Empirical model for the temperature dependence of silicon refractive index from O to C band based on waveguide measurements.

An accurate model for the silicon refractive index including its temperature and wavelength dependence is critically important for many disciplines of science and technology. Currently, such a model for temperatures above 22°C in the optical communication bands is not available. The temperature dependence in the spectral response of integrated echelle grating filters made in silicon-on-insulator is solely determined by the optical properties of the slab waveguide, making it largely immune to dimensional uncertainties. This feature renders the echelle filters a reliable tool to evaluate the thermo-optic properties of silicon. Here we investigate the temperature dependence of silicon echelle filters for the wavelength range of both O and C bands, measured between 22°C to 80°C. We show that if a constant thermo-optic coefficient of silicon is assumed for each band, as is common in the literature, the predictions show an underestimate of up to 10% in the temperature-induced channel wavelength shift. We propose and assess a model of silicon refractive index that encompasses both the wavelength and temperature dependence of its thermo-optic coefficients. We start from literature data for bulk silicon and further refine the model using the echelle filter measurement results. This model is validated through accurate predictions of device channel wavelengths and their temperature dependence, including the quadratic term, over a wide wavelength and temperature range. This work also demonstrates a new high-precision method for characterizing the optical properties of a variety of materials.

Athermal echelle grating filter in silicon-on-insulator using a temperature-synchronized input.

Athermal design of integrated photonic devices can reduce the need for active temperature stabilization and consequently the energy required to operate photonic integrated circuits. For silicon photonic filters such as AWGs which employ wire or ridge waveguides, temperature insensitivity can be achieved using cladding materials with negative thermo-optic coefficients. On the other hand, in echelle grating filters the inteference takes place in the slab free-propagation region, and therefore the modal overlap with the cladding is small, rendering this method ineffective. In this work we present an approach to design an athermal echelle grating filter exploiting a temperature-synchronized Mach-Zehnder interferometer as input. This reduces the spectral shift over a temperature range of 20 K to less than ±45 pm compared to the 1.6 nm shift for the same echelle grating with a conventional waveguide input. Furthermore, the proposed design relies exclusively on a standard fabrication process for silicon-on-insulator photonic devices and exhibits a good tolerance to fabrication uncertainties.

Optical fiber interferometer array for scanless Fourier-transform spectroscopy.

We report a spatial heterodyne Fourier-transform spectrometer implemented with an array of optical fiber interferometers. This configuration generates a wavelength-dependent stationary interferogram from which the input spectrum is retrieved in a single shot without scanning elements. Furthermore, fabrication and experimental deviations from the ideal behavior of the device are corrected by spectral inversion algorithms. The spectral resolution of our system can be readily scaled up by incorporating longer optical fiber delays, providing a pathway toward surpassing current spectroscopy resolution limits.

High-resolution Fourier-transform spectrometer chip with microphotonic silicon spiral waveguides.

We report a stationary Fourier-transform spectrometer chip implemented in silicon microphotonic waveguides. The device comprises an array of 32 Mach-Zehnder interferometers (MZIs) with linearly increasing optical path delays between the MZI arms across the array. The optical delays are achieved by using Si-wire waveguides arranged in tightly coiled spirals with a compact device footprint of 12 mm2. Spectral retrieval is demonstrated in a single measurement of the stationary spatial interferogram formed at the output waveguides of the array, with a wavelength resolution of 40 pm within a free spectral range of 0.75 nm. The phase and amplitude errors arising from fabrication imperfections are compensated using a transformation matrix spectral retrieval algorithm.

Simultaneous retrieval of fluidic refractive index and surface adsorbed molecular film thickness using silicon wire waveguide biosensors.

For silicon wire based ring resonator biosensors, we investigate the simultaneous retrieval of changes in the fluidic refractive index ∆n(c) and surface adsorbed molecular film thickness ∆d(F). This can be achieved by monitoring the resonance shifts of the sensors operating in the TE and TM polarizations at the same time. Although this procedure is straightforward in principle, significant retrieval errors can be introduced due to deviations in the sensor waveguide cross-sections from their nominal values in the range commonly encountered for silicon photonic wire devices. We propose a method of determining the fabricated waveguide size using the group indices derived from measured free spectral range (FSR) of the resonators. We further demonstrate that using experimentally measured group index values, the waveguide size can be determined to accuracies of ± 2 nm in width and ± 1 nm in height. By using this procedure, ∆n(c) and ∆d(F) can be obtained to a precision of within 10% of the true values using optically measurable parameters, improving the retrieval accuracy by more than 3 times.

Demonstration of a curved sidewall grating demultiplexer on silicon.

We experimentally demonstrate a new type of waveguide multiplexer device designed for silicon photonics, with a crosstalk level as low as -35 dB and an operational wavelength range of 300 nm. A compact device footprint of only 100 × 160 µm2 offers an excellent potential for integration with other silicon nanophotonic circuits.

Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide.

We report on the experimental demonstration and analysis of a new waveguide principle using subwavelength gratings. Unlike other periodic waveguides such as line-defects in a 2D photonic crystal lattice, a subwavelength grating waveguide confines the light as a conventional index-guided structure and does not exhibit optically resonant behaviour. Subwavelength grating waveguides in silicon-on-insulator are fabricated with a single etch step and allow for flexible control of the effective refractive index of the waveguide core simply by lithographic patterning. Experimental measurements indicate a propagation loss as low as 2.1 dB/cm for subwavelength grating waveguides with negligible polarization and wavelength dependent loss, which compares favourably to conventional microphotonic silicon waveguides. The measured group index is nearly constant n(g) ~1.5 over a wavelength range exceeding the telecom C-band.

Refractive index engineering with subwavelength gratings for efficient microphotonic couplers and planar waveguide multiplexers.

We use subwavelength gratings (SWGs) to engineer the refractive index in microphotonic waveguides, including practical components such as input couplers and multiplexer circuits. This technique allows for direct control of the mode confinement by changing the refractive index of a waveguide core over a range as broad as 1.6-3.5 by lithographic patterning. We demonstrate two experimental examples of refractive index engineering, namely, a microphotonic fiber-chip coupler with a coupling loss as small as -0.9dB and minimal wavelength dependence and a planar waveguide multiplexer with SWG nanostructure, which acts as a slab waveguide for light diffracted by the grating, while at the same time acting as a lateral cladding for the strip waveguide. This yields an operation bandwidth of 170nm for a device size of only approximately 160microm x100microm.

Subwavelength grating crossings for silicon wire waveguides.

We report on the design, simulation and experimental demonstration of a new type of waveguide crossing based on subwavelength gratings in silicon waveguides. We used 3D finite-difference time-domain simulations to minimize loss, crosstalk and polarization dependence. Measurement of fabricated devices show that our waveguide crossings have a loss as low as -0.023 dB/crossing, polarization dependent loss of < 0.02 dB and crosstalk <-40 dB.

Archimedean spiral cavity ring resonators in silicon as ultra-compact optical comb filters.

We present an ultra-compact comb filter using an add-drop ring resonator with an Archimedean spiral cavity. The cavity consists of two interleaved spiral branches which are connected in the center using arcs of circle of a radius that causes minimum bend loss. We describe the design procedure and examine the physical parameters governing the resonator performance. As an example, we demonstrate experimentally a comb filter with a 25 GHz channel spacing made of silicon photonic wires and only occupies an area of 80 x 90 microm(2), approximately a 70 fold size reduction compared to a racetrack resonator. The filter transmission is free of spurious reflections, attesting to the smooth transition between different sections of the resonator cavity. Over a 40 channel wavelength span, the filter exhibits a quality factor Q > 35,000, extinction ratios > 10 dB, and an excellent power uniformity with variations < 0.5 dB for both the through and drop ports.

Compact and low power thermo-optic switch using folded silicon waveguides.

By exploiting the small bend radius achievable using high-index-contrast silicon photonic wire waveguides, we demonstrate a new low power thermo-optic switch arranged in a dense, double spiral geometry. Such a design permits the waveguide length to be extended for increased phase shift, without the need for increased heated volume. This provides an effective means to reduce the power consumption of thermo-optic switches, as well as a compact geometry desirable for the development of switch arrays. A low switching power of 6.5 mW was obtained for a spiral-path Mach-Zehnder interferometer device having a 10% - 90% rise time of 14 micros. The switching power is shown to be reduced by more than 5 times compared to a Mach-Zehnder interferometer employing a conventional straight waveguide geometry.

Sub-wavelength grating mode transformers in silicon slab waveguides.

We report on several new types of sub-wavelength grating (SWG) gradient index structures for efficient mode coupling in high index contrast slab waveguides. Using a SWG, an adiabatic transition is achieved at the interface between silicon-on-insulator waveguides of different geometries. The SWG transition region minimizes both fundamental mode mismatch loss and coupling to higher order modes. By creating the gradient effective index region in the direction of propagation, we demonstrate that efficient vertical mode transformation can be achieved between slab waveguides of different core thickness. The structures which we propose can be fabricated by a single etch step. Using 3D finite-difference time-domain simulations we study the loss, polarization dependence and the higher order mode excitation for two types (triangular and triangular-transverse) of SWG transition regions between silicon-on-insulator slab waveguides of different core thicknesses. We demonstrate two solutions to reduce the polarization dependent loss of these structures. Finally, we propose an implementation of SWG structures to reduce loss and higher order mode excitation between a slab waveguide and a phase array of an array waveguide grating (AWG). Compared to a conventional AWG, the loss is reduced from -1.4 dB to < -0.2 dB at the slab-array interface.

Tilted fiber Bragg grating sensor interrogation system using a high-resolution silicon-on-insulator arrayed waveguide grating.

We report a compact high-resolution arrayed waveguide grating (AWG) interrogator system designed to measure the relative wavelength spacing between two individual resonances of a tilted fiber Bragg grating (TFBG) refractometer. The TFBG refractometer benefits from an internal wavelength and power reference provided by the core mode reflection resonance that can be used to determine cladding mode perturbations with high accuracy. The AWG interrogator is a planar waveguide device fabricated on a silicon-on-insulator platform, having 50 channels with a 0.18 nm wavelength separation and a footprint of 8 mmx8 mm. By overlaying two adjacent interference orders of the AWG we demonstrate simultaneous monitoring of two widely separated resonances in real time with high wavelength resolution. The standard deviation of the measured wavelength shifts is 1.2 pm, and it is limited by the resolution of the optical spectrum analyzer used for the interrogator calibration measurements.

Demultiplexer with blazed waveguide sidewall grating and sub-wavelength grating structure.

We propose an original diffraction grating demultiplexer device with a very small footprint, designed for the silicon-on-insulator waveguide platform. The wavelength dispersive properties are provided by a second-order diffraction grating designed to be lithographically defined and etched in the sidewall of a curved Si waveguide. The grating is blazed to maximize the -1st order diffraction efficiency. The diffracted light is coupled into the silicon slab waveguide via an impedance matching subwavelength grating gradient index antireflective interface. The waveguide is curved in order to focus the light onto the Rowland circle, where different wavelengths are intercepted by different receiver waveguides. The phase errors were substantially reduced using an apodized design with a chirped grating, which assures a constant effective index along the grating length. The simulated crosstalk is -30 dB. The device has 15 channels with a spacing of 25 nm, thus a broadband operational bandwidth of 375 nm. Its performance approaches the diffraction limit. The layout size is 90 microm x 140 microm, which is the smallest footprint yet reported for a mux/dmux device of a similar performance.

High bandwidth SOI photonic wire ring resonators using MMI couplers.

A ring resonator in SOI photonic wire waveguides is demonstrated using a compact MMI coupler with 3mum x 9 mum footprint as the coupling element. We achieved high bandwidth of 0.25 nm, and a quality factor Q of ~ 6000 for rings with a radius of 50 mum. Unlike directional coupler based rings, these resonators have a wavelength independent Q and extinction ratio over more than 30 nm wavelength range, and there is no loss penalty for increasing the bandwidth. Compared to their directional coupler based counterparts, these resonators also have less demanding fabrication requirements and are compatible with high speed signal processing and optical delay lines.