Sampled Bragg gratings in chalcogenide ( As 2 S 3 ) rib-waveguides

We have written a sampled Bragg grating into a highly photosensitive chalcogenide (As2S3) rib-waveguide using a scanning Sagnac interferometer. The grating exhibits evenly spaced rejection peaks over a 40 nm bandwidth. We estimate the induced refractive index change of the waveguide to be over 0.03 by matching the measured spectrum to numerical solutions of the coupled mode equations while accounting for an induced chirp. The sampled Bragg grating presented is comparable in strength and bandwidth to the best sampled Bragg gratings obtained to date in silica optical fibre. © 2006 Optical Society of America OCIS codes: (090.2880) Holographic interferometry; (160.2750) Glass and other amorphous materials; (230.1480) Bragg reflectors. References and Links 1. A.R. Hilton, “Nonoxide Chalcogenide Glass as Infrared Optical Materials,” Appl. Opt. 5, 1877-1882 (1966). 2. Y. Ruan, W. Li, R. Jarvis, N. Madsen, A. Rode, and B. 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Introduction
Chalcogenides are an amorphous glass containing at least one of the chalcogen elements (S, Se or Te), that have, for the past five decades, been used primarily for mid-IR free-space optics [1].Following recent processing advances, chalcogenides can now be fabricated into low loss waveguide structures [2,3], making it possible for the development of chip-based alloptical devices for both telecom and mid-IR applications.Chalcogenide glasses have a number of attractive properties: they are transparent across the telecom range and through the mid-IR [1,4]; they can be processed into rib-waveguide or photonic crystal structures using the same equipment and similar techniques as with conventional silicon lithography [2,5]; they possess a large refractive index contrast that enables strong optical confinement in narrow waveguides; they possess an ultrafast Kerr nonlinearity which, depending on composition and stoichiometry, can range from 100-1000x larger than in silica [2] making them useful for nonlinear signal processing [6], such as all-optical switching [7] and alloptical signal regeneration [8]; and they are strongly photosensitive with photo-induced refractive index changes as large as 0.04 typically available [2,9,10].
The photosensitivity of a chalcogenide glass is comparable only to the "hero" results observed in specially processed silica optical fibre [11] and is among one of its most striking properties.Some devices have already taken advantage of this large photosensitivity, including laser-written waveguides [12,13], surface gratings [14] and integrated Bragg gratings [10,[15][16][17], although none have yet offered an improvement to what is currently available in silica fibre or silicon waveguides.Structures that can benefit particularly well from the large refractive index change in chalcogenides are sampled Bragg gratings (SBGs) [18].These provide a comb shaped transmission spectrum for which a large index change can extend the useable bandwidth and increase the strength beyond that possible in silica or silicon.SBGs open a new platform for WDM on-chip signal processing, providing a larger bandwidth response in a short, integrated device.Since chalcogenides can also be doped with rare-earth elements [19] and exhibit strong Raman gain [20] they show potential for hosting on-chip multi-wavelength lasers.
In this paper we explore the linear spectral response of a holographically written SBG in a chalcogenide-based As 2 S 3 rib-waveguide.We describe the fabrication of high-quality As 2 S 3 rib-waveguides and the scanning Sagnac interferometer used to write the SBG.We find the spectrum to be comparable to the broadest and strongest SBGs written in silica to date, and, by matching the measured spectrum to numerical results, we estimate the photo-induced refractive index change to be approximately 0.03.

Background
SBGs are formed by the on/off modulation of a Bragg grating written holographically into the core of a waveguide.Figure 1(a) is a schematic of the resulting refractive index profile of a typical SBG, outlining the key parameters of its design: the period of the underlying Bragg grating, Λ; the overall device length, L; the sampled period by which the Bragg grating is modulated, P; the "on" length of each Bragg region, P o ; the nominal waveguide refractive index n o ; the average ("DC") refractive index in the on-part of the grating, n dc ; and finally the amplitude of the refractive index change, ∆n, in these regions.numerically from the coupled mode equations [21], consist of evenly spaced rejection peaks separated by [18] where λ B is the underlying Bragg wavelength and corresponds to the central rejection peak.
Note that the rejection peaks are bound to an outer envelope which, to first order, is the Fourier transform of the modulating function [18]; here, a square wave modulation profile yields a sinc shaped spectral envelope.By using a more complex modulation function the spectral response can be tailored to follow any desired envelope [22].The bandwidth of the central rejection band can be increased by lowering the duty cycle of the square wave, albeit reducing the strength of the grating in the process.As is the case for Bragg gratings, the strength of the individual rejection peaks of a SBG is proportional to the product of L and ∆n, but where for a Bragg grating L is its entire length, it is the sum of the "on" sections, i.e., L•P o /P, for a SBG.This is evident in Fig. 1(b)-(d) where the response weakens as the duty cycle is reduced.Since the objective is to integrate SBGs eventually into compact on-chip devices, the natural aim is to obtain a strong comb filter response over a wide bandwidth, while keeping the device length small.Chalcogenides are able to compensate a short device length and low duty cycle through a large ∆n.

Waveguide Fabrication
A detailed description of As 2 S 3 waveguide fabrication has been given by Ruan et al [2] and Li et al [3].Briefly, waveguides are fabricated via ultra-fast pulsed laser deposition (UFPLD) of As 2 S 3 onto an oxidized silicon wafer and processed into rib structures using standard photolithography and reactive ion etching.Figure 2(a) shows a scanning electron microscope (SEM) image of a typical waveguide prior to the application of its protective inorganic polymer glass (IPG) coating.Using the convention shown in Fig. 2(b), the SEM image shows a rib-waveguide having a rib width, w = 7.0 μm, rib height, H = 3.3 μm and slab height, h =2.1 μm.Propagation loss through these waveguides has been reported as low as 0.25 dB/cm [2], but, likewise with silicon waveguides, the loss is strongly influenced by the surface quality of the sidewalls [23].

Experiment
The set-up used to write SBGs is shown in Fig. 3(a) and is based on the system previously described by Shokooh-Saremi et al. for writing short Bragg gratings into As 2 S 3 ribwaveguides [17].In this system, an incoming laser beam is split by a phase mask into two equal ±1 orders that form the arms of a modified Sagnac interferometer with an As 2 S 3 waveguide mounted at the point where the two arms interfere.Using a 532 nm CW frequency doubled Nd:YAG laser (with a photon energy below the material bandgap), a photo-induced refractive index change occurs within the waveguide at each maximum of the incident fringe pattern.The angle at which the two beams overlap determines the spacing of the fringe pattern and sets the Bragg period, Λ.
A few changes to this system were necessary to permit the writing of long SBGs.Since the interference pattern formed by the overlapping beams results from a path-length difference within the two arms of the interferometer, a single longitudinal mode 532 nm CW laser was selected to ensure a coherence length much longer than the grating being written, while the footprint of the grating writing area was increased by switching to 100 mm diameter mirrors in the Sagnac loop.A stepper-motor driven translation stage was included to scan the incoming beam across the phase mask, allowing for the localized control of Δn by adjusting the stage velocity throughout the scan.While a photolithographically etched chrome amplitude mask with periodic vertical slits was positioned directly in front of the waveguide to modulate the Bragg grating, resulting in a SBG.
In our experiment the shadow mask had 25 μm wide slits periodically separated by period, P = 500 μm, giving a duty cycle of 5%.The waveguide used was 18 mm long and of similar dimensions to that shown in Fig. 2, except we chose w = 2.3 μm to minimize contributions from modes other than the fundamental [24].The output of the laser was spatially filtered and then collimated to a diameter of 0.5 mm with each interfering arm carrying 3 mW of optical power.It was scanned across the waveguide at 10 μm/s for 30 minutes.The waveguide was characterized before, during and after writing using two butt-coupled optical fibres.The first was used to inject C-band light from a broadband EDFA source into the waveguide while the second fibre collected the transmitted spectrum and delivered it to an optical signal analyzer (OSA).The insertion loss caused by a mode-field diameter mismatch between the 2.3 μm wide waveguide and 10 μm diameter core SMF-28 fibre was quite large, so an intermediate stage was used to step-down the mode size and provide more efficient coupling.This was accomplished by fusion splicing a short length of high-NA fibre, having a 4 μm core diameter, to each end of the butt-coupled fibre.The insertion loss was further reduced through the precision alignment of the fibre to waveguide using an in-house built auto-alignment system.A polarization controller was used at the input to isolate the desired polarization state (TE) and to mitigate any polarization mode dependence that may have been present in the waveguide.The characterization system is shown in Fig. 3(b).

Results and analysis
The spectral response of a SBG written into an As 2 S 3 rib-waveguide is shown in Fig. 4(a).This spectrum has ∆λ s = 0.966 nm and a 3 dB bandwidth that spans almost 40 nm, where the central 11 rejection peaks are each over 20 dB strong.To our knowledge the strength and bandwidth of this grating is comparable to the best results observed in optical fibre [18,25,26].Using Eq. ( 1), with λ B = 1548.8nm and P = 500 μm, we determine n dc = 2.48, which is independently confirmed as the effective modal index by measuring the free spectral range of the Fabry-Perot cavity formed by the end facets of an adjacent, unexposed waveguide.duty cycle = 5% and Δn = 0.002.Inset: an enlargement of one rejection peak showing (i) the measured spectrum, and the calculated effect of tilting the mask by (ii) 0° with Δn = 0.002, (iii) 0.075° with Δn = 0.01, and (iv) 0.125° with Δn = 0.016.Figure 4(b) shows the calculated spectrum for two SBGs having L = 18 mm, P = 500 μm and a duty cycle of 5%.The blue dashed line represents the calculated spectrum for a grating written having a slight misalignment of the shadow mask, such that the normal to the mask has been offset from the normal to the As 2 S 3 waveguide by 0.125°, while the red solid line represents the ideal case where the mask and As 2 S 3 waveguide are parallel.Though the effect of tilting the mask is discussed in detail below, it is briefly mentioned here to emphasize that since we have positioned the shadow mask manually in front of the As 2 S 3 waveguide, it is unlikely that perfect parallelism between the two has been obtained, and this has a detrimental effect on the resulting spectrum.For a given tilt of the shadow mask, the only unknown parameter required in calculating the grating spectrum [21] is the modulation depth of the refractive index, Δn, and is therefore used as a fitting parameter to match the strengths at λ B to the measured value of -23 dB.A best fit to the measured spectrum is found by calculating the resulting spectra over a wide range of mask tilts.Returning to Fig. 4 (b), in the ideal case with 0° tilt, setting Δn = 0.002 provides the desired -23 dB response at λ B but the widths of the individual peaks and the span of the total bandwidth do not match well to the measured spectrum.Incorporating a tilt of only 0.125° and setting Δn = 0.016, a good match is found in both strength and width.Although this represents a net refractive index change equal to 0.032, which compared to silica fibre is very large, it remains within the reported range for this material [2,9] and is consistent with our previous measurements [10].
An enlargement of one of the rejection peaks is shown in the inset to Fig. 4(a).Note how the measured width, (i), is substantially broader than that for the ideal spectrum where the waveguide and shadow mask are parallel, (ii).By incorporating a slight tilt to the mask, at 0.075° and 0.125° for (iii) and (iv), respectively, the width of the calculated profile is shown to increase substantially with the latter providing a satisfactory fit to (i).
To explain the observed broadening we determine that the SBG has been inadvertently chirped, which would result in precisely such broadening [27].However, chirping is usually achieved through the variation of P over the length of the grating [27] whereas the period of the shadow mask is known to be uniform throughout.We believe that the chirping results from an effective change in P within the waveguide, whereby the background refractive index actually changes between each of the "on" regions of the SBG over its entire length.This causes the effective optical path length to differ between each "on" region, hence chirping the grating.We discuss below how a slight misalignment of the shadow mask can cause this effect.
To understand this effect, note that at the waveguide where the two incident beams overlap their angles of incidence are the same giving each an identical spot size.However, at the mask, as it is tilted towards one of the incoming beams, the angle of incidence between each beam and the mask will differ and, consequently, so too will their spot size.Since at the waveguide the spot sizes are the same but each beam has passed through a different fraction of the mask, both beams have effectively been modulated with a different period.Where the modulated beams do overlap at the waveguide they interfere to form an "on" region, but from their difference in periods the overlap is not maintained along the length of the waveguide (as it would in the ideal case) and instead walks apart.The first effect is then a reduction in the actual length of the SBG.The second effect comes from a non-interfering "DC" refractive index change within the walk-off region and is the cause of the effective optical path length change.Figure 5 is an exaggerated illustration showing the resulting DC refractive index change formed in a 4.5 mm length of waveguide by two incident beams, the red (dot-dashed) and green (dashed), passing through a shadow mask tilted towards the green beam.Here the mask has P = 500 μm and, for illustration purposes, a duty cycle of 30% and a tilt of 1°.
Where the two beams overlap they interfere to form a SBG, outlined by the solid black line.Note the regions where the interference zone becomes narrower and where the refractive index change on either side is purely DC.Then, in terms of the effective optical path length, P does in fact change from one interference region to the next.This is analogous to chirp and leads to the observed spectral broadening.
In matching the calculated spectrum to the one measured we have had to account for both the tilt and ∆n parameters.Although the width of the individual rejection peaks are partially influenced by the magnitude of ∆n, they are most strongly influenced by the chirp.And so, in matching the calculated and measured widths, we determine the mask has been tilted by approximately 0.125°.The walk-off from the mismatched periods explains why ∆n becomes so large for such a marginal tilt.For the ideal case, with a tilt of 0°, the overlap is maintained over the entire 18 mm length of waveguide, while for a tilt of 0.125° and a 5% duty cycle the device length reduces to only 8 mm and hence ∆n must be increased to compensate [21].shadow mask (green) (red) Fig. 5. Schematic demonstrating the interference walk-off caused by a misalignment of the shadow mask.Top: two incident beams (green and red) are modulated through a shadow mask, tilted towards the green beam by 1°.Below; the corresponding DC refractive index within the waveguide caused by the green (dashed) and red (dot-dashed) incident beams.The regions where two beams interfere to form the SBG is represented by the solid black line.

Discussion
To eliminate the chirping effect and to realize a long, uniform SBG would require a more elaborate mask positioning system than currently available.Alternatively, it may be possible to pattern the mask directly onto the waveguide which would eliminate the need for such precise alignment altogether.In either case, if a ∆n of approximately 0.03 could be observed in a SBG longer than 8 mm, the resulting spectrum's strength and bandwidth would increase well beyond that possible in silica fibre.Additionally, through the elimination of chirp the spectral features become narrower and the SBG is much better suited for applications to devices such as the on-chip multi-wavelength Raman laser mentioned previously.However, prior to any such major advancement, further investigations need to be made into the stability and robustness of chalcogenides in general.Although they display very promising optical properties, chalcogenides are still very much in their infancy in terms of hosting integrated all-optical signal processing devices.To date, very little has been reported on the long term stability of the photorefractive index change, including its response to standard processing techniques such as annealing, or even the fluence threshold dividing the reversible and irreversible photorefractive index change regimes.Some common problems that have been reported in As 2 S 3 chalcogenides include: photodarkening of the material by moderate intensities of the carrier signal at frequencies well below the material's bandgap (1.5 μm) [28], which leads to a low damage threshold and a possible photo-induced crystallization [29]; positive or negative photorefractive index changes reported in similarly prepared materials where the as-deposited film stoichiometry varied by only a few percent [30], as well as a host of other interesting phenomena that are not well understood, though all seem to depend heavily on all the subtleties of the material preparation and handling [31].Of the many different groups reporting on chalcogenides, most employ slightly different processing techniques and material stoichiometries [31], making direct across-the-board comparisons of results difficult.Needless to say, as progress is made into proof-of-principle devices (such as the SBG discussed here) and the potential uses of chalcogenides continues to gain interest amongst those with a focus on commercial applications, further studies into their viability are bound to result.This was the case with the commercialization of fibre Bragg gratings, which led to not only a better understanding of the photo-refractive index change, but also to enhancements in photosensitivity through fibre-hydrogenation [32] and improvements longterm stability through post-process annealing [33].

Conclusion
We present a sampled Bragg grating written into a highly photosensitive As 2 S 3 rib-waveguide that is 23 dB deep and has a 3 dB bandwidth spanning 40 nm.From it we infer a net refractive index change of approximately 0.03 by accounting for the induced chirp and a resulting 8 mm long grating.We believe that through a modest modification to the writing system a significantly stronger and broader response can be obtained, well surpassing what can be achieved in silica fibre or silicon waveguides.The integration of SBGs into a chalcogenide waveguides provides a new platform to both IR and telecommunications based WDM systems, and provided the material proves robust enough for commercial use, has a wide range of practical applications.

Figure 2 (Fig. 2 .
Fig. 2. (a) SEM image of a rib-waveguide prior to the IPG application.(b) schematic of a ribwaveguide structure.c) enlarged image from (a) showing minimal sidewall roughness.

Fig. 3 .
Fig. 3. (a) Scanning Sagnac interferometric grating writing system showing modulating shadow mask for sampled Bragg grating fabrication.The irradiating beams move in the opposite direction to the translation stage as shown by the solid and dashed lines; (b) waveguide characterization system for measuring throughput of chalcogenide waveguide