## Abstract

Stimulated Brillouin scattering was investigated for the first time in As_{2}S_{3} single-mode fibers, and also in As_{2}Se_{3}. The propagation loss and numerical aperture of the fibers at 1.56 µm, along with the threshold intensity for the stimulated Brillouin scattering process were measured. From the threshold values we estimate the Brillouin gain coefficient and demonstrate record figure of merit for slow-light based applications in chalcogenide fibers.

©2006 Optical Society of America

## 1. Introduction

The observation of slow light has been recently demonstrated in optical fibers by using the dispersion associated with laser-induced amplification of a material resonance as is the case in stimulated Brillouin scattering (SBS) [1, 2] and stimulated Raman scattering (SRS) [3, 4]. The slow-light technique based on SBS in optical fibers is particularly of interest as it allows a very simple and robust implementation of tunable optical pulse delays, using mostly standard telecom components.

Previously reported results deal with either long standard telecom fibers (tens of meters to kilometers) or with rather large pump powers (hundreds of milliwatts to watts), values which will negatively impact the cost and also the performance of the system, in terms of pulse distortion, stability of the delay, and onset of other nonlinear effects. The length of the delay fiber and the amount of pump power are generally considered key parameters which determine qualitatively and quantitatively the optical pulse delay. These parameters are ultimately determined by the fiber properties (propagation loss, numerical aperture) and by material properties (refractive index, Brillouin gain coefficient). Since the standard silica fibers have a very small Brillouin gain coefficient, there is a need for alternative materials with higher values of the gain coefficient which will enable low-power solutions. There have been reports of very efficient slow-light generation in Bi-oxide high-nonlinearity fiber [5] and in As_{2}Se_{3} chalcogenide fiber [6]. A figure of merit (FOM) has also been proposed in order to easily quantify the degree of usefulness of a given fiber when considered for slow-light applications [6].

We measured, for the first time to the best of our knowledge, the Brillouin gain coefficient of single-mode As_{2}S_{3} fiber. We have also measured the Brillouin gain coefficient in As_{2}Se_{3} in order to compare it with the As_{2}S_{3} result and with the previously reported result from literature [7]. We demonstrate a significant increase in the figure of merit in the case of this particular As_{2}S_{3} fiber when slow-light applications are considered.

This letter continues with section 2 on fiber characterization, section 3 on SBS threshold measurements, followed by a discussion of the figure of merit in section 4, and conclusions in section 5.

## 2. Fiber characterization

Two fibers, drawn in-house, were used in this work, and their main physical properties are given in Table 1 below. The core refractive index was measured with an ellipsometer using glass sample from the core preform.

The numerical aperture (NA), essentially the contrast in index between the core and the clad, is an important parameter. It determines the mode-field diameter and hence the effective area of the fundamental mode, with direct implications on the threshold power estimation. It also determines the number of modes supported by the fiber at a given wavelength, λ. The V-number for a step-index fiber is a function of NA as given in the equation below, where d is the core diameter:

Careful measurements of the far-field angular dependence of the fundamental mode exiting the fiber were used for NA determination. Light from a temperature stabilized, fiberpigtailed laser diode was coupled with free-space optics into 1-m long sections of fiber. The radiation escaping into the cladding was stripped out by coating a 10-cm long portion of fiber with liquid gallium at each end. The data for both fibers is shown in Fig. 1 below. The V-number of ~ 2.8 for the As_{2}S_{3} fiber suggests a second mode could be excited at 1.56 µm. In practice, the second mode was not observed. During the experiments, nevertheless we monitored the mode field pattern by imaging the output on a vidicon camera to make sure we launched only in the fundamental mode.

Using the V-number, the MFD for the fundamental mode will be given by Eq. (2) below [7]:

The propagation loss is also an important parameter as it defines the effective interaction length for the Brillouin scattering process. The loss was measured using the cutback method and the data for the As_{2}S_{3} fiber is shown in Fig. 2.

## 3. Measurement of Brillouin gain coefficient

In order to determine the Brillouin gain coefficient, we measured the threshold power of the stimulated Brillouin scattering (SBS) process using the experimental setup detailed below in Fig. 3. In doing so we are following the approach established in previous work [7] in order to be able to compare our results with previous results, although a more exact analysis was proposed elsewhere [8]. The threshold power is easily determined by monitoring the spectrum of the reflected light using a high-resolution optical spectrum analyzer (OSA) as sampled by the circulator which is the interface between the pump delivery system (DFB laser source plus Er amplifier, EDFA) and the chalcogenide fiber. We choose this method due to its simplicity although more careful schemes are usually employed in the case of silica fibers [9].

The fiber was coated with liquid gallium on 10-cm lengths on each end to eliminate the radiation leaking into the cladding. The fiber ends were not anti-reflection coated and hence cavity effects were significant due to the high refractive index of the fiber. The losses in the fiber (given above), and the coupling optics (4% for the focusing lens, 14% for the collimating objective), along with the Fresnel loss at the fiber ends (17.7% for As_{2}S_{3} and 22.6% for As_{2}Se_{3}) are all taken into account in throughput measurements used to estimate the coupling efficiency, and hence the amount of pump launched into the core. We estimate 45% coupling efficiency in the As_{2}S_{3} case, and 37% in the As_{2}Se_{3} case. In future, coupling efficiency can be optimized and hence the SBS threshold power can be reduced, which is a desired trend from a system design perspective.

The spectral changes of the backward wave propagating through the chalcogenide fiber, as sampled by the circulator, are shown in Fig. 4 for the As_{2}S_{3} fiber, and in Fig. 5 for the As_{2}Se_{3} fiber. The cavity effects reduced the accuracy with which we were able to determine the threshold as indicated in the captions. Nevertheless, the threshold is easily identified by the significant jump in the peak of the Brillouin-shifted signal monitored on the OSA. Additionally, we observed the clamping of the pump output power as, once the threshold is reached, most of the pump power is transferred to the Stokes wave [10]. From these experimentally determined threshold values, one can estimate the Brillouin gain coefficient using the equation below [7, 11]:

In the Eq. (3), k is a constant which reflects whether the polarization is maintained constant throughout the interaction (k = 1) or not (k = 0.5, our case). Also, the Aeff and Leff are the effective area of the fundamental mode, and the effective interaction length, respectively.

These are given by Eq. (4) and Eq. (5) below, where L is the fiber length, α is the propagation loss, and the 1.e^{-2} mode-field diameter is determined by Eq. (2) above.

Using Eqs (3)–(5), the parameters from Table 1, and the fiber lengths and pump threshold values indicated in Fig. 4 and Fig. 5, we determined the Brillouin coefficient to be (3.9±0.4) × 10^{-9} m.W^{-1} for the As_{2}S_{3} and (6.75±0.35)×10^{-9} m.W^{-1} for As_{2}Se_{3}. The value for the As_{2}Se_{3} is close to the only other previously published result [7]. The value for the As_{2}S_{3} fiber, although lower than the one for As_{2}Se_{3}, is still two orders of magnitude higher than that for fused silica (~4.4×10^{-11} m.W^{-1}) [6, 12].

## 4. Discussion of figure of merit for slow-light applications

The very large Brillouin gain coefficient presents the chalcogenide fibers as alternatives to silica fiber for slow-light applications. A figure of merit (FOM) has been proposed [6] in order to quantify the usefulness of a given fiber for slow-light based applications. The Brillouin gain is considered a positive factor while the length, the refractive index, and the power are considered as negative factors impacting the response time and the onset of additional nonlinear effects in the system. The FOM as defined in Ref. [6] requires the knowledge of the actual Brillouin gain which has to be measured, and takes into account the effective length instead of the total length of fiber.

We propose to compare various fibers by using the theoretical small-signal gain, G_{th}, which is the small-signal gain for a standard length of fiber of 1 m, at a standard pump power of 1 mW. The expression for the small-signal gain expected in a fiber is given by:

Therefore Gth will be given by:

In order to take into account the previous comparasion of chalcogenide fibers against silica fiber [6], we re-write the FOM proposed in Ref. [6] such as to reduce it to the primary quantities qualifying the fiber (effective area, length and propagation loss, refractive index, and Brillouin gain coefficient expressed in dB):

It is important to keep in mind that this FOM contains the large-index penalty and determines what length and power are needed in a system to achieve a certain gain, and hence a certain time delay. It does not allow, however, to accurately assess the effect of the loss coefficient when comparing different fibers. Hence for strictly comparing fibers one should use the gain in the fiber for a standard length, under a standard power as proposed in Eq (7). We used both parameters, the FOM and G_{th}, to compare the most representative fibers considered so far: silica [1], high-nonlinearity bismuth fiber [5, 13], As_{2}Se_{3} fiber [6, 7], along with the results reported here. The comparison is provided in Table 2 below, with all the data reported for experiments without polarization control (k=0.5). One can easily notice the significant increase in the theoretical gain (or FOM) for this particular As_{2}S_{3} fiber due to its smaller core, lower loss and slightly reduced refractive index.

It needs to be mentioned that actually a As_{2}Se_{3} fiber with similarly smaller core size and same loss figure as the small-core As_{2}S_{3} fiber would perform even better, given the larger nonlinearity of the selenide-based chalcogenide! Our first trial in obtaining such a fiber resulted in a fiber with a higher loss though, which would lower its overall FOM. Efforts to obtain an optimized small-core As_{2}Se_{3} are currently under way.

## 5. Conclusion

The stimulated Brillouin scattering process was studied for the first time in As_{2}S_{3} fiber, and the Brillouin gain coefficient was measured to be (3.9±0.4)×10^{-9} m.W^{-1}. Similar measurements were done also in As_{2}Se_{3}, and the determined Brillouin gain coefficient of (6.75±0.35)×10^{-9} m.W^{-1} is comparable with the only other result recently published in literature [7]. An analysis of the figure of merit for slow-light based applications indicates that, to date, the smaller core As_{2}S_{3} fiber performs best due to the reduced core size coupled with the fact that it has a low loss. The configuration using the small-core As_{2}S_{3} fiber yields a figure of merit which is about 140 times larger, or a theoretical gain about 45 times larger, than the similar quantities for the best silica-based configurations reported to date.

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