We demonstrate C-band wavelength conversion in Si photonic-wire waveguides with submicron cross-section by means of nonresonant, nondegenerate four-wave mixing (FWM) using low-power, cw-laser sources. Our analysis shows that for these deeply scaled Si waveguides, FWM can be observed despite the large phase mismatch imposed by strong waveguide dispersion. The theoretical calculations agree well with proof-of-concept experiments. The nonresonant character of the FWM scheme employed allows to demonstrate frequency tuning of the idler from ~20 GHz to>100 GHz thus covering several C-band DWDM channels.
©2005 Optical Society of America
During the past few years, silicon has emerged as an important material of choice for the development of integrated photonics circuits . The maturity of silicon technology has been an impetus behind the search for new optical functionalities that can work in concert with integrated microelectronics . Recently, many new types of active Si devices have been developed such as a Raman amplifier [3, 4, 5, 6], a Raman laser [7, 8], a wavelength converter , modulators based on free-carrier dispersion or absorption [10, 11], and thermooptic switches [12, 13, 14]. Most of these devices have been fabricated on Si waveguides with crosssectional areas of ~1 µm2. However deeper scaling of the waveguide dimensions is possible. The capability of Si for deep scaling offers many important optical properties. First its small cross-sectional area enhances the nonlinear response of the medium thereby permitting the use of low power, cw laser sources. Second, reduced cross sectional area allows for the possibility of dispersion engineering to tailor the optical properties of the device according to the desired functionality. Third, deeply scaled devices have an inherently reduced photogenerated carrier lifetime; these carriers can increase absorption even at moderate laser power levels [15, 16, 17].
In this paper we investigate and demonstrate wavelength conversion within the C-band in deeply scaled silicon waveguides. Since Si is a centrosymmetric material, its second-order nonlinear susceptibility, which has been the basis for various functionalities such as electro-optic modulation and wavelength conversion, is extremely weak. Thus Si becomes impractical as a wavelength converter using second-order nonlinear optics. Silicon’s third-order optical nonlinearity, on the other hand, can be exploited for wavelength conversion by means of techniques such as four-wave mixing (FWM) or by electric-field-induced harmonic (SHG, sum-, or difference-frequency) generation . In this work we focus on the former. Recently Fukuda et al. gave an interesting, preliminary report, which showed the possibility of FWM in silicon waveguides for frequency conversion . In their scheme, they demonstrated conventional FWM wherein two input beams at frequencies ω 1 and ω 2 interact in the Si waveguide to generate new output frequencies at 2ω 1-ω 2 and 2ω 2-ω 1. In this work, we employ a general FWM process (Fig. 1(a)), wherein three beams of different wavelengths, for example, two pump lasers (p1 and p2) and a signal laser (s), interact in a χ (3) medium to produce an output (o)”idler” beam. For the same pump and signal wavelengths, two wavelength mixing processes are possible as seen in Fig. 1(a), hence two output idler beams are generated. The advantage of this scheme over the conventional FWM process is that the former allows for operation of the pump (control) laser wavelengths outside of the C-band while keeping the phase mismatch minimal for efficient conversion. This is an important consideration in a strongly dispersive medium, such as in the case of our Si waveguide, discussed below.
In certain FWM schemes, resonances may play a role in enhancing the nonlinear optical susceptibility, as in the case of coherent anti-Stokes Raman scattering (CARS). Figure 1(b) illustrates the energy diagram for the CARS process wherein the photon-energy difference between the pump and signal matches the phonon (Raman) energy. In such a process, two photons derived from the same pump laser (p) interact with the (Stokes) signal photon in the medium to produce an output photon whose angular frequency is given by ω CARS=2ωp -ωs . Recently, Claps et al. have demonstrated wavelength conversion in a 5.4-µm2-crosssection Si waveguide through CARS . Wavelength conversion from λs =1542 nm to λ CARS=1329 nm using a pump laser at λp =1427 nm was achieved with a -50 dB efficiency corresponding to a phase mismatch of |Δβ|=27 cm-1.
For the case of a deeply scaled waveguide, as used in our study, it would seem that CARS should be directly applicable and perhaps more efficient because of the tighter optical confinement afforded by the scaled waveguide. However, in fact, waveguide dispersion dominates the modal dispersion thus making it difficult to achieve efficient phase-matched conversion. For example, using full-vector, three-dimensional beam propagation simulations to calculate the relevant effective refractive indices and using the values for λs , λp , and λ CARS above for our waveguide, we obtain a phase mismatch of |Δβ|≈600 cm-1 for the CARS process! In addition, for a fixed signal wavelength, λs , the CARS process is nontunable since the resonance condition requires that ωp -ωs =ΩRAMAN. Because of these difficulties, we employ, here, the FWM scheme described above to demonstrate wavelength conversion within the C-band (1530 -1570 nm) in a short Si photonic-wire waveguide fabricated on silicon-on-insulator (SOI). Despite the fact that the nonresonant susceptibility is much weaker than resonant Raman susceptibility, by ~1/44 [2, 20], the decreased crosssectional area of the waveguide compensates for the weak such that FWM is easily observed in our devices.
For our FWM demonstration, two pump sources having a small frequency separation of Δν, are combined with a C-band signal source in the SOI waveguide. The FWM process, as indicated above, yields two idler outputs that are shifted in frequency from the signal by an amount ±Δν. In our proof-of-concept experiment, we employ pump beams arising from the different longitudinal modes present in a single diode laser and a tunable single-mode C-band signal source. Since any two longitudinal modes of the pump laser are separated by nΔν where n is an integer, the mixing of the signal with these two pump modes has provided a way to test and demonstrate the tunability of the FWM process in our system. Our measured value of FWM conversion efficiency agrees well with our numerical simulations. The useful functionality described here should be contrasted with FWM in long-haul fiber WDM systems where FWM can become a major source of crosstalk and signal degradation through interactions between channels .
Before we describe the details of the experiment, we first perform an analysis of the FWM scheme appropriate for our system. The energy conservation and phase matching conditions of our conversion scheme are listed below :
where p1, p2, s, and o correspond to the two pumps, signal, and output fields, respectively and βi =n eff(ωi )ωi/c where n eff is the effective refractive index obtained using a three-dimensional beam-propagation simulation. For the (+) configuration of Eqs. 1 and 2, the propagation properties and the interchange of energy between these four fields within the waveguide are described by four nonlinear, coupled-mode differential equations given by 
αi and γi =n 2 ωi /(cA eff) are the propagation loss and the nonlinear coefficient, respectively, corresponding to wavelength λi . The parameter n 2 (∝χ (3)) is the intensity-dependent refractive index, which we take as n 2=4.5×10-18m2/W, and A eff=0.06 µm2 is the effective modal area . Since the nonlinear coefficient γi ∝, we immediately see that the FWM conversion efficiency should be enhanced as the cross-sectional area is decreased. On the right-hand side of Eqs. 3–6, the first, second to fourth, and fifth terms correspond to the self-phase modulation (SPM), cross-phase modulation (XPM), and FWM contributions, respectively. The effects of two-photon absorption (TPA) and TPA-induced free-carrier absorption (FCA) [15, 16] are neglected because of the low powers (maximum pump power, Pp =38 mW) considered in this experiment [4, 17]. For the case of the (+) configuration of Eqs. (1) and (2), the idler wavelength (λ o+) and the corresponding phase mismatch, Δβ, are shown in Fig. 2(a). Numerically
solving Eqs. 3-6 using our pump source spectral profile at the maximum coupled pump power and taking the propagation loss as α=3.5dB/cm, we obtain the conversion efficiency as shown in Fig. 2(b). As an example, for pump wavelengths of λ p1=1435 nm and λ p2=λ p1+Δλ, where Δλ=0.148 nm, a signal wavelength of λs =1550.5 nm, and the output wavelength of λo +=1550.3 nm, we obtain a phase mismatch of |Δβ |=0.6 cm-1 and a conversion efficiency of -20 dB. The corresponding analysis for the (-) configuration yields similar results.
Each of our experiments used a single-mode silicon photonic-wire waveguide with a cross-section of 220 nm×445 nm and length of L=4.2 mm fabricated on Unibond SOI having a 1-µm-thick oxide layer and aligned along the  crystallographic direction. In addition, each end of the waveguide incorporates an inverse taper/polymer mode converter for efficient coupling to and from fiber. A low sidewall roughness (<3 nm) yielded a waveguide loss of approximately 3.5 dB/cm for TE polarization at λ=1550 nm. The devices were fabricated using the state-of-the-art E-beam and CMOS process line at the IBM TJWatson Research Center [23, 24]. The experimental setup, shown in Fig. 3(a), consists of pump and signal laser sources that are multiplexed and launched into the waveguide using a tapered fiber. The optical output from the waveguide was coupled into a receiving tapered fiber and wavelength demultiplexed. The outgoing pump power was measured with a photodetector and the signal power with an optical spectrum analyzer (OSA) with a resolution of 0.01 nm. The pump laser is a Bragg-grating-stabilized Fabry-Perot diode laser centered at λ=1435 nm having multiple longitudinal modes with a mode spacing of Δν=21.6 GHz (Δλ=0.148 nm) as shown in Fig. 3(b). The signal laser is a single-mode and tunable Fabry-Perot laser with a bandwidth of <0.05 nm. The signal wavelengths were tuned from λs =1545 to 1555 nm. The experiments were performed with the pump and signal lasers in a copropagating configuration (shown in Fig. 3(a)) and in a counterpropagating configuration (not shown).
4. Results and discussion
We now discuss the experimental results for the copropagating configuration. Figure 4 shows the output spectra using several signal wavelengths ranging from 1545.5 to 1555.5 nm. Notice the presence of the newly-generated satellite peaks on each side of the signal wavelength employed. These features are the FWM peaks that arise primarily from the interaction of the main pump mode and its nearest neighboring modes, with the signal laser in the SOI waveguide. The main mode contains approximately 40% of the total pump power. As expected, the satellite FWM peaks are clamped to the signal, i.e., they shift by approximately the same amount as the shift in signal wavelength. The magnitude of the satellite peaks remain nearly constant for all the wavelengths studied, which indicates a nonresonant process. In the absence of the pump laser and in the presence of only the signal laser, FWM modes are nonexistent. In the absence of the signal laser but in the presence of the pump laser, no FWM peaks are observed except for a Raman feature near 1550.5 nm as previously demonstrated . These properties are succinctly demonstrated through the power dependence of the idler output with respect to either the pump or signal powers below. Figure 5(a) shows a more expanded spectrum for one particular choice of signal wavelength, λs =1550.5 nm. We have chosen this signal wavelength since it fortuitously coincides with and can be compared with a simple Raman-scattered output for a pump centered at λ=1435 nm. The spontaneous Raman emission appears as a weak, broad Raman peak beneath the FWM lines. Analyzing the generated satellite FWM peaks shown in Fig. 5(a) which have been designated as ±1,±2, …,±5, we find that they correspond to peaks expected from the FWM scheme due to the mixing of the different modes of the pump and the signal and obey the relation ωo,n =ωs ±2πnΔν, in accordance with Eq. 1. Each of the five peaks on either side of the signal corresponds to FWM between the signal laser and two pump modes that are separated by nΔν where n=1, 2, …, 5. Since the phase mismatch is fairly constant for all pump separation, the variation in the efficiency arises from the uneven power distribution of the various pump modes. These results directly demonstrate the tunability of FWM process for this system for pump separations ranging from 21.6 GHz to 108 GHz.
In the counterpropagating geometry, the calculated phase mismatch is Δβ=41 cm-1, which is larger than the phase mismatch in the forward geometry by a factor of ~70. This corresponds to a conversion efficiency of approximately -40 dB, which renders the FWM in the backward geometry undetectable with our detection system. As expected from these phase matching considerations, there are no FWM peaks in the counter-propagating geometry as shown in Fig. 5(b) at all pump and signal powers used. In addition to the signal, Fig. 5(b) now reveals the broad spontaneous Raman background, illustrating the much larger Raman linewidth compared to the FWM modes observed in the forward geometry.
We have also performed power-dependence measurements to elucidate further the FWM scheme. Figs. 6(a)-6(b) show the dependence of one of the output modes (designated as FWM peak 1 in Fig. 5(a)) on the pump and signal powers, respectively. The mode power is found to scale quadratically and linearly with the pump and signal laser powers, respectively, and no saturation effects were observed because of the relatively low pump powers used. The power dependence behavior follows directly from Eq. (6), which describes the evolution of Eo . From this equation, we can estimate the contributions from the other nonlinear processes to Eo . In terms of the field strength, the contribution arising from FWM is over five times larger than the contribution from the XPM and four orders of magnitude larger than that of the SPM. In terms of the power, FWM is, indeed, the dominant contribution over the next strongest effect (XPM) by more than an order of magnitude. Since the SPM and XPM terms are negligible compared to the FWM term, Eq. (6) becomes
Since the power Pi ∝|Ei |2, and P p1∝P p2∝Pp , Eq. 7 can be solved to yield the relation Po ∝Ps in agreement with Figs. 6(a) and 6(b). Keeping the power at its maximum, Pp =38 mW and taking the slope of the output vs. signal power in Fig. 6(b), we obtain a conversion efficiency of -21±3 dB, in good agreement with our calculations. The relatively low conversion efficiency is due partly to the low pump powers used and partly to the relatively low value of the nonresonant . This represents, however, a~30 dB improvement in the conversion efficiency over the previous CARS-based scheme utilized in a larger cross-section waveguide , despite the order-of-magnitude lower power used here in our studies.
Significant improvement in the conversion efficiency can be achieved by using larger pump powers in accordance with the relation Po ∝P p1 P p2. At high powers, however, other nonlinear optical processes, such as TPA, stimulated Raman scattering (SRS), and FCA arising from TPA can contribute to loss. The effect of TPA become significant at much higher powers . The effect of SRS may be eliminated by using pump sources that are nonresonant with the idler or signal wavelengths. A rigorous analysis of pulse propagation in deeply scaled waveguides indicates that the effects arising from these nonlinear optical processes depend sensitively on the waveguide dimensions, wavelength, carrier lifetime, and laser beam characteristics . The most significant contribution to the loss mechanism is the TPA-induced FCA, which can produce substantial loss even at moderate powers [15, 16, 17]. However, because of the small size of the waveguide cross-section, the lifetime of the carriers is estimated to be less than 1 ns due to diffusion of carriers to the waveguide boundary . Consequently, for the powers used in this experiment, the effect of TPA-induced FCA is negligible. In addition, this loss mechanism can be further mitigated through the application of an electric field that serves to sweep the carriers and, hence, further reduce the effective carrier lifetimes for higher pump power applications.
Our results demonstrate the feasibility of using a dual pump FWM scheme in deeply scaled Si waveguides for C-band frequency interconversion with a frequency spacing that is comparable to DWDM, i.e., ~50 GHz, systems. While our conversion output spacing is 21.6 GHz, a frequency spacing about half of the state-of-the-art DWDM spacing of 50 GHz, the parameters and phase-matching scheme used in our experiment can be applied to the design of a practical wavelength converter. Further analysis indicates that a more efficient wavelength converter is possible simply through the use of two single-mode pump lasers operating at modestly higher powers compared to the ones used in this experiment. In addition, the tuning range for this process can be further increased by means of dispersion engineering, i.e., by choosing the appropriate waveguide dimensions and geometry.
In conclusion, we have shown that in the presence of strong waveguide dispersion and finite phase-mismatch, C-band wavelength conversion is feasible in a deeply scaled SOI waveguides by means of a general FWM scheme using low-power, cw pump laser sources operating outside of the C-band. We have also demonstrated tuning from 21.6 GHz to 108 GHz. Such capability for tuning is not possible for a CARS-based scheme. Our results that agree well with our coupled-mode calculations. More practical and efficient wavelength conversion can be achieved through the appropriate choice of device dimensions and geometry in conjunction with periodic structures, such as Bragg gratings, ring resonators, and photonic crystal structures, or integrated with Raman amplifiers. The novelty of this method is the fact that high-speed, tunable narrow band conversion can be accomplished with deeply scaled, on-chip devices with the prospect of integration onto future WDM telecommunications systems.
This work was partially supported by DARPA/MTO University Opto Centers under Contract BROWNU-1119-24596. We thank JDS Uniphase for graciously providing optical components and equipment used in our testing lab. We also acknowledge helpful discussions with Dr. Idan Mandelbaum and Dr. Nicolae Panoiu.
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