Thermo-optic coefficient and nonlinear refractive index of silicon oxynitride waveguides

A. Trenti; M. Borghi; S. Biasi; M. Ghulinyan; F. Ramiro-Manzano; G. Pucker; L. Pavesi

doi:10.1063/1.5018016

Research · Publication & note

Thermo-optic coefficient and nonlinear refractive index of silicon oxynitride waveguides

Research article

A. Trenti, M. Borghi, S. Biasi, M. Ghulinyan, F. Ramiro-Manzano, G. Pucker and L. Pavesi

AIP Advances 8, 025311 (2018) · Published 12 February 2018

Abstract

Integrated waveguiding devices based on silicon oxynitride (SiON) are appealing for their relatively high refractive index contrast and broadband transparency. The lack of two photon absorption at telecom wavelengths and the possibility to fabricate low loss waveguides make SiON an ideal platform for on-chip nonlinear optics and for the realization of reconfigurable integrated quantum lightwave circuits. Despite this, very few studies on its linear and nonlinear optical properties have been reported so far. In this work, we measured the thermo-optic coefficient dn/dT and the nonlinear refractive index n₂ of relatively high (n ∼ 1.83 at a wavelength of 1.55 μm) refractive index SiON by using racetrack resonators. These parameters have been determined to be dn/dT = (1.84 ± 0.17) × 10⁻⁵ K⁻¹ and n₂ = (7 ± 1) × 10⁻¹⁶ cm² W⁻¹.

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Figures

Figure 1. Racetrack resonator, device cross-section, thermo-optic setup and interferometric setup. — **Figure 1.** (a) Top-view of the side-coupled racetrack resonator (R = 50 µm and L = 20 µm). The coupling gap is 1.05 µm. (b) Device cross-section. The waveguide cross section is 1.2 × 0.55 µm². BPSG: Borophosphosilicate glass. (c) Sketch of the experimental set-up used for the thermo-optic and n₂ SiON coefficients. PL: Pump Laser, IL: Idler Laser, BPF: Band-pass Filter, FPC: Fiber Polarization Controller, FBG: Fiber Bragg Grating, 3PC: Three Port Circulator, BS: Beam-splitter, TEC: Temperature Controller, PeC: Peltier Cell, AS: Alignment Stage, GD: Germanium Detector, DWDM: Dense Wavelength Division Multiplexing, PhC: Photon Counter. (d) Sketch of the interferometric experimental set-up for the intensity/phase measurement of the racetrack transmittance as a function of the wavelength. TL: Tunable Laser, OB: Objective, DL: Delay Line, MS: Movable Shutter, M: Mirror.

Resonance spectral shift with temperature — **Figure 2.** Simulation of the quantity Δn_eff/ΔT as a function of the thermo-optic coefficient of the waveguide core material. The red dot shows the experimental value, which is found from the analysis of the shift of the resonance wavelength as a function of temperature (shown in the inset). The solid blue lines mark the values of the thermo-optic coefficient of silica and of stoichiometric silicon nitride reported in Ref. 15.

**Figure 3.** (a) Normalized transmission of the resonator, with the polarization set to TM. The signal (blue), pump (yellow) and idler (red) resonance orders involved in the FWM process are highlighted with different colors. (b) Measured (black) and simulated (red) intensity and phase of the light transmitted. From left to right, the panels refer respectively to the signal, the pump and idler resonance orders.

Research fields

Top-down

PECVD silicon oxynitride is patterned into channel waveguides and side-coupled racetrack resonators on silicon, then clad and interfaced for fibre access. The resonator converts small refractive-index changes into accurately measurable spectral shifts.

Simulations & fits

Finite-element mode calculations provide the SiON confinement factor used to recover material coefficients from effective-index measurements. Power-dependent resonance models separate Kerr and thermal contributions and support extraction of the nonlinear refractive index.

Characterization

Temperature-controlled resonance tracking determines a thermo-optic coefficient of about 1.84 × 10⁻⁵ K⁻¹, while a pump–probe experiment measures an isotropic nonlinear index near 7 × 10⁻¹⁶ cm² W⁻¹. Both are obtained on the same integrated material platform.

RESEARCH TOPICS

MaterialsThe waveguide core is silicon oxynitride with an effective refractive index near 1.83 at 1.55 μm. Heating shifts both the core and cladding indices and also creates a much smaller photoelastic contribution from thermally induced stress. By tracking resonances at controlled temperatures, the study obtains dn/dT = (1.84 ± 0.17) × 10⁻⁵ K⁻¹, close to stoichiometric silicon nitride. Separating this material coefficient from thermal expansion and stress is essential before using the same resonator to quantify optical nonlinearity.

NonlinearThe nonlinear refractive index is extracted through stimulated four-wave mixing rather than from a simple power-dependent resonance shift, which would mix Kerr, thermal and carrier effects. Pump and idler lasers excite three resonant wavelengths, and the generated signal is compared with a cavity-enhanced FWM model using measured coupling and quality factors. The resulting isotropic value, n₂ = (7 ± 1) × 10⁻¹⁶ cm² W⁻¹, is about three times that of silica and establishes SiON as a useful moderate-index nonlinear platform.

ResonatorsAn all-pass racetrack resonator turns small index changes into measurable spectral shifts and simultaneously enhances the pump, idler and generated FWM fields. The total and extrinsic quality factors are extracted from transmission and phase; the phase jump remains below π at all three wavelengths, identifying the device as undercoupled. Those measured cavity parameters are fed back into the nonlinear analysis rather than treating field enhancement as an adjustable constant. The resonator is therefore both the sensor for thermo-optic response and the calibrated interaction volume for n₂.

SetupsTemperature measurements use a Peltier-controlled chip and follow resonance displacement while accounting for expansion and photoelasticity. For n₂, a second continuous-wave tunable laser supplies the idler; pump and idler are combined, polarization adjusted and injected through the bus waveguide. Fiber Bragg and dense-wavelength-division filters suppress the strong inputs so the weak generated band can be counted. A free-space phase-delay measurement determines the coupling regime, giving the experiment the independent quantities needed to avoid fitting the nonlinear coefficient from power alone.