We, for the first time, present the ultrafast optical nonlinear response of a hydrogenated amorphous silicon (a-Si:H) wire waveguide using femtosecond pulses. We show cross-phase and cross-absorption modulations measured using the heterodyne pump-probe method and estimate the optical Kerr coefficient and two-photon absorption coefficient for the amorphous silicon waveguide. The pumping energy of 0.8 eV is slightly lower than that required to achieve two-photon excitation at the band gap of a-Si:H (~1.7 eV). An ultrafast response of less than 100 fs is observed, which indicates that the free-carrier effect is suppressed by the localized states in the band gap.
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Third-order nonlinear effects in semiconductors have been studied for all-optical switching devices. Cross-phase modulation (XPM) and cross-absorption modulation (XAM) are used for ultrafast signal processing where light is controlled by another light. In recent years, the efficient nonlinear interactions in silicon waveguides have been investigated because the strong optical field confinement in a core with a small cross section allows a pulse to have high power density with relatively low injected power [1–10]. The dominant nonlinear effects in crystalline Si (c-Si) are ultrafast Kerr nonlinearity, two-photon absorption (TPA), and slow effects of free carriers generated by TPA. Therefore, the response time of a nonlinear interaction is limited by the free-carrier lifetime of several hundred picoseconds in c-Si. To avoid the influence of free carriers, ion implantation of the silicon waveguide , carrier reduction by reverse-biasing the p-i-n diode in the waveguide [12,13], and using high-bit-rate signals where the free-carrier density is saturated  have been reported.
An alternative approach is to employ another material such as amorphous silicon (a-Si), which has a wider band gap and shorter carrier lifetime owing to the localized state in the band gap, as a high-index contrast waveguide. Since hydrogenated amorphous silicon (a-Si:H) has low absorption loss because of the terminating dangling bond in a-Si, it has recently attracted attention for the interconnection or three-dimensional integration of high-index contrast waveguides [15–19]. However, there has been little investigation of the optical nonlinearity in a-Si at telecom wavelengths. Ikeda et al. investigated nonlinear optical absorption in a-Si:H films using a Z-scan technique and in a hybrid waveguide of a-Si and c-Si with a short response time of ~30 ps .
In this paper, we present ultrafast nonlinear responses in an a-Si:H wire waveguide measured using heterodyne pump-probe methods and femtosecond pulses. This is the first report of Kerr nonlinearity in an a-Si:H waveguide at a telecom wavelength. Ultrafast response of less than 100 fs without slow free-carrier relaxation is observed.
2.1 Fabrication of amorphous silicon wire waveguide
A hydrogenated amorphous silicon layer was deposited by plasma-enhanced chemical vapor deposition with SiH4 and H2 mixture at 250 °C on a silicon wafer with a 2-μm-thick thermal oxide layer [15,16]. The band gap energy was ~1.7 eV and the absorption coefficient at 0.8 eV (λ = 1550 nm) was measured to be ~10−2 cm−1 using the constant photocurrent method. The refractive index was determined to be 3.516 at a wavelength of 1550 nm by spectroscopic ellipsometry. The waveguide core was formed by electron-beam lithography and reactive ion etching with SF6 gas. After RCA cleaning, 1-μm-thick SiO2 was deposited as over-cladding by electron cyclotron resonance sputter deposition. Each end of the waveguide had a spot-size converter with a narrowed waveguide for field enlargement. Figure 1(a) shows a scanning electron microscope (SEM) image of the cross section of the 400 nm × 250 nm waveguide.
Propagation losses of 14 dB/cm for the transverse electric-like (TE) mode and 7 dB/cm for the transverse magnetic-like (TM) mode were measured using the cut-back method with fiber-to-fiber alignment using continuous-wave light at λ = 1550 nm as shown in Fig. 1(b). The coupling loss between the a-Si:H waveguide and the lensed fiber was estimated to be 8 dB/facet. The power confinement of the TE mode within the a-Si:H core was three times that of the TM mode for the core dimensions used in this study, and therefore, the TE mode was more sensitive to waveguide loss because of the sidewall roughness. This should explain the larger loss in the TE mode.
2.2 Heterodyne pump-probe measurement
The ultrafast optical nonlinearity of the a-Si:H wire waveguide was measured using the heterodyne pump-probe method and femtosecond pulses [10,21]. Our experimental setup is shown in Fig. 2 . An optical parametric oscillator (OPO), which is synchronously pumped by a mode-locked Ti:sapphire laser, provides 150-fs optical pulses at a wavelength of 1550 nm and repetition rate of 80 MHz. The OPO output is split into three beams as pump, probe, and reference pulses. The probe and reference beams pass through acousto-optic modulators (AOMs), where the frequencies are shifted by + 75 and + 85 MHz respectively. The probe and reference pulses were broadened from 150 fs to 240 fs by chromatic dispersion in the AOMs. The three beams are recombined so that the reference pulse leads the pump and probe pulses by ~600 ps. The time delay Δt between the pump and probe pulses is controlled with the motorized translation stage. The pulses are launched into the device under test and they transmit through the 2-mm-long waveguide. A Michelson interferometer induces interference between the output reference and probe pulses with a 10-MHz beat signal, which is detected by a radio-frequency lock-in amplifier. By comparing the beat signals with and without the pump pulse, the changes in amplitude and phase of the probe pulse due to the pump pulse are obtained. The pulse energies of the probe and reference were set at 1.75 pJ. The pulse energy of the pump was varied from 1.25 to 10 pJ. All the beams were polarized so as to excite the TE mode. The coupling loss between the objective lens in this measurement and the waveguide is estimated to be ~6 dB/facet, which is better than the measured loss shown in Fig. 1(b).
Figure 3 shows the results of the measurement. A positive delay time means the pump pulse leads the probe pulse. For comparison, figures in the insets show the experimental results for c-Si, i.e., measurements for a Si-wire waveguide composed of a silicon-on-insulator wafer taken using the same method for the pump pulse energy of 2.0 pJ . The XAM is due to TPA or two-step absorption  across the band gap of a-Si:H. The XPM is due to the optical Kerr effect. In the case of c-Si, free carriers generated by TPA affect the loss due to free-carrier absorption (FCA) and a negative refractive index change by free-carrier plasma effect (FCP) with a slow response of several hundred picoseconds, as shown in Figs. 3(a’) and 3(b’), respectively. In the case of a-Si:H, the pumping energy of two-photon excitation for light of 0.8 eV (λ = 1550 nm) is slightly less than the band gap energy of a-Si:H (~1.7 eV). Therefore, the number of excited carriers is less than that in the case of c-Si and the carriers are instantaneously trapped in the localized state (tail state) in the band gap, which prohibits the slow relaxation of free carriers. Consequently, an ultrafast nonlinear response of less than 100 fs was observed.
The slight rebound of the amplitude for the positive delay time is to be noted. It is known that one-photon absorption due to a defect state results in a background loss over a wide range of wavelengths. We presume the rebound represents the pump-induced saturation of such one-photon resonance. A slightly longer trailing edge in XPM indicates that there is a change in the index with the same sign as the Kerr effect. This is also due to the generated carrier. Although we cannot provide a clear explanation, we believe it is worth mentioning that the absorption saturation and the increase in the index are consistent with the trend that the Kramers-Kronig relation predicts for the range of anomalous dispersion.
For more quantitative analysis, we show the plots of measured XAM and XPM as functions of the incident pump peak power in Fig. 4 . First, we consider the XAM due to the TPA of the a-Si:H wire waveguide using coupled differential equations :Eqs. (1) and (2) as the cross term. When βT = 0.08 cm/GW, the calculation result for z = 2.0 mm agrees with the measurement result as shown by the dashed line in Fig. 4(a).
XPM induced by the Kerr effect is given byEqs. (1), (2), and (3) for z = 2.0 mm agree with the measurement results as shown by the dashed line in Fig. 4(b). Estimated nonlinear coefficients of a-Si:H are one-tenth those of c-Si.
In this analysis, we neglect the effects of free carriers because they were observed to be small compared with the Kerr effect and the effect of TPA. Instead, we can say that the contribution is quite different from that for c-Si since free carrier transition occurs in lower energy states than the conduction band state. We speculate that the small mismatch in XAM may be the contribution of free carriers. However, at this time, there is little information that can be used to determine the carrier effect and the precise energies and densities of the localized states, which may strictly depend on the condition of a-Si:H deposition. We leave it to a future study to establish a model that can explain the carrier dynamics.
We studied the ultrafast nonlinear effects in an a-Si:H wire waveguide using femtosecond pulses. We fabricated an a-Si:H wire waveguide and characterized the nonlinear effect using the heterodyne pump-probe method. A high-speed response of less than 100 fs without slow free-carrier relaxation was observed for a photon energy of 0.8 eV. Nonlinear coefficients of βT = 0.08 cm/GW and n 2 = 0.5 × 10−18 m2/W were estimated, and thus, this is the first report with regard to Kerr nonlinearity in an a-Si:H waveguide at a telecom wavelength. The ultrafast response will be useful for all-optical signal processing.
This study was supported in part by Special Coordination Funds for Promoting Science and Technology from the Ministry of Education, Culture, Sport, Science and Technology, Japan.
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