H Boutayeb

K Mahdjoubi

A.-C Tarot

MULTI-LAYER CRYSTALS OF METALLIC WIRES: ANALYSIS OF THE TRANSMISSION COEFFICIENT FOR OUTSIDE AND INSIDE EXCITATION

This paper proposes a new analysis of the transmission coefficient at normal incidence for 2-D periodic crystals (also called Electromagnetic Band Gap (EBG) structures), which are finite in the direction of wave-propagation and are composed of metallic wires. The crystal is considered as a set of parallel Partially Reflecting Surfaces (PRSs), whose transmission and reflection characteristics are obtained rigorously using the Finite Difference Time Domain (FDTD) method. The transmission coefficient of the EBG structure is then obtained by using a plane-wave cascading approach considering single mode interactions between PRSs. The accuracy of the results given by the hybrid method is assessed compared to those obtained directly by the Finite Difference Time Domain (FDTD) method. The minima and maxima envelops and the resonance frequencies of the transmission coefficient are studied, with analytical expressions, for both, excitation from outside and excitation from inside. A discussion is also presented concerning the strength of the coefficient greater than one obtained when the plane-wave source is inside the EBG structure. In addition, by using a transmission line model, a normalized version for this coefficient is proposed, which considers the available power by the source.

INTRODUCTION

Electromagnetic bandgap (EBG) materials, also known as photonic crystals [START_REF] Yablonovitch | Inhibited spontaneous emission in solid state physics[END_REF][START_REF] Joannopoulos | Photonic Crystals: Molding the Flow of Light[END_REF], have been the subject of intensive research in the past few years. An important feature of these structures is their ability to open a bandgap that is a frequency range for which the propagation of electromagnetic waves is forbidden whatever the direction of propagation and the polarization. EBG materials are periodic structures composed of dielectric and/or metallic elements. Potential applications have been suggested in microwave and antenna domains, such as suppressing surface waves [START_REF] Yang | Microstrip antennas integrated with electromagnetic bandgap (EBG) structures: a low mutual coupling design for array applications[END_REF], creating controllable beams [START_REF] Poilasne | Active metallic photonic band-gap materials (MPBG): experimental results on beam shaper[END_REF][START_REF] Lourtioz | Toward controllable photonic crystals for centimeter and millimeter wave devices[END_REF], and designing high-gain antennas with a single feed [START_REF] Thevenot | Directive photonic band-gap antennas[END_REF][START_REF] Cheype | An electromagnetic bandgap resonator antenna[END_REF][START_REF] Biswas | Exceptionally directional sources with photonic band-gap crystals[END_REF][START_REF] Akalin | A highly directive dipole antenna embedded in a fabry-perot type cavity[END_REF][START_REF] Enoch | A metamaterial for directive emission[END_REF].

To analyze crystals with a rectangular lattice, various methods have been proposed for calculating the scattering of the periodic structures, e.g., the rigorous scattering matrix method [START_REF] Felbacq | Scattering by a random set of parallel cylinders[END_REF], and the generalized scattering matrix method with a cascading approach [START_REF] Hall | Analysis of multilayered periodic structures using generalized scattering matrix[END_REF], where the periodic structure is made from the cascading of multiple layers of PRSs, also called Frequency Selective Surfaces (FSSs) [START_REF] Munk | Frequency Selective Surfaces: Theory and Design[END_REF]. These methods are rigorous but they are typically time-consuming. In this paper, a simple modeling method based on a spectral planewave generalized-ray analysis with a cascading process is presented to predict the characteristics of a rectangular crystal. The proposed method does not consider the higher Floquet modes interactions between PRSs, but it reduces considerably the computational time compared to the preceding methods and it is well suited for the design process of the structure.

To our knowledge, the shapes and the resonance behaviors of the transmission coefficient for rectangular periodic crystals, which are finite in the direction of propagation, have not been studied enough. Indeed, it is of a lot of interest to be able to predict the stop-bands level and the locations of the transmission peaks in order to simplify the design process. For double layer structures, the Fabry Perot approach has been used in references [START_REF] De Lima | Fabry-Perot approach to the design of double layer FSS[END_REF][START_REF] Lee | Simple formulas for transmission through grids or plates[END_REF]. In this paper, new analytical results and a new parametrical study of multi-layers structures are proposed, in order to simplify the design of such structures.

Furthermore, to analyze EBG-antennas, many authors have used the characterization of the EBG structure when it is excited by a plane-wave from outside, and with an observation point outside the structure also [START_REF] Thevenot | Directive photonic band-gap antennas[END_REF][START_REF] Cheype | An electromagnetic bandgap resonator antenna[END_REF]. However the exciting source in the proposed antennas was inside the EBG structure. Because of the principle of reciprocity, the analysis of the transmission coefficient for a source located inside an EBG structure is equivalent to the calculation of the total wave inside an EBG structure excited from outside. This second analysis has been presented in [START_REF] Ozbay | Microwave applications of photonic crystals[END_REF], by using a ray method and in [START_REF] Guida | Time reversal symmetry, microcavities and photonic crystals[END_REF], where a numerical method has been proposed. However, the minima and maxima envelop and the resonance frequencies of the transmission coefficient have not been studied enough. In addition, the reason of the strength of the transmission coefficient greater than one, obtained for inside-excitation, has not been sufficiently developed and the physical insight of this anomaly has not been sufficiently explained. In this paper, a new analysis of the frequency response of a crystal with a rectangular lattice, excited from its interior, is presented, and a discussion is also proposed concerning the strength of the coefficient greater than one obtained when the plane-wave source is inside the EBG structure. In addition, a normalized version for this coefficient is proposed, by using a transmission line model and considering the available power by the source.

CHARACTERIZATION OF A SINGLE PARTIALLY REFLECTING SURFACE

The Partially Reflecting Surface (PRS) of infinite and perfectly conducting metallic wires, illuminated by a plane wave at normal incidence as illustrated in Fig. 1, is considered. In this figure, P t is the transversal period and a is the wire diameter. The coefficients t and r = |r|e jϕr are the complex transmission and the reflection coefficients of the surface, which are computed rigourously with the Finite Difference Time Domain (FDTD) method. In the FDTD code, Floquet boundaries conditions and a thin mesh ( = P eriod/80) are used. For the considered PRS, the magnitude of the transmission and reflection coefficients are plotted in Figs. 2 and

EXCITATION FROM OUTSIDE

In this section, the previous results for the PRS, are used for the characterization of EBG structures composed of multiple layers of PRSs. The EBG structures are illuminated by a plane wave from outside, and they are finite in the direction of wave-propagation. In the following subsections, and in all the paper, the energy conservation relation |t 2 | = 1 -|r| 2 , which is verified because no absorption occurs, will be used to simplify analytical expressions.

Two Layer Structure

The Fabry-Perot cavity composed of two layers of PRSs separated by the distance D, and illuminated by a plane wave at its left, as illustrated in Fig. 5, is considered. Considering the multiple reflections inside the cavity, and considering only single mode interactions between layers, the amplitude of the total transmitted wave t 2 in the right part and of the total reflected wave in the left part r 2 can be written as following [START_REF] Hecht | Optics[END_REF]:

t 2 = t 2 ∞ n=0 r 2n e -jk(2n+1)D = t 2 e -jkD 1 -r 2 e -j2kD = t 2 e -jkD 1 -|r| 2 e -j(2kD-ϕr) (1)
r 2 = r + t 2 re -j2kD 1 -r 2 e -j2kD
(2) where k is the free space wave number.

In Figs. 6 to 8, are compared the coefficients |t 2 | given by FDTD and those obtained by the hybrid method, for a/P = 0.5%. Different values of the distance D are tested: D = 0.5P t , D = P t and D = 2P t . From these figures, it can be seen that semi-analytical method gives the same results than the full-wave method (FDTD) for P t < 0.8λ. In Figs. 9 to 11, the ratio a/P = 30% is now considered, and D vary by the same way than previously. One can note that for D = 0.5P t the hybrid method is less accurate. But for D ≥ P t and P t /λ < 0.8λ, the two method present the same results. Eq. ( 1) is now used in order to study the shape and the resonance frequencies of the transmission coefficient t 2 . The resonance picks, are obtained when all the transmitted partial waves have the same phase. This can be written as following:

ϕ r = kD -nπ, n = 0, ±1 . . . ( 3
)
where ϕ r is the phase of r. At the resonance frequencies, the maximum value achieved by magnitude of the transmission coefficient t 2 is then given by: The envelop of the minima is obtained when the transmitted partial waves have opposite phase. This condition can be written as following:

|t 2 | max = |t| 2 1 -|r| 2 = 1 -|r| 2 1 -|r| 2 = 1 (4) 0
ϕ r = kD + π/2 -nπ, n = 0, ±1 . . . ( 5
)
The envelop of the minima can then be expressed as following:

|t 2 | min = |t| 2 1 + |r| 2 = 1 -|r| 2 1 + |r| 2 (6)
Fig. 12 shows t 2 , the phase of r (ϕ r ) and the lines kDnπ (n = 0, 1 . . .), for D = P t and a/P t = 5%. The intersections between ϕ r and kDnπ correspond to the resonance peaks. Fig. 13 illustrate the envelop of the minima and of the maxima for |t 2 |. Fig. 14 illustrates that the intersections between ϕ r and kD +π/2-nπ correspond to the minima of |t 2 |. Fig. 15 illustrates the influence of a/P t in the position of the resonance peaks.

Multilayered Structures

In this section, the study is extended to multilayered structures. The structure of three layers equally spaced with the longitudinal period P l , as illustrated in Fig. 16 is considered. By replacing the two first layers by an equivalent surface of characteristics t 2 and r 2 , the coefficients of the three layers structure are written as following: hybrid method those obtained by FDTD. From these curves, Eq. ( 7) is exact until the normalized frequency P t /λ < 0.7.

t 3 = t 2 te -jkP l 1 -r 2 re -j2kP l (7)
r 3 = r 2 + t 2 2 re -j2kP l 1 -r 2 re -j2kP l (8)
|t 3 | has two peaks in each sides of the peaks of |t 2 | (see Fig. 18). By observing that when |t 2 | = 1, and then |r 2 | = 0, |t 3 | is in a minimum between the resonance peaks, the envelop of this minimum is then given by: By generalizing to n layers, it is obtained the following iterative equations, for the transmission and reflection coefficients: In Fig. 19, the magnitude of |t n | is plotted, for n = 5, using both, FDTD and semi-analytical methods, showing the accuracy of the hybrid method for P t /λ < 0.7. It is interesting to note that the transmission peaks of |t n | appear at the intersections between |t n-1 | and |t|. Indeed, this conducts to

|t 3 | = |t|/(1 -0) = |t|.
t n = t n-1 te -jkP l 1 -r n-1 re -j2kP l (9)
r n = r n-1 + t 2 n-1 re -j2kP l 1 -r n-1 re -j2kP l ( 10
|t n | = |t n-1 ||t|/(1 -|r n-1 ||r|) = |t n-1 | 2 /(1 -|r n-1 | 2 ) = 1, at these resonance frequencies.
From Eq. ( 9), the envelop of the minima for |t n | can be written as following:

|t n | min = |t n-1 t| 1 + |r n-1 r| (11)
To obtain a simpler expression, the corresponding maxima of |r n | are first calculated. By using 2 , the following relation is obtained:

|r n | 2 max = 1 -|t n | 2 min , |t n-1 | 2 = 1 -|r n-1 | 2 and |t| 2 = 1 -|r|
|r n | max = |r| + |r n-1 | 1 + |r n-1 r| (12)
In order to simplify this equation, we consider the coefficient

f n = 1-|rn|max 1+|rn|max .
After some algebra, it is obtained

f n = 1-|r| 1+|r| 1-|r n-1 | 1+|r n-1 | , and then f n = 1-|r| 1+|r| n
. From this, the envelop of the maxima for |r n | is given by

|r n | max = 1 -1-|r| 1+|r| n 1 + 1-|r| 1+|r| n ( 13
)
The corresponding envelop of the minima for |t n | is then written as following:

|t n | min = 2 1-|r| 1+|r| n/2 1 + 1-|r| 1+|r| n ( 14
)
The

EXCITATION FROM INSIDE

In this section, the plane-wave source is considered inside the Fabry-Perot cavity or the EBG structure. For this case, the same ray analysis than previously is carried out.

Analysis of the "Transmission" Coefficient

Two Layers Structure

Two layers of PRSs are considered at the same distance D/2 at each side of the source as illustrated in Fig. 22(a). The source is considered transparent to electromagnetic waves and it sends two plane waves on each side. In the FDTD code, the source is modeled with a plane of current sources. Another model of the source, which considers the interactions of the source with the electromagnetic waves inside the cavity will be presented later in this paper. Because of the reciprocity principle, this analysis is equivalent to the one of the problem illustrated in Fig. 22(b), where the Fabry-perot cavity is excited from outside and the total wave is calculated at the center of the cavity. As referring to Fig. 22(a), the amplitude of the total transmitted wave T 2 is calculated by summing the rays outside the

T 2 = t ∞ n=0 r n e -jk(2n+1)D/2 = te -jkD/2 1 -re -jkD ( 15
)
|T 2 | is plotted in Fig. 23, for a/P t = 5% and D = P t , by using FDTD and semi-analytical method. For T 2 , the resonance condition is written:

ϕ r = kD -2nπ, n = 0, ±1 . . . ( 16
)
This condition is illustrated in Fig. 24 for D = P t . In this figure, the coefficient |t 2 | is also plotted, in order to show that |t 2 | has twice more resonance frequencies than |T 2 |. The minima envelop is written as following:

ϕ r = kD -(2n + 1)π, n = 0, ±1 . . . ( 17
)
The envelop of maxima for |T 2 | is given by:

|T 2 | max = |t| 1 -|r| = 1 -|r| 2 1 -|r| = 1 + |r| 1 -|r| ( 18
)
From Eq. ( 18), |T 2 | max is equal or greater than one and can theoretically become very large if |r| is near one (note that 0 ≤ |r| < 1). This means that the source inside the cavity can supply more power in the presence of the cavity than without the cavity. This is due to the fact that the cavity modifies the matching of the source to free space. Taking into account the available power from the source, a normalized version for the transmission coefficient will be proposed later in this paper.

The envelop of minima for |T 2 | is expressed as following: The coefficient |T 2 |, the envelops of minima and maxima are plotted in Fig. 25, for D = P t , and in Fig. 29, for D = 2P t .

|T 2 | min = |t| 1 + |r| = 1 -|r| 2 1 + |r| = 1 -|r| 1 + |r| = 1 |T 2 | max ( 19
)

Multilayered Structure

Multiple PRSs are on each sides of the source. The case P l = D = 2P t is considered. For n layers periodically spaced by the distance P l , at the distance P l /2 at each sides of the source, one can show that the coefficient T 2n is written:

T 2n = t n e -jkP l /2 1 -r n e -jkP l (20)
In Eq. ( 20), t n and r n are obtained from Eqs. ( 9) and [START_REF] Enoch | A metamaterial for directive emission[END_REF]. The coefficient |T 2n | for n = 4 is plotted in Fig. 26. In this figure, this coefficient is compared to the transmission coefficients of the cavity walls (i.e., |t n |) and in Fig. 27, it is compared to the transmission coefficient of the all structure excited from outside (i.e., |t 2n |). From these curves, the coefficient |T 2n | has one more peak than |t n | in the first pass-band, but the two coefficients have the same number of peaks in the second pass-band (Fig. 26). In addition, the first peak of |T 2n | occurs at the same frequency that the first peak of |t 2n | (Fig. 27).

Concerning the Strength of "Transmission" Coefficient Greater than One

The strength of the coefficient greater than one is due to the fact that the power supplied by the source has not been considered. In the next sub-sections, a normalized version for this coefficient, which take into account the power available by the source is proposed, by using a transmission line model.

Power Normalization

The Fabry-Perot cavity excited from its inside (see Fig. 22(a)) is represented by the transmission line model as illustrated in Fig. 28(a). In Fig. 28(b), the transmission line model of the source with its matched impedance is also presented in order to calculate the available power from the source. Z c is the free-space characteristic impedance (Z c = 120π). Z is the equivalent circuit model of the PRS. Z s and e s are the equivalent impedance and equivalent tension of the source, respectively.

To calculate the transmission coefficient outside the cavity, the available power P i (see Fig. 28(b)) is first calculated [START_REF] Pozar | Microwave Engineering[END_REF]:

P i = 1 2 |V i | 2 Z * s = 1 2 |Z * s | 2 Z * s |Z * s + Z s | 2 |e s | 2 (21)
where e s , Z s and V i parameters are shown in Fig. 28(b). Then, referring to Fig. 28(a), the transmitted power P t for one side of the transmission line is given by:

P t = 1 2 |V t | 2 Z c ( 22
)
The transmission and reflection coefficients t and r can be expressed as functions of Z as following [START_REF] Pozar | Microwave Engineering[END_REF]:

t = 2Z 2Z + Z c (23) r = - Z c 2Z + Z c (24)
t s and r s are the transmission and reflection coefficients of the source and can be written as functions of Z s

t s = 2Z s 2Z s + Z c (25) r s = - Z c 2Z s + Z c (26)
By using Eqs. ( 23)-( 26), and after simplification (see Appendix), one can show that Eq. ( 22) can be written

P t = 1 2 Z c |2Z s + Z c | 2 |te -jkD/2 | 2 |1 -r(r s + t s )e -jkD | 2 |e s | 2 (27)
Taking into account the power transmitted from the both sides of the line, the normalized squared magnitude of the transmission coefficient

|T 2 | 2
Norm,max can be expressed as following:

|T 2 | 2 Norm,max = 2P t P i = 2Z c Z * s |Z * s + Z s | 2 |Z * s | 2 |2Z s + Z c | 2 |te -jkD/2 | 2 |1 -r(r s + t s )e -jkD | 2 (28)
For the case of real Z s , Eq. ( 12) becomes

|T 2 | 2 Norm,max = 4|r s ||t s | |te -jkD/2 | 2 |1 -r(r s + t s )e -jkD | 2 (29)
The maximum is then written

|T 2 | 2 N orm,max = 4|r s ||t s | 1 -|r| 2 (1 -|r||r s + t s |) 2 (30)
In Fig. 29 Norm,max is always limited to 1, as expected.

Discussion

To analyze the directivity of an antenna embedded inside a Fabry-Perot cavity, one can use Eq. ( 15), where the variable D is replaced by D cos(θ), and θ is the angle of the transmitted waves. This analysis has been recently presented in [START_REF] Boutayeb | Directivity of an antenna embedded inside a Fabry-Perot cavity: Analysis and design[END_REF]. The directivity has been predicted by considering the angular dependance of the transmission coefficient. The Fabry-Perot cavity increases the directivity of the antenna and then its gain. Indeed, the relationship between directivity and gain for highly directive antennas is well known [START_REF] Balanis | Antenna Theory: Analysis and Design[END_REF]. However, it can be noted that the strength of the coefficient of Eq. ( 15), can not be interpreted has the gain of this antenna, because it does not consider the power available by the source.

Theoretically the coefficient of Eq. (29), is more correct than the coefficient of Eq. ( 15). However, it is less applicable in practice, because we don't have necessarily access to the transmission and reflection coefficients of the source.

A rapid comparison between Eq. ( 15) and Eq. ( 29) shows that the normalized version (Eq. ( 29)) has two factors more: 4|r s ||t s | and (r s + t s ) (in the denominator). For directive-antennas incorporating a Fabry-Perot cavity, we focus on the angular dependence of the transmission coefficient. If the source is omnidirectional, the factor 4|r s ||t s | is independent on transmitting angle and can then be omitted. Furthermore, as the source can usually considered as a point source, it can be considered having negligible interaction with the reflecting plane-waves inside the cavity, which leads to r s ≈ 0, t s ≈ 1 and r s + t s ≈ 1. From these, using the coefficient version presented in Eq. ( 15) for predicting the radiation patterns of directive-antennas based on a Fabry-Perot cavity excited internally is justified. However, the strength of this coefficient should not be considered as the gain of these antennas. The observed improvement of the gain of these antennas is more associated with the enhancement of their directivity that can be evaluated by calculating the half power beamwidth by using Eq. ( 15) (with D replaced by D cos(θ)) as has been demonstrated in [START_REF] Boutayeb | Directivity of an antenna embedded inside a Fabry-Perot cavity: Analysis and design[END_REF].

CONCLUSION

A new analysis of Electromagnetic Band Gap structures (EBGs) composed of multiple Partially Reflecting Surfaces (PRSs) of metallic wires has been presented. Transmission coefficients, for a plane-wave excitation, obtained with a semi-analytical method, which considers only the fundamental mode interaction between PRSs, have been validated by comparing them with the results of a full-wave method (FDTD). The shape and the resonance frequencies of the transmission coefficients have been studied by using analytical expressions. The two cases, excitation from outside and excitation from inside, have been treated. For the inside-excitation case, the transmission coefficient presents a different number of resonance peaks than for the outsideexcitation case. A discussion is also presented concerning the strength of the coefficient greater than one obtained when the plane-wave source is inside the EBG structure. In addition, by using a transmission line model, a normalized version for this coefficient is proposed, which considers the available power by the source. This work is useful for the design process of multilayered periodic structures and for physical study of crystals excited internally, which has applications in the design of high-gain antennas. The expression for the voltage V 1 (see Fig. A1) can be written:

V 1 = Z Z + Z s e s = Z c (1 + re -jkD ) (2Z s + Z c ) -(2Z s -Z c )re -jkD e s (A2)
And the current I 1 is expressed as following:

I 1 = V 1 Z = 2 1 -re -jkD (2Z s + Z c ) -(2Z s -Z c )re -jkD e s (A3)
Then the voltage V t (Fig. 28(a)) is deduced from these results:

V t = V 1

Figure 6 .

 6 Figure 6. Coefficient |t 2 | for D = P t /2, a/P t = 5%: FDTD (solid line) and semi-analytical model (dashed line).

Figure 7 . 2 Figure 8 .

 728 Figure 7. Coefficient |t 2 | for D = P t , a/P t = 5%: FDTD (solid line) and semi-analytical model (dashed line).

2 Figure 9 .Figure 10 .

 2910 Figure 9. Coefficient |t 2 | for D = P t /2, a/P t = 30%: FDTD (solid line) and semi-analytical model (dashed line).

Figure 12 .Figure 13 .

 1213 Figure 12. The intersections between ϕ r and kDnπ, n = 0, 1, . . ., correspond to the transmission peaks of |t 2 |.

Fig. 15 2 Figure 14 .Figure 15 .

 1521415 Fig. 15 shows results for the coefficient |t 3 | obtained with the

Figure 16 .Figure 17 .

 1617 Figure 16. Three layers of partially reflecting surfaces excited by a plane-wave source from outside.

Figure 18 .Figure 19 .

 1819 Figure 18. Coefficients |t|, |t 2 |, and |t 3 |. The intersections between |t| and |t 2 | correspond to the peaks of |t 3 |. The minimum between two peaks of |t 3 | is determined by |t|.

  coefficients |t 2 |, |t 3 |, |t 4 |, and |t 5 | and their minima envelops are reported in Fig. 20. The coefficients |r 2 |, and |r 5 | and their maxima envelops are plotted in Fig. 21.

Figure 20 .Figure 21 .

 2021 Figure 20. Coefficients |t 2 |, |t 3 |, |t 4 |, and |t 5 | and their minima envelops.

Figure 22 .Figure 23 .

 2223 Figure 22. Two equivalent problems: (a) Fabry-Perot cavity excited by a plane wave source from its inside. Calculation of the total transmitted wave outside the cavity (b) Fabry-Perot cavity excited by a plane wave source from outside. Calculation of the wave inside the cavity.

  cavity:

Figure 24 .

 24 Figure 24. Intersections between ϕ r and kD -2nπ, n = 0, 1, . . ., correspond to transmission peaks of |T 2 |. |t 2 | has one more peaks than |T 2 |.

Figure 25 .

 25 Figure 25. Coefficient |T 2 |, envelops of minima and maxima.

Figure 26 .Figure 27 .

 2627 Figure 26. Coefficient |T 2n |, for n = 4 and coefficient |t 4 |. P l = D = 2P t and a/P t = 5%. In the first pass-band, |T 2 * 4 | has two more peaks than |t 4 |. In the second pass-band the two coefficients have the same number of peaks.

Figure 28 .

 28 Figure 28. Transmission line models: (a) Source-fabry perot cavity structure (b) Source with matched impedance.

Figure 29 .

 29 Figure 29. |T 2 | 2 N orm,max coefficient versus Z s for different values of |r|.

1 Figure A1 .

 1A1 Figure A1. Equivalent transmission line model of Fig. 28(a).

  cos (kD/2) + jZ c I 1 /2 sin (kD/2) = Z c (1 + r)e -jkD/2 (2Z s + Z c ) -(2Z s -Z c )re -jkD = Z c 2Z s + Z c (1 + r)e -jkD/2

  3, versus normalized frequency P t /λ, for different values of the ratio a/P t . The phase of the Phase of the reflection coefficient ϕ r versus normalized frequency P t /λ for different values of a/P t (FDTD).

	1 π				|t| ϕr
	0.8 π/2		a/Pt = 5% 10% a/P t = 5%	25%	30%
	0.4 0.6 0		15% 25% 20% 10% 15% 20% 40% 35% 30%
	0.2 -π/2				45% 50%	45% 50%
	0 -π		0 0	0.2 0.2	0.4 Pt /λ P t / λ 0.4	0.6 0.6 35%	0.8 0.8 40%	1	1
	Figure 2. Coefficient |t| versus normalized frequency P t /λ for different values of a/P t (FDTD). Figure 4.
					|r|
	1						50%
	0.6 0.8	a/P t = 5% 10% 15% 20% 30% 25% 35% 40% 45%
	0.4
	0.2			∞	y
	0	Incident 0 plane wave 0.2	0.4 P t / λ P t	0.6	x 0.8	1
	t Figure 3. Coefficient |r| versus normalized frequency P t /λ for
	r different values of a/P t (FDTD).
	reflection coefficient r, ϕ r , is also reported in Fig. 4, versus normalized
	∞ frequency P t /λ, for different values of the ratio a/P t . These results Metallic wire will be applied in the next sections in order to characterize structures of diameter a with multiple layers of PRSs.
	Figure 1. Partially Reflecting Surface of metallic wires.

  , |T 2 | 2 Norm,max is plotted versus Z s for different values of |r|. From these curves, one can see that the strength of |T 2 | 2

APPENDIX A.

The details for the calculation of the variable V t (see Fig. 28(a)) are given in this appendix. Fig. A1 presents the equivalent model for the circuit of Fig. 28(a).

In this Figure, the impedance Z can be written as following:


Prachi A Gaidhani

S B Bagal

Implementation of Sketch Based and Content Based Image Retrieval

Keywords: Sketch based image retrieval, Content based image retrieval, Feature extraction, Line segment based descriptor, object boundary selection

In this paper we propose a novel approach to combine Sketch Based and Content Based Image retrieval. The database of the images is growing rapidly and there is huge demand in the enhancement of the retrieval of the images. Color, shape, texture, spatial layout are the main attributes to represent as well index the images. These features of images are extracted to check similarity between the images. Generation of special query is the chief trouble of content based image retrieval. By using different algorithms the similarity between the extracted features from the images are checked. Sketch based image retrieval is efficient and main method which are not necessarily having a high skill to draw the query sketch. To overcome these disadvantages we proposed combination of Sketch Based and Content Based Image retrieval. Experimental results show that proposed system is much better than the single systems.

I. INTRODUCTION

Sketch Based Image Retrieval (SBIR) and Content Based Image Retrieval (CBIR) problems are discuss by many researchers in different ways and numbers of techniques are proposed to retrieve images effectively from the databases. All the existing systems are independent like some retrieve the content based images and some retrieve sketch based images. To improvise the search efficiency we come up with a effective way by combining the sketch and content based techniques. An image retrieval system provides an effective way to access, browse, and retrieve a set of like images in the real-time applications. We can easily recognize objects from other people's sketches, and this form of expression is arguably the most common interaction tool for people who speak different languages. Compared with keywords, a sketch is generally more descriptive, breaking down the language barrier. Content-based image retrieval (CBIR) is the application of computer sight to the image retrieval trouble, so as to the hard of searching for digital image in big databases. "Content-based" means with the purpose of explore will examine the literal contents of the image. Here the term content in this context might submit to shade, figure, surface, or some other information that can be derived from the image itself [START_REF] Ait-Aoudia | YACBIR: Yet another Content Based Image Retrieval system[END_REF].

Implementing SBIR and CBIR together will increase the searching efficiency of the system. Several approaches for SBIR have been proposed. However, to attain interactive query reply, it is impossible to compare the sketch to all images in the database right away. Instead, descriptors are extracted in a preprocess and stored in a data structure for fast access. Very commonly, the descriptors are interpreted as points in a high-dimensional space and finding close matches means searching for nearest neighbors in this space. Researchers have developed many offline as well as online CBIR systems using a combination of two or more image features and some have been successful in retrieving similar images with good precision and recall values. Several CBIR systems such as VIR image engine from Virage Inc., IBM's QBIC and Excalibur from Excalibur technologies are available as commercial packages. Many systems such as Visual SEEK, Surf image, Photo book, Chabot, Netra and MARS have been developed on experimental basis by academic institutions and researchers to demonstrate the feasibility of new techniques. Working demonstrations of many of these are available on the web.

II. LITERATURE SURVEY

Many research attempts have been committed in addressing the Content Based Image

Retrieval (CBIR) problem [START_REF] Guo | Improved block truncation coding based on the void-and-cluster dithering approach[END_REF] ans Sketch Based Image Retrieval (SBIR). Various methods have been proposed in the literature for sketch-based and content based Retrieval. The main aspect of image retrieval system is to offer an efficient way to access, browse, and find similar images in the real-time applications.

Content Based Image Retrieval (CBIR):

(CBIR) is a method that is used to look at image features like (color, shape, texture) to find a query image from database. The difficulties of CBIR lie in reducing the differences of contents based feature and the semantic based features. This problem in giving effective retrieval images and channelize the researchers to use (CBIR) system ,to take global color and texture features to achieve, the good retrieval, where others used local color and texture features [START_REF] Datta | Image retrieval[END_REF].The method in [START_REF] Oliva | Modeling the shape of the scene: "A holistic representation of the spatial envelope[END_REF] presented the holistic representation of spatial envelop with a very low dimensionality for making the incident image. This approach presented an outstanding result in the scene categorization. The method in [START_REF] Jia | Beyond spatial pyramids: "Receptive field learning for pooled image features[END_REF] proposed a modern approach for image classification with the open field design and the concept of over-completeness methodology to achieve a preferable result. As reported in [START_REF] Jia | Beyond spatial pyramids: "Receptive field learning for pooled image features[END_REF], this method achieved the best classification performance with much lower feature spatiality compared to that of the former schemes in image classification task.

Tiwari et al developed a CBIR system [PATSEEK] for US based patent database as a patent always consists of an image along with textual information. For similarity search [START_REF] Tiwari | PATSEEK: Content Based Image Retrieval System for Patent Database[END_REF] the user need to enter keywords along with the query image that might appear in the text of patents. Krishnan et al developed CBIR based on color, based on the rife colors in the foreground image which gives only the semantics of the image. Dominant color identification by using foreground objects alone is able to retrieve number of similar images considering the foreground color irrespective of size. Higher average precision and recall rates compared to the traditional Dominant Color method were obtained successfully [START_REF] Krishnan | Content Based Image Retrieval Using Dominant Color Identification Based on Foreground Objects[END_REF].In another system the image is represented by a Fuzzy Attributed Relational Graph (FARG) that describes each object in the image, its attributes and spatial relation. The texture and color attributes are computed in a way that model the Human Vision System (HSV) [START_REF] Heba | A New Approach in Content-Based Image Retrieval Using Fuzzy Logic[END_REF].

Sketch Based Image Retrieval (SBIR):

Sketch-based image retrieval (SBIR) is a relevant means of querying large image databases. All of researches focus on how to solve the gap between sketch and image matching problem. The Sketch-based image retrieval (SBIR) was introduced in QBIC [START_REF] Menp | Multiscale binary patterns for texture analysis[END_REF] and Visual SEEK [START_REF] Smith | VisualSEEK: a fully automated contentbased image query system[END_REF] systems. In these systems the user draws color sketches and blobs on the drawing area. The images were divided into grids, and the color and texture features were determined in these grids. The applications of grids were also used in other algorithms, for example in the edge histogram descriptor (EHD) method [START_REF] Eitz | An evaluation of descriptors for large-scale image retrieval from sketched feature lines[END_REF]. The disadvantage of these methods is that they are not invariant opposite rotation, scaling and translation. Lately the development of difficult and robust descriptors was emphasized. Another research approach is the application of fuzzy logic or neural networks. In these cases the purpose of the investment is the determination of suitable weights of image features [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF].Early sketch based image retrieval systems were typically driven by queries comprising blobs of color or predefined texture [START_REF] Ashley | The query by image content (QBIC) system[END_REF] [START_REF] Smith | Visualseek: a fully automated content-based image query system[END_REF]. Later systems explored shape descriptors [START_REF] Sciascio | Content-based image retrieval over the web using query by sketch and relevance feedback[END_REF] and spectral descriptors such as wavelets [START_REF] Jacobs | Fast multiresolution image querying[END_REF]. Eitz et al. [START_REF] Eitz | A descriptor for large scale image retrieval based on sketched feature lines[END_REF] introduced a grid based approach to shape retrieval, dividing the image into regular grids and locate photos using sketched depiction of object shape. Sciascio et al. [START_REF] Sciascio | Content-based image retrieval over the web using query by sketch and relevance feedback[END_REF] investigate extracting shape feature in photo-realistic images using image segmentation. Ma et al. [START_REF] Ma | Sketch retrieval via dense stroke features[END_REF] proposed a Poisson-based HOG and organized the codebook in a hierarchical vocabulary tree. To better measure visual similarity, Shrivastava et al. [START_REF] Shrivastava | Data-driven visual similarity for cross domain image matching[END_REF] learned the data driven uniqueness (weights) for blocks of HOG. Gong et al. [START_REF] Gong | Multi-feature canonical correlation analysis for face photo-sketch image retrieval[END_REF] combined HOG and MLBP [START_REF] Menp | Multiscale binary patterns for texture analysis[END_REF] for face image retrieval. In addition to HOG based descriptors, Eitz et al. [START_REF] Eitz | Sketch-based image retrieval: Benchmark and bagof-features descriptors[END_REF] utilized shape context [START_REF] Salve | Shape matching and object recognition using shape contexts[END_REF] to perform retrieval.

III. PROPOSED SYSTEM

Figure 1. General Architecture of sketch and content based image retrieval system

Figure shows a typical architecture of a sketch and content based image retrieval system. In this system the query sketch was taken by translating original image into sketch image. Then we propose a new line segment-based descriptor named histogram of line relationship (HLR).our line segment-based descriptor HLR has two advantages. First, it focuses on directly capturing higher level information. Since the object shape is determined by these relationships, our HLR is better able to describe the sketches/object boundaries. Second, since our HLR is a line segment-based descriptor, it is able to selectively capture a subset of neighboring line segments rather than capturing all of them, which makes it quite flexible and serve as the basis for noise impact reduction. The sampling strategy has a significant influence on performance. Noisy edges widen the appearance gap between sketch images and photorealistic images and subsequently degrade retrieval performance. However, the human visual system is not usually impacted by these noisy edges since humans can differentiate the shaping edges and noisy edges based on their inference ability. Inspired by this observation, we propose a novel object boundary selection algorithm to predict the shaping edges. To the best of our knowledge, this object boundary selection algorithm is the first method to aim to reduce the impact of noisy edges in a SBIR system. Then images are retrieved for SBIR system. These digital images are given to content based image retrieval system(CBIR).Content based means that search will analyze the actual content of the image. The term content in this context might refer colors, shapes, texture or other information that can be derived from the image itself.

The CBIR system uses ordered-dither block truncation coding (ODBTC) for the generation of image content descriptor. In the encoding step, ODBTC compresses an image block into corresponding quantizers and bitmap image. Two image features are proposed to index an image, namely, color co-occurrence feature (CCF) and bit pattern features (BPF), which are generated directly from the ODBTC encoded data streams without performing the decoding process. Then images are retrieved for CBIR system. CBIR systems can make use of relevance feedback; Relevance feedback retrieval systems prompt the user for feedback on retrieval results and then use this feedback on subsequent retrievals with the goal of increasing retrieval performance.

IV. RESULTS

V. CONCLUSION

In the proposed system we have merged Content based and Sketch based techniques. The results shown in the result section shows the comparison of the existing system with the proposed systems. 0.5% of efficiency is increased as per the data table discussion.

Figure 2 . Performance Graph 4 . 1

 241 Figure 2. Performance Graph

Table 1 . Comparison table

 1


H Boutayeb
email: boutayeb@inrs-emt.uquebec.ca.

K Mahdjoubi

A.-C Tarot

T A Denidni

Directivity of an Antenna Embedded Inside a Fabry-Perot Cavity: Analysis and Design

Keywords: Periodic structures, Fabry-Perot cavity, Directive antennas

The enhancement of directivity of a monopole located in a Fabry-Perot type cavity is studied. The analysis is based on the response of the cavity excited from its inside by electromagnetic waves. To validate the proposed antenna, an experimental prototype was designed, fabricated and measured.

Introduction

Directive and low-cost antennas composed of a single feed present an attractive solution for several wireless communication systems, such as high-speed wireless LANs, satellite systems and point-to-point links. Their single-feed system allows to increase the gain with low complexity compared to feeding networks used in conventional antenna arrays. In this paper, a directive antenna composed of a monopole embedded inside a Fabry-Perot cavity is proposed.

Recently, several authors have developed techniques to obtain high directive antennas by embedding a dipole inside a Fabry-Perot cavity [START_REF] Akalin | A Highly Directive Dipole Antenna Embedded in a Fabry-Perot Type Cavity[END_REF][START_REF] Biswas | Exceptionally directional sources with Photonic Band-Gap crystals[END_REF][START_REF] Boutayeb | Design of a Directive and Matched Antenna with a planar EBG structure[END_REF]. In [START_REF] Akalin | A Highly Directive Dipole Antenna Embedded in a Fabry-Perot Type Cavity[END_REF], a relation between the half power beamwidth and the quality factor of the cavity (at the resonant frequency of the cavity) has been proposed and validated numerically, whereas in [START_REF] Biswas | Exceptionally directional sources with Photonic Band-Gap crystals[END_REF], it has been demonstrated that this directivity improvement has an analogy with past research in optical physics. In [START_REF] Boutayeb | Design of a Directive and Matched Antenna with a planar EBG structure[END_REF], a study on the input impedance of the antenna has been presented. In [START_REF] Thevenot | Directive Photonic Band-Gap Antennas[END_REF][START_REF] Serier | 1D photonic bandgap resonator antenna[END_REF], an antenna based on a Electromagnetic Band Gap (EBG) material with a defect has been proposed. The antenna consists of a Fabry-Perot cavity between a patch antenna and the EBG material.

Another way for producing a high-gain antenna has been introduced in the 50's [START_REF] Trentini | Partially reflecting sheet arrays[END_REF]. This technique uses a Partially Reflecting Surface (PRS) to introduce leaky waves and beamforming effects when placed in front of a grounded waveguide aperture. A ray theory has been proposed, showing that the directivity of the antenna increases when the reflectivity of the PRS increases. This kind of antenna has been revisited recently [START_REF] Feresidis | High gain planar antenna using optimized partially reflective surfaces[END_REF], where the PRS has been optimized to enlarge the antenna bandwidth.

To our knowledge, the directivity at different frequencies of antennas based on a Fabry-Perot cavity has not been sufficiently studied. Indeed, the directivity (or the beamwidth) is often calculated at the resonant frequency of the cavity. However, as it is shown in this paper, the maximum of the directivity (or minimum of the beamwidth) is obtained at another frequency. In this contribution, a ray method is applied to predict the focusing characteristics of the proposed antenna. To demonstrate the proposed approach, an antenna prototype was build and measured, and the experimental results show a good agreement with the predicted ones.

Analysis

The analysis procedure for the proposed antenna is given in the following sections. In Section 2.1, the structure is characterized using the frequency and angular responses of the Fabry-Perot cavity to a plane wave excitation, which is in the center of the cavity. This frequency and angular function is called T. Usually, in the Fabry-Perot interferometer, the source is outside the Fabry-Perot cavity [START_REF] Hecht | Optics[END_REF], whereas here the source is placed inside the cavity, which necessitates new formulas for the characterization. Using the calculated function T, in Sections 2.2 and 2.3, the relationships of the bandwidths at the half-power and at an arbitrary power ratio are developed and presented. In Section 2.4, these relations are then used to calculate new results for the half power beamwidth of the radiation pattern of the Fabry-Perot-antenna, and the main results are finally applied in Section 2.5 for the antenna design.

Characterization

Figure 1(a) shows the geometry of the proposed structure. This structure consists of two metallic wire rows located on each side of a point source, where a TM-wave excitation is considered. The wires are spaced periodically with the period P , the distance between the two rows is and the diameter of the wires is a. In order to characterize the structure in terms of frequency and radiation pattern, the rays going at the direction D θ are considered (Fig. 1(b)). The rows of wires act as partially reflecting surfaces to these rays, with the complex reflection and transmission coefficients r and t . An infinite number of rays exit from the cavity at the direction θ . The amplitude of the direct transmitted ray ( t ), using an arbitrary reference of phase, is equal to t .

The amplitude of the once-reflected ray ( t ) can be written as

0 1 ( ) ( ) ( ) ( ) θ - θ θ + θ - = = cos sin tan 2 / cos 2 1 jkD jkD jkD tre tre t ( 1
)
where

c f k π = 2
is the free space wave number, is the frequency and is the velocity of wave propagation in free space. In Eq. ( 1),

f c ( ) θ - 2 cos kD n
represents the phase variation during displacement and is the path difference between ray 1 and ray . Thus, the amplitude of the nth-reflected transmitted ray ( t ) is written

( ) ( ) θ θ sin tan 2 / kD 0 (2) ( ) θ - = cos jnkD n n e tr t
The total transmitted amplitude is then written as

( ) ( ) θ - ∞ = θ - ∞ = - = = = ∑ ∑ cos 0 cos 0 1 jkD n jnkD n n n re t e r t t T (3) 3
Using the energy conservation relation

2 2 1 r t - =
[8] and after simplifications, the squared modulus of T can be written

( ) ( ) r kD r r r T ϕ - θ - + - = cos cos 2 1 1 2 2 2 (4)
where ϕ is the phase of r r .

In order to obtain simple analytical results, the reflection and transmission coefficients r and are considered constant (i.e. independent of the frequency and angle). This approximation is usually considered valid in the frequency band of interest [START_REF] Trentini | Partially reflecting sheet arrays[END_REF][START_REF] Feresidis | High gain planar antenna using optimized partially reflective surfaces[END_REF]. T versus frequency at its half squared maximum amplitude is defined as 1 , where is the quality factor of the cavity [START_REF] Akalin | A Highly Directive Dipole Antenna Embedded in a Fabry-Perot Type Cavity[END_REF]. Figure 3 shows

Q / Q
T versus angle at different frequencies. These radiation patterns exhibit directive beams at the normal directions ( θ and °= 0 °= θ 180 ) for frequencies lower than . For frequencies greater than , lobs appear on each side of the normal axis.

0 f 0 f dB 3 θ ∆
is defined as the half power beamwidth of the main lobs at the normal directions (see Fig. 3). In the next sections, the quality factor is first written as function of the reflection coefficient Q r , and then, the interrelation between the half power beamwidth and the quality factor Q is developed.

Half power bandwidth

To find the expression of 1 as a function of the reflection coefficient

Q / r ,
( )         - - ± ϕ = ψ ± r r r 2 1 2 1 1 cos arc ( 7
) Q / 1
can be expressed as

( ) r r r r f f f f r r ϕ - ≈         - - ϕ = + - = ψ + ψ ψ - ψ = - + - + - + - + 1 2 1 2 1 1 cos arc 2 2 2 Q 1 2 (8)
The approximate relation is obtained by considering r close to 1, which is the condition to obtain high directivity [START_REF] Trentini | Partially reflecting sheet arrays[END_REF][START_REF] Feresidis | High gain planar antenna using optimized partially reflective surfaces[END_REF].

Bandwidth for an arbitrary power ratio x

The half power bandwidth 1 is obtained for

Q / 2 / 2 max

T

. We can also define a bandwidth 1 determined for

x Q / x T / 2 max
. For this, we have to resolve the following equation :

( ) r r x r r r r x - + = ϕ - ψ - + - ± 1 1 1 cos 2 1 1 2 2 (9)
which leads to the following expression of 1 :

x Q / ( ) Q x r r x r x x x x 1 1 1 ) 1 ( 2 1 1 cos arc 2 2 Q 1 2 x - ≈         - - - ϕ = ψ + ψ ψ - ψ = - + - + (10) where 2 2 max / T T x =
. The approximate relation is obtained by considering r close to 1 and is such that

x ( ) 1 1 ) 1 ( 2 << - - r r x
. Then, the approximate relation is valid for frequencies near the resonance.

Half power beamwidth

The bandwidth obtained for

) 2 /( 2 max x T
is noted 1 . To resolve the interrelation between the angular beamwidth and the frequency bandwidth, a graphical method that is described in this x Q 2 / section is used. Two cases are considered: the case 0 f f ≤ , and the case . Note that is not defined at , because for these frequencies, the level of

+ ≤ ≤ f f f 0 dB 3 θ ∆ + > f f 2 T at normal is inferior to the half of 2 max

T

. The link between the beamwidth

dB 3 θ ∆
and the bandwidths 1 and 1 is shown in Fig. 4, for

x Q / x Q 2 / 0 f f ≤ . From this figure, the following relation can be obtained    θ ∆ 2 cos = - Q 1 x 2    dB x Q 1 ≈ - Q x 1 2 - - f f dB 0 , ≈ ≤ dB x Q / 1    θ ∆ 2 cos 3dB = - 2 Q 1 f 0 Q x 1 + - 0 f f f f f dB 0 , ≤ ≤ dB 3 θ ≤ 5 . 1 ≈            - 1 2 Q 1 3 2x dB (11)
With the approximation of a small beamwidth, the relation can be written :

3 2x 2 Q 1    θ ∆ ( 12
)
Using Eq. ( 10), the beamwidth is then given by

x 1 2 3 - θ ∆ (13)
Figure 5 shows the relationship between the beamwidth 3 θ ∆ and the bandwidths 1 and when . From the curve presented in Fig. 5, the following equation can be obtained

Q / + ≤ ≤ f f f 0            - 1 Q 1 x (14)
Then, at , with the approximation of a small beamwidth, and using Eq. ( 10), the beamwidth can be expressed as

+ ≤ ≤ f f 1 2 3 ≈ θ ∆ (15)
Now, the link between ∆ and 1 is obtained for all frequencies . Figure 6 exhibits the beamwidth versus frequency using Eqs. ( 13) and (15). From this figure, it can be seen that the minimum of is obtained for

Q / + ≤ f f dB 3 θ ∆
. By minimizing Eq. ( 13), one can see that the minimum of is obtained for

dB 3 θ ∆ = x
, and then it can be written

Q dB 2 min 3 θ ∆ (16)
The frequency corresponding to this value is obtained from

min 3 dB f θ ∆ Q Q f f f dB 5 . 0 1 2 5 . 1 0 0 min 3 ≈ = -θ ∆ (17) Then         - ≈ θ ∆ Q f f dB 2 2 1 1 0 min 3 (18)
For r close to 1, the quality factor is high and then is close to .

Q min 3dB f θ ∆ 0 f 2.

Applications

From the previous results, considering r close to 1, the minimum of the beamwidth

dB 3 θ ∆ is
obtained at a frequency , which is slightly smaller than the resonance . This frequency can be written as

min 3dB f θ ∆ 0 f         - ≈ θ ∆ Q f f dB 2 2 1 1 0 min 3 (19)

At

, the beamwidth is given by

min 3 dB f θ ∆ dB 3 θ ∆ Q dB 2 min 3 ≈ θ ∆ (20)
At , using Eq. (15) with , the following relation is obtained

0 f 1 = x Q f dB 1 2 0 , 3 ≈ θ ∆ (21)
The quality factor Q is obtained from the following equation

r r Q r ϕ - ≈ 1 2 1 ( 22
)
The knowledge of the reflection coefficient r allows then to obtain important parameters of the radiation patterns of the proposed antenna. For this, numerical simulations using the Finite Difference Time Domain (FDTD) method were carried out to obtain the reflection coefficient r , of an infinite grid of metallic wires with the following characteristics: and . In Fig. 7,

mm P 20 = mm a 2 =
T is plotted using Eq. ( 4) and the computed coefficient r , which is considered now dependent on the frequency.

GHz

In the following section, results from Eqs.( 19)-( 21) are compared with experimental data.

Experimental results

To validate our approach, a prototype of the structure was fabricated and measured. A monopole is used as an excitation source. Figure 8 gives the photograph of the fabricated antenna. The wires are 50 length and diameter, the number of wires in each row is 28 , the cavity is width, the period is , the monopole is 15 length and diameter.

The dimensions of the ground plane are . The radiation patterns of the proposed antenna were measured in an anechoic chamber located at INRS, in Montreal. As an example, the measured radiation patterns of the antenna in the H-plane and E-plane at are plotted in Fig. 9, showing two directive beams at the normal directions. Figure 10

°41

To conclude the experimental part, note that the matching of the antenna can be done at the frequency of maximum directivity using conventional techniques (e.g., stubs on the feeding line).

Conclusion

An analysis for enhancing the directivity of an antenna based on a Fabry-Perot cavity has been presented. The frequency of maximum directivity and the beamwidth at different frequencies have been predicted with new analytical expressions. An antenna prototype has been fabricated

and tested, and a good agreement has been achieved between theoretical and experimental results

showing the usefulness of the proposed approach.

t. 2 ,

 2 When T is plotted versus frequency at in the first abscise, and versus °= θ 0 ( ) θ cos at the resonant frequency in the second abscise. The bandwidth of GHz f 3 0 =

2 T

 2 values of ψ corresponding to the half of the maximum of . Then, resolving Eq. (6) gives

Figure Captions : FIG. 1 :FIG. 2 :FIG. 3 :FIG. 4 :FIG. 7 :FIG. 8 :FIG. 9 : 2 FIG. 10 :

 :1234789210 Figure Captions:

  From this figure, the resonant frequency of the

	structure is	f	0 =	3	GHz	. The modulus and phase of	r at	f	0	are	0	.	824	and 2	.	52	rad	,
	respectively. These values are used to calculate 1	/	Q	in Eq. (22). Then, it is possible to evaluate
	the frequency of maximum directivity and the beamwidth at this frequency and at the resonant
	frequency using Eqs.(19)-(21).
		cm
															mm
								cm	2
			2	.	85	GHz
																			.	85	GHz
									GHz
									28	.	8	.	2		.	85	GHz
														.	8	°		43	.	6	°

  exhibits the measured directivity versus frequency. From this curve, the maximum of directivity (corresponding to the minimum of beamwidth) is obtained at 2 .

	From Eq. (19), it is obtained	f	3 ∆ dB θ	min	≈	2	.	846	, which shows a good agreement with
	measured ones. The measured beamwidths are	°	and	at 2	and 3	,
	respectively. The results obtained from Eqs. (20) and (21) are 30	and	, these show also
	a good agreement with the previous experimental data.

FIG. 8 FIG. 9


Murat Bronz

Antoine Drouin

Experimental Verification of a Semi-Empirical V/STOL Aircraft Performance Analysis Method

Verification of a previously developed semi-empirical Vertical/Short Takeoff and Landing (V/STOL) aircraft performance analysis program is discussed. The proposed method uses actuator disk theory for the propeller slipstream velocity calculations starting from an input thrust. Semi-empirical formulations are used in order to estimate the forces and moments generated by the highly coupled propeller and wing interaction. The main objective of this study is to compare the results of the method with existing experimental measurement and determine the validity to use this method of calculation for the design optimization of V/STOL vehicles. Two existing NASA experiment cases are investigated and compared.

I. Introduction

V/STOL aircrafts offers unique mission characteristics with wide-speed flight envelope. Several configurations of V/STOL exists, and for a long time there have been an idea of distributing the propulsion system over the wings in order to enhance the performance. The idea of Distributed Electric Propulsion (DEP) was not feasible previously, where reciprocating and turbine engines used simply did not make it possible to practically build the vehicles. However, the possibility of using a DEP system has been widely investigated [START_REF] Deckert | Large-scale wind-tunnel tests of a deflected slipstream STOL model with wings of various aspect ratios[END_REF][START_REF] Kuhn | An investigation of a wing-propeller configuration employing largechord plain flaps and large-diameter propellers for low-speed flight and vertical take-off[END_REF][START_REF] Draper | Investigation of the Aerodynamic Characteristics of a model wingpropeller combination and of the wing and Propeller Separately at Angles of Attack up to 90 degrees[END_REF] . Recently, with the improvements on the electric propulsion systems, the use of electric system makes it possible to design an airframe that is well integrated with the propulsion system 4 in order to achieve big aerodynamic performance improvements. LEAPTech, [START_REF] Stoll | Drag Reduction Through Distributed Electric Propulsion[END_REF] shown in Figure 1, is a good example of a highly-DEP configuration. The complete wing is immersed inside the distributed propeller slipstream which increases the dynamic pressure over the wing. This results a significant wing surface reduction which makes the aircraft more efficient during the cruise flight conditions as the drag caused by the unnecessary wing surface that is needed only for the take-off and landing conditions is reduced. The V/STOL configuration with DEP is also interesting on the small scale, such as ISAE's tilt-body MAVION, which is a good example of a hand-release vertical take-off and afterwards transition to cruise flight concept. The GL-10, also shown in Figure 1, that is capable of vertical take-off by tilting its wing and then transition for an efficient cruise by adapting its multiple propellers located on the leading edge of the wing. Finally, the Pterosaur from ONERA is shown as an example for unconventional use of DEP system.

A. Problem Definition

The design of the mentioned configurations requires a good understanding of the interaction between the DEP system and the airframe. The propeller wing interaction is highly complex to solve without simplifications. Jameson 6 has developed semi-empirical formulations in order to estimate the force and moment generation on V/STOL vehicles which is the basis of the used method in this study. The inclined propeller forces are estimated based on De Young's method. [START_REF] De Young | Propellers at High Incidence[END_REF]

B. Present Work

Comparison with previous experimental measurements from NASA are presented following the brief explanation of the semi-empirical method that is used for the analyses. Last part of the paper discusses the intended use and the limits of the method.

II. Aerodynamic Model for Propeller Wing Combination

The semi-empirical estimation method of forces and moments of a propeller wing combination will be described briefly here for the consistency of the paper, interested readers should refer to the basis of the method by Jameson, [START_REF] Jameson | The Analysis of Propeller Wing Flow Interaction, Analytic Methods in Aircraft Aerodynamics[END_REF] and with additional moment and viscous drag contribution to Bronz and Drouin. [START_REF] Bronz | Preliminary Design Estimation of the V/STOL Airplane Performance[END_REF] An arbitrary number of propeller slipstreams is defined, with individual thrust, actuator disk area, position and orientation. The method is mainly based on momentum theory, so that the swirl effects of the propeller slipstream are not modeled. Inclined propeller thrust is estimated by DeYoung's method.

A. Propeller Forces

Blown Sections Unblown Sections

Figure 2. Showing the creation of wing sections according to the fully developed propeller slipstream width. Note that for each thrust value the sections will dynamically be changed in order to take into account the contraction.

The propeller forces are modeled according to actuator disk theory, for a given propeller thrust T , the ratio µ, between the free stream V ∞ and propeller jet slipstream V j , for a given actuator area of S p is given by

µ = V ∞ V j = 1 - T 0.5ρV 2 j S p (1)
Each individual slipstream is taken as circular form, and their contraction is estimated with

b pc = b p 1 + µ 2 (2)
where, b p is the propeller disk diameter or width, and b pc is the fully developed contracted slipstream diameter or width. Once the contracted slipstream diameter is calculated, the wing can be separated into sections, as shown in Figure 2, that are inside the propeller slipstream or outside. Note that the propeller slipstream is taken as fully developed for simplification reasons. Inclined propellers will deflect the free stream, which will change the angle of attack of the wing inside this slipstream. This downwash can be determined according to the inflow angle of the propeller α j as = Eα j according to Ribner 9 and De Young.

7 ∞ V L T j V ϵ N α + i w D α + i j Figure 3
. Shows the wing incidence angle iw, jet incidence angle i j , angle of attack of the fuselage α with the resultant lift L, drag D, thrust T and the propeller normal force N , propeller downwash , jet slipstream V j .

B. Actuator Inflow Angle Change due to Wing, Fuselage and Other Propeller Jets Upwash

Each actuator will be influenced by the fuselage, wing, and the other propeller jets. Taking these into effect, the inflow angle for each jet will be the sum of

α j = α + i j + U w (α + i w ) + U f α + otherjets U o j (3)
where, U w is the upwash due to wing, U f is the upwash due to fuselage and U 0 j is the upwash due to the other propeller slipstreams.

For each propeller slipstream , α j can be written as

α j1 = α + i j 1 + U w (α + i w ) + U f α + U oj 12 2 + • • • + U oj 1n n α j2 = α + i j 2 + U w (α + i w ) + U f α + U oj 21 1 + • • • + U oj 2n n α j3 = α + i j 3 + U w (α + i w ) + U f α + U oj 31 1 + • • • + U oj 3n n . . . α jn = • • •
for a half wing with n propellers mounted on the leading edge. U oj 12 presents the upwash effect of the second actuator on the first one. As long as there is a fuselage between the propellers separating the slipstreams, the upwash effects coming from the other wing can be neglected. Substituting from = Eα j , results a set of linear equations in the form of Ax = b.

Once the set of linear equations solved, and therefore the inflow angles α j can be found. Similarly, wing inflow angles for sections that are inside the freestream and that are inside the propeller slipstream will be

α w j1 = α + i w + U f α and α w jµ = α w j1 -+ jets U ∞ j (4)
Propeller normal force can be calculated with the assumption of being proportional to inflow angle α j as in C N = C Nα sin α j .

Resulting Lift Slope in a Slipstream is a function of the influenced mass flow around the wing. The essential difference between a wing in free stream of speed V ∞ , and a stationary wing immersed in a slipstream of the same speed V, is the reduction of the mass flow outside the slipstream and also a reduction in the mass flow influenced by the wing. The wing in free stream is influenced from a mass flow that is passing through a tube surface S ∞ of πb 2 /4 containing the wing tips. However, the wing in a slipstream passing through surface S j influences a smaller mass flow resulting a reduction in the effective span or aspect ratio of the wing.

In the case of a stationary wing immersed in a slipstream, compared to a wing in free stream, the same amount of lift has to be generated by deflection of a smaller mass flow through a greater downwash angle. Assuming that the additional downwash angle due to the slipstream is a constant fraction of the downwash of the wing in free stream, with a value of p, then the Aspect Ratio (AR) reduces to

AR 0 = AR 1 + p (5)

C. Partially Immersed Wing in Arbitrary Number of Slipstreams

The slipstream over the wing will be generated by individual propellers, and also there will be different propulsion configurations for different flight phases, hence an approximation in order to calculate the highly complex force, moments, and interactions. A simple estimation can be made by superposition of forces over the wing in free stream and the individual parts that are immersed in slipstreams. The individual parts that are immersed in slipstream are calculated as isolated planforms. Thus, the additional increase on each isolated planform will simply be the difference between the planform in free stream V ∞ , and the planform immersed in a jet slipstream V j moving with a forward speed of V ∞ . The difference in lift will be

∆L = 1 2 ρS w j (V 2 j CL α jµ α w jµ -V 2 ∞ CL α∞ α w j∞ ) (6)
where CL α jµ is the lift slope of the wing part that is inside the jet slipstream with a velocity ratio of µ = V ∞ /V j by taking the aspect ratio as b j /S w j . CL α∞ is the lift slope of the same wing part in a freestream, or in other words when µ = 1, α w jµ is the angle of attack of the wing in jet slipstream, and α w j∞ is the angle of attack of the same part in free stream. It should be noted that the angle of attack of the wing portion in jet slipstream is reduced compared to the angle of attack in the free stream by the slipstream downwash of . Additionally, an inclined slipstream to the free stream will generate an external upwash, which can be approximated by assuming the slipstream as a falling cylinder model. The upwash at a distance y from the center axis of the slipstream is b 2 j /2/y 2

According to, [START_REF] Jameson | The Analysis of Propeller Wing Flow Interaction, Analytic Methods in Aircraft Aerodynamics[END_REF] the average upwash over the external part of the wing will approximately be Sw j S . Taking all upwash effects of propeller jets, the increase in lift can be calculated by multiplying the sum of all slipstream upwash angle with the unblown surface area and the lift slope of the complete wing in freestream CL α∞ For the small angle of attack, lift force generated by the wing can be found by adding up the freestream lift of the complete wing, the additional lift created from the unblown parts of the wing because of the upwash effects of the jets, and finally the additional lift on the blown sections coming from dynamic pressure increase because of the jet velocities.

L = 0.5ρV 2 ∞ SCL α∞ + 0.5ρV 2 ∞ SCL α∞ S - jets S w j jets S w j S + jets ∆L j (7)
A similar approach can be used to calculate the additional induced drag for the wing section that are inside the slipstream. ∆D i can be calculated as the freestream lift of this section multiplied by the in induced downwash angle, plus the new induced downwash angle multiplied by the change in the lift ∆L.

∆D i = 0.5ρV 2 ∞ S w j CL j∞ (α i j -α i∞ ) + ∆Lα i j (8)
Finally, induced drag D i can be found by summing up the induced drag of the whole wing in freestream as if there were no propeller slipstreams on it, and the additional induced drag

∆D i D i = 0.5ρV 2 ∞ SkCL 2 ∞ + jets ∆D i j (9)
It should be noted that each wing section inside the propeller slipstream generates a lift force perpendicular to the local flow velocity and the drag force parallel to flow velocity. Therefore they should be rotated back by the propeller slipstream downwash angle and then summed in order to obtain the total lift force L ∞ and drag force D ∞ .

D. Effect of Flaps

The effect of flaps are modeled by an increase on the wing angle of attack as presented by Jameson. 6 α/δ ∞ being the flap effectiveness of three dimensional wing in free stream, effective wing incidence angle i w∞ becomes

i w∞ = i w + α/δ ∞ δ f (10)
where δ f is the flap deflection and,

α/δ ∞ = α/δ 2D + α/δ 2D AR+4.5 AR+2 AR α/δ 2D + AR+4.5 AR+2 AR (11)
Likewise for a wing section inside propeller slipstream, effective wing incidence i w jµ becomes

i w jµ = i w + α/δ jµ δ f (12)

III. Total Forces and Moments

A. Forces

For now, only longitudinal flight dynamics is considered, so that the lateral force and moments are assumed to be zero F y = M x = M z = 0 as in equilibrium. Contribution of the wing lift L ∞ , drag D ∞ , propeller thrust T , and propeller normal force N will be taken into account as The pitching moment is calculated by the resultant wing forces and moments as well. However, as the aircraft is capable of increasing its pitch attitude up to 90 degrees, the moment arm between the wing aerodynamic center and the center of gravity of the aircraft changes during this rotation as shown in Figure 4. The variation on pitch does also effects the position of aerodynamic center of the wing as experimentally tested by Draper and Kuhn. [START_REF] Draper | Investigation of the Aerodynamic Characteristics of a model wingpropeller combination and of the wing and Propeller Separately at Angles of Attack up to 90 degrees[END_REF] However we will assume it to be fixed. The thrust moment arm d T j does not change during the pitch variation. However lift force moment arm d L and drag force moment arm d D has to be calculated at every angle of attack as a result of moment arm length variation. Finally, the total pitching moment of the aircraft is found by

F z = L ∞ + jets T sin(α + i j ) + jets N cos(α + i j ) (13)
F x = D ∞ - jets T cos(α + i j ) + jets N sin(α + i j ) (14) B. Moment ∞ V T L ∞ D ∞ d L d D d T M y L ∞ D ∞ T d L d D d T
M y = M wing AC - jets T j d T j -L ∞ d L + D ∞ d D (15)

IV. Experimental Comparison

Explained method is parametrized in order to accept multi-variable input, such as the number of propellers, diameter, pitch, position and orientations, wing surface, different thrusts, etc... and written into a FORTRAN code. 5. The correlation between the theory and the experimental measurements shows an acceptable relation, especially on the C T = 0.91 case. However there are still some problems to be solved (mainly on the code) for the drag contribution when the wing is partially stalled.

Aerodynamic coefficients shown in the Figure 5 refers to the propeller slipstream velocity instead of freestream velocity as some of the experimental measurements done in static conditions where the freestream velocity is equal to zero. The drag coefficients shown, are calculated including the propeller thrust contribution too as the wing and the propellers work together in the system. The negative drag coefficients results from excessive amount of thrust contribution. The lift curve behavior is well estimated with the semi empirical theory. After the sharp high lift portion of the first lift curve (C T = 0.5), the estimations mismatch the experiment, and the drag coefficient of that case also have a huge error, which is still under investigation. Another experimental comparison is selected to be done with a four propeller wing from NASA TN-D-4448 Report. The general specifications of the test model is represented in Table 2. Two test case is examined, with thrust coefficient C T = 0 and C T = 0.856. Likewise, the lift coefficient C L versus angle of attack α variation, and drag coefficient C D is plotted respectively which are shown in Figure 6. There is no flap deflection on the wind-tunnel model, however the wing section airfoil camber is represented by flap deflection for the theoretical calculations. Lift curve slope match is visible for the two cases, however there is still some problems with the drag estimation.

V. Conclusion

A brief description of the semi-empirical method for estimating force and moments generated by a wing partially or fully immersed inside distributed propeller slipstream is given. The results obtained by the method is compared with experimental measurements coming from NASA TN3307 2 and TN-D-4448 1 reports for verification purpose. The wing configurations are simulated by the proposed method and comparison are shown. The program is capable of estimating the lift curve correctly, which will be useful during the conceptual design phase, however there is still some mismatch on the drag force estimations. Further verifications will continue as a future work through additional comparison with experimental measurements and numerical (such as CFD) simulations.

Figure 1 .

 1 Figure 1. Tilt-Body micro air vehicle MAVION from ISAE, a small demonstrator of NASA's GL-10, the LEAPTech Program from JobyAviation, and the Pterosaur from ONERA.

Figure 4 .

 4 Figure 4. Illustration of the moment arm length variation during pitch attitude change.

Figure 5 .

 5 Figure 5. Theory and experimental measurement correlation is shown for TN-3307, where the reference velocity is taken from the propeller slipstream velocity.

Figure 6 .

 6 Figure 6. Theory and experimental measurement correlation is shown for TN-D-4448, where the reference velocity is taken from the propeller slipstream velocity.

Table 1 .

 1 The final program is capable of analyzing any given configuration within the explained limitations. Comparison of the program with experimental measurements, and with other reliable numerical simulations is a must. Therefore, two comparison with NASA experiments are used as a test case. Further comparisons, with LEAPTech blown wing, both numerical simulations and experimental measurements are in progress. General specifications of the TN-3307 wind-tunnel model.

	A. Comparison with NASA TN3307 Report
	Experimental measurements are digitized
	by using the original report obtained from
	NASA Technical Report Service. The test	Wing Span	4.16	[m]
	case presented here is a two engined con-	Wing Surface Area	0.952	[m 2 ]
	figuration, with a +20 deg flap. The gen-	Mean Aero. Chord	0.457	[m]
	eral specifications of the test model is rep-resented in Table 1. Two different cases are simulated, with thrust coefficient C T = 0.5	Prop Diameter Section Airfoil	0.61 NACA0015	[m]
	and C T = 0.91. Lift coefficient C L versus	Section α C Lmax	14.0	[-]
	angle of attack α variation, and drag coef-
	ficient C D is plotted respectively which are
	shown in Figure

  B. Comparison with NASA TN-D-4448 Report

	Wing Span	13.19	[m]
	Wing Surface Area	30.56	[m 2 ]
	Mean Aero. Chord	2.31	[m]
	Prop Diameter	2.83	[m]
	Fuselage Diameter	0.91	[m]
	Section Airfoil	NACA63 2 416
	Section α C Lmax	16.0	[-]

Table 2 .

 2 General specifications of the TN-D-4448 wind-tunnel model.

Acknowledgments

The authors would like to thank Alex Stoll of JobyAviation for sharing the geometrical and aerodynamic specifications of the LEAPTech demonstrator wing with simulated results and experimental measurements. However, the authors have not finish the analyses therefore the results are not presented on the paper.


Debajit K Lakshmanaswamy

Das Gupta

Sailesh Toppo N

Biswajit Senapati

Multi-Layered Security by Embedding Biometrics in Quick Response (QR) Codes

Keywords: Authentication, Biometrics, QR codes, AES, Signal Processing

Biometrics is nowadays becoming more popular and prolific in highly secured areas where security is concerned with much priority. But with the advancement in technology, fingerprints can be easily duplicated & secured areas can be trespassed. QR code is another important innovation in the field of data storage which stores data in 2D format containing alphanumeric characters arranged in a matrix order. Moreover the disadvantage of misusing biometrics can be overcomed. Keeping in mind with the fact, the authors come up with the idea of transfusing Biometrics in QR codes which would not only provide much security to the prevailing system, but also reduce in many cost factors and complicacies. Such a kind of system can be used in highly authenticated areas where security is highly concerned. This system can also be implemented in MNC's where employees' need to shift to other branches or departments for a particular span of time.

I. INTRODUCTION

In this present world of technology and highly advanced secured services, biometrics has been widely used in many national and international organizations, agencies and bureaus. The main purpose of this biometric system is manifold including data entry of the inflow and outflow of persons in the organization, entry of only authorized personals, also in some areas used for mode of attendance too. Despite the advantages of biometrics, the data is very sensitive in the sense that a person cannot change a biometric trait. Biometric recognition systems should preserve the users' privacy by storing data in a much procured way. Fingerprint is considered highly risky as it can be traced easily. It means that fingerprint data may be seized without knowledge or consent, and used for unrevealed purposes. QR (Quick Response) Code is a type of 2-D bar code in the form of Matrix which was developed by Denso Wave. It is composed of black and white modules which became wildly known and used because of its reading speed, accuracy and functionality characteristic. It contains information in both vertical and horizontal direction. The maximum data capacity, within version 40 of the QR Code, is 7,089 numeric characters or 4,296 alphanumeric characters. QR Codes provides information for products in industry, data on a mailing label, or information on a business card. It is small in size and the pattern can be hidden or integrated into an aesthetically attractive image in any printed form such as newspapers, magazines, or clothing. Data can be converted into QR code by any means of QR generator which can be later electronically displayed or printed. In this paper, the authors propose the idea of collaborating biometrics within a QR code so as to overcome the disadvantages of the former. In the proposed system, the security would be two fold, i.e. the fingerprint of user will be loaded into the database and the overall information of the user including his/her name, designation, department, and etc. along with the user's fingerprint will be embedded into a QR code. As a user try to access permission for an authenticated service, he/she would be asked for a fingerprint scan. As the scan goes through the database, it asks for the QR code which contains the overall information of the user. Then the system compares with the output of the data from the fingerprint scan in the database and the QR code data, if both the data matches 100%, the person is allowed to access the service.

Advantages of biometrics

Biometrics is a feature which identifies and authorizes an individual over information using physiological features such as iris scans, face recognition, voice recognition, fingerprint scans and DNA tests. The main advantage of biometrics is that it uniquely identifies an individual even when there are variations in time. It minimizes ID fraud, buddy punching. Biometrics eliminates the problems when an ID card is lost or the password is forgotten by the user.

Disadvantages of biometrics

The disadvantage in biometrics is that 2D recognition it affected when a person's hair colour is changed and when the persons age increases. Sometimes when a person's voice changes due to cold he/she cannot be recognized by the biometric system.

Advantages of QR codes

QR codes stores information's that appear in magazines, business cards or any product that the user needs to know about.

Disadvantages of QR codes

The main disadvantage of QR code is sometimes it takes a lot of time to process identifying the data.

II. PROPOSED AUTHENTICATION SYSTEM A. SYSTEM ARCHITECTURE

We are proposing a new system which will strengthen the privacy of the user. In our implementation, we are combining the biometrics with that of QR codes so that forgery may be reduced. Firstly we are going to process the user's biometric data for use by system in subsequent authentication operations. Then, we are going to extract the biometric features and store it in the database/repository. Then we are going to create a QR code based on the user's information and store it in the software so that it may be a two tier security system which will be easier to find the forgery done by people. Fig 1: The tier 1 architecture shows that the biometric of a person is collected and then it is sent to a transmission which contains compression, encryption, decryption and decompress. We are going to use an AES algorithm which is encrypted to each data block so that it can prevent attacks from the outside world. After the encryption and decryption the signal is processed and sent to a quality checker where it checks whether the quality of the biometric is good or not. If the quality is bad the biometric device asks the user to give the input again. If the quality is sufficient it generates a template and matches with that of user's data residing in the database. Fig 3: The tier 2 architecture shows that the data is encrypted in the form of QR codes using a QR code generator. Once the user wants to get authorization the QR code reader will scan the data through a QR code reader. If the data matches the user is authorized.

Advantages of proposed system

The system thus so proposed has many advantages over the conventional usage of biometrics. Two tier authentication Enhanced security level Lower complicacies III. APPLICATIONS The proposed system has many applications in the daily life: E.g.: an employee of a company is requested to offer service for another branch or department of the same organization for a limited period of time till the project or the service work sustains. For this, the company has to provide the employee with a new set of ID card & also has to amend changes in the authenticated entrance in respective branch or department to authorize the employee. According to the conventional method, the organization just needs to change in the biometric system so as to allow the employee which can be misused. But the proposed system manages change in the biometric system database for the specific period of time providing a unique key in the QR code which would enhance the authentication of entrance. The system would also create a session timing of the entry and exit of the new alien employee which can be viewed by the database administrator. The key in the QR code would expire for the specific newly assigned location after a stipulated period of time, which would prevent further entry of that employee into the said location. If the service or the project work's designated time needs to be extended, both the departments, or the branches need to agree for the extension of the expiry of the key in the QR code. This system can also be used in many highly secured, authenticated and authorized areas where security is highly mattered like in defense and research areas.

Fig. 1 :

 1 Fig.1: QR code architecture

IV. CONCLUSION

The conventional mode of authentication is pretty unsecure where security systems can be bypassed and misused. By providing such an updated and highly secured two tier system, would not only bring a change in the security service but also provide the ease in many areas. The proposed system would be helpful in many of key security prioritized areas and also in many of organizations.


Cylindrical Periodic Structures of Metallic wires

Halim Boutayeb and Kouroch Mahdjoubi IETR -Institut d'Electronique et de Télécommunication de Rennes, Université de Rennes 1, Bât. 11 C, Campus de Beaulieu, 35042 Rennes -France. Halim.Boutayeb@univ-rennes1.fr

Abstract-First, we calculate the total field for an outgoing or an incoming TM cylindrical incident wave illuminating a cylindrical periodic structure of metallic wires. Then, we give analytical formulas to extract the characteristics (reflection and transmission) of the cylindrical periodic structure. To finish, we extend the study to infinite radius periodic structure by given an approximation of the dispersion diagram.

I-Introduction

Cylindrical periodic structures are not often used in antenna devices. Before associating this type of structures with an antenna it is important to understand there characteristics.

In part II, we calculate the total field due a cylindrical periodic structure of metallic wires illuminated by an outgoing cylindrical wave or an incoming cylindrical wave, outside and inside the cavity. Unlike in the plane case, in the cylindrical structure we have not access directly to the characteristics of the cylindrical surface because of the multiples reflections between the center and the surface. In part III, we show how to extract the reflection and transmission characteristics of a single cylindrical surface by the knowledge of the preceding results. In part IV, the multiple layer periodic structure characteristics are deduced from one surface characteristics.

II-Calculation of the total field

The cylindrical periodic structure of infinite long metallic wires (figures 1) have the following parameters : C is the radius of the cylinder, a is the diameter of the wires, P θ is the angular period, P t is the transversal period (P t =P θ *C) and N=360/P θ is the number of wires.

In figure 1a the structure is illuminated by a TM outgoing cylindrical wave and in figure 1b we consider a TM incoming cylindrical incident wave. For these two cases (case 1a and case 1b) we will calculate the total Electric field inside and outside the cylindrical cavity.

Figure 1 (b) Cylindrical periodic structure of metallic wires illuminated by an incoming cylindrical incident wave

Let us call E(ρ) the tangential composing of the total electric field in function of the distance ρ to the center The total field is the sum of the incident field and the diffracted field [START_REF] Harington | Time Harmonic Electromagnetic Field[END_REF].

For case 1a the expression of E is :

is : (1a) ( ) ( ) ( ) ∑ = ρ + ρ = ρ N 1 n dn n inc E K E E
For case 1b the expression of E is :

(1b) ( ) ( ) ( ) ( ) ∑ = ρ + ρ η - + ρ = ρ N 1 n dn n 0 a inc E K k j 2 exp( r 1 E E () Where ( ) ( ) ρ = ρ k H E 2 0 inc
for the outgoing cylindrical incident wave or

( ) ( ρ = ρ k H 1 0 ( ) ) E inc for the incoming cylindrical incident wave, ( ) ( )         x J x N 0 0 = arctan x 0 η
, J 0 (x) and N 0 (x) are the Bessel functions of order 0, and k is the free space wave number. r a is the reflection coefficient in the center which is equal to one when no object is placed in the center. E dn is the electric field diffracted by wire number n (n=1,…N). K n represent the unknown factors which contain the coupling between wires. Because of the symmetry theses factors don't depend on the wire considered :

(2)

( ) ( ) ∑ ∑ = = ρ = ρ N 1 n dn N 1 n dn n E K E K
K is determined by imposing zero to E at a surface of a metallic wire :

( ) ( ) 2 / a C N 1 n dn inc E E K + = ρ = ∑ ρ ρ - = , for case 1a, or ( ) ( ) ( ) ( ) 2 / a C N 1 n dn 0 a inc E k j 2 exp( r 1 E K + = ρ = ∑ ρ ρ η - + ρ - =
, for case 1b

(3)
In fact, for all wires but one this condition will be took in the center of a wire and for this wire the condition is took at a distance a/2. For small diameter of wire a comparing to the wavelength, E dn are approximated by the Hankel function of first order . The formulation of E 2 0 H dn are given below :

( ) ( )               π - ρ - ρ + = ρ N 2 1 i cos C 2 C k H E 2 2 2 0 di , i=1,…N. (4)
The total field E(ρ) is then given by (1a) or (1b) for the two cases 1a and 1b respectively.

Let us call T the total transmission coefficient outside the cylindrical cavity and R the total reflection coefficient inside the cavity at a distance D (<C) from the center :

( ) ( )

t inc P C , E E T + > ρ ρ ρ = (5) ( ) ( ) t inc P C D , E E R - < = ρ ρ ρ = (6)
We call T o the value of T when the incident wave E inc is an outgoing wave (case 1a) and T i when it is an incoming wave (case 1b). Similar definitions are given for R o and R i .

III-Characterization of a cylindrical periodic surface

(r, t) are the complex reflection and transmission coefficient of the cylindrical periodic structure of metallic wire for an outgoing cylindrical wave (figures 1a). (r', t') are the complex reflection and transmission coefficient of the structure for an incoming cylindrical incident wave (figures 1b). The purpose of this part is to determine (r, t) and (r', t') by the knowledge of T o , T i , R o and R i . Let us insist that the method that we will describe can be used even if the total field is calculated by an another method that the method of part II. In [START_REF] Cwick | Coupling into and scattering from cylindrical structures covered periodically with metallic patches[END_REF][START_REF] Mokhtar | Analysis of Cylindrical Frequency Selective Surfaces[END_REF] the problem of a source inside a cylindrical periodic surface have been also treated but the characteristics of the surface have not been given.

T o can be expressed in terms of (r, t) and r a (see figure 2a) :

( ) ( ) ( ) ( ) kC 2 j exp rr 1 t kC 2 jn exp r r t T 0 a 0 n 0 n a n o η - - = η - = ∑ +∞ = , where ( ) ( ) ( )         = η x J x N arctan x 0 0 0 (7)
R o is the wave at a distance D from the line source inside the cavity, normalized by the incident wave (figure 2b). R o can be expressed in terms of (r, t) and r a :

( ) ( ) ( ) ( ) ( ) kC 2 j exp rr 1 kD 2 j kC 2 j exp . r 1 R 0 a 0 0 o η - - η + η - + = (8)
With expressions ( 7) and (8), we can calculate the reflection and transmission coefficients (r, t) if we know R o and T o :

( ) C * D o a o B B R r 1 R + - r = , ( 9)

Figures 3 : (a) : Partial terms of the "total" transmission coefficient T i (b) : Partial terms of the "total" reflection coefficient R i inside the cavity

In figure 3a we can see that T i can be expressed in terms of (r', t') , (r, t) and r a :

( ) ( ) ( ) ( ) ( ) ( ) ( ) kC 2 j exp rr 1 kE 2 j exp tr ' t kC 2 j kE 2 j exp ' r 1 T 0 a 0 a 0 0 i η - - η - + η + η - + = (11)
1 R i can be expressed in terms of t', r and r a (figure 3a) :

( ) ( ) ( ) ( ) ( ) kC 2 j exp rr 1 kD 2 j exp r 1 ' t R 0 a 0 a i η - - η - + = (12)
With expressions ( 11) and ( 12), we can calculate the reflection and transmission coefficients (r', t') if we know R i and T i and (r, t):

( )

D a i C B r 1 R rB 1 ' t + - = ,       - - - = C a E a i * C E B rr 1 B r ' tt 1 T B B 1 ' r (13) where , B , ( ) ( )
kC j 2 exp B 0 C η - = ( ) ( ) kE j 2 exp 0 E η - = ( ) ( ) kD j 2 exp B 0 D η - = , ( ) ( ) kC j 2 exp B 0 * C η = (14)
-2

IV-Radius periodic structures

In Figure 4a and Figure 4b, we plot the magnitudes of (r, t) and (r', t') and the phases of r and r' obtained with R 0 ,T 0 , R i and Ti (obtained in part II) for two examples : C=40mm and C=120mm respectively , with P t constant. We see that (r', t') tend to (r, t) as C increase. In Figure 5 we can see that the resonances of T o are well given by the intersections of the phase of r and 2kη 0 (kC). The condition of continuity r+1=t have been verified also.

The value of |T o | superior to one (Figure 5) correspond to a matching of the ideal source (r a =1) and must not be took as a gain enhancement. We can note that an enhancement of the bandwidth of the resonance of [T o | can be obtain if ϕ r increase with frequency. This can be obtained with a negative index material as it is observed in [START_REF] Ziolkowski | Artificial material that exhibit electromagnetic responses generally not found in nature[END_REF] . ) )

If we consider, now, two surfaces 1 and 2 (Figure 6), and if we consider only the reflections between these two surfaces (considering a matched source, i.e. r a =0), then the transmission coefficient must be equal to : Figure 6 represent a cylindrical structure of two layers with a source in the center. Figure 7 give an example of the transmission coefficient of this structure if r a =0.

( ) ( ) ( ( ( ) r 0 0 2 1 2 1 2 P C k 2 j exp kC 2 j exp r ' r 1 t t T + η - η - = (
The case of multiple surfaces is easy to obtain (by recurrence) and it is not necessary to develop it.

We consider, now, an infinite number of cylindrical surfaces. In the same way than in the plane case, we can consider that the cylindrical wave propagate in the structure with a constant of propagation β (cylindrical Floquet equivalent theorem). We can see [START_REF] Boutayeb | Radius Periodic Cylindrical Structures[END_REF] also that the dispersion equation of the plane case is a good approximation of the dispersion equation :

) P k sin( 2 y j ) P k cos( ) P cos( r r r + = β (16)
Where k is the wave number, P r the radius period and y=2(1-t)/t the normalized equivalent impedance of a cylindrical surface. The cylindrical surfaces have the same period P t and then the same characteristics when C is sufficiently large. Figure 8 represent a radius periodic cylindrical structure of multiple layers. Figure 9 give the modulus of M=cos(kP r )+jy/2sin(kP r ) (16), βP r and also the magnitude of the reflection coefficient r 6 of a six layer structure of metallic wires. A frequency band gap appears when |M|>1 (no real solution for β) where |r 6 | is near 1.

V-Conclusion

We have seen how to obtain the mains characteristics of a cylindrical periodic surface of metallic wires and of multiple layer radius periodic cylindrical structure. These methods will be used to design new types of antennas.

Figure 1

 1 Figure 1(a) Cylindrical periodic structure of metallic wires illuminated by an outgoing cylindrical incident wave

Figures 2 :

 2 Figures 2 : (a) : Partial terms of the "total" transmission coefficient T o (b) : Partial terms of the "total" reflection coefficient R o inside the cavity

Figure 4 :

 4 |t|,|t'|, |r|, |r'|, ϕ r et ϕ r' for (a) : C=40mm (b) : C=120mm (a, b) Pt=pi/6*40mm constant

Figure 5 :

 5 Figure 5: the resonances of |T o | correspond to the intersections between ϕ r and 2η 0 (kC) (C=200mm, a=1mm, P θ =30°, P t =pi/6*200mm ≈105mm)

  15)This is the cylindrical equivalent of the Fabry-Perot cavity in the plane case.

Figure 7 :

 7 Figure 6 : Two layer cylindrical periodic structure

Figure 9 :

 9 Figure 8 : Multiple layer cylindrical periodic structure