In this paper we describe a new modulation scheme using stimulated Raman scattering in conjunction with a reverse biased p-i-n diode embedded in a silicon waveguide. We show optical modulation of a weak probe beam by modulating the reverse bias voltage of the silicon waveguide excited by a strong pump beam. The probe beam modulation is due to the two-photon absorption-induced carrier density modulation in the waveguide. By tuning the probe wavelength to the Stokes wavelength, we demonstrate for the first time a lossless optical modulator in silicon with modulation speeds up to 80-MHz.
©2005 Optical Society of America
Research into optical modulation in silicon has primarily focused on two physical mechanisms: the free carrier plasma-dispersion effect  and the thermo-optic effect  because silicon possesses no electro-optic effects [3, 4]. Plasma-dispersion modulators use charge injection and/or removal to cause either direct absorption or phase modulation of an optical beam. The conventional approach to charge injection is achieved by using a forward biased p-i-n embedded in a silicon waveguide [5, 6, 7]. The fastest experimental demonstration of this type of modulator is 20-MHz [6, 7]. To achieve high speeds using this architecture the p- and n- dopants have to be placed close to the optical waveguide, which produces additional loss. Other modulator architectures, eg CMOS capacitor based schemes, have exhibited high speeds , but like all modulators based on silicon the device is not completely transparent to light and suffers from residual transmission loss. Thermo-optic modulators, while potentially low loss, unfortunately suffer from low modulation speeds [11, 12]. Here we demonstrate a new modulation scheme for a silicon optical modulator with >0-dB transmission using stimulated Raman scattering (SRS) and a reverse biased p-i-n diode.
Stimulated Raman scattering in silicon waveguides allows the formation of active optical components e.g. chip-scale optical amplifiers [13, 14, 15], and lasers [16, 17] in silicon. However, to achieve net gain, high pump intensities (>10-MW/cm2) are used and two-photoninitiated free carrier absorption has to be mitigated [18, 19, 20, 21]. One way this has been achieved is by using a reverse biased p-i-n device embedded in a silicon waveguide to sweep out two-photon induced free-carriers. Recently this approach has demonstrated net CW Raman gain in a silicon waveguide . Direct modulation of a silicon Raman laser has also been achieved by modulating the forward bias voltage of an intra-cavity p-i-n device . In this paper we demonstrate net Raman gain modulation in a silicon waveguide by modulating the reverse bias voltage on the p-i-n. Modulating the reverse bias voltage alters the rate at which the two-photon induced free-carriers are swept out of the waveguide, which in turn modifies the free carrier absorption. By this method we experimentally demonstrate electrically controlled modulation of the net Raman gain in a silicon waveguide, and, for the first time demonstrate a lossless optical modulator in silicon. We also show that the modulation speed for the reverse biased scheme is faster compared to the conventional, current injection, scheme in a forward biased p-i-n diode.
2. Device fabrication and characterization
The silicon rib waveguide is fabricated on the (100) surface of an un-doped silicon-on-insulator (SOI) substrate using standard photolithographic patterning and reactive ion etching techniques. The rib waveguide width is 1.5 µm, the rib height is 1.55 µm, and the etch depth is 0.7 µm. A schematic of the waveguide cross-section is shown in Fig. 1(a), and a scanning electron microscope (SEM) image of the same waveguide is shown in Fig. 1(b). The effective core area of the waveguide is calculated to be ~1.6 µm2 by using a fully vectorial waveguide modal solver . A small waveguide cross-section is advantageous as it increases the pump intensity for a given pump power and enables high Raman gain, as it is the optical intensity and not power of the pump that determines the Raman scattering efficiency. To increase the interaction length, and in turn achieve larger total Raman gain, the waveguide was formed in an S-shaped curve with a total length of 4.8 cm and a bend radius of 400 µm. The straight sections of the waveguide are oriented along the  direction. A reverse biased p-i-n was fabricated in order to reduce the nonlinear optical loss due to the TPA-induced FCA.
As shown in Fig. 1(a), the silicon rib waveguide has a heavily doped p and n type region in the slab, with a doping concentration of ~1×1020 cm-3. The separation between the edge of the p and n type doping regions is ~6 µm. Aluminium films are deposited on the p and n doped regions to form ohmic contacts. It has been experimentally verified that the presence of these doped regions and metal contacts has negligible effect on the waveguide loss; which is due to the tightly confined mode for the waveguide being used. The linear optical transmission loss of the S-bend waveguide is 0.4±0.1 dB/cm; measured using the Fabry-Perot resonance technique  prior to anti-reflection coating the silicon waveguides. The 0.1 dB/cm uncertainty in the linear optical loss includes the experimental error and waveguide-towaveguide variations.
3. Experimental results and analysis
The net Raman gain is measured by performing a pump-probe experiment; a pump laser at 1548-nm is used to amplify a probe laser at the Stokes wavelength of 1684-nm. The achievable net gain is measured as a function of pump power and reverse bias condition of the silicon waveguide. The experimental setup is shown in Fig. 2.
Pump and probe lasers are combined with a wavelength multiplexer and coupled to the waveguide under investigation using a lensed single-mode fiber; the measured coupling loss for both pump and probe beam is 3.9-dB. The output of the waveguide is collimated by a 50× objective lens, and the pump and probe beams are separated using a long-wavelength pass optical filter. The probe beam passes through the filter and is detected with a 125 MHz bandwidth photo-detector while the pump beam is blocked by the filter. Fiber polarization controllers at the input to the device-under-test allow both probe and pump beam polarizations to be independently controlled. The device-under-test is mounted on a Thermo-Electric Cooler (TEC) and kept at a constant temperature of 25 °C. For the DC gain measurements, the pump laser is a CW tunable external cavity laser emitting around 1548.3 nm, which is amplified using two EDFA’s to a maximum output power of 3 W. The probe laser is a 2 mW, external cavity tunable diode laser operating at around 1684 nm. Both the pump and probe laser sources have line-widths of ≤100 MHz. The polarization of the probe and the pump beam are aligned with the TE mode of the waveguide.
To measure the SRS gain, the transmitted probe power is measured at the peak of the Raman gain profile (at the Stokes wavelength) and compared to the input probe power. The input probe power is determined from the measured transmitted probe power without the pump beam by factorizing out the linear transmission loss of the waveguide. The net optical gain is given by:
where Ps(L) is the probe output power after traversing the waveguide of length L.
Figure 3 shows the net CW Raman gain of the probe beam when it is tuned to the Stokes wavelength as a function of the DC reverse bias voltage on the p-i-n for various pump powers inside the 4.8 cm long waveguide. The pump power is the power of the pump coupled into the waveguide, and is determined by measuring the power exiting the lensed fiber and factorizing out coupling loss into the waveguide.
As the reverse bias voltage is increased, two-photon induced free carriers are swept out of the waveguide and the net gain increases until saturation occurs. Higher pump powers result in higher saturated gains. For a pump power of 945mW a net gain of 3.5-dB is achievable in this 4.8-cm long waveguide. As can be seen from Fig. 3, for a pump power of 945-mW a 5-dB modulation of the net gain could be achieved with a 0 to 8V reverse bias voltage swing.
To obtain a qualitative understanding of this net gain saturation, we modeled the carrier density in the waveguide as a function of the reverse bias for different pump powers by using a 2D semiconductor device modeling package ATLAS/SILVACO. In the modeling, we used the photo-generation rate (ζ) due to the TPA process given by 
where β is the TPA coefficient, h is Planck’s constant, ν the optical frequency, P is the pump intensity and Aeff is the effective core area of the waveguide. Fig. 4 shows the modeled results for pump powers of 945 and 669 mW used in our experiment. We see that the photo-generated carrier density inside the waveguide is nonlinearly dependent on the reverse bias voltage. It decreases rapidly with increasing the bias when the reverse bias voltage is small, and tends to saturate at higher bias voltages. From Fig. 4 one observes that the higher the pump power, the higher the reverse bias voltage is for carrier density saturation. Since the FCA is proportional to the carrier density, one would expect that the net gain follows the same trend of the carrier density dependence. This is in qualitative agreement to the results shown in Fig. 3.
Taking advantage of the voltage dependent net gain in this silicon waveguide device, one can obtain optical modulation by varying the reverse bias voltage, as shown in Fig 5. This Fig. shows the drive voltage and net gain modulation of this modulator for a pump power of 954-mW inside the waveguide. The drive voltage is a 10-MHz square wave reverse bias voltage, as can be seen the net gain is modulated from 0.5 to 2.5-dB by the 1 to 6V reverse bias voltage swing. This demonstrates the lossless optical modulation achievable with this device.
To determine the speed of the current device the modulation depth of the optical modulation was monitored as a function of drive voltage frequency for a 3-V peak to peak sinusoidal drive voltage at a DC reverse bias of 2V. Figure 6(a) shows a typical trace obtained for 579-mW pump power coupled into the p-i-n waveguide. To obtain the frequency response of the device the optical signal is normalized to the on-chip AC voltage, as shown in Fig. 6(b). For 579-mW pump power in the waveguide the 3dB modulation speed is measured to be 57-MHz.
This measurement was repeated for various pump powers coupled into the waveguide and the results are shown in Table 1. The highest 3-dB bandwidth achieved is 80-MHz, for a pump power of 283-mW inside the waveguide, and a small signal modulation depth of 0.3-dB. As can be seen in Table 1, as the pump power is increased the 3-dB bandwidth of the device decreases. This is due to the photo-generated carriers shielding the applied field and reducing the carrier velocity across the waveguide. This can be compensated for by increasing the DC bias on the modulating voltage, as shown by the speed increase from 47-MHz to 71-MHz when the DC bias increased from 1.5V to 7.5V for a pump power of 950-mW inside the waveguide. The drawback to both decreasing the pump intensity and increasing the DC bias voltage is the reduction in achievable modulation depth. For all three pump powers we achieve net gain in the waveguide, meaning that this modulator has no transmission loss excluding the fiber chip coupling loss. With rapid development of silicon waveguide tapers, efficient fiber chip coupling (with <1 dB/facet loss) is achievable .
Further work and investigation is underway to both improve gain and modulation speed. For example, we could scale down the waveguide dimension so that the p and n doping separation is reduced while keeping the optical transmission loss low. As a result, the carrier transit time (or effective carrier lifetime) can be reduced. One could also optimize the doping profile in the PIN device to maximize the electric field due to the reverse bias. This would potentially enhance the modulation bandwidth of the modulator. In addition, rather than using a purely amplitude modulation scheme, one can configure this device as an interferometer such as a Mach-Zehnder Interferometer (MZI), allowing operation based on phase modulation to produce much larger modulation depth. We expect the extinction ratio of such a MZI modulator is higher, since it is mainly determined by the phase difference between the two arms as compared to the direct amplitude modulation of the waveguide used in our current experiment. For comparison we also show the modulation speed of this device when it is run in the conventional forward biased scheme (0.5–0.9V drive voltage), with no pump beam in the waveguide. As can be seen, although the modulation depth is enhanced compared to the reverse biased case, the 3-dB bandwidth of 14 MHz is much lower and the transmission loss is >3dB worse than our new scheme of modulation.
In conclusion we have constructed a lossless modulator in a silicon-on-insulator waveguide. Using stimulated Raman scattering in conjunction with a reverse bias p-i-n device we have demonstrated an 80-MHz small-signal modulator that has no net transmission loss. Increasing the pump power or the DC bias voltage leads to higher modulation depths at the expense of device bandwidth. Running the p-i-n in reverse bias and using pump-induced injection of free carriers produces faster device performance compared to running the p-i-n in forward bias. Modulation depth improvements could be obtained by using the index change due to the free carriers rather than the absorption modulation. This could be done in an interferometer such as a MZI device, and allows for the possibility of a lossless planar waveguide switch or modulator based in silicon.
We acknowledge A. Barkai for etch development; L. Peremislov for SEM images; J. Tseng and D. Tran for assistance in device fabrication and sample preparation; D. Samara-Rubio for help with the electrical characterization of this device; S. Koehl for data collection software development; and M. Morse and G. T. Reed for helpful discussions.
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