Pulsed heterodyne interferometry for nonlinear SOI waveguide characterization

. Silicon waveguides are a promising candidate for integrated nonlinear optics applications. Nonlinear coefficients of Silicon on Insulator (SOI) waveguides have been previously measured using techniques such as Z-scan, D-scan, Four Wave Mixing (FWM) and Self-phase modulation. However, they have several drawbacks such as they operate at high power or are cumbersome to setup and require multiple measurements to determine all the coefficients. In this work, we develop a direct and single measurement technique to characterize the nonlinear processes in SOI waveguides. This is achieved by employing a heterodyne interferometric technique to accurately measure minute nonlinear response. The measured nonlinear amplitude and phase shifts are fit to extract third-order nonlinear coefficients of Two-photon absorption, Kerr nonlinear index, Free carrier absorption and Free carrier dispersion. The obtained coefficients for SOI waveguides are close to that found in literature measured using the above-mentioned techniques. The advantages of this method include easy interpretation of the output signal and relatively low power of operation. It is especially advantageous for studying materials such as Phase Change Materials (PCM) in which phase changes occur dynamically. This aspect is quite promising for characterizing emerging materials for integrated photonics applications.


Method
SOI technology has been used extensively for photonic integrated circuits owing to its ease of fabrication and CMOS compatibility.Nonlinear effects in Silicon waveguides such as Two-photon absorption, Stimulated Raman scattering, Optical Kerr effect etc have been largely studied for a decade.However practical applications are still limited by nonlinear losses and free carrier effects.Hence new materials compatible with CMOS technologies such as Silicon Nitride, chalcogenides among the other are emerging to overcome silicon limitations.On the route of new materials development and optimization, accurate and reliable measurement techniques of the nonlinear parameters are thus needed.This is precisely what we address in this work by heterodyne interferometry in pulse regime.
Heterodyne detection is convenient for detecting ultraweak signals [1] and interferometry can be performed by comparing the sample signal with a frequency shifted reference.We have implemented this reliable technique for precise measurement of nonlinear phase and amplitude of Silicon waveguides as a reference since its nonlinear parameters are well documented.
As shown in figure 1, the sample is placed in one of the arms of a Mach-Zehnder interferometer and the reference arm is frequency shifted by ε= 43 MHz using an Acousto-Optic Modulator (AOM) and synchronized to the other one with a delay line.The interferences at the beating frequency ε are recorded with a balanced photodiode and amplitude and phase are recovered by demodulating the signal with a lock-in amplifier.

Fig. 1. Heterodyne interferometer setup. EOM-Electro-Optic Modulator, AOM -Acousto-Optic Modulator, D1, D2 -Photodiode, BPD-Balanced Photodiode
A picosecond fiber laser producing 0.79 ps pulses at 1550 nm with a 80 MHz repetition rate is used to feed the interferometer [2] and Silicon on insulator (SOI) Rib waveguides of different lengths (L=2mm, 2cm, 4cm and 6cm) were tested.The nonlinear processes involved in the Silicon waveguides are the Kerr nonlinearity, the Two Photon Absorption (TPA) and the Free Carrier Absorption (FCA).Respectively, the nonlinear power (P) and the nonlinear phase transmitted by the silicon waveguides are given by [3] : (1) Here, P stands for peak power, L-length along the waveguide, α -linear absorption coefficient, βTPA-two photon absorption coefficient, Aeff -effective mode area, αFCA -free carrier absorption coefficient, ϕ -nonlinear phase, γeff -effective Kerr coefficient and μ is a parameter governing free carrier dispersion equal to 7.5 for SOI waveguides at 1550 nm wavelength.

Results
The experimentally measured nonlinear power and phase are shown in figure 2 a) and b) respectively for waveguides of different lengths.The increasing absorption for longer lengths is expected from Two photon absorption process.Whereas, in the nonlinear phase, Kerr effect and Free carrier absorption are the competing processes.The initial rise in phase is due to increase in refractive index from Kerr effect and at higher input powers, FCA dominates which tends to decrease the waveguide refractive index.By solving the above differential equations, the experimental curves are fit to determine the nonlinear coefficients as shown in figure 2  c) and d) for L=2cm.A satisfactory fit is achieved and the retrieved values βTPA = 5.4 ± 1.6 e-12 m/W and nonlinear refractive index (which is obtained from γeff) n2 = 2.0 ± 0.1 e-18 m 2 /W -1 from different waveguides are in good agreement with the values from literature.Additionally, FCA coefficient can also be estimated by this method, which gives an insight into carrier densities and lifetimes.However, further measurements are still ongoing to estimate different sources of uncertainties and evaluate error bars for reporting an accurate value of FCA coefficient which is not intrinsic to silicon but also depends on the laser pulse train itself.In this work, we have demonstrated the capability of pulsed heterodyne interferometry for measuring minute nonlinear phase and power and retrieve nonlinear parameters in a single shot measurement.Compared to other techniques of characterization such as D-scan, Four wave mixing etc, the reported method has the advantage of being easy to setup, interpret and works at relatively low power.Moreover, it can be equally effective on active optical materials such as phase change materials to dynamically measure nonlinearities.

Fig. 2 .
Fig. 2. a), b) -Experimentally measured nonlinear power and phase respectively for different waveguide lengths of 2mm, 2cm, 4cm and 6cm.c), d) Power and phase fits for L=2cm waveguide.The shaded region in phase plot corresponds to the standard deviation after different cycles of input power.