Analog-to-digital optical waveguide conversion at sampling periods greater than the free-space wavelength

Nyquist sampling theorem reveals the possibility of sampling the continuous refractive index profiles of optical waveguides at periods greater than the free-space wavelength, λ(o). Binary encoding of these analog waveguides is investigated using the zero-order effective medium theory, while conserving the quantization of the modal spectrum implied by their boundary conditions. Both analytical and numerical approaches are developed for this analog-to-digital (A-to-D) conversion. An example is presented for the A-to-D conversion of a graded index waveguide with a hyperbolic secant profile at a sample period of 1.3λ(o). The results are confirmed using a beam propagation method.