An 80 MHz pulse train of ~100 fs optical pulses centred at ~1.5 µm is propagated through a variety of high-index-contrast silicon-on-insulator waveguide structures less than 1 mm long. All-optical power limiting and negative differential transmission, based only on the intrinsic nonlinear response of the untextured waveguides near 1.5 µm, are demonstrated for average in-guide power levels of ~1 mW. Superlinear transmission is observed in a textured silicon waveguide for power levels less than 20 µW.
©2004 Optical Society of America
Photonic crystals, or, more generally, high-index-contrast (HIC) optical waveguides, offer a means by which to integrate a number of signal processing functions in small (~cm2) “optical chips”. This is fundamentally due to the fact that optical pulses propagating in these strongly-confining, dispersive waveguides can be efficiently filtered and re-routed over distances of only a few wavelengths, with low intrinsic loss. Numerous geometries have been proposed for realizing the key building blocks of integrated optical chips in HIC waveguides, including; high-transmission bends, splitters, dispersion compensators, filters etc .
Over the past few years, silicon-on-insulator (SOI) based nanostructures have attracted much interest as potential candidates for highly efficient and low-cost optical circuits due to silicon-based electronic chip technology. Low-loss bends with very small radius of curvature have already been demonstrated in SOI-based photonic crystal waveguides [2–4] and several schemes for coupling light in and out of these waveguides have recently been realized including the use of photonic crystal technology [5–8]. An integrated optical circuit in SOI consisting of waveguides, mode converters, and input/output couplers to single mode fibres with relatively low overall loss has been demonstrated .
Although much progress has been made towards achieving low-loss performance that approaches the intrinsic limits of this technology [9,10], the fabrication tolerances on surface roughness and lithographic accuracy are extreme. Even straight HIC ridge waveguides require the roughness to be less than ~5 nm to keep losses below the dB/mm level . Substantial investment would be needed to develop manufacturable processes of sufficient quality to make high-density optical chips commercially viable. Unless such chips can offer completely new functionality, rather than just a higher degree of integration on a smaller footprint, the required level of investment is unlikely to be made.
A qualitatively different level of functionality could be realized if electronically-controlled functions (switching, variable attenuation, wavelength shifting etc.) were replaced with “all-optical” elements. This can be achieved in principle by combining nonlinear optical response with optical gain. The HIC waveguide structures are ideally suited for yielding nonlinear response at moderate optical powers, because of their small mode areas (in the case of guides), and mode volumes (in the case of 3D microcavities). It has been shown theoretically how devices such as all-optical analog-to-digital converters, hard limiters, and logic gates could be created using periodic changes in the refractive index . An all-optical transistor with low switching powers has been simulated in a two-dimensional photonic crystal waveguide geometry . Wavelength conversion with an efficiency of 10%  and stimulated Raman scattering  based on the nonlinear susceptibility of silicon have also been demonstrated.
Other work has focused on two-photon absorption and self-phase modulation of 1.5 µm pulses in silicon, and the possibility of building a fast optical switch based on these effects [8,15–17]. The figure-of-merit obtained in two of the three studies suggests that optical switching in intrinsic silicon might be possible at this wavelength. Previously published  nonlinear propagation studies of ~100 fs pulses through 200 nm high by 1.6 µm wide silicon ridge waveguides illustrated how compact optical limiters can be realized in SOI. These proof-of-principle devices incorporated 2D photonic crystal input and output “grating” couplers, combined with parabolic-shaped taper sections that adiabatically couple the ~10 µm wide output of the grating coupler into the narrow ridge waveguides .
This paper describes a number of nonlinear responses obtained by propagating an 80 MHz pulsetrain of ~100 fs optical pulses centred at ~1.5 µm, through HIC integrated silicon waveguide structures less than 1 mm long. All-optical power limiting and negative differential transmission, based only on the intrinsic nonlinear response of the untextured silicon waveguides near 1.5 µm, are demonstrated for average in-guide power levels of ~1mW. Superlinear transmission in a textured silicon waveguide is observed for power levels less than 20 µW. The principles used to achieve these nonlinear transmission responses are quite generic: qualitatively similar, and perhaps even better nonlinear behaviour could be expected in HIC waveguides made from other semiconductors, such as AlxGa1-xAs, or by integrating resonant media, such as semiconductor quantum dots, with the waveguides.
Laser pulses of 100-fs duration (80 MHz repetition rate) are launched into HIC waveguide structures of different lengths and widths. The SOI wafer used to fabricate the optical circuits consists of a silicon substrate, a 1000-nm-thick SiO2 layer, and a 200-nm-thick layer of silicon with surface normal in the <100>-direction. The rectangular channel waveguides are fabricated by etching grooves all the way through the top 200 nm layer of silicon, so that the resulting silicon cores have an air cladding on top and on the sides, and an SiO2 cladding layer on the bottom. All waveguides have a height of 200 nm but their widths vary. One group of single mode waveguides studied in this paper have a width of 425 nm and vary in length from 0.05 mm to 1.00 mm. These waveguides have a photonic crystal grating coupler-tapered waveguide section at each end in order to couple 1.49-µm-wavelength light efficiently and conveniently in and out of the waveguides. This geometry allows near normal incidence coupling that is very tolerant of misalignment. With minimal effort, input coupling efficiencies of ~4% for the 100 fs pulses can be achieved, while the output coupling efficiency of light transmitted through the ridge waveguide segments is ~25% . This group is used for the systematic study of nonlinear transmission through straight, single mode waveguides, as described in section 3.
The second group of waveguides have polished facets at each end. The laser light is end-coupled into the waveguides using an f/2-lens. The input coupling efficiency is approximately 0.2%, which is a factor of 20 less than the photonic crystal couplers and, in addition, alignment is much more challenging. The waveguides are 3-µm-wide at both ends and taper down to a (single mode) width of 580 nm in the center. The total length including the tapered ends is approximately 1.0 mm. In one of the waveguides studied in this paper, the 10-µm-long single mode section is patterned with a Bragg grating of 25 periods, 400 nm pitch, and a 50% duty cycle. The resulting photonic band gap has its lower energy edge near 1.5 µm. The transmission properties of this structure are discussed in section 4.
All spectra are recorded with a Fourier transform spectrometer using f/7 reflective optics. Power measurements are performed with an InGaAs photodiode that is cross-calibrated against a power meter. Only TE-polarized modes are excited in all experiments reported here.
3. Nonlinear effects in silicon waveguides
Figure 1 shows (in open red symbols) the transmitted power through a 1.6-µm-wide guide, as a function of the incident power (defined as the average power of the 80 MHz pulse train external to the sample in all figures), from Ref. . Also shown in Fig. 1 are a series of similar response curves obtained with identical input-output coupling regions, but where the silicon ridge is a single (TE) mode guide (near 1.5 µm) 200 nm high by 425 nm wide. Note that for short lengths of the single mode waveguide, these structures also offer almost ideal optical limiting behaviour. The new result of interest here is that for longer lengths of single mode waveguide, the nonlinear transmission actually turns over, and for single mode guides longer than 200 µm, negative differential transmission is observed. For an 800-µm-long single mode guide (see Fig. 2), there is a five times reduction of the transmitted power from its peak value at Pin ~8 mW to the saturated value for Pin>50 mW.
In Ref.  it was possible to fit both the saturated transmission and the corresponding nonlinear transmission spectra through the 1.6 µm wide guides using a fairly simple numerical model that included the influences of third-order self-phase modulation and two-photon absorption (the real and imaginary components of χ(3) for silicon), and the iterative effect of the free carriers generated via the two-photon absorption. The free carriers had to be included in order to simulate the plateau-like behaviour at high powers, which is parabolic when only the instantaneous χ(3)-term is included in the pulse propagation equations. At the highest powers achieved in the 1.6 µm guides, the agreement between this model and the experiment was satisfactory, but not perfect, with the biggest problem being that there was a slight bit of negative differential transmission even in the 1.6 µm guides at elevated power levels, which is not reproduced by the model. Figure 3 compares the output spectra obtained in the 1.6 µm and 425 nm wide guides of similar length when the input powers are scaled by the respective mode areas to yield in-guide intensities. For intensities below ~150 GW/cm2, the spectra evolve nonlinearly in an almost identical fashion. These are power levels where the simple model described in Ref.  is in reasonable agreement with the results. At higher intensities there are clearly additional effects present that influence the nonlinear propagation, with the net result that negative differential transmission occurs both in the multimode and single mode guides, with the effect being more pronounced in the single mode case.
The onset of nonlinear behaviour that goes beyond that predicted by third-order perturbative models occurs at intensities where the effective two-photon absorption length becomes comparable to the optical pulse length. Several non-perturbative effects may be contributing to the observed nonlinear response when the slowly varying envelope approximation is invalid. The fact that the nonlinear response depends on the waveguide length in this regime, despite identical input coupling geometries, seems to rule out an essential role of the tapered coupling region. The difference in behaviour between the 425 nm and 1.6 µm wide guides may be due to nonlinear mode conversion in the wider (multimode) guides. It is interesting to note (see Fig. 4), that in the saturated transmission regime in samples where a large negative differential transmission is observed, the transmitted spectra appear more symmetric than at lower powers, suggesting perhaps that the free carrier influence is saturating (see Ref. ).
4. All-optical functionality
Figure 5 shows two absolute transmission spectra through the 800-µm-long single mode guide discussed above. If this waveguide was followed by a bandpass filter that has high transmission from 6750 cm-1 to 6850 cm-1, there would be a decrease in transmission of ~20 times on going from an input power of 12 mW to 30 mW. This type of response could be used to realize an all-optical exclusive OR gate if an upstream combiner was integrated to route two inputs into a single mode waveguide section. Other applications such as inverted operational amplifiers, inverters, and NAND gates result from the combination of negative differential transmission with amplifiers [18–20].
A method for utilizing an in-line filter to achieve a different, superlinear response (i.e., a more than linear increase in transmission with increasing input power) is illustrated in the following: consider the spectra shown in figure 6, which shows the transmission at relatively low powers through a 250-µm-long, 510-nm-wide (single mode) waveguide with 100-µm-long adiabatic input and output tapers connecting the guide to 325-µm-long, 3-µm-wide multimode guides at either end. The laser pulses are coupled into the input multimode guide by an f/2-lens. While the total transmitted power saturates for increasing input power, the transmitted power at 6575cm-1 (detuned 178 cm-1 from the center exciting wavelength) evolves as shown in Fig. 7.
At low input powers the transmitted power at this wavelength grows super-linearly. As the power increases the propagating pulse broadens and thus an increasing amount of the energy in the pulse is found at this wavelength. At higher powers the strong saturation processes dominate and the response curve (at this particular frequency) again saturates. A narrow bandpass filter situated at 6575 cm-1 would result in the nonlinear transmission response illustrated in Fig. 7. This would be useful as an all-optical AND gate where the individual input channels would have powers below the threshold for nonlinear transmission.
In order to demonstrate this concept of achieving nonlinear all-optical functionality by integrating a nonlinear waveguide with an in-line filter, the structure illustrated schematically in Fig. 8 was fabricated. It consists of a 3-µm-wide 395-µm-long multimode guide that couples to a 580-nm-wide 10-µm-long section of HIC periodic Bragg grating waveguide through a 100-µm-long adiabatic taper.
The Bragg grating waveguide is out-coupled through an identical 100-µm taper and a 3-µm-wide waveguide. The entire structure is coated with a ~1-µm-thick layer of photoresist (AZ 4110, Clariant Inc., baked for 10 min. at 100°C). The HIC Bragg grating waveguide consists of 25 periods with a pitch of 400 nm, a duty cycle of 50%, and a silicon-to-photoresist index ratio of 3.47:1.64. Using UV lithography a 4-µm-wide trench of the photoresist is removed from the center of the grating leaving approximately 3 µm (5–6 pitches) of photoresist-coated barriers on either side. The photonic band edge of the structure without photoresist (index ratio of 3.47:1 in the grating teeth) is located at 1.45 µm (6900 cm-1); with the photoresist layer it shifts to 6450 cm-1 (1.55 µm). Hence the resulting structure comprises a coupled waveguide-resonator system in the wavelength range (1.45–1.55) µm. The photoresist-coated parts of the grating at either side act as barriers through which the light tunnels from the waveguide into the cavity. In Fig. 9, the low power normalized transmission spectrum for this waveguide-resonator system is presented. Between 6450 cm-1 and 6900 cm-1 there are two resonances corresponding to localized modes supported by the cavity. The feature just above 6400 cm-1 is at the band edge of the barrier regions.
The resonance located at 6592 cm-1 has a Q-value of 180 while the other at 6771 cm-1 has a Q-value of 250. Transmission spectra for (external) incident powers of (1-28) mW, and an incident centre wavelength of 1.477 µm (6771 cm-1), are shown in figure 10. As predicted there is a nonlinear increase in the power transmitted through the lower energy mode at 6592 cm-1 as the input power is increased.
The power transmitted through the 6592 cm-1 mode as a function of input power is shown in figure 11. Up to incident powers of ~10 mW (corresponding to average in-guide power levels of ~20 µW) the output power grows super-linearly. This behaviour is attributed to spectral broadening in the waveguide, followed by filtering by the micro-resonator. It is very unlikely that there is a significant nonlinear response in the cavity region itself, since two-photon absorption in the 3-µm-wide, 490-µm-long input section (including taper) of the structure, substantially reduces the power reaching the cavity. The amount of spectral broadening appears to be enhanced in the photoresist-clad waveguide, as compared to uncoated guides, likely due to the nonlinear response of the photoresist. For all incident powers the localized mode resonances neither shift nor broaden, further indicating that the nonlinear effect occurs in the waveguide preceding the cavity.
The measurements presented in this work show that the filtering characteristics of such a resonator combined with the intrinsic nonlinear properties of the in-coming waveguide, can exhibit response curves that are useful for optical switching and logic applications. To the authors’ knowledge this is the first demonstration of an integrated optical device using the nonlinearity of a waveguide, followed by the filtering characteristics of a resonator. Note that the device studied here is different from a design by Raynolds and LoCascio, in which optical switching is based on the nonlinear properties of nanocrystals incorporated into a Bragg cavity written into a planar waveguide . Their device relies on the saturable absorption properties of the nanocrystals not on the nonlinear properties of the waveguide.
In conclusion, efficient coupling of ~100 fs pulses centred near 1.5 µm has been achieved to single-mode silicon ridge waveguides, 200 nm tall, and varying from 425 to 510 nm wide. These rectangular cross section silicon channels are fabricated in the top layer of an SOI wafer containing a 1-micron-thick SiO2 layer. At power levels corresponding to ~1 mW inside the waveguides, strong negative differential transmission is observed in the total transmission through single mode guides of length longer than 200 microns. By placing a bandpass filter at the output, the spectral modulation of the spectrum can be exploited to obtain negative differential contrasts as high as 20 times. A structure that integrates a nonlinear waveguide with an in-line, 1D photonic crystal is used to demonstrate superlinear transmission for average in-guide optical powers less than 20 µW. Thus by integrating differently textured single mode waveguides on SOI, it is possible to achieve a variety of nonlinear transmission responses that could be used for all-optical gates.
The authors wish to thank the Natural Sciences and Engineering Research Council, the Canadian Institute for Advanced Research, and the Canadian Foundation for Innovation for financial support, and Galian Photonics Inc. for the SOI chip.
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