6/2017

This example demonstrates numerical design of a single-layer antireflection coating for the waveguide specified in the data input file. Irrespective of the coating information provided in the input file, a single-layer coating is used. This simple command line specifies the data-input file name, which reflection model to use (AR = Kendall, ARF = Fresnel, ARV = Vassallo), and the Smax/beta range and Sstep/beta increment resolution used in integrating the modal reflection expressions. With the parameters used in the example, Smax/beta = 5 and Sstep/beta = 0.002, the coating refractive index and thickness are both within about 1 part per million of the fully converged values FOR THAT MODEL. However, these calculated coating parameters depend on the model used due to different residual effects inherent in the models, particularly at extreme minimum "perfect" design coatings with R<1e-10. In many practical cases, considering realistic control accuracy of the coating process, Sstep/beta can be increased to ~ 0.01 resulting in considerably faster execution with results convergent to about 1 part in 1000 of the fully converged result for that model:

The chart below compares the results predicted for a PERFECT single layer TE0 AR coating (with R<1e-12) for the 3 approximate models with the exact rigorously calculated result for the same waveguide (Vassallo 1988). For each of the 3 models, a low resolution and a high resolution iteration computation result is shown rounded to the final figure. In all cases, the search convergence is achieved (to well within the results shown). The variation of the predicted coating layer index and thickness is evident:

The plots below show how the optimum single-layer refractive index and (normalized) thickness of a "perfect" TE0 antireflection coating (using Kendall model) depends on the active layer thickness of a typical waveguide (Vassallo, Electronics Letters, V21 1985 p. 333). As the waveguide core layer thickness tends to zero and the mode becomes increasingly unconfined and tends towards a plane wave with near-zero normal incidence, the optimum coating index tends to the plane wave value of √3.17 (index of waveguide cladding region) and the normalized thickness tends to 1/4:

Finally, the plot below demonstrates the changes to modal reflectance of an otherwise ideal zero reflectance single-layer coating with changes to the vertical waveguide-structure. The example uses the ideal Kendall coating parameters above for a symmetric waveguide but also includes an additional bottom waveguide region of index 2.0 (close to a SiNx dielectric). The lower waveguide cladding layer of index 3.17 is varied in thickness Tb with Tb-> ∞ reducing to the perfect symmetric waveguide layer example above with mode reflectance of < 1e-15. The inset shows the corresponding result for the uncoated waveguide: