![]() At larger incidence angles, and longer wavelengths, larger surface heights will result and vice versa as the incidence angle approaches 0 degrees and for shorter wavelengths.įor a perfectly reflecting surface, the infinite sum over orders for ![]() For order of magnitude h = 100 nm, the 3rd-order is starting to pick up power, but the second and lower orders carry most all the power. Under these assumptions, a 10 nm height is relatively smooth and the 0th-order dominates. ![]() Is calculated assuming incidence in glass with refractive index n = 1.46. For our numerical examples, the value of h (nm) for a free space wavelength Where the diffracted orders are “locally paraxial” with respect to the specular reflection axis, is a/2 = 0.142. 1 orders under a “locally paraxial” constraint, defined by Under the GO approximation, surface scattering is driven by the distribution of the surface slope. Beyond the GO simulation, the next step is to evaluate the potential for diffraction-based scattering effects that could introduce wavelength-dependent losses in the light pipe. We have implemented a geometrical optics (GO) simulation to compare the expected surface scattering loss to our experimental measurement results. The light is guided via total internal reflection as it propagates along the light pipe and undergoes numerous sidewall reflections that vary in number depending on the incident ray angles. For example, we have fabricated glass light pipes with millimeter-scale cross-sections that are several centimeters in length. For applications with numerous surface reflections, such as light pipes based on total internal reflection at the interface, a simpler surface scattering model is desired that can be combined with ray tracing simulations for the overall device. Optical surface scattering analyses are often conducted using a diffraction-based approach for single surface light scattering, as opposed to using geometrical optics approximations (GOA). Close agreement is shown between the DO and GO solutions for the same surface rms slope scattering loss due to angular filtering near the critical angle of a total internal reflection (TIR) glass-to-air interface. The conditions under which the diffraction-based solution closely approximates the GO solution, as predicted by the rms slope, are identified. The scatter angle’s mean and rms width are evaluated over a range of grating amplitudes and periods using scalar theory and full vector simulations from the COMSOL® wave optic module for a sinusoidal reflection grating. ![]() A formula for the root-mean-square (rms) scattered angle width of a sinusoidal reflection grating that depends only on the surface rms slope is derived from the nonparaxial scalar diffraction theory, thereby linking it to GO. A better understanding of the link, or transition, between DO and GO scattering domains would be helpful for efficiently incorporating scattering loss analyses into ray trace simulations. In the DO case, surface scattering analyses depend on the spatial frequency distribution and amplitude as well as wavelength, with the sinusoidal grating as a fundamental basis. Light pipes are often simulated with geometric optics (GO) using ray tracing, where surface scattering is driven by the surface slope distribution. Optical surface scattering analyses based on diffractive optics (DO) are typically applied to one surface however, there is a need for simulating surface scattering losses for devices having many surface interactions such as light pipes. ![]()
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