We have studied low-dispersion slow light and its nonlinear enhancement in photonic crystal waveguides. In this work, we fabricated the waveguides using Si CMOS-compatible process. It enables us to integrate spotsize converters, which greatly simplifies the optical coupling from fibers as well as demonstration of the nonlinear enhancement. Two-photon absorption, self-phase modulation and four-wave mixing were observed clearly for picosecond pulses in a 200-μm-long device. In comparison with Si wire waveguides, a 60 − 120 fold higher nonlinearity was evaluated for a group index of 51. Unique intensity response also occurred due to the specific transmission spectrum and enhanced nonlinearities. Such slow light may add various functionalities in Si photonics, while loss reduction is desired for ensuring the advantage of slow light.
©2011 Optical Society of America
With the rapid increase in photonic network traffic and related power consumption, advanced optical signal processing requiring fewer O/E conversions is desired, and thereby nonlinear optical devices are studied for all optical wavelength conversion, signal regeneration, and fast photonic switching. Many studies have exploited optical fibers and semiconductor optical amplifiers as bulky nonlinear devices. However, the total system usually becomes large because the signal processing needs many other optical components. Therefore, on-chip compact nonlinear devices are worth studying toward their full integration. Recently, such on-chip devices have become available in Si photonics. A small modal cross-section of Si wire waveguides enhances the internal optical density to 1000 times higher than that in fibers and easily generates stimulated Raman scattering, two-photon absorption (TPA), self-phase modulation (SPM) and four-wave mixing (FWM) [1–4]. They will be more attractive if their operating power and device length currently of watt- and centimeter-order, respectively, are drastically reduced, and/or their narrow working spectra in resonant structures is moderately expanded. Low-dispersion (LD) slow light, usually with a group index ng of several tens and a bandwidth of several nanometers, compresses optical pulses in space and enhances the longitudinal optical density, resulting in further nonlinear enhancement. Photonic crystal waveguides (PCWs) have been studied extensively for generating such LD slow light [5–10]. The lattice-shifted photonic crystal waveguide (LSPCW) we have developed so far exhibits LD slow light with a simple parameter tuning .
While many groups are still fabricating Si photonics devices using their own facilities, the future breakthrough depends on whether advanced CMOS (-compatible) process for Si electronics can be exploited for photonics. The CMOS process ensures large-scale photonic integration with high uniformity, high reproducibility, and low cost. It is already used for fabricating Si wire and rib waveguides on silicon-on-insulator (SOI) substrate [11–13]. However, it is not suitable for fabricating commonly-used air-bridge PC slabs. Here, the thick silica box layer in the SOI substrate needs to be etched chemically in the backend process, but this often damages other devices. This difficulty hampers the integration of spot-size converters (SSCs)  with PCWs. Without SSCs, the optical coupling loss between a lensed fiber and a cleaved PCW is usually as high as 15 − 20 dB/facet. This is a severe disadvantage for nonlinear experiments which require a high input power..
In this work, we applied CMOS-compatible process optimized for fabricating air-clad (air-bridge slab) and silica-clad LSPCWs integrated with SSCs and Si wires. Consequently, the optical coupling was significantly improved and the nonlinear enhancement was observed much more clearly than ever. In this paper, we first show the device design, which partly overlaps with previous reports for the air-clad LSPCW  but is a new study for the silica-clad LSPCW. Then, we describe the fabricated device and the linear characteristics. In particular we estimate the loss at each part of the device, because this is the first experiment, for which we can discuss the fiber-to-fiber insertion loss of PC devices. In the later part, we show the nonlinear characteristics such as TPA and SPM for short optical pulses, and estimate their enhancement brought from slow light. We also demonstrate unique intensity response and FWM, which may be applicable for signal processing.
The normal PCW consists of a line defect in a triangular lattice of holes with the period a and hole diameter 2r . In the LSPCW, the third rows of holes are shifted along the line defect by s. Figure 1(a) shows photonic bands of the guided mode for the air-clad device. When s is increased slightly (B), the straight section of the band (red line) representing LD slow light appears. When s is increased further (C, D), the LD band becomes more sloped, so the group index ng decreases and the normalized LD bandwidth ΔλLD/λ increases. In addition, a horizontally flat band appears at higher frequencies. These behaviors have been explained by the interaction of the slab and guided mode bands [6,16]. Let us define ΔλLD as the range that ng falls within a ± 10% change. Then, we can estimate ng = 79 − 23 for ΔλLD/λ = 0.2 − 0.6% (ΔλLD = 3.6 − 8.8 nm at λ = 1.55 μm), respectively. Thus we can control ng and ΔλLD just by changing s. In addition, the band-edge wavelength is almost unchanged when s is changed. These are important advantages that simplify the experimental observation of LD slow light at a target wavelength. The figure of merit (FOM) of slow light is often evaluated by the normalized delay-bandwidth product ng(ΔλLD/λ) . In the band diagram, it is proportional to the lateral width of the LD band. It is seen from Fig. 1(a) that a smaller s gives a larger FOM.
For the silica-clad device, parameters are optimized so that the LD band is located at frequencies lower than the silica light line . As shown in Fig. 1(b), the fundamental behaviors are the same as those of the air-clad devices. In general, however, the guided mode band is 3 − 5 times more sloped because of the lower index contrast, resulting in a smaller ng of 15 − 30 and wider ΔλLD/λ = 0.6 − 1.2% (ΔλLD = 9 − 18 nm at λ = 1.55 μm). These parameters are more insensitive to s while the band-edge wavelength shifts with s. Thus advantages of the LSPCW are weakened.
We employed SOI substrate with a 220 nm thick top Si layer and 2 μm thick silica box layer. Devices were fabricated by using CMOS-compatible process with KrF stepper exposure (180 nm resolution), as shown in Fig. 2 . The LSPCW of length L = 200 μm is sandwiched by 50 μm-long chirped LSPCWs explained below and Si wire waveguides, which are then terminated by SSCs at the end facets. In air-clad devices, the air-bridge is formed by etching the top silica cladding and bottom box layer using the multi-step masking and etching process, which has been optimized for protecting the Si wires and SSCs. Figure 2(a) shows the overview of a single chip separated by dicing. It includes more than a hundred devices with different parameters. (b)−(d) show top views of the SSC, air-clad LSPCW and silica-clad LSPCW, respectively. The SSC consists of inverse-tapered Si wire of 180 nm tip width and 200 μm length, buried by a silica waveguide of 4 μm square cross-section. The taper is butt-joined to the silica-clad Si wire. In samples only including the Si wire and SSCs, the width of the Si wire is maintained to be 400 nm. In LSPCW samples, on the other hand, the straight part of the Si wire is laterally expanded to 4 μm through a taper in order to suppress the nonlinearity. At the junction between the Si wire and chirped LSPCW, another taper of the Si wire is inserted, where the width at the junction is . While s = 0 at the junction, s is increased linearly in the chirped LSPCW, and finally connected to the LSPCW with a constant s. The output side is symmetric to the input side. The distance between input and output end facets of the SSCs is 1.93 mm, while a crank pattern that offsets the SSCs is inserted to the output side in order to avoid the direct coupling of stray input light to the output fiber. Thus, the total waveguide length including SSCs is 1.95 mm.
4. Linear characteristics
In the measurement of the linear characteristics, transverse-electric polarized light from a tunable laser was coupled to the SSC through a lensed fiber with a 1/e2 spot diameter of 3 μm or a 20 × objective lens. The optical output from the other SSC was detected through similar optics. The group delay Δt was measured by using the modulation phase shift method. The transmission of short optical pulses was observed using mode-locked fiber laser, erbium-doped optical amplifier, band-pass filter (BPF), and auto-correlator. Refer to Ref . for further details.
Figure 3 shows transmission and group delay spectra for three LSPCW samples, which were used for overall measurements in this study. Two air-clad devices and one silica-clad device have parameters similar to those in Fig. 1. ng was estimated from cΔt/L, where c is the light velocity in vacuum. In the air-clad devices, the transmission spectrum is separated into two distinct regimes by a dip. As inferred from Fig. 1(a) and Ref , the dip corresponds to the horizontally flat band, and the short and long wavelength sides correspond to the low-ng band and high-ng LD band, respectively. The dip which varies in depth from −15 to −25 dB is caused by the mode mismatch in the chirped LSPCWs and the propagation loss in the LSPCW, both of which are enhanced particularly for the large ng of the flat band. Large dispersion occurs at both edges of the LD band, while ng is near-constant and takes the minimum value around the center wavelength. Here let us define ng as the minimum value after taking a moving average (thick line). From Figs. 3(a) and (b), we evaluate ng = 51, ΔλLD = 5.6 nm and ng = 36, ΔλLD = 7.4 nm, respectively. To confirm the low dispersion at wavelengths indicated by arrows in Fig. 3(a), we observed the short pulse transmission for the former sample. For an input pulse width (FWHM) of 3.1 ps, the dispersion was almost negligible in the low-ng band. The dispersion was not severe even in the LD band; the output pulse length increased to 4.0 ps. In the silica-clad device, the spectral shape is different, as shown in 3(c). Only one transmission maximum appears with slightly intense background. Figure 1(b) suggests that the low-ng band is suppressed because it is located above the silica light line, and therefore the transmission maximum corresponds to the LD band. As the delay changes slowly in this band, we can estimate ng = 24 and Δλ = 6.6 nm. The background noise comes from the propagation of leaky modes in the silica cladding. The oscillation is caused by the Fabry-Perot resonance in the cladding overlapping with the LSPCW.
Output intensities were measured and compared between many different waveguides of different parameters, and the loss at each part was evaluated. This is summarized in Fig. 4 for the above three samples. The coupling loss from the lensed fiber to the SSC is 3.0 ± 1.0 dB. It is mainly caused by the scattering at the tip of the inverse taper, and can be reduced to < 0.5 dB by narrowing the tip using higher resolution lithography . The average loss in the Si wire is 4.2 ± 0.1 dB/cm. While it is higher than the lowest value of < 2 dB/cm for similar Si wires , it already gives a small total loss of less than 1 dB for L = 1.95 mm. The loss at each junction between the Si wire and air-clad PCW in the high-group-velocity band is < 0.5 dB. This means that, when the first Si wire is short enough to neglect the propagation loss, we can launch light from the fiber to the PCW within 3.5 dB loss. This value is roughly 15 dB lower than that for the cleaved PCW without the SSC. When the air-clad chirped LSPCW and LSPCW are inserted instead of the PCW, the loss increases by more than 2 dB. This should be reduced to < 1 dB by further optimizing the structure . In any case, we can launch light from fiber to the LSPCW with a 5 − 6 dB loss. The propagation loss α in the LSPCW is rather severe −− it is ~47 dB/cm in the high-group-velocity band, and ~130 and 210 dB/cm for ng = 36 and 51 in the LD band, respectively. The corresponding losses for the three LSPCWs (L = 200 μm) are 0.9, 2.4, and 4.2 dB. They are much larger than that of the Si wire and the reported value of < 5 dB/cm for the low-ng band of a PCW fabricated by using e-beam lithography . This is partly due to different resolutions of KrF stepper and e-beam, but may also be affected by the imperfect etching of the box layer, which is still under optimization. In the silica-clad device, the propagation loss is only ~12 dB/cm and < 0.3 dB for L = 200 μm. This is attributed to the reduced light scattering at the lower-index-contrast boundaries  as well as fewer process issues than in the air-clad devices.
5. Nonlinear enhancement
Nonlinear characteristics were measured for high-intensity optical pulses of 3.1 ps width. Measurement setups were the same as in Ref . Thanks to the SSC, a pulse peak power of up to 80 W could be launched into the Si wire even when SPM in the preceding fibers was suppressed. However, we actually limited the launched power to < 30 W to avoid damaging to the first SSC. In LSPCW samples, nonlinear effects in the expanded Si wires were negligible at this power level. The center wavelength of the pulse, λp, was centered at the LD band.
Figure 5 shows intensity response, where the abscissa denotes the input power Pin launched inside each main device, which is estimated from Fig. 4. In the sample of Si wire used for comparison, the output starts to saturate gradually at Pin ~1 W due to TPA. The output from the air-clad LSPCWs is by 8 − 10 dB further reduced on the output side, due to linear absorption. Here, the saturation starts at Pin ~0.1 W although LSPCWs are approximately 10 times shorter than the Si wire. Let us define the saturation-starting power Psat as Pin that reduces the output to 90% of the linear response. Then, Psat = 0.12 and 0.055 W are evaluated for ng = 36 and 51, respectively. In general, Psat is expected to decrease in proportion to ng−2 . The two evaluated Psat satisfy this relation very well. At higher powers, the response exhibit very clear saturation followed by unexpected rise up, which cannot be explained simply by TPA. We will discuss this in the next section. In the silica-clad LSPCW, Psat increases to 0.30 W, but still maintains the ng−2 dependence approximately.
Figure 6 shows the output spectra corresponding to Fig. 5. The spectra in the linear regime were formed by a box-like response of the BPF (2 nm transmission window) and some specific response of devices. In the Si wire, the spectrum was broadened slightly by SPM at Pin = 0.86 W. The spectral width at −10 dB intensity, Δλ10dB, broadened to 3 nm at 2.7 W. Since TPA occurred simultaneously, carriers were excited and dynamic blue-shift occurred through the carrier plasma effect. On the other hand, the spectra of LSPCWs look noisy. This originates from the oscillating spectra in the linear regime and increases further in the nonlinear regime. Neglecting this noise, the spectra overall exhibit larger broadening, which also indicates the nonlinear enhancement. In the air-clad LSPCW, Δλ10dB broadened to 5 − 7 nm at similar Pin and a spectral dip appears. This dip is considered to show the 1.5π phase shift of the SPM, although it is slightly offset from the spectral center due to the carrier plasma effect and seems to be initiated from some dips and peaks of the oscillating linear spectrum. In the silica-clad device, similar wide broadening and dip appear but require a much higher power because of the low ng. Let us evaluate the nonlinear coefficient γeff = ΔϕNL/PinLeff, where ΔϕNL is the 1.5π phase shift, Pin is the corresponding input power, and Leff is the nonlinear effective length given by for the linear loss coefficient α in the unit of inverse length. For the Si wire, Leff is calculated from the aforementioned propagation loss to be 1.8 mm, and γeff is evaluated to be ~600 W−1m−1 from a higher Pin showing the 1.5π phase shift. For LSPCWs, on the other hand, Leff is 130, 150 and 180 μm, Pin is 0.50 − 0.99 W, 0.92 − 1.85 W and 1.4 − 2.2 W (the lowest power is evaluated from that exhibiting a clear dip and the highest power is that not exhibiting the next peak of ΔϕNL > 1.5π), for ng = 51, 35, and 24, respectively. They give γeff = 3.6 − 7.1 × 104, 1.7 − 3.4 × 104, and 1.1 − 1.7 × 104 W−1m−1, and the corresponding enhancement factors against that of the Si wire are approximately 60 − 120, 30 − 60 and 20 − 30. Theoretically the enhancement factor is proportional to ng2/Aeff where Aeff is the effective modal area. For the Si wire in this study, ng and Aeff are calculated to be 4.2 and 0.12 μm2 at λ ~1.55 μm. For LSPCWs, Aeff depends on s and ng, but usually increases to 2 − 3 fold larger than that of Si wires [6–8]. Therefore, the ng2/Aeff enhancement factors are expected to be 49 − 74, 23 − 35 and 11 − 16. The experimental results are slightly larger than these values, even considering the uncertainties in the power of the 1.5π phase shift and the modal area. They might be caused by the nonuniform localization of slow light in the devices with some disordering, which is suggested by the oscillating linear spectrum and unusual formation of the spectral dip. The highest value of γeff in the experiment is comparable to that in the LSPCW made of highly nonlinear chalcogenide glass Ag-As2Se3 with ng = 20 ; the chalcogenide glass has 10-fold higher nonlinear index n2 than that of Si. This result suggests that the smaller n2 of Si is compensated by the larger ng..
Note that the reduction ratio of the effective length Leff/L is 0.91 for the Si wire, while 0.65, 0.75, and 0.90 for the LSPCWs. This means that 1.95 mm Si wire is too short and 200 μm LSPCWs of larger ng are too long to compare the nonlinearity with each other. Considering the loss coefficients, three-fold longer Si wire would be fair for comparison. In addition, a low loss of ~1 dB/cm is reported for the state-of-the-art Si wire with the similar design. In this case, the length giving Leff/L = 0.65 is elongated to 4.1 cm and we can expect a 21-fold nonlinear enhancement. This discussion suggests that 200 μm is a reasonable length for the LSPCWs to obtain nonlinearities for the high propagation loss, and that, even compared with the best Si wire to date, the LSPCWs with a large ng maintain their advantage on the nonlinear enhancement. The advantage will be larger if the propagation loss is reduced so that a longer devices becomes meaningful. For example, 2 × , 5 × , and 10 × higher nonlinearities than those for ng = 51 are estimated when (L [mm], α [dB/cm]) are (0.4, 100), (1, 40), and (2, 20), respectively. Disadvantages of the LSPCW are the limited bandwidth and spectral oscillation. The former is essential and it must be balanced with the nonlinear enhancement by optimizing s and other structural parameters toward each target application. The latter is a technical issue, but not simply improved as it strongly depends on the accuracy of the CMOS-compatible process. More advanced process would be effective, whole we have to improve the waveguide design so that the oscillation is moderated.
6. Nonlinear response
In Fig. 5, we showed the distinct output saturation in the air-clad LSPCWs. This is not simply caused by TPA but the combination of the specific transmission spectrum in Fig. 3 and SPM in Fig. 6, in addition to the TPA. It changes the intensity response at different wavelengths λp. Figure 7 summarizes the nonlinear response and output spectra in the LSPCW of ng = 51. When λp is set at the high-group-velocity regime (indicated by symbol A), the TPA gradually saturates the output intensity. The spectral broadening mainly occurs toward shorter wavelengths because of the SPM, carrier plasma effect and dip at longer wavelengths. When λp is inside the dip (B), the output is suppressed in the linear regime, while it increases rapidly once the spectral broadening reaches the low-ng band. When λp is set at the long wavelength edge of the dip (C), rapid saturation occurs rapidly once the spectral broadening starts but blocked by the dip. Complete saturation occurs at Pin < 0.3 W. After the spectral broadening crosses the dip, the output increases again. When λp is at the center of the LD band (D), the complete saturation is delayed until the spectral broadening reaches to the dip. Thus B shows the threshold behavior, and C and D show a limiter-like function. If the device spectrum is shifted for example by heating, the desired response can be tuned to the desired operating wavelength.
7. Four-wave mixing
FWM has been observed for two synchronized slow light pulses in chalcogenide glass PCWs [8,21] and also for cw pump and pulsed signals in a SOI PCW . To maximize the slow light enhancement, we employed two synchronized pulses in the LD band of the LSPCWs. Although the material nonlinearity is 10 times lower than chalcogenide glass reported, our device compensates for the disadvantage by the efficient light coupling using the SSC and the higher ng. The synchronized pulses with a 6.6 ps length and different λp were generated in a setup shown in Ref . Figure 8 shows the output spectrum when the input total power was limited so that FWM do not occur in the preceding fibers. In the Si wire, we can confirm four spectral peaks of FWM with a conversion efficiency η of −14 dB when Pin of the pump pulse is 1.32 W. Previously, a high η of −10.6 dB has been reported for a similar Si wire of 2.8 cm length . Our η is slightly lower but seems reasonable because our Si wire is 14 times shorter. For the LSPCWs, Pin cannot be comparably high because the spectral broadening of SPM became severe and overlapped with converted signals. We limited the pump power to less than 0.9 W and observed η = −13 to −18 dB for different ng. Considering that the LSPCW is 10 times shorter than our Si wire and 140 times shorter than that in Ref , comparable η in the LSPCWs supports the nonlinear enhancement.
Using CMOS-compatible process, we fabricated the lattice-shifted photonic crystal waveguides which exhibit low-dispersion slow light and nonlinear enhancement. The integration of spot size converter enable us to input light from fiber to the photonic crystal waveguides with a loss of 5 − 6 dB. Slow light pulses of 3.1 − 6.6 ps length were observed with a group index of around 24 − 51. Even when the device length is as short as 200 μm, TPA, SPM and FWM were observed clearly at an incident peak power of 100 mW order. The nonlinear coefficient was enhanced by slow light up to 130 times higher than that in Si wires. The combination of the specific transmission spectrum and these nonlinearities gives unique nonlinear response, some of which may be applicable for signal processing. This study shows an example of advanced photonic crystal devices fabricated by using CMOS-compatible process. Another example is presented elsewhere .
This work was partly supported by the FIRST Program of Japan Society for the Promotion of Science.
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