Advances in the development and manufacturing of photonic processors have reached a critical stage where their mass applications are becoming commercially viable. LNL Optenia utilized the FEMLAB multiphysics package from COMSOL to design inexpensive planar-lightwave photonic processors based on planar Echelle grating technology. One major challenge in the design and manufacture of devices with a large contrast in the refractive index of the constituent materials is that as they get smaller, it becomes more difficult to obtain the desired optical characteristics.
The design of planar lightwave circuits typically begins with an analysis of the waveguide mode structure, that is, looking at the distribution of light within the waveguide. The determination of propagation along optical waveguides requires solving Maxwell's vector wave equations for a given complex permittivity tensor. Due to coupling of the six components (three electric and three magnetic field vectors) along with the complicated cross-sectional geometries of refractive-index profiles, the solution to the vector wave equation presents a formidable computational challenge.
In this instance, FEMLAB software was used to create a series of algorithms based on the finite element method with a set of absorbing, periodic, metallic, and magnetic boundary conditions to successfully model arbitrarily shaped waveguides. Creating these structures can be complicated; arbitrary intensity distributions through the core must be generated, in effect achieving desired spectral passband performance in the devices.
A Matlab algorithm was written to create various device geometries. Each time an algorithm was used, Matlab called on FEMLAB to investigate device performance by computing the waveguide modes and their propagation properties. In a typical device simulation 4,000 mesh elements are used to create a cross-section model for transverse modeling and Eigenvalue analysis. For a given geometry, it took roughly two minutes to arrive at the Eigenvalue solution of a mode. At this rate hundreds of geometries were run through in a short period of time (24 to 48 hours).
The computational program was augmented with adaptive mesh capabilities that work equally well for waveguides of any geometry and refractive-index contrast, including those that consist of very thin layers or composite cores. Variable-sized mesh capabilities enable the effects of any element to be captured (see Figure 1). If the mesh were not constant, focus could not be placed on specific regions of a device's geometry, disallowing accurate analysis of optical properties. For instance, the metal electrode layer on the top of a photonic processor can be as thin as 20 nm to 200 nm, but in the optical domain it is a crucial element because it influences the properties of light in the waveguide core.
Periodic boundaries are also an issue of concern. A device might have a large number of waveguide cores next to each other that extend across the width of a device. Because of memory restrictions and computational time, however, it is reasonable to perform detailed modeling only on a small region (see Figure 2). The software allowed boundaries to be set so that they acted as a mirror on each side, roughly approximating how cores in the actual device function. The approximation is realistic because the cores were sufficiently far away from the edges of the device so that boundary effects are negligible.
Most modeling codes approach Maxwell's equations as scalar functions, even though an electric or magnetic field is actually a vector. In contrast, FEMLAB allowed full vectorial descriptions for realistic birefringence analysis. As a result, the software revealed vector-related phenomenon such as the coupling of components of the electric and magnetic fields, and how they interact.
FEM algorithms were generalized in order to solve optical modes of inhomogeneous and anisotropic materials. This allowed mechanical stresses to be included in the waveguide analysis, thereby modeling the impact of material manufacturing processes at different growth and annealing temperatures. Such computations yielded precise values for the stress-induced birefringence in planar lightwave circuits.
Using the software's Structural Mechanics module, a value was predicted for a device's inherent birefringence, allowing core geometry to be determined with a form birefringence that can compensate for the inherent value to produce a device that is essentially polarization-insensitive. Inherent birefringence arises during the manufacturing process, in particular the stresses that occur when hot wafer material cools down. Form birefringence varies with the core geometry and is one variable over which the designer has some control.
Another critical operating parameter in these devices was how much attenuation or amplification was applied to lightwaves. The complex part of the refractive index was analyzed, and the resulting value was used to predict loss. Device engineers could then dope the core material during manufacturing in order to alter its amplification or attenuation properties.