## Abstract

We study out-of-plane coupling and switching in a semiconductor periodic waveguide structure, with attention given to both dispersion within the structure and impedence matching of an external wave with a guided mode. We show nanosecond-scale optical switching and discuss the implications for Bragg soliton excitation.

© 1998 Optical Society of America

## 1. Introduction.

One-dimensional periodic structures which exhibit third-order optical nonlinearities are interesting for their technological applications and for the fact that they exhibit many classic properties of nonlinear systems with feedback. Theoretical investigations dating back to 1979 have predicted optical bistability [1], switching [2], and a variety of effects linked to the excitation of gap soliton [3–9]. The first experimental efforts were successful in demonstrating much of the general predicted behavior [10–14] but suffered from difficulties due to the impedance mismatch encountered by a propagating wave incident on a periodic structure. This impedance mismatch is responsible for the near band-edge oscillations which appear in the linear response of periodic structures, and, in the nonlinear regime, presents difficulties in launching Bragg solitons.

Solutions to the impedance mismatch problem employ either tapered gratings (in order to provide an adiabatic transition) or sections of linear gratings fabricated or fused at either end of the nonlinear grating section. The tapered grating is especially suited for fiber experiments, and has been successfully employed in several recent experimental efforts [14–16]

In this paper we analyze an optimized out-of-plane excitation geometry which exhibits nanosecond-scale all-optical switching and may also be suitable for the distributed excitation of a Bragg soliton within a periodic planar waveguide structure. It differs from the well-studied nonlinear grating coupler by employing nearly degenerate coupling from an external wave (e.g. a radiation mode of the cover) to a local wave (e.g. a guided mode within the periodic structure) such that the local wave is nearly Bragg resonant at a higher order resonance of the periodic structure. For example a grating coupler designed for first-order diffraction from a radiation mode to a guided mode will, for normal incidence coupling, also provide a second-order Bragg reflection to the guided mode. In some cases, the grating period can be chosen to provide second-order coupling from the cover and a fourth-order Bragg resonance for the guided mode. In the following sections, we will consider the dispersion curves, optimized conditions for coupling from an external, out-of-plane, source, and the implications for all-optical switching and out-of-plane launching of Bragg solitons.

## 2. Sample Design and Fabrication

The particular examples examined in this paper employ a metal-semiconductor-metal silicon-on-insulator (MSM/SOI) waveguide designed for excitation at near-normal incidence to the surface of the structure. Figure 1 shows a typical scanning electron micrograph cross-section. We have employed such structures in previous in-plane switching experiments [17] and one preliminary demonstration of out-of-plane self-modulation[18]. This is one of a class of device geometries which employ an optically-resonant periodic-electrode (ORPEL) structure on a waveguide in order to achieve suitable resonances. The practical advantages of electrode proximity (for tuning), high speed (for carrier injection and extraction) combine with the optical resonances to produce a highly versatile building block for detectors, modulators, and, in the present application, optical switches.

The general design goal was to achieve a high reflectance for radiation modes not resonantly coupled to the waveguide while achieving maximum coupling effiency on resonance. This was achieved by choosing the multilayer/overcoat thicknesses to maximize the reflectance both in the metallic and nonmetallic regions of the coupler. The details of this design procedure are out of the scope of this study and will be discussed in another paper. Suffice it to say that the inclusion of a high-index overcoat to clad both the metal and the waveguiding layer provides the structure with enough degrees of freedom to provide an off-resonance reflectance which is typically greater than 95%.

Before fabrication, the linear properties of the structures were analyzed using rigorous coupled-wave analysis (RCWA) in which periodic boundary conditions are imposed on a plane wave incident from the cover region. This particular algorithm, which was introduced by Peng and Morris[19], provides excellent, fast convergence even for metallic structures. In our case, the RCWA was integrated into an analysis/optimization loop using MatLab^{™} software tools.

Figure 2a shows the calculated (normal-incidence) reflectance of a gold-fingered structure equipped with an amorphous silicon overcoat. The grating period (Λ=680 nm) was chosen to provide second-order coupling from the cover and a fourth-order Bragg resonance for the guided mode. There is clearly a rich spectrum of mode excitations. Tabulating the mode resonances as a function of excitation angle produces the dispersion plot of figure 2b. We have added the lines as a guide to the eye indicating the propagation direction and slope (group velocity) of the various interacting modes. A majority of the avoided crossings are attributable to interactions between counterpropagating waves, which show clear energy gaps typical of Bragg reflectors at lower orders. There is one case of co-propagating interactions evident and one triple interaction involving two co- and one counter-propagating waves. The nature of the avoided crossings in these cases are not simple ω- or k-gaps, perhaps due to high-order coupling. Discontinuities in the dispersion relation correspond to regions with no identifiable resonance in the reflectance spectrum. While it should be emphasized that this does not imply any discontinuity in the actual dispersion relation it does indicate that the guided mode is isolated from any interactions with cover-radiation modes.

For the purpose of impedance matching at a specified design wavelength, it is helpful to apply a merit function to the coupling resonance and employ a multiparameter optimization. Two important properties of the coupling are the damping (quantified by the width of the resonance) and the impedance mismatch (quantified by the reflectance at the center of the resonance). The optimization was guided by a merit function consisting of a weighted sum of the normalized width of the resonance and the contrast ratio between the maximum off-resonance reflectance and the minimum on-resonance reflectance.

Samples were fabricated from commercial SOI material (SiBond) with layer thicknesses as close as possible to optimum coupling for design wavelengths of λ=1064 nm and λ=1550 nm. In some cases, the starting c-Si layer was thickened slightly with a deposition of amorphous silicon in order to meet the design specifications. In all cases, the sample received a uniform gold deposition at the specified electrode thickness.

Holographic gratings were recorded in photoresist using a Lloyd’s mirror arrangement and the exposed gold was selectively etched in a Chlorine-Assisted Ion-Beam Etching system. The remaining gold grating was then stripped of photoresist and overcoated with amorphous silicon. The amorphous silicon was deposited at approxmately 0.5 nm/s in an electron beam evaporation system. In order to minimize the background oxygen content, the chamber was first gettered with a pre-deposition prior to opening the shutter. The resultant films showed the high visible reflectance characteristic of amorphous silicon.

## 3. Experimental Results and Discussion

The dispersion plot of figure 2b suggests that this sample geometry may be suitable for optoelectronic switching, all optical switching or, on a shorter time scale, Bragg soliton excitation. We discuss each of these applications in turn. It is well known that a change in refractive index can be accomplished by current injection or, for certain materials, by the application of an electric field. This change in refractive index can be the basis for optoelectronic switching[16], through the resulting change in waveguide mode resonance.

All-optical switching is accomplished by an intensity induced change in refractive index in the waveguide region. The combination of an Nd:YAG (λ=1064 nm) laser pulse with crystalline silicon results in an absorption-induced change in carrier density which, in turn, alters the refractive index. This type of nonlinearity is appropriate for switching at sub-nanosecond to microsecond time scales (depending on the native response time of the MSM device), but the time scales are much longer than those considered suitable for Bragg soliton excitation.

We investigated the all-optical switching characteristics of MSM/SOI waveguide structures designed for operation near λ=1064 nm. The apparatus was similar to that used in earlier investigations,[10,11,15,16] in which the sample was controlled on a five-axis translation stage and the reflectance from a diode-pumped Nd:YAG source (1 KW peak power) was monitored. It was observed that, despite the fact that the sample was fabricated for optimum linear coupling at normal incidence, the optimum angle for switching was always slightly off-normal incidence. Figure 3 shows a traceof the incident and reflected pulse at an angle of 2.3° to the surface normal. The reflected pulse shows a transition from high to low reflectance near the peak of the incident pulse, along with hysteresis similar to that seen in earlier, in-plane switching

We now consider the possibility of accomplishing out-of-plane, distributed excitation of Bragg solitons. For such an application it is appropriate to examine the characteristics of MSM/SOI samples in the high transparency region of silicon, λ=1550 nm. The paragraphs which follow describe an experimental characterization of the linear properties in order to assess the possibility of carrying out nonlinear Bragg-soliton experiments. Samples were fabricated in a manner identical to those designed for near band-edge interaction, but with the grating period Λ=895 nm chosen for first-order radiation mode/waveguide coupling and second-order Bragg reflection.

The experimental apparatus shown in figure 4 was used to characterize the linear response of the periodic structure over a wavelength range centered 1550 nm. Light from a broadband fiber-coupled LED was connected to a 2 × 2 splitter, collimated, and passed through a polarizer before striking the sample at normal incidence. Reflected light was then collected by the fiber and passed through the second arm of the splitter and passed to an optical spectrum analyzer.

Figure 5 shows a comparison between the theoretical and experimental TE reflectance spectra for a sample optimized for λ=1550 nm. The width of the measured resonance, Δλ, is somewhat larger than that predicted by theory, but we note that the depth is even deeper than that predicted by the theory. Origins for the broadening could include sample inhomogeneity╌very small thickness variations will result in a spatially varying mode resonance. Other possible origins for this are homogeneous: waveguide scattering and beam size effects, neither of which are treated in the RCWA.

It is instructive to consider the impedance matching conditions necessary for linear and nonlinear out-of-plane coupling in periodic waveguide structures. For linear coupling, resonant impedence matching can be understood as destructive interference between the specularly reflected amplitude and that portion of the wave which scatters into the waveguide mode and back out into the cover. When this condition is met, the energy must either remain in the guide and be dissipated (absorbed or scattered) or be diffracted into a transmitted order in the substrate. The combination of these (dissipation and substrate-coupling) will define the characteristic ‘interaction length’ within the structure. As with any spectral filter, the interaction length measured in wavelengths is approximately equal to the resolving power λ/Δλ. The resonance shown in figure 5 indicates an interaction length of approximately 300 wavelengths which corresponds to 85 μm in a material of refractive index n=3.5.

A similar coupling process is expected for out-of-plane Bragg soliton excitation, but with a resonance condition which undergoes a discrete shift reflecting the difference between thegroup velocity of the envelope soliton and that of the linear waveguide mode. We can use the interaction length as the effective grating length for out-of-plane coupling, and estimate the strength of in-plane contradirectional coupling using the splittings observed in the dispersion relations of figure 3. The fractional gap width Δω/ω is 0.03 for near-normal incidence coupling, yielding a coupling coefficient-length product of kL≈9. Nonlinear index changes in semiconductors can be as high as 0.01. We can then take the gap-soliton figure of merit proposed by deSterke and Sipe, modified to use the interaction length as the effective grating length:

in which N represents the number of grating periods in the interaction length. We expect that Bragg solitons excited by out-of-plane coupling would exhibit a ‘signature’ shift in resonance wavelength defined by the group velocity of the soliton.

In summary, we have presented a study of out-of-plane coupling in MSM/SOI waveguide structures applied to optical switching and Bragg soliton excitation. The calculated dispersion curves show a rich variety of interactions that may provide the necessary dispersion for Bragg soliton interaction, and the samples exhibit nanosecond time scale optical switching near the semiconductor band edge.

## Acknowledgments.

The authors are indebted to Dr. Song Peng, Professor G. M. Morris, and Dr. Scott Norton for providing the core RCWA software, and to Al Heaney and Prof. Turan Erdogan for invaluable experimental assistance.

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