details). The plot of the PE as a function of a time shift 𝜏 used to define the ordinal patterns can show well-defined dips that allow to unveil periodicities in the dynamics [START_REF] Toomey | Mapping the dynamic complexity of a semiconductor laser with optical feedback using permutation entropy[END_REF][START_REF] Aragoneses | Unveiling Temporal Correlations Characteristic of a Phase Transition in the Output Intensity of a Fiber Laser[END_REF]. Here we compute the normalised PE with patterns of length 𝐷 = 5.

Figure 4 shows PE with time shifts 𝜏 in the range 0-50 µs, for the times series shown in Fig. 2. We note that 𝜏 represents an effective sampling time, as the ordinal patterns are defined in terms of the relative ordering of the intensity values 𝐼 (𝑡), 𝐼 (𝑡 + 𝜏), 𝐼 (𝑡 + 2𝜏) . . . 𝐼 (𝑡 + 4𝜏). For fully random signals, PE ≈ 1, and lower values reveal the presence of temporal ordering in the sequence of data points. The signals analysed in this paper are highly random, therefore, PE values close to 1 are expected. Because the data acquisition system and the characteristics of the datasets (length and resolution) are the same for the SBSOF and COF setups, we can make a fair comparison, even if the differences found are very small.

For the COF setup in Fig. 4(a), a dip at 𝜏 𝑒𝑥𝑡 = 21.09 µs (see the inset of the figure) confirms the presence of TDS. Additional dips are seen at 7.03 µs, 14.06 µs, 42.18 µs, which correspond to 𝜏 𝑒𝑥𝑡 /3, 2𝜏 𝑒𝑥𝑡 /3 and 2𝜏 𝑒𝑥𝑡 , respectively. The baseline value (for 𝜏 ≠ 𝑛𝜏 𝑒𝑥𝑡 with 𝑛 an integer number) PE ≈ 0.9996 reveals a high degree of randomness, when the intensity sampling time is not an exact multiple of the delay time. For the signal generated with the SBSOF setup, Fig. 4(b), dips occurring at 𝜏 = 𝑛𝜏 𝑒𝑥𝑡 are not observed, confirming the total suppression of TDS. However, the baseline PE value is ≈ 0.9925, slightly lower than that of the COF signal. We speculate that the slight decrease of the entropy is due to the fact that the SBSOF dynamics has oscillations at the BFS, which are not present in the dynamics induced by COF.

We have mapped the PE as a function of the laser current and feedback strength in the COF and SBSOF setups. The maps, depicted in Fig. 5, are established by scanning the laser current from 100 mA to 1000 mA at every 2 mA and the feedback ratio from 0.005 % to 0.2 % at every 0.005 %. For each feedback configuration, a total of 18048 intensity time-traces of 2M samples have been recorded. The entropy values obtained with time shift 𝜏 = 𝜏 𝑒𝑥𝑡 = 21.09 µs are coded in colour scale. In both maps the laser threshold reveals clearly: the PE values are represented with light green colour. The reason for which the entropy, when the laser is below the threshold, is not higher is due to the resolution of the data acquisition system: all readings were done using the same amplitude scale on the oscilloscope (8 bits). This results in very small amplitude fluctuations below the threshold, that lower the PE (this is in contrast with the procedure followed in Ref. [START_REF] Toomey | Mapping the dynamic complexity of a semiconductor laser with optical feedback using permutation entropy[END_REF], where the PE maps do not unveil the threshold).

The map patterns are very different. Particularly the SBSOF map pattern in Fig. 5(b) appears irregular unlike the one for the COF setup in Fig. 5(a). PE drops are seen in the SBSOF map (blue dots). It seems that the PE values decreases in the early process of SBS, but increase rapidly with the laser current, reaching values close to 1. In the COF map it can also be noticed that the PE values decrease slightly after the threshold with a feedback stronger than 0.15 %, showing a green zone surrounded by the yellow zone. In fact, the well-known dynamical regime of low frequency fluctuations [START_REF] Ohtsubo | Semiconductor Lasers: Stability, Instability and Chaos[END_REF] is observed in this parameter region.

Conclusions

We have compared the permutation entropies of the output of a high power laser diode with optical feedback from a standard optical fibre in two configurations: when the light transmitted through the fibre is re-injected into the laser (conventional optical feedback, COF) and when the light backscattered from the fibre is re-injected into the laser (stimulated Brillouin scattering optical feedback, SBSOF). While it was expected that the SBSOF setup would produce a more random output than the COF one (because in the SBSOF setup TDS is fully suppressed), we have found that the SBSOF setup produces signals that are, on average, less random than those produced by the COF setup. Therefore, our results indicate that COF and SBSOF generate chaotic signals with different characteristics, that might have advantages and drawbacks for different applications of optical chaos [START_REF] Sciamanna | Physics and applications of laser diode chaos[END_REF][START_REF] Brunner | Parallel photonic information processing at gigabyte per second data rates using transient states[END_REF][START_REF] Kim | Massively parallel ultrafast random bit generation with a chip-scale laser[END_REF] [?].

Funding. ECOS-Nord programme (M19P03); Mexican Consejo Nacional de Ciencia y Tecnología (CONACyT, 465594); Spanish Ministerio de Ciencia, Innovación y Universidades (PGC2018-099443-B-I00); ICREA ACADEMIA, Generalitat de Catalunya.

Disclosures. The authors declare no conflicts of interest.

Fig. 1 .

 1 Fig. 1. Schematics of the (a) COF and (b) SBSOF setups. OC: optical circulator, PC: polarisation controller, VOA: variable optical attenuators, PD: photo-detector. (c) Spectrum of the free-running laser.

Fig. 2 .

 2 Figure1illustrates the experimental setups (they were described in detail in Ref.[START_REF] Correa-Mena | Investigation of the Dynamical Behavior of a High-Power Laser Diode Subject to Stimulated Brillouin Scattering Optical Feedback[END_REF]). A high-power multimode laser diode emitting at 1450 nm with a mode-spacing of 0.1 nm is used together with a standard 4 km-long optical fibre spool. The spectrum of the free-running laser diode is displayed in Fig.1(c). The maximum free-running power of the laser diode is 𝑃 0 = 270 mW for a pump current of 1000 mA, but the power injected into the fibre is around 140 mW (21.5 dBm) because of the components losses. The light backscattered by SBS from the fibre is injected back into the laser diode as optical feedback forming a closed-loop in Fig.1(b). In the COF setup, as seen in Fig.1(a), only the light transmitted through the fibre is injected back into the laser diode. In both setups the time delay is around 21 µs. We note that the SBS threshold power for chaotic laser light in a fibre of 4 km is higher than 30 dBm[START_REF] Fu | Broadband optical chaos for stimulated Brillouin scattering suppression in power over fiber[END_REF]; therefore, with an injected power of 21.5 dBm, SBS is not present in the COF setup. In contrast, in the SBSOF setup, the SBS threshold power is 16 dBm; therefore, the injected power, 21.5 dBm, is higher than the SBS threshold. Rayleigh scattering also exists in the setup, but SBS is almost 12 dB greater than Rayleigh scattering[START_REF] Correa-Mena | Investigation of the Dynamical Behavior of a High-Power Laser Diode Subject to Stimulated Brillouin Scattering Optical Feedback[END_REF] and thus dominant in dynamics.The dynamical behaviours in the time domain for both the setups appear complex, but very different as shown in Figs. 2(a) and 2(b). The time traces are recorded with 8M sample points

Fig. 3 .

 3 Fig. 3. Auto-correlation functions obtained at 1000 mA and 0.2 % for (a) COF and (b) SBSOF setups, respectively. The ACFs are zoomed in a range of 0.006 µs in the insets.

Fig. 4 .

 4 Fig. 4. Permutation entropies obtained from the time traces recorded at 1000 mA and 0.2 % for (a) COF and (b) SBSOF setups in the ordinal pattern length 𝐷 = 5. The insets show PE from 21.08 µs to 21.10 µs for zoom-in purpose.

Fig. 5 .

 5 Fig. 5. Permutation entropy maps for (a) COF and (b) SBSOF setups.

Data availability. Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.