Florian De

Francesco Salvarani
email: francesco.salvarani@unipv.it

GPU-ACCELERATED NUMERICAL SIMULATIONS OF THE KNUDSEN GAS ON TIME-DEPENDENT DOMAINS

Keywords: Transport equation, Particle methods, GPGPU, moving domains. monocomponent gases

We consider the long-time behaviour of a free-molecular gas in a time-dependent vessel with absorbing boundary, in any space dimension. We first show, at the theoretical level, that the convergence towards equilibrium heavily depends on the initial data and on the time evolution law of the vessel. Subsequently, we describe a numerical strategy to simulate the problem, based on a particle method implemented on general-purpose graphics processing units (GPGPU). We observe that the parallelization procedure on GPGPU allows for a marked improvement of the performances when compared with the standard approach on CPU.

Introduction

In this paper we consider an ideal rarefied gas contained in a deformable vessel with absorbing boundary, kept at a uniform temperature.

When the mean free path of the gas molecules has the same order of magnitude of a characteristic macroscopic length (for example, the size of the vessel), continuum fluid dynamics is not valid, and we need to use a kinetic description, as described, for example, in [START_REF] Cercignani | Rarefied gas dynamics[END_REF][START_REF] Cercignani | The mathematical theory of dilute gases[END_REF].

However, since kinetic equations are defined on the phase space of the system, the number of independent variables makes, from a computational point of view, their numerical simulation much more expensive than the numerical computations of standard fluid mechanics.

A popular strategy for the numerical study of kinetic equations is the particle method, which has been declined in a number of interesting variants, such as, for example, the Bird method [START_REF] Bird | Molecular gas dynamics and the direct simulation of gas flows[END_REF] and the Nanbu-Babowski method [7,[START_REF] Babovsky | On a simulation scheme for the Boltzmann equation[END_REF].

The particle method is based on the physical ground that leads to write the equations (and not on the equations themselves); among the main quantities used in the simulations, indeed, one can find the mean free path between collisions, the particle free flow and the collision frequency.

In practice, the particle method simulates a gas, composed by a number of particle that is not far from the Avogadro number, by a reduced set of particles (whose number can be handled by a computing machine) that simulate the global behaviour of the whole gas.

It is clear that such a method can obtain great benefits from a parallelization procedure.

Indeed, the evolution of the particles is caused by the free flow (which can be treated in a completely parallel way) and, in the case of collisional gases, by the mutual interactions between particles, which are instantaneous in time, local in space, and involving only a pair of particles in each collision.

In the situation studied in the paper, we consider the case where the gas is so rarefied that the interaction between the gas molecules is neglected. Such a gas is called the free-molecular gas or the Knudsen gas and, in the case of moving domains, exhibits a variety of different behaviours in what concerns its long-time evolution.

After a theoretical analysis of the long-time asymptotics of the Knudsen gas in a moving vessel, we implement a simulation algorithm of the problem suitable to run on a general purpose GPU (GPU-based architecture dedicated to high performance computing).

GPUs today reach a performance up to 3 TFLOPS at a fraction of the cost of CPU-based architectures of similar performance. The use of this kind of hardware architectures allows one to handle a greater number of numerical particles (up to 10 8 per board) and hence to noticeably improve both the speed and the precision of the numerical results.

Finally, we notice that, the free transport equation being the first step of a splitting method concerning the numerical simulation of the Boltzmann equation, the results presented here can be useful in the simulation on GPU of the full Boltzmann equation on moving domains.

The paper is organized as follows: in the next section we provide the theoretical background of the problem; then, in Section 3, we explain the numerical method. Finally, in Section 4, we show and analyse our numerical simulations.

Basic mathematical properties of the problem

In order to give a solid benchmark framework for our computations, we first set up the theoretical aspects of the problem, and prove the main results that we will reproduce in the numerical simulations.

Consider an open bounded domain Ω 0 ⊂ R d , d ∈ N, with a regular boundary Γ 0 = ∂Ω 0 , at least of class C 1 , which evolves with respect to time.

The deformation of Ω 0 that leads to the domain

Ω t ⊂ R d , t ∈ R + is described by a function Φ : R + × R d → R d .
In other words, for any x 0 ∈ Γ 0 , the vector x t 0 = Φ(t, x 0 ) defines the surface Γ t = ∂Ω t , which is the boundary of the domain of the problem at time t.

We suppose that Φ is regular, at least of class C 1 , and moreover that ∂ t Φ(t, x 0 ) R d ≤ c (c > 0), uniformly for all x 0 ∈ Ω 0 and for all t ∈ R + . In other words, we suppose that the velocity of the boundary is finite.

The problem considered in the paper consists in studying the time evolution of a collisionless gas, described by the classical transport equation

(2.1) ∂f ∂t + v • ∇ x f = 0, (t, x, v) ∈ R + × Ω t × R d ,
where f := f (t, x, v) is the density of particles which at time t and point x move with velocity v.

The problem is supplemented with the initial and boundary conditions

(2.2) f (0, x, v) = f in (x, v) ∈ L p (Ω 0 × R 3 ), f (t, x, v)| x∈Γ t = 0 where 1 ≤ p ≤ +∞.
Restrictions on the regularity of the initial data and on the properties of the domain Ω t will be consider later on, when focusing on some special features of the problem.

A crucial tool in studying Equation (2.1) is the forward exit time for a particle starting from x ∈ Ω 0 in the direction v ∈ R d , defined as

τ Ω t (x, v) = inf{t > 0 : x + tv ∈ Γ t }.
In what follows, we denote by B q (s) the ball centred in s ∈ R d of radius q ∈ R + and its volume by meas(B q (s)), that is

meas(B q (s)) = π d/2 Γ(n/2 + 1)
.

The proof of the following theorem is immediate:

Theorem 2.1. Suppose that ∂ t Φ(t, x 0 ) R d ≤ c uniformly for all x 0 ∈ Ω 0 and for all t ∈ R + . Then, Problem (2.1)-(2.
2) admits a unique solution for any p ∈ [1, +∞] and for all t ∈ R + . Moreover, the only stationary solution of this problem in the class of L p -functions is f = 0.

Proof. The unique explicit solution of the problem is

(2.3) f (t, x, v) = f in (x -vt, v)1 τ Ω t (x,v)>t ,
as shown by the method of characteristics. It is finally straightforward to prove that the only possible stationary solution of Equation (2.1), with vanishing boundary condition is f = 0, since the stationary version of equation (2.1)

reduces to v • ∇ x f = 0.
Hence the theorem is fully proven.

Another important feature of the problem is its long-time asymptotics. The situation is more complex than the corresponding problem in a fixed domain, and a variety of behaviours occurs: sometimes the convergence to zero is achieved in a finite time, in some other cases the speed of convergence is algebraic, sometimes there is no convergence towards equilibrium.

We point out that the possibility of algebraic convergence is not surprising, as shown by Bernard and Salvarani in [START_REF] Bernard | On the convergence to equilibrium for degenerate transport problems[END_REF] for the linear transport equation and by Aoki and Golse [START_REF] Aoki | On the speed of approach to equilibrium for a collisionless gas[END_REF] for the Knudsen gas in a vessel whose wall is kept at a uniform and constant temperature, assuming diffuse reflection on the vessel wall.

We have the following result:

Theorem 2.

Let us consider the initial-boundary value problem (2.1)-(2.2). The following behaviours concerning the long-time asymptotics of the problem are possible:

1) If Ω t is uniformly bounded for all t ∈ R + by an hypersphere B R (0), with R > 0, and there exists V > 0 such that supp (f in ) ⊂ Ω 0 × (R d \ B V (0)), then the extinction time of the solution f is finite. 2) If Ω t is uniformly bounded for all t ∈ R + by an hypersphere B R (0), with R > 0, and f in ∈ L ∞ (Ω 0 × R d ), the solution converges to zero. Moreover, we have the following estimate on the speed of convergence towards the asymptotic state:

f (t, • , • ) L 1 (Ω t ×R d ) ≤ meas(B R (0)) f in L ∞ (Ω 0 ×R d ) 4R t d .
3) If Ω t is not uniformly bounded by an hypersphere B R (0), with R > 0, then it may exist no stationary state.

Proof. The strategy of proof is different in the three cases. 1) Since Ω t is uniformly bounded for all t ∈ R + by the hypersphere B R (0), and v ∈ (R d \ B V (0)), by looking at the explicit solution (2.3) we can deduce that the worst forward exit time is τ B R (0) (x, v) ≤ 2R/V , and hence the extinction time is finite. 2) We use a technique based on an upper solution of the problem, defined on a fixed hypersphere B R (0), with R > 0 (which is such that Ω t ⊂ B R (0) uniformly for all t ∈ R + by hypothesis). We hence consider the function g, solution of the problem

∂g ∂t + v • ∇ x g = 0, (t, x, v) ∈ R + × B R (0) × R d ,
with the initial conditions g(0, x, v) = f in (x, v) when x ∈ Ω 0 and g(0, x, v) = 0 when x ∈ B R (0) \ Ω 0 , and with absorbing boundary data

g(t, x, v)| x∈∂B R (0) = 0.
It is straightforward to prove that

g(t, x, v) = f in (x -vt, v)1 τ B R (0) (x,v)>t ,
and that g ≥ f for a.e. (t,

x, v) ∈ R + × Ω t × R d . In general, we have that g(t, • , • ) L 1 (B R (0)×R d ) ≤ f in L 1 (Ω 0 ×R d )
. We now suppose that t > 0. Thanks to the explicit form of g and the fact that its domain of definition is fixed, we have that

g(t, • , • ) L 1 (B R (0)×R d ) ≤ B R (0)×R d f in (x, v)1 x∈Ω 0 dxdv ≤ f in L ∞ (Ω 0 ×R d ) B R (0) 2R/t -2R/t . . . 2R/t -2R/t dxdv 1 . . . dv 1 dv d = Vol(B R (0)) f in L ∞ (Ω 0 ×R d ) 4R t d ,
which is the desired result.

3) We give the following counterexample: Ω t = B 1+2t (0) and

f in = 1 v R d ≤1 on B 1 (0) × R d . The explicit form (2.
3) of the solution implies that

R d ×R d f dxdv = meas(B 1 (0)) 2
for all time t > 0, and hence there exists no extinction time.

Remark 2.3. The situations listed on Theorem 2.2 are not exhaustive nor optimal. They depend, indeed, on the geometry of the moving domain, together with the functional form of the initial conditions.

The numerical strategy

The basic point of a particle method is the discretization of the unknown function f by means of a sum of Dirac masses, centred in (x k (t), v k (t)) 1≤k≤N , which represent a set composed by N ∈ N macro-particles that evolve in the phase space of a system.

More precisely, our working hypothesis is the approximation

f = N k=1 ω k δ(x -x k (t)) δ(v -v k (t)),
where ω k is the weight of the k-th particle.

Once the number N of numerical particles has been chosen, we initialize the problem by approximating the initial condition f in by means of

f in (x, v) = N k=1 ω k δ(x -x 0 k ) δ(v -v 0 k ),
and then the time evolution of the system is obtained by deducing the time evolution of the macro-particles on the characteristic curves of the problem (2.1)-(2.2). In our case, we obtain the following evolution rule for the free flow of the numerical particles:

   x ′ k (t) = v k (t), v ′ k (t) = 0, under the initial conditions (x k (0), v k (0)) = (x 0 k , v 0 k ), for all 1 ≤ k ≤ N .
The method is naturally conservative and highly parallelizable. In the next section, we shall give the details of the numerical strategy.

Implementation and benchmarks

We have produced two different codes, the first one is a classical sequential code, and the second one is based on a thread-based GPU parallelization technique.

The numerical tests on the long-time asymptotics of the problem allow to evaluate the mean GPU speedup factor compared to a sequential monothread CPU computation. The speedup factor is evaluated as a function of the number of particles N . The hardware being used is a PC with an Intel Xeon CPU E56202.40 GHz and a nVIDIA GPGPU TESLA C2070, 448 cores with 6 GB memory, 14 multiprocessors, 510 Gflop/s in double precision and 960 Gflop/s in single precision.

All the computations presented here have been performed in single precision. The nVIDIA CUDA toolkit 4.1 is used.

In all computations, we have considered a three-dimensional spatial problem, i.e., all positions and velocities of the particles belong to a subset of R 3 . This means that each particle is individuated at each time instant t by a set of six independent variables in the phase-space R 3 × R 3 .

We have then performed three numerical tests which represent the three prototypes of the behaviours described in Theorem 2.2.

Let x = (x 1 , x 2 , x 3 ) ∈ R 3 and v = (v 1 , v 2 , v 3 ) ∈ R 3 .
We first consider the sphere B r (0), where the radius r = r(t) is given by

r 2 (t) = e -t + 2(1 -e -t ), t ≥ 0.
We numerically studied the time evolution of the problem with two different initial data,

f in 1 = 1 {(x,v)∈R 3 ×R 3 : |x i |≤1/2, 1/4≤v i ≤1, i=1,2,3} and f in 2 = 1 {(x,v)∈R 3 ×R 3 : |x i |≤1/2, |v i |≤1, i=1,2,3}
, by using 2 20 = 1, 048, 576 numerical particles, and for t ∈ [0, 10].

We observe the finite in time extinction of the solution for the initial condition f in 1 (Figure 1) and the extinction with time rate t -3 for the initial condition f in 2 , as expected, the latter plotted both in linear and in logarithmic scale (Figures 2 and3). In this case we have also computed the numerical decay rate with a least square methods on the time interval t ∈ [START_REF] Cercignani | The mathematical theory of dilute gases[END_REF]10]. The numerical decay rate is equal to 2.98, a value which is very close to the theoretical one, d = 3.

We finally consider the domain B 1+3t/5 (0), with initial data f in 1 . In Figure 4 we recover the behaviour predicted by the third point in Theorem 2.2, namely the absence of an asymptotic equilibrium state (which should have L 1 -norm equal to zero). Again, in the simulation shown in Figure 4 we have used 2 20 numerical particles. In all cases, the GPU results are identical to the CPU ones up to the rounding error.

On each time step the particles are moved according to their velocity. The particle weight is set to zero once a particle leaves the sphere of interest.

In the parallelized code, this task is done in parallel on the GPU. For each discrete instant, we also compute the L 1 -norm of the distribution according to the discrete formula:

f (t, • , • ) L 1 (R 3 ×R 3 ) = 1 N N i=1 1 ( x i (t) ≤r(t)) .
This GPU parallel reduction requires particular attention for performance purpose. Actually we use the GPU shared memory for partial reduction on each CUDA block. We based our implementation from the CUDA GPU Computing SDK 4.1, reduction example. The numerical complexity of a reduction operation (sum, max, . . . ) on an array of size N over P processors is known to be O(N/P + log(N )).

The CUDA kernel function of the particle positions and the weight update are given by the following instructions: We have then compared the results of the parallel code with respect to a standard C sequential code.

The GPU parallel code does not take into account the reduction of the active particles due to the absorbing moving boundary. Indeed, a dynamical particle table would require many memory accesses to be managed, that would lead either to a loss of performance with respect to the code without particle reduction or a strong implementation effort, requiring high GPU programming skills.

On the other hand, the sequential code can be easily optimized by remapping the particles with positive weight and by eliminating the particles that are absorbed by the boundary.

The algorithm that reduces the current number N of active particles has been implemented in C language as follows:

j=0; for(i=0;i<N;i++) { if ( weight[i] > 0.0) { x1[j] = x1[i]; v1[j] = v1[i]; x2[j] = x2[i]; v2[j] = v2[i]; x3[j] = x3[i]; v3[j] = v3[i]; weight[j]= weight[i]; j=j+1; } } N=j;
In what follows, we consider only the simulation generated by the initial condition f in 2 into the sphere B r(t) (0). The other tests give very similar results, and hence they are not reported here.

On Table 1, we give the mean speedup factor obtained on the C2070 board, where the number of particles N varies from N = 2 19 = 524, 288 to N = 2 23 = 33, 554, 432 particles, with t ∈ [0, 4]. In all tests, the number of particles with positive weight at the final time t = 4 is only the 6.37% of the initial particles.

One can observe a speedup factor of over 25 for N = 2 25 particles. For relatively small numbers of particles, the speedup varies between 17 and 25. This behaviour is certainly due to a stronger rate of memory communication. We would like to end this section with a general comment and a deep question about code comparability.

It is, of course, difficult to define an absolute measure of performance speedup between a sequential code and a GPU-accelerated one.

It has indeed been shown that code optimizations which may be done on the sequential code are not always relevant for GPU implementations: the constraints on the algorithm are strongly depending on the physical behaviour of the problem and some strategies, that are very efficient in a sequential code, can be counter-productive on a parallel code (for example, when they would imply a lot of memory rearrangement).

An example of this behaviour can be seen when compared the sequential code that we used here with the same code without particle reduction: we found that the speedup factors are very sensitive to the initial condition, on the evolution law of the moving domain and the on time interval.

By using as initial condition f in 2 into the sphere B r(t) (0), with 10 5 particles, the code with particle reduction is 1.45 times faster than the code without reduction when the simulation covers the time interval [0,5], whereas the code without reduction is twice faster than the code with reduction when the simulation covers the time interval [0,1].

Moreover, because CPU are generally made of 4 or 6 cores, researchers are disputing the fact that performance speedup should be measured from a monothread computation rather than a multithreaded run (using openMP for example).

For that reason, it is of course of paramount importance to clearly specify the comparison methodology.

Conclusions

We have presented an implementation of a GPU-accelerated particle method to numerically simulate a Knudsen gas in a vessel with moving boundary with absorbing boundary conditions.

After proving some possible dynamics of convergence to equilibrium, we have recovered, in the numerical simulations, the theoretical results.

The parallelized code gives a considerable improvement of the performances of the code (up to a factor 26) and allows us to handle a greater number of numerical particles than those allowed by standard sequential programming. Since the free transport step is also an essential part of any particle method for space-inhomogeneous kinetic system, this improvement of the performances will be useful also for the simulation of collisional gases.

Figure 1 .

 1 Figure 1. Evolution of the L 1 -norm of the discrete distribution generated by the initial condition f in 1 into the sphere B r(t) (0).

Figure 2 .

 2 Figure 2. Evolution of the L 1 -norm of the discrete distribution generated by the initial condition f in 2 into the sphere B r(t) (0) (linear scale).

Figure 3 .

 3 Figure 3. Evolution of the L 1 -norm of the discrete distribution generated by the initial condition f in 2 into the sphere B r(t) (0) (logarithmic scale).

Figure 4 .

 4 Figure 4. Evolution of the L 1 -norm of the discrete distribution generated by the initial condition f in 1 into the sphere B 1+3t/5 (0).

  float)exp(-1.0*k)*1.0 + (1.0-exp(-1.0*k))*2.0; // xupdate<<<grid, block>>> (dev_x1, dev_x2, dev_x3, dev_v1, dev_v2, dev_v3, dev_weight, c); reduce<float>(N, numThreads, numBlocks, whichKernel, dev_weight, d_odata); // // sum partial sums from each block on CPU // copy result from device to host // (of size numBlocks*sizeof(float)) cudaMemcpy(h_odata, d_odata, numBlocks*sizeof(float), cudaMemcpyDeviceToHost); gpu_result = (float)0.0; // small loop for (int i=0; i<numBlocks; i++) {gpu_result += h_odata[i]; } This has to be compared with the C code of the time loop including the call of the particle update kernel and the reduction kernel for the computation of the L 1 -norm: __global__ void xupdate(float *x1, float *x2, float *x3, float *v1, float *v2, float *v3, float *weight, float c) { int tid = threadIdx.x + blockIdx.x * blockDim.x; while (tid < N) { x1[tid] += dt * v1[tid]; x2[tid] += dt * v2[tid]; x3[tid] += dt * v3[tid]; weight[tid] *= (x1[tid]*x1[tid] + x2[tid]*x2[tid] + x3[tid]*x3[tid] < c); tid += blockDim.x * gridDim.x; } }

Table 1 .

 1 Total GPU time computation and speedup factor relatively to a sequential (optimized) CPU computation.

	Nb of particles N GPU time (sec) GPU/CPU speedup factor
	2 19	0.99	17.6
	2 20 = 1, 048, 576	1.96	18.0
	2 21	3.89	18.7
	2 22	7.37	22.6
	2 23	14.78	24.4
	2 24	29.60	24.7
	2 25 = 33, 554, 432	60.39	26.3

Acknowledgements

The authors would like to thank nVIDIA for the TESLA equipment Grant in 2011 that made this work possible.


P Pe T E R K A ,

P N A V R Átil

J Maria

B Dussardier

R Slavík

P H O N Z Átko

V Kubeček

Self-induced laser line sweeping in double-clad Yb-doped fiber-ring lasers

Keywords: fiber laser, ring cavity, long-period fiber grating, claddingpumping, ytterbium, tunablelaser

Experimental observation of the self-induced laser line sweeping (SLLS) in fiber ring lasers is presented. The SLLS with the same gain fiber is studied in Fabry-Perot cavity for comparison. The SLLS effect manifests itself as a laser wavelength drift with speed of the order of nanometer per second from shorter to longer wavelengths across several nanometers and fast backward jump. Recently, the dynamics of the SLLS in a Fabry-Perot cavity fiber laser was qualitatively described by a dynamic grating induced by spatial-hole-burning in the ytterbium doped fiber where the lifetime of the grating was related to the self-sustainedrelaxation oscillations. In this paper we address possible discrepancies between the published theoretical model and earlier observations of SLLS, particularly in fiber-ring lasers. We show that the qualitative theoretical model developed for explaining SLLS in the Fabry-Perot cavity can be used also to explain the SLLS effect we observed earlier in fiber-ring lasers.

Introduction

In recent years we have been witnessing stunning achievements in rising power of cw fiber lasers and also in substantial increase of their share in global laser markets. On the other hand, rare-earth doped fiber lasers are subject to instabilities and various self-pulsation regimes which can lead to catastrophic damage of concerned components and relatively little work has been reported on these damage mechanisms. Particularly notorious in this regard are ytterbium-doped fiber lasers (YDFLs) [1]. The self-pulsation regimes have been attributed, e.g., to reabsorption in an unpumped part of the YDF [2], external perturbations like pump instabilities [3], scattering processes [4] and ion-pairs formation [5].

An interesting self-pulsing regime accompanied with laser line drift with time was observed in solid-state lasers in early days of lasers [6,7]. Despite several decades of intensive research of fiber lasers, the first detailed description of this so-called self-induced laser line sweeping (SLLS) in fiber lasers appeared only very recently [8]. The main characteristic of this effect is the self-scanning of laser line from shorter to longer wavelength, spanning over several nanometers, and its instantaneous bouncing backward. The time period of this sweeping is usually quite long, of the order of seconds. Kir'yanov and Il'ichev attributed this spectacular effect to spatial-hole burning (SHB) caused by standing-wave in the Fabry-Perot cavity. Kir'yanov and Il'ichev also noted that the effect was already mentioned in our previous work dealing with ringcavity YDFL [9]; with sweep achieved over a relatively broad range of 1076 -1084 nm.

Other important reports about the SLLS were published shortly after [8] by Lobach et al. [START_REF] Lobach | Proc. of 20th International Laser Physics Workshop (LPHYS'11)[END_REF][START_REF] Lobach | [END_REF]. They proposed a qualitative theoretical model of the SLLS and their theoretical findings correspond well to the experiments reported in the paper. However, there are two issues that need to be addressed. First, the fiber-laser in [8] is supposed to oscillate in continuous-or quasi-continuous-wave (cw) mode, while for the description in [START_REF] Lobach | Proc. of 20th International Laser Physics Workshop (LPHYS'11)[END_REF] the self-pulsing laser dynamics plays a fundamental role in the SLLS. The quasi-cw mode in [8] was described as "self-spiking with the characteristic times in a 1µs range" and pulse energies were much weaker than those arising at the spectral bursts regime. This description can be in principle coherent with the self-sustained relaxation oscillations supposed in the model of Lobach et al. However it was not specified whether the SLLS was observed uniquely in quasicw mode or also in truly cw mode. The other issue is that the SLLS effect reported in [9] deals with a unidirectional ring-cavity laser that generally does not involve any SHB. Therefore building of the dynamical grating in the cavity cannot be explained by the standing wave of the Fabry-Perot cavity and it is a question whether the recent explanations [8,[START_REF] Lobach | Proc. of 20th International Laser Physics Workshop (LPHYS'11)[END_REF] can describe the observed effect in fiberring lasers. In this paper we address the two above mentioned issues with particular emphasis on explaining the SLLS origin in fiber-ring laser cavities.

Laser setups and the SLLS theory

The effect of SLLS was observed up to now principally in two configurations of fiber lasers which are schematically shown in Fig. 2. The gain fiber was always an ytterbiumdoped double clad fiber. The Fabry-Perot setup in [8] differs from the one in Fig. 2a in that the GT-Wave ytterbium doped fiber bundle was used thus eliminating the need of the pump and signal combiner. In addition to the setup in Fig. 2a, Lobach et al. tested also a fiber-Bragg grating or fiber-loop-mirror as one of the Fabry-Perot resonator mirrors. The ring laser studied in [9] exploited one or more long-period fiber gratings (LPFGs) for selection of the laser wavelength or the ring laser was left lasing without any wavelength selective element.

In this paper we study both the Fabry-Perot and ring laser setups shown in Fig. 2. In both cases, the gain medium was a double-clad YDF (Liekki-nLight Yb1200-6/125DC) with nominal 2.6d B /m peak absorption in the inner cladding and 1200 dB/m in the core. The inner cladding has an octagonal shape with 125 µm average diameter and the core has the diameter of 6 µm and numerical aperture of 0.13.T h eo u t e rc l a d d i n gi sm a d e from low refractive index polymer. The laser output of the Fabry-Perot laser was obtained from perpendicularly cleaved fiber ends and in the case of ring YDFL the output was obtained from a fused optical fiber coupler. Usually, the 80% branch of the coupler was used for the output. Apigtailedopticalfiberisolatorwasinsertedintothering cavity to ensure unidirectional propagation of the laser signal. The fiber isolator was the main lossy element in the cavity and as such it was placed behind the output coupler where the laser signal is minimal. Such a position also helped to prevent damage of the isolator by eventual self-Q-switched pulses. This configuration is commonly used for high-power fiber-ring lasers [3]. In the experiments, we used one multimode-pump laser diode pigtailed with multimode fiber of 105 µm core diameter. Unless otherwise stated, the temperature of the pump laser diode was stabilized to 25 • C and its central wavelength at maximum output power of 6Wis 975 nm.TheLPFGwasinscribedonto the passive fiber (Fibercore PS1250/1500) by CO 2 laser with the grating period of 177 µm and length of 16.5mm providing a band stop filter centered at 1070 nm with 3dB and 10 dB suppression width of 32 nm and 18 nm,respectively. Insertion of the LPFG into the ring resonator leads to modification of the net spectral gain of the laser. In such aw a yt h eo p e r a t i n gw a v e l e n g t ho ft h er i n gl a s e rc a nb e selected in a wide range [9].

The SLLS effect was explained by Kir'yanov and Il'ichev by strong interference of narrow-linewidth, contra-propagating beams inside Fabry-Perot cavity. Superposition of the bouncing beams inside the Fabry-Perot cavity would create an interference pattern of nodes and antinodes in the YDF and consequently it would make a grating of higher signal gain (at nodes) and lower gain (at antinodes). This grating in turn causes movement of the longitudinal laser modes to the modes with better spatial overlap of higher gain areas in the YDF. From the spectral point of view the self-written grating exhibit itself as an inhomogeneous gain broadening. The gain/loss spectrum is then modulated by a function proportional to sinc(C(λλ 0 )) where the constant C depends primarily on the grating length and λ 0 is the wavelength of the narrow-bandwidth, high-power beam. The strength of the modulation depends on amplitudes of the interfering waves, rare-earth ions concentration, grating length and eventually on other factors. Such a spectral modulation is well known from applications in erbium doped fiber lasers, e.g., narrowing and stabilization of the linewidth of erbium doped fiber laser can be achieved by standing-wave saturation effect in an unpumped section of erbium doped fiber [12] or by SHB in twin-core fiber with cores doped with erbium [13].

Explanation of the sweeping dynamics was proposed by Lobach et al. [START_REF] Lobach | Proc. of 20th International Laser Physics Workshop (LPHYS'11)[END_REF]. Similarly to the early works on ruby lasers [7] they noticed that the SHB leads to self-sustained relaxation oscillations and therefore the laser generation occurs in the spiking mode. They observed square root dependence of both the sweep rate and frequency of selfpulsation on the laser output power. Based on this observation they linked the frequency of relaxation oscillations and the sweeping rate and they found that the sweeping rate is proportional to P out /L,w h e r eP out is the laser output power and L is the cavity length.

Experimental results

For studying of the issue of the pulsed or cw operation of the SLLS, we have first built the Fabry-Perot YDFL according to Fig. 2a. The YDF length was 5m .F o rm o nitoring of the laser output spectra and temporal behavior we used one of the unused branches of the pump and signal combiner. About 0.5% of the laser signal is coupled into one pump branch of the combiner. The output spectrum was monitored by the CCD type spectrometer Ocean Optics HR2000CG-UV-NIR with 1nmresolution. Under certain conditions, namely above laser threshold, we observed a drift of the laser wavelength with stable speed. The drift period is of the order of seconds; see the video sequence captured by the spectrometer in Fig. 2. The period of this particular SLLS is 3.24 s.W ed e t e c t e dt h e spectra also with a grating-monochromator-based optical spectrum analyzer (OSA) ANDO AQ-1425. spectra for several pump power levels are shown in Fig. 3a. The OSA resolution was set to 0.2nm.Measuringofone spectrogram in high-sensitivity mode of the OSA takes 44 s.T h e r e f o r e ,t h ec o m bl i k es t r u c t u r eo ft h es p e c t r ao f 0.88 W of the pump power may indicate a periodic effect with period of the orders of seconds. The periodic effect is even more clearly manifested when the OSA is set to power meter mode, so that the output at a preset wavelength is recorded with time, see Fig. 4a. The resolution of the OSA was widened to 0.5nmin order to avoid misdetection of the sweeping because of too narrow entrance slit of the OSA. The temporal behavior of the laser output was also detected by an InGaAs photodetector with 1.2GHzbandwidth and displayed by a digital oscilloscope (100 MHz bandwidth, 1G S a /s). Typical oscillogram of the SLLS regime is shown in Fig. 5a. Beating between neighboring longitudinal modes of the laser is apparent from the detail of one of the peaks in the inset of Fig. 5a. The separation of the longitudinal modes of 9.82 MHz was detected. This value corresponds to a 10.5m -long cavity. The SLLS mode of operation was observed for pump power just above threshold to about 0.9Was it is marked in the laser output characteristic vs. input pump power in Fig. 6. For higher pump powers, the SLLS regime disappeared and instead, a chaotic self-pulsation regime was established, with peak power higher than that of the peaks in Fig. 6 by several orders of magnitude. The characteristic pulse width was less than 10 ns.

For studying of the SLLS in fiber ring lasers, we added af u s e dfi b e rc o u p l e ra n da ni s o l a t o rt ot h eF a b r y -P e r o t laser setup to form a ring cavity as shown in Fig. 2b. The laser outputs measured by the OSA are shown in Fig. 3b and Fig. 4b. No LPFG was included in the cavity. Similarly to the OSA measurements of the Fabry-Perot laser shown in Fig. 3a and Fig. 4a, the SLLS effect is clearly manifested even in the ring-laser setup. The SLLS effect disappeared for pump powers above 0.95 W and instead we observed competition of cw lasing at various wavelengths. It can be seen in the laser spectrum for the pump power of 1.82 W in Fig. 3b. We also observed the effect of SLLS in the ring YDFL configuration with LPFG, though weaker than in the two preceding laser configurations. Incorporation of LPFGs into the fiber laser cavity can shift the laser wavelength, while preserving possibility of relatively wide laser-line sweeping range. This feature may be found useful in eventual application of SLLS where a specific wavelength range of sweeping would be needed. As an example we present evidence of SLLS in ring YDFL with one LPFG in the cavity. The laser setup is shown in Fig. 2b. The YDF length was 3m .T h ec a l c u l a t e dg a i np r o fi l eo ft h e combined YDF and LPFG is shown in Fig. 7 together with spectral characteristics of the LPFG sample and the calculated gain of the YDF itself. The laser output spectrum is also shown in the figure to pinpoint the position of the maximum cavity gain. The 3-dB gain bandwidth of the combined YDF and LPFG is about 20 nm, i.e., less than a half of the 3-dB gain bandwidth of the YDF itself. The temperature of the pump laser diode was stabilized to 30 • C in order to enhance the pump absorption in the shorter fiber at lower pump powers. The laser outputs measured by the OSA in power meter mode are shown in Fig. 4c for the pump power just above threshold and in Fig. 4d for the pump power close to the upper limit of SLLS regime. The observed wavelength range of SLLS was about 1n m .T y p i c a lo s c i l l o g r a m sa r es h o w n in Fig. 5b. The temporal characteristics of the SLLS in Fig. 5b are consistent with the two preceding laser configurations, i. e., the laser output is a train of 1-2slong pulses envelopes with apparent beating of longitudinal modes of the ring laser cavity.

Discussion

The issue of the cw or pulsed operation of the SLLS regime of laser operation we studied in case of the Fabry-Perot and ring laser without LPFG. We have carefully scanned through the pump powers within the range of the SLLS and observed the time behavior of the laser output. We have never obtained cw mode of laser oscillation in this range. The laser was always in pulsed regime similar to that shown in Fig. 5a. This correspond well to the regime described as quasi-cw regime in [8] or as the selfsustained relaxation oscillations [START_REF] Lobach | Proc. of 20th International Laser Physics Workshop (LPHYS'11)[END_REF]. Our observations are consistent with the model proposed by Lobach et al.

The SLLS in a unidirectional fiber ring laser could have been attributed to various sustained self-pulsing instabilities or to temperature drift. For example, similar time period was observed in time fluctuations of interference fringes of the all-fiber Michelson interferometer used for measuring of the chromatic dispersion of optical fibers [14]. However, time period of these fluctuations changes in time or the fluctuations are not periodic at all, while the SLLS in ring lasers described here exhibits good long-term stability. It should be mentioned that the thermal effects as a cause of the SLLS in Fabry-Perot fiber lasers were excluded in discussion in [8].

Following the detailed reports and investigations for the origins of the SLLS in [8,[START_REF] Lobach | Proc. of 20th International Laser Physics Workshop (LPHYS'11)[END_REF], we have tried to find the parasitic Fabry-Perot cavity in our ring YDFL. Possible sources of reflections could be the non-ideal splices and perpendicularly cleaved ends of the output coupler and the pump and signal combiner. Although the main portion (about 89%)ofthelasersignalistransmittedthroughthe signal port of the combiner, about 0.5% of the laser signal arrives at each of the pump branches too and can be reflected. One of the main sources of reflection would be the perpendicularly cleaved end of the output coupler. Taking into account the transmission of the combiner and the coupler and neglecting the splice losses of the YDF and the combiner, about 1.5% of the laser output can be reflected back to the YDF. Indeed, after addition of a fiber terminated with an angle-polished connector to the 80% branch of the output we achieved cw regime of operation of the ring YDFL for the whole range of available pump power. In contrast to observation of SLLS in Fabry-Perot cavities, where the SHB is caused by standing wave between both cavity mirrors, in the case of the ring laser the standing wave responsible for SLLS was created by interference of the laser signal wave and its single weak reflection at the output coupler. It means that the interference between only two counter-propagating laser signal waves in the ring YDFL may lead to sufficient modulation of the ytterbium population inversion and create the dynamical grating responsible for the SLLS.

Conclusions

We reported details about the observation of SLLS in three different fiber laser configurations: Fabry-Perot, ring without wavelength selective element and ring laser with LPFG. We have found that the SLLS effect in ring cavities can be explained also by creating a dynamical grating in longitudinal distribution of population inversion of ytterbium along the gain fiber as it was explained recently for the Fabry-Perot cavities. However, in contrast to the papers of Kir'yanov and Il'ichev and Lobach et al., the dynamical grating in the YDF was not created by the standing wave of the laser signal oscillating between the two mirrors of the Fabry-Perot cavity, but instead by relatively weak interference of the laser signal with reflection from the output coupler. We have observed that a sustained self-pulsing is acharacteristicfeatureoftheSLLSregime,whichisconsistent with the findings of Lobach et al. The turning-up of SLLS in fiber lasers may help laser designer to find source of possible parasitic reflections and sources of instabilities. Although the SLLS is an undesired effect in YDFL intended for cw mode of operation, this effect may find useful in interrogation of optical fiber sensor systems. Indeed, the cavity and pump power regions of YDFL can be optimized to provide relatively wide and stable SLLS output. One particular advantage of such a swept source is its simplicity as it does not require any external driving electronics, apart from the pump laser diode driver.

Figure 1

 1 Figure 1 Setup of the fiber laser in Fabry-Perot (a) and ring configuration (b).

Figure 3

 3 Figure 3 Fiber laser output spectra measured by the monochromator-based OSA: (a) Fabry-Perot and (b) ringlaser cavity.

Figure 4

 4 Figure 4 Fiber laser output measured by the monochromatorbased OSA in power-meter mode: (a) Fabry-Perot resonator, (b) ring-laser cavity, and (c, d) ring laser with LPFG.

Figure 5

 5 Figure 5 Oscillograms of the laser output: (a) Fabry-Perot resonator, pump power 0.6W,and(b)ringlaserwithLPFG,pump power 0.74 W.Thefinestructureofpulsesisshownintheinsets.

Figure 6

 6 Figure 6Output power characteristics versus pump power for various cavity configurations. The SLLS mode of operation exists up to pump power level depicted with an arrow.

Figure 7

 7 Figure 7 Transmission of the LPFG used in the and calculated gain of the YDF. The net gain bandwidth is limited by the LPFG. The position of the laser wavelength is on a side of attenuation band of the LPFG.

  Figure 2Video recording of the time drift of the laser wavelength of the Fabry-Perot fiber laser for pump power of 0.8W . The video was captured by the CCD-type spectrometer (video is available on-line).

		1000			0.000 s 0.615 s
					1.229 s
	Intensity, a. u.	250 500 750			1.843 s 2.458 s
		0
		1070	1075	1080	1085	1090
			Wavelength, nm
	The recorded

manuscript version

Acknowledgments This work was supported by the French-Czech program Barrande (EGIDE-France, project No. 17360VA and Czech Ministry of Education, Youth and Sports, project No. ME10119); and by the European action COST TD1001.


Wilfried Blanc
email: wilfried.blanc@unice.fr

Valérie Mauroy

Bernard Dussardier
email: bernard.dussardier@unice.fr

Valerie Mauroy
email: valerie.mauroy@unice.fr

Erbium-doped nanoparticles in silica-based optical fibres

Keywords: Optical fibres, Erbium, Spectroscopy, Nanoparticles, Phase separation, Silica, Alkaline-earth elements

Developing of new rare-earth (RE)-doped optical fibres for power amplifiers and lasers requires continuous improvements in the fibre spectroscopic properties (like shape and width of the gain curve, optical quantum efficiency, resistance to spectral hole burning and photodarkening,…). Silica glass as a host material for fibres has proved to be very attractive. However some potential applications of RE-doped fibres suffer from limitations in terms of spectroscopic properties resulting from clustering or inappropriate local environment when doped into silica. To this aim, we present a new route to modify some spectroscopic properties of rare-earth ions in silicabased fibers based on the incorporation of erbium ions in amorphous dielectric nanoparticles, grown in-situ in fiber preforms. By adding alkaline earth elements, in low concentration into silica, one can obtain a glass with an immiscibility gap. Then, phase separation occurs under an appropriate heat treatment. We investigated the role of three alkaline-earth elements: magnesium, calcium and strontium. We present the achieved stabilization of nanometric erbium-doped dielectric nanoparticles within the core of silica fibers. We present the nanoparticle dimensional characterization in fiber samples. We also show the spectroscopic characterisation of erbium in preform and fibre samples with different compositions. This new route could have important potentials in improving rare-earth doped fibre amplifiers and laser sources.

Introduction

Developing of new rare-earth (RE)-doped optical fibres for power amplifiers and lasers requires continuous improvements in the fibre's spectroscopic properties (like gain and efficiency characteristics, resistance to spectral hole burning and photodarkening,…) besides reduction in device size and economical efficiency. Silica glass as a host material for fibres has proved to be very attractive. However some potential applications of REdoped fibres suffer from limitations in terms of spectroscopic properties resulting from clustering or inappropriate local environment when doped into silica. Several mixedoxide and non-oxide alternatives to silica have been successfully proposed to obtain spectroscopically improved amplifying singlemode fibres, however inducing fabrication difficulties and high cost.

The route of interest here consists of using silica as a mechanical host and support of the fibre optical waveguide, and of embedding RE-ions within oxide nanoparticles of composition and structure different from those of silica, and small enough to induce acceptable scattering loss. When nanoparticles have a crystalline structure the term Transparent Glass Ceramics (TGC) is used [START_REF] Clara Gonçalves | Rare-earth-doped transparent glass ceramics[END_REF], however they may also be amorphous, such as those obtained by phase separation [START_REF] Zarzycki | Glasses and the vitreous state[END_REF]. In the following we use the term TGC in both cases for convenience.

Scarce reports on RE-doped TGC singlemode fibres use low melting mixed oxides prepared by a rod-in-tube technique [START_REF] Samson | Nickel-doped nanocrystalline glass-ceramic fiber[END_REF], or mixed oxyfluorides using a double-crucible technique [START_REF] Samson | Efficient neodymium-doped glass-ceramic fiber laser and amplifier[END_REF], both with a subsequent ceramming stage. However the low melting point of these materials causes low compatibility with silica components. Transition metaldoped silica-based TGC fibres were prepared by MCVD (Modified Chemical Vapour Deposition) and using a slurry method [START_REF] Yoo | Development of a glass optical fiber containing ZnO-Al2O3-SiO2 glass-ceramics doped with Co 2+ and its optical absorption characteristics[END_REF], i.e. the particles were synthesized before insertion into the silica tube-substrate. We have proposed a more straightforward technique allowing to embed RE ions within in-situ grown oxide nanoparticles in silicabased preforms [START_REF] Acapito | Role of CaO addition in the local order around Erbium in SiO 2 -GeO 2 -P 2 O 5 fiber preforms[END_REF]. The implemented principle is the spontaneous phase separation process [START_REF] Zarzycki | Glasses and the vitreous state[END_REF] : Silicate systems can exhibit strong and stable immiscibility when they contain divalent metals oxides (MO, where M= Mg, Ca or Sr). For example, if a silicate glass containing few mol% MO is heated it will decompose into two phases : one silica-rich and one MO-rich in shape of spherical particles. Two key advantages of this process are that (i) nanoparticles are grown in-situ during the course of the fabrication process and (ii) there is no need (and associated risks) of nanoparticles manipulation by an operator. Further, the process takes advantage of the high compositional control and purity typical of the MCVD technique.

In the present paper, we aim at showing the potential of a simple technique to produce silica-based fibres with the core made of a spectroscopically-modified RE-doped TGC. We report on the growth of erbium-doped MO-silicate nanoparticles, that are stable after the fibre drawing stage using the MCVD and solution doping techniques. The nanoparticles mean diameter varies strongly with the composition. Losses as low as 0.4 dB/m at 1350 are reported, acceptable for fibre amplifier or laser applications. Further it is shown that the Er 3+ emission band is broadened when compared to a standard Erdoped fibre. This demonstrates the potentiality of this fabrication technique for applications such as fibre amplifiers.

Experimental details

Preforms were fabricated by the conventional MVCD technique. In this process, gaseous chlorides (SiCl 4 , GeCl 4 , POCl 3 ) are passed through a rotating silica tube, heated by an external burner in translation along the tube. Due to the high temperature, chlorides oxidize, forming particles which deposit on the inner wall. This porous layer turns into a glassy layer when the burner passes over it (the tube external temperature is around 1500 °C). In the final stage, the tube is collapsed into a rod at a temperature higher than 1800°C. Fibres were obtained by stretching preforms in a drawing tower at temperatures higher than 2000 °C under otherwise normal conditions. Opto-geometric properties of the perform (or fibre) are determined by adjusting the composition and number of layers. In our samples, phosphorous and germanium concentrations are ~1 mol% and 2 mol%, respectively.

Erbium and alkaline-earth ions were incorporated through the solution doping technique. An alcoholic solution (of desired strength of ErCl 3 .6H 2 O or MCl 2 .6H 2 O) is soaked for two hours in the unsintered core layer. After removing the solution, the layer is dried and sintered. Erbium concentration is estimated through absorption spectra to be around 100 ppm. Three alkaline-earth concentrations in the solution were prepared: 0, 0.01 and 0.1 mol/l. The core diameter in the preforms was measured with a preform analyzer (York Technology P 101 ) to be 1 mm. It is about 8 m in fibres.

Nanoparticles and attenuation characterizations

The fibres were characterized through scanning electron microscopy (SEM, backscattered electrons). One typical SEM picture from the exposed core section of a cleaved fibre is shown on Fig. 1. The nanoparticles are visible as bright spots, showing the important composition contrast compared to the silica background. The fibre core corresponds to the grey disk. The dark central part of the core is caused by the evaporation of germanium and alkaline-earth elements; this is a common artifact of the MCVD technique. It can be corrected by process optimization. The nanoparticles formation is linked to the addition of alkaline-earth ions.

Analysis of SEM images reveals that nanoparticle mean size depends on the alkalineearth elements and its concentration. In the case of calcium and strontium incorporation, nanoparticle mean size is around 100 nm, and bigger nanoparticles are observed. This leads to a high level of scattering of light. In the case of magnesium incorporation, nanoparticles with a mean size of ~40 nm are obtained and the inter-particle distance is within the 100-500-nm range. No particle bigger than 100 nm was observed in these MgO-doped fibres, unlike the case of CaO and SrO-doped fibres. When the solution concentration increases from 0.1 to 1 mol/l, the density of particles remains nearly the same but the mean particle diameter almost doubles to ~ 80 nm. For laser and amplifier fibres, the most promising composition is based on the magnesium incorporation. The scattering loss in Mg-doped fibre was measured through the cut-back method. The fibre bending radius was kept > 20 cm to minimize bend loss. The 0.1 mol/l Mg-doped fibre attenuation spectrum is displayed in Fig. 4. At the wavelength of 1350 nm, losses were measured to be 0.4 dB/m only. This value is comparable with the attenuation measured in low-melting temperature transparent glass ceramics fibres [START_REF] Samson | Nickel-doped nanocrystalline glass-ceramic fiber[END_REF] and is compatible with amplifier applications. It is considered as a promising result. The Increase in loss with decrease in wavelength is attributable to stronger light scattering induced by the nanoparticles. Due to the small particle size we assume Rayleigh scattering to be the major source of scatter loss, which was estimated according to the formula: (dB/m)=4.34.C Rayleigh .N., where N is the DNP density (m -3 ), is the overlap factor between the field and the core containing the DNP ( = 0.3 in fiber A) and C Rayleigh (m 2 ) is the Rayleigh scattering coefficient [START_REF] Bohren | Absorption and scattering of light by small particles[END_REF]:

(

) 1
where d is the nanoparticle diameter, n m and n n the host material and particles refractive indices, respectively. The actual particle composition is not known but a high content of MgO is expected [START_REF] Stebbins | Characterization of Phase Separation and Thermal History Effects in Magnesium Silicate Glass Fibers by Nuclear Magnetic Resonance Spectroscopy[END_REF]. The nanoparticle refractive index is estimated at ~ 1.65, like that of Mg-based oxide such as Mg 2 SiO 4 [START_REF] Burshtein | Refractive index dispersion and anisotropy in Cr 4+ :Mg 2 SiO 4[END_REF]. Under these considerations, fitting of the experimental data with Eq. 1 yields a particle density N~ 0.4 10 20 m -3 , or equivalently a mean inter-particle distance ~300 nm. These values agree well with the results collected from the SEM pictures taken from cleaved fibres.

At 1350 nm, the normalized frequency V was lower than 1.3 (LP 11 mode cut-off wavelength is 700 nm). The difference between experimental data and Rayleigh scattering curve above 1350 nm is attributed to bending loss only. However for practical application, the presented fabrication technique allows any necessary waveguide optimization without preventing the TGC growth. The attenuation of 1 mol/l Mg-doped fibre was extremely high (several 100s dB/m), in agreement with the Rayleigh formula (120 dB/m) assuming large monodisperse 100 nm particles. This shows that the particle mean size must be less than 50 nm for potential applications, and that the technique presented here is able to produce fibres with acceptable scattering loss. The composition of a Ca-doped sample was investigated by EDX analyses. When nanoparticles are analyzed, Ca, P and Si is found while only Si is detected outside of the particles. Germanium seems to be homogeneously distributed over the entire glass. When erbium is added to the composition, it is found to be inserted into the particles as it is presented on figure 5. Such conclusion was also drawn when emission intensity of Er 3+ was mapped on the end-face of a cleaved fibre under a confocal microscope [START_REF] Blanc | Erbium emission properties in nanostructured fibers[END_REF]. No erbium fluorescence is detected outside the DNP. This result was expected due to the low solubility of silica (or even germano-silicate) for rare-earth ions, whereas strongly modified and amorphous silicates, such as in the DNP, have a high solubility for these ions. These results indicate that erbium ions are located inside or very close to the DNP. At room temperature, it was observed that erbium emission depends on calcium concentration. For the lowest concentration (0.01 mol/l), when no DNP are observed, erbium emission is similar to that from a standard silica erbium-doped preform where no calcium is added to the core composition (Figure 6). However, when calcium concentration is 0.1 mol/l, erbium emission spectrum is broadened (Figure 6). At very low temperature, the same was observed (not shown here). Such a broadening is also observed for different concentrations of Mg in fibres (figure 7). It is assumed that the change of local order around the erbium ions embedded into the alkaline-earth ions rich phase is responsible of the observed broadening. This luminescent broadening is the signature of a sensible modification of the close environment of rare earth ions in DNP-doped fibres, compared to standard silica fibres. Such assumptions were also supported by RFLN and EXAFS spectroscopy [START_REF] Blanc | Erbium emission properties in nanostructured fibers[END_REF][START_REF] Acapito | Role of CaO addition in the local order around Erbium in SiO 2 -GeO 2 -P 2 O 5 fiber preforms[END_REF].

Conclusion

A method to fabricate nanostructured Er 3+ -doped fibres entirely through the MCVD process is demonstrated. By adding magnesium to the silica-based composition, nanoparticles of 40 nm in diameter are obtained through in situ growth without requiring a separate process to realize nanoparticles (such as post-process ceramming). Such fibres have low-loss. Moreover, a broadening of the emission spectrum by as much as almost 50% is observed with attractive features to realize gain flattened fibre amplifiers. More generally, this concept has great potentials as possible solutions to nowadays issues in amplifying fibres, including (but not limited to) amplifiers intrinsic gain flattening and/or spectral hole burning, amplifiers irradiation strengthening, photodarkening in fibre lasers, etc.

Figure 1

 1 Figure 1 SEM pictures of fibres doped with 0.1 mol/l of calcium.

Figure 2

 2 Figure 2 SEM pictures of fibres doped with 0.1 mol/l of magnesium.

Figure 3

 3 Figure 3 SEM pictures of fibres doped with 0.1 mol/l of strontium

Figure 4

 4 Figure 4 Transmission spectrum of a Mg-doped fiber (0.1 mol/l). Dots: experimental data, full line: calculated Rayleigh scattering curve.

Figure 5

 5 Figure 5 Energy Dispersive X-ray Analyses spectra of the preform sample doped with Ca and Er. (a) within a nanoparticle, (b) in the surrounding host, away from nanoparticles.

Figure 6

 6 Figure 6 Room temperature erbium emission spectra in standard preform (dashed line) and DNPdoped preform with 0.01 and 0.1 mol/l of calcium (grey and black line, respectively). Excitation wavelength is 980 nm.

Figure 7

 7 Figure 7 Room temperature emission spectra from Mg-doped fibres. The Mg concentration in the doping solution is 0.1 (A) and 1.0 (B) mol/l, respectively. Excitation wavelength is 980 nm.

Acknowledgements

This work was partly supported by CNRS (France), the Ministère des Affaires Etrangères (France) and Department of Science and Technology (India) through an Indo-French Research Network 'P2R' program. LPMC is a member of the GIS 'GRIFON' (http://www.unice.fr/GIS/). The authors thank Michèle Ude and Stanislaw Trzésien (LPMC, Nice, France) for samples preparation and Luan Nguyen (CRHEA, Valbonne, France) for SEM Analyses.

he commenced with the Centre National de la Recherche Scientifique (CNRSmade by using a Modified Chemical Vapour Deposition (MCVDnanostructuration of optical fibre by phase separation.


Ali Makke

Nicolas Le Sommer

Yves Mahéo
email: yves.maheo@univ-ubs.fr

Nicolas Makke

Le-Sommer

TAO: A Time-Aware Opportunistic Routing Protocol for Service Invocation in Intermittently Connected Networks

Keywords: Service invocation, Opportunistic Networking, Disconnected Mobile Ad hoc Networks

Handheld devices owned by nomadic people can form intermittently connected mobile ad hoc networks spontaneously. Such networks appear as an attractive solution for service providers, such as local authorities, in order to extend a pre-existing infrastructure-based network composed of several infostations so as to provide nomadic people with application services in a large scale area (e.g., a city). In such hybrid networks, intermittent connections are prevalent, and end-toend paths between clients and providers cannot be maintained all the time. Service provisioning thus remains a challenging problem today in these networks. In this paper, we propose a new time-aware opportunistic routing protocol called TAO. TAO is designed for service invocation in intermittently connected hybrid networks. This protocol makes it possible to select the best next message forwarder(s) among a set of neighbor nodes based on the dates of contacts of these nodes with infostations, and tends to implicitly estimate the distance separating these mobile nodes and the infostations. This paper gives a detailed description of this protocol supported with some simulation results.

I. INTRODUCTION

With the increasing proliferation of handheld devices equipped with a wireless interface, such as smart-phones or internet tablets, new kinds of applications, services or networks relying on spontaneous communication, interaction and collaboration can be considered. Such devices, which can form mobile ad hoc networks spontaneously, can be exploited in order to extend networks composed of some sparsely distributed infostations across a large area, (e.g., a city), and so to create hybrid networks in which infostations can act as service providers and mobile devices as service clients. This kind of networks, illustrated in Figure 1, is said hybrid because they are formed of a fixed part (the set of infostations connected together via a wired infrastructure) and a mobile part (the ad hoc network of mobiles nodes). Hybrid networks could appear as an opportunity for service providers, such as local authorities, to provide nomadic people with new ubiquitous services, without resorting to any expensive infrastructure, such as those provided by Global System for Mobile Communications (GSM) operator companies.

The fixed part of these hybrid networks can obviously present various topologies. For instance, the services can be provided by dedicated servers that can be accessed by the mobile devices through the infostations, which act as gateways. We focus in this paper on message routing in the mobile part of the hybrid network. Consequently, we will assume, without loss of generality, that a service is provided by an infostation, directly or via another infostation.

Both the free movements of people and the short communication range of Wi-Fi wireless interfaces accompanied with the radio interferences induce some frequent and unpredictable disruptions in the communication links. These disruptions entail the creation of disconnected communication-islands formed near or far from the infostations embedded in the physical environment (see Figure 1). Moreover, the volatility of the devices, which are frequently switched off due to their limited power budget, increases the number of changes in the network topology. In these networks, which we will qualify as intermittently connected hybrid networks (ICHN), it is difficult, and most often even impossible, to maintain an endto-end path between two devices thanks to traditional routing protocols designed for wired networks or thanks to dynamic routing protocols such as Ad hoc On Demand Distance Vector (AODV) or Optimized Link State Routing Protocol (OLSR).

To cope with these issues, routing protocols devised for networks that suffer from frequent and unpredictable disruptions, such as delay tolerant and opportunistic networks, implement the "store, carry and forward" general principle. When two devices cannot communicate directly because they are not in the transmission range of each other, these protocols make it possible to exploit other mobile nodes as intermediate relays that can carry a copy of a message when they move and forward it afterwards to other nodes so that it eventually reaches its destination. The provision of application services with this kind of opportunistic and asynchronous communications has been addressed so far only by a few number of research works [START_REF] Mahéo | Service Invocation over Content-Based Communication in Disconnected Mobile Ad Hoc Networks[END_REF], [START_REF] Sommer | A Middleware Support for Location-Based Service Discovery and Invocation in Disconnected MANETs[END_REF], [START_REF] Conti | Opportunities in Opportunistic Computing[END_REF], [START_REF] Conti | From opportunistic networks to opportunistic computing[END_REF]. Mahéo and Said [START_REF] Mahéo | Service Invocation over Content-Based Communication in Disconnected Mobile Ad Hoc Networks[END_REF], and Conti and Kumar [START_REF] Conti | Opportunities in Opportunistic Computing[END_REF] focus on service provisioning in opportunistic networks composed solely of mobile nodes. In [START_REF] Mahéo | Service Invocation over Content-Based Communication in Disconnected Mobile Ad Hoc Networks[END_REF], the authors propose content-based service discovery and invocation solutions in order to exploit the redundancy of the services offered by the mobile devices that can move freely (i.e., no assumptions are made regarding the mobility of the devices). Conti and Kumar [START_REF] Conti | Opportunities in Opportunistic Computing[END_REF] target networks relying on social interactions between mobile nodes that act as both clients and providers of services. Due to the volatility and the limited resources of the mobile devices, the number of relevant services that can be offered by these devices are limited in comparison to those that could be offered in hybrid networks. Unlike [START_REF] Mahéo | Service Invocation over Content-Based Communication in Disconnected Mobile Ad Hoc Networks[END_REF] and [START_REF] Conti | Opportunities in Opportunistic Computing[END_REF], in Le Sommer et al. [START_REF] Sommer | A Middleware Support for Location-Based Service Discovery and Invocation in Disconnected MANETs[END_REF] the services are provided by fixed infostations in limited geographical areas. In [START_REF] Sommer | A Middleware Support for Location-Based Service Discovery and Invocation in Disconnected MANETs[END_REF], mobile devices and infostations are aware of their own location. Mobile devices can invoke remote infostations thanks to an opportunistic and location-aware forwarding protocol. In contrast with the environments we consider, in [START_REF] Sommer | A Middleware Support for Location-Based Service Discovery and Invocation in Disconnected MANETs[END_REF], the infostations were not connected together. We believe that the design of routing protocols suited for service discovery and service invocation in ICHN should take the specificity of ICHN into account, namely the interconnection of the infostations, in particular when defining heuristics or functions that allow to select among a set of neighbor nodes the node(s) that are considered as the best relay(s) to reach one of the infostations.

In this paper, we propose TAO, a new opportunistic and time-aware routing protocol devoted to service invocation in ICHN. TAO adopts a temporal heuristic to perform efficient message forwarding decisions. The basis of our approach is to take into account the disconnection dates between the fixed infostations and the mobile nodes. Assuming a homogeneous speed of the mobile nodes, a node implicitly estimates the distance from its neighbors to the target infostation and is able to select the best carriers among them. Our proposal applies to situations in which routing decisions cannot be taken according to geolocation information.

The rest of the paper is structured as follows. Section II describes protocol TAO, and Section III the evaluation of this protocol. Related works are discussed in Section IV. Section V presents our conclusions and gives some perspectives.

II. THE TAO PROTOCOL

TAO aims at supporting the invocation of software services in ICHN such as those formed by fixed infostations and portable devices used by nomadic people. The description of the discovery phase that should occurs before the invocation is not in the scope of this paper. The remainder of this section details how service invocation requests and responses are forwarded by TAO in an ICHN.

A. Assumptions

TAO relies on four main assumptions: 1) Mobile hosts are able to perceive their one-hop neighborhood. 2) Each mobile host is able to temporarily store the messages it receives, and can associate to each of them some pieces of information. 3) All the infostations are continuously running and are connected to each other using a backbone. An infostation is never out of order and can provide services itself, or can act as a proxy to another infostation. 4) The time synchronization between mobile devices does not need to be very accurate, given the low movement speed of the mobile devices, which are carried by pedestrians. We can legitimately consider that TAO can tolerate a clock-shift on the order of half a minute.

B. Overview of TAO

TAO implements the "store, carry and forward" principle, a multiple-copy message forwarding algorithm, source routing mechanisms and a time-stamping-based heuristic that aims at selecting the best next message forwarder(s) among a set of neighbor nodes. This heuristic relies on lists of last dates of contact of a node with its neighbors. Mobile nodes are expected to use these lists when they are solicited by a neighbor node that wants to forward a message to an infostation or to a given mobile node, and to return to this node their last date of contact with an infostation. These pieces of information are then processed by the mobile node that must forward the message in order to select the best next forwarder(s) to deliver the message to an infostation. Such an algorithm tends to reduce progressively the area where the messages are disseminated until reaching their destination (i.e., a fixed infostation). Indeed, from a logical point of view, a node will disconnect from an infostation when it starts moving away from it, and the distance separating them is increasing progressively.

In order to improve the service delivery and to avoid the bad carrier dilemma (i.e., delivering the message to a mobile node abruptly moving in the wrong way), TAO implements a multiple-copy message forwarding algorithm. The source node is first expected to forward a copy of this message to its best neighbors. Later these carriers, and the source node, will forward a copy of this message only when they encounter a better carrier than themselves, while a limited number of copies will be forwarded toward bad carriers. A neighbor will be considered as a good carrier by a node if the last date of contact of this neighbor with an infostation is more recent than its own date of contact, or if this neighbor is a new neighbor and its last date of contact with an infostation is more recent than those of the other neighbors. This classification aims at estimating the ability of these intermediate nodes to deliver the message to an infostation. Furthermore, sometimes it might be critical to forward copies exclusively to good carriers, especially if the source node is located remotely from an infostation. In this case, the major number of neighbors might be classified as bad carriers, while the contact with a good carrier is uncertain. Thus in TAO, each mobile node has a stock of a few number of copies dedicated to bad neighbors. This number of copies is limited in order to avoid network overload and resource consumption on mobile devices. Finally, TAO makes it possible to control the propagation of messages in the network using two parameters: a lifetime and a number of hops. When the lifetime is expired or when the number of hops is zero, the message is removed from the local cache and will not be forwarded anymore.

Unlike Prophet [START_REF] Lindgren | Probabilistic Routing in Intermittently Connected Networks[END_REF], PropicMan [START_REF] Nguyen | Probabilistic Routing Protocol for Intermittently Connected Mobile Ad hoc Network (PROP-ICMAN)[END_REF] or HiBOp [START_REF] Boldrini | HiBOp: a History Based Routing Protocol for Opportunistic Networks[END_REF], TAO needs neither to record any large set of history values nor to use complex algorithms to select the next message carriers. In TAO, each node maintains 3 kinds of lists: a neighbor list, a list of last local contacts with infostations and a list of the last remote contacts with the infostations. These 3 lists will be referred to as NL, LLCI and LRCI respectively in the remainder of this section. NL contains the one-hop neighbors of the node and the date of reception of their last beacon. This set is obtained thanks to a background beaconing performed periodically by each node. Furthermore, mobile nodes or infostations are considered disconnected from the neighborhood of a mobile node if no beacons have been received from them during a time gap superior to an already define disconnection time threshold.

The LLCI list contains a limited number of entries (on the order of the number of two-hop neighbors). Each entry includes the IDs of the infostations the node has encountered and the time of the last beacon it received from these infostations. The LRCI list is similar to the LLCI list, but it is related to the neighbor nodes found in the NL list. Each entry of the LRCI represents the ID of the most recent infostation each neighbor had contact with and the value of the last contact date.When a new neighbor joins the one-hop neighborhood of the node it will directly send the ID and the most recent time of contact with an infostation to be registered in the LRCI.

TAO is a reactive and an event-driven protocol. Five events are considered in TAO:

1) The emission of an invocation request by a local client application.

2) The reception of an invocation request sent by a neighbor node.

3) The reception of a service response sent by a neighbor node. 4) The arrival of a new neighbor node. 5) The disappearance of a neighbor node.

C. Forwarding of service invocation requests

When a node receives an invocation request from a local application for a service provided by a remote infostation (event 1), or when it receives such a request from one of its neighbors (event 2), the node will process this request according to the forwarding Algorithm 1. On each message reception, a mobile node will forward a copy of this message to E emit direct neighbors at the most. In this algorithm, the good carriers will always obtain a copy of the message. The Algorithm 1 Emission or forwarding of an invocation request. infostation contact time of the best carrier of each invocation request will be recorded in the lists of the local node in order to be compared later with those of the new nodes that appear in the neighborhood of the current carrier. A copy of each invocation request will only be forwarded toward a new neighbor if its infostation contact time is more recent than the locally recorded value. As a result, this process prevents from forwarding multiple copies to the same node. On the other hand, bad carriers will receive a copy from the stock of copies dedicated to them only when the number of good carriers is less than E emit in the neighborhood of the carrier node. The stock will be decremented, and when this stock is empty no more copies of the message will be forwarded to the bad carriers.

In order to select the best next carriers among its neighbors, the local host checks the content of the LRCI list and chooses the nodes with the most recent infostation contact time. Service invocation messages will be stored, carried and forwarded by intermediate carriers in the same manner.

When a node discovers that it exists in its one-hop neighborhood an infostation, it forwards to this infostation all the service invocation requests it has in its cache and that are still valid, and removes them from its cache of messages. This infostation is expected to either deliver the service itself or forward the request to the appropriate infostations.

Any invocation request copy will stay alive until its lifetime expires or its number of hops is zero. Moreover, each message will store in its header the route it followed to reach the infostation.

D. Forwarding of service responses

The next event is the reception of the reply from the infostation toward the client node. The infostation will send the reply message with a reverse routing, in other words, send the message back on the route it has just traversed. Reverse source routing can be reliable if the mobility of the nodes in the network is relatively slow. In fact, TAO is designed to function in ICHN, where mobile nodes are volatile and endto-end paths between nodes cannot be maintained all the time.

As a result, a forwarding mechanism must be applied when the reverse source routing fails at some point (i.e., a disconnection in the route is encountered).

Algorithm 2 Management of the forwarding mechanism of the service response. When such a disconnection occurs, the node carrying the message will perform a multiple-copy message forwarding algorithm dedicated to the service responses (Algorithm 2). A copy of the service response will be forwarded to the best neighbors (setting higher priority to the nodes closer to the destination). Thus, all of the new carriers will try to resume the source routing process. If they cannot resume this process, they forward a copy of the message when they encounter a better carrier than themselves.

E. Management of neighborhood changes

Algorithm 3 Management of the service messages after the contact with a new neighbor. The last two above-mentioned events are triggered when changes occur in the one-hop neighborhood of a node. When a new neighbor joins the one-hop neighborhood of another node, the LLCI and LRCI lists are updated using the pieces of information obtained from the beaconing process. Then, the current carrier is expected to check if it exists in its local cache some messages (requests or responses) that should be delivered. If so, it conditionally forwards copies of these messages to its new neighbor using Algorithm 3. If the new neighbor has a date of contact with an infostation that is more recent than those of the other neighbors of the current carrier, this one will forward to this new neighbor all the service invocation requests it has and that are still valid. The service responses stored locally will be forwarded by the current carrier to this new neighbor only if this one is the destination or has been used as intermediate node to forward the request (i.e., if this one appears in the reverse source path header of the response).

Algorithm 4 Management of the disappearance of a neighbor to the mobile node. As Algorithm 4 shows, when a node is notified of the disappearance of an infostation from its one-hop neighborhood (i.e., from the neighbor set NL), it updates its LLCI list with the ID and the date of the last beacon of the infostation, that has been removed from the neighbor set. Otherwise, if the disconnected neighbor is a mobile node, all the related information will be removed from the NL and LRCI lists.

III. SIMULATION

In this section, we present the simulation results we obtained for TAO regarding the service delivery performances in comparison with a simple routing protocol RANDOM. The RANDOM routing protocol has the same characteristics as TAO, but instead of relying on the time heuristic implemented in TAO, RANDOM relies on a random mechanism in choosing the next carriers of the service invocation messages. The main objective of these simulations is not to compare the global performance of TAO with other protocols such as [START_REF] Boldrini | HiBOp: a History Based Routing Protocol for Opportunistic Networks[END_REF], [START_REF] Zhao | A Message Ferrying Approach for Data Delivery in Sparse Mobile Ad Hoc Networks[END_REF] and [START_REF] Vahdat | Epidemic Routing for Partially Connected Ad Hoc Networks[END_REF], but instead to assess the effectiveness of the time heuristic in delivering messages between a mobile node and a fixed infostation. The simulations have been performed on the OMNeT++ network simulator. In these simulations, we focus on a simple, but realistic, hybrid network composed of only one infostation providing a service and a set of mobile devices carried by pedestrians. A part of these pedestrians act as clients, forming a set of nodes that request services from the infostation.

A. Setup

The simulation environment we consider is a square open area of 1 km 2 . The infostation is located in the middle of this area. All mobile nodes move according to a random waypoint mobility model with a speed of 0.5 m/s. The communication range of the mobile devices and of the infostation is approximately 30 m. After discovering the service they are looking for, the mobile clients invoke this service every 3 minutes. In our experiments, we have not assigned any lifetime or maximum number of hops to any message for both protocols.

We ran the simulations for each routing protocol, varying the number of nodes forming the network. For each setup, we made 10 simulation runs with a different random seed. A warm up period of 10 minutes is used in the beginning of the simulations before clients start to generate invocation request messages, to allow LLCI, LRCI and NL lists to be initialized. The simulation is run for another 1 hour before stopping all the invocation requests from all the clients. Finally, the simulation is left for 10 minutes to allow all the messages to be delivered.

We present below the obtained results. The objectives of these experiments was to measure the ability to satisfy the client service delivery with a small number of message copies, where we have fixed the number of copies (size of the stock) to 3 copies for both protocols and the maximum number of emissions E emit to 3.

B. Results

Each of the following graphs contain curves for both TAO and the RANDOM routing protocols, while changing both the number of clients and the number of mobile nodes forming the network. The two metrics we are studying are the satisfaction ratio and the delay. The satisfaction ratio is the percentage of successful service invocation (i.e., the number of invocations for which a client node receives their response from an infostation), while the delay is the total time needed by a successful invocation message to travel from the client node toward an infostation and on the way back toward the same client node. First, we analyze the satisfaction ratio of each of the protocols in order to study the impact of increasing the number of nodes forming the network on the performance of each protocol. Three scenarios for each protocol are presented in Figure 2, where each scenario is characterized by the number of clients found in the network. As we notice, when having few nodes in the network, the satisfaction ratio of both protocols is almost the same. This observation is coherent with what is expected, because, due to the limited number of neighbors, TAO and RANDOM will select most of the time the same carriers. The performance of TAO increases with the number of nodes forming the network due to the selection of good carriers among a large set of neighbors. On the contrary, the performance of RANDOM decreases due to the bad selection of next carriers. Based on (Figure 3), we notice that when the network is formed of a few number of nodes, the delay values are relatively high. This is totally normal, since few nodes with limited transmission range and random waypoint mobility have to cover a large area. When the number of mobile nodes increases in the network, the average delay of RANDOM remains relatively high due to the random choices of carriers that contribute in transmitting the invocation messages toward the infostations. On the contrary, the average delay of TAO decreases due to the presence of more carriers that can fill the gap between the client and the infostation and the ability of TAO in choosing good carriers to perform this operation. As a result, the mechanism used by TAO to choose among the carriers of service invocation messages results in shorter delays and higher delivery ratio than what RANDOM can offer.

Satisfaction Ratio

Average Delay

Finally, the application we utilized in these primary simulations was simply a mobile node invoking an infostation and waiting for the response back. This was done to study the effect of the time heuristic implemented in TAO. Since the number of hops and the lifetime message parameters are directly related to the application and the expected delays in the targeted network, we did not specify any limits over these two parameters. So, the number of messages that are disseminated in the network increases continuously. That's why we do not give in this paper details about the network load and the efficiency of TAO regarding this point precisely. Nevertheless, the measurements we conducted show that the number of messages disseminated by TAO and RANDOM is approximately the same.

IV. RELATED WORK

TAO combines the originality of being designed to support service invocation and to specifically target hybrid intermittently connected MANETs. Indeed, most of the research work concerning intermittently connected MANETs consider networks solely formed of mobile devices and multi-purpose communication. However TAO uses the "store, carry and forward" principle and several techniques that are shared with many protocols in delay-tolerant and opportunistic networking. In the remainder of this section, we present some representative routing protocols.

The Message Ferrying paradigm is a mobility-assisted approach [START_REF] Zhao | A Message Ferrying Approach for Data Delivery in Sparse Mobile Ad Hoc Networks[END_REF]. It introduces non-randomness to the node mobility and exploits it to provide physical connectivity among nodes. Two variations are introduced both with movement constraints. The first is targeting the message ferries, which are special nodes introduced as data carriers toward specific positions to collect data. The second forces the clients to move toward the ferries in order to send and receive messages. Although this approach ensures reliability, it introduces a lot of constraints on the mobility of clients, which is considered disturbing and impractical in real life.

The constraint of intervening with clients' mobility was addressed by other protocols that aimed to benefit from the natural uncontrolled movements of nodes. The most general attempt is the flooding-based routing protocols such as Epidemic Routing [START_REF] Vahdat | Epidemic Routing for Partially Connected Ad Hoc Networks[END_REF]. In such types of protocols, messages are flooded in the network and stored by all available neighbor nodes. No precautions are considered to limit the number of messages exchanged and forwarded. Therefore, network congestion is very likely to happen, especially in high density regions. Some approaches resort to probabilistic solutions [START_REF] Lindgren | Probabilistic Routing in Intermittently Connected Networks[END_REF], [START_REF] Nguyen | Probabilistic Routing Protocol for Intermittently Connected Mobile Ad hoc Network (PROP-ICMAN)[END_REF] and prediction techniques [START_REF] Musolesi | CAR: Context-Aware Adaptive Routing for Delay Tolerant Mobile Networks[END_REF] to choose the best relay nodes for each specific message. For routing, these protocols rely on the context and history information in order to compute delivery probabilities and predictabilities. A history-based approach such as the one described in [START_REF] Boldrini | HiBOp: a History Based Routing Protocol for Opportunistic Networks[END_REF] relies on an algorithm to predict the future movements and patterns of the node and route packets according to these predictions. Such algorithms can achieve high efficiency and delivery ratio, but the major drawback is assuming that a node is able to register a large amount of contact history in its buffers, taking into consideration that the majority of the devices forming such networks are small portable devices with limited capabilities and capacities. Moreover, computing histories and predicting movement patterns is a tricky problem, especially in environments composed of numerous mobile devices that move following irregular patterns, such as those held by pedestrians in a city. On the contrary, TAO simply utilizes recent history to predict near future. TAO tends to estimate the distance separating the nodes and the infostations in the network, relying on the disconnection times recorded locally by the mobile nodes. By this approach we aim to reduce the complexity and the resources needed to take correct routing decisions.

V. CONCLUSION

Intermittently connected hybrid networks is a quiet original perspective that can be exploited to provide nomadic people with a wide access to pervasive services, eliminating the need for any expensive infrastructures, such as those provided by GSM operators.

In this paper, we have proposed a new simple time-aware opportunistic routing protocol, called TAO, devoted to service invocation in ICHN. TAO implements a multiple-copy message forwarding algorithm, source routing mechanisms, and a time-stamping-based heuristic that aims at selecting the best next message forwarder(s) among a set of neighbor nodes.

TAO is a recent work, and its evaluation through real conditions is still in progress. TAO will shortly be included in a service-oriented middleware platform. Furthermore, in the future, we would like to improve the service delivery process by implementing a handover mechanism in the infostations, thus allowing to provide nomadic people with a continuous access to a given service. Then, a service will be delivered all the time to the client by the best infostation, which will be, the most of the time, the nearest infostation.

Figure 1 .

 1 Figure 1. Example of an intermittently connected hybrid network.

Figure 2 .

 2 Figure 2. Satisfaction ratios of TAO and RANDOM Routing Protocols

Figure 3 .

 3 Figure 3. Delay of TAO and RANDOM Routing Protocols

  emission or forwarding of a Service Invocation Message : if it exists an infostation in the one-hop neighborhood then forward request to the infostation remove the Service Invocation Message from the cache else check LRCI list for good carriers for number of emissions is less than E emit if good carriers are found then forward a copy of the Service Invocation Message Update the best contact time with an infostation relative to this

	invocation message
	else
	if local stock related to this Service Invocation Message > 0
	forward a copy of the Service Invocation Message
	decrement the stock
	endif
	endif
	endfor
	endif