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.

Optimum phase for rugate filter synthesis by Fourier transforms.

An optimum phase is developed for the synthesis of rugate reflectors by a simple Fourier transform. This phase belongs to a complex function of the desired spectral characteristics and is usually a free parameter. In general, it receives much less attention than the function magnitude, which is not known exactly. The current work shows that phase shaping alone produces surprisingly good results and has other advantages in rugate filter synthesis. In addition, the operating mode of this design procedure is quite unusual and interesting in itself.

Hybrid approach for rugate filter design.

Fourier techniques and direct optimization are applied to the synthesis of complex rugate filters. A hybrid approach is presented. The design strategies are illustrated numerically for different spectral shapes.

Fourier transform approach for thickness estimation of reflecting interference filters. 2. Generalized theory.

A Fourier transform (FT) approach based on the evaluation of optical-density-bandwidth products in the spectral region of interest was recently proposed for the thickness estimation of reflecting thin-film dielectric filters. For simplicity, the initial discussion was limited to a particular type of immersed coating. The theory is generalized to more realistic filter configurations and confirmed by numerical examples. It is shown that good results are possible although the problem is more complex from a FT point of view.

Fourier transform approach for thickness estimation of reflecting interference filters.

An empirical procedure based on optical-density-bandwidth products was recently proposed for thickness estimation of dielectric thin film reflectors. A parallel is established with new results derived from the Fourier transform thin film synthesis technique. Two Fourier-transform approaches are proposed and justified by numerical examples.

Optical interference coatings design contest 2004.

A manufacturable, broadband, broad-angle antireflection (AR) coating for the visible (13 designs submitted) and a minimum-shift immersed short-pass filter (12 designs submitted) were the subjects of the design contest held in conjunction with the 2004 Optical Interference Coatings topical meeting of the Optical Society of America. Under the specified constraints, the broadband, broad-angle AR coating could be made more than 65 nm wide. The statistical stability of manufacturing simulations is discussed. The short-pass filter could operate up to a +/- 5.5 degree angular range. The submitted designs are described and evaluated.

Design of a robust thin-film interference filter for erbium-doped fiber amplifier gain equalization.

Gain-flattening filters (GFFs) are key wavelength division multiplexing components in fiber-optics telecommunications. Challenging issues in the design of thin-film GFFs were recently the subject of a contest organized at the 2001 Conference on Optical Interference Coatings. The interest and main difficulty of the proposed problem was to minimize the sensitivity of a GFF to simulated fabrication errors. A high-yield solution and its design philosophy are described. The approach used to control the filter robustness is explained and illustrated by numerical results.