Quasi-Vector Model of Propagation of Polarized Light in a Thin-Film Waveguide Lens

Dmitriy Divakov,Edik Ayryan,Mikhail Malykh,Anton Sevastianov,Leonid Sevastianov,Gh Adam,D Podgainy,M Hnatič,J Buša

doi:10.1051/epjconf/201817302007

Dmitriy Divakov, Edik Ayryan + Show 7 more

Open Access

https://doi.org/10.1051/epjconf/201817302007

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Abstract

Maxwell equations describe the propagation with diffraction of waveguide modes through a thin-film waveguide lens. If the radius of the thin-film lens is large, then the thickness of the lens varies slowly in the yz plane. For this case we propose the model, which is based on the assumption of a small change in the electromagnetic field in a direction y. Under this assumption the vector diffraction problem is reduced to a number of scalar diffraction problems. The solutions demonstrate the vector nature of the electromagnetic field, which allows us to call the proposed model a quasi-vector model.

Highlights

The first and the second Maxwell equations in the component representation in the Cartesian coordinate system for time-harmonic fields have the following form [1]: ∂Hz ∂y − ∂Hy ∂z = −ik0εEx, ∂Hx ∂z ∂Hz ∂x −ik0εEy, ∂Hy ∂x ∂Hx ∂y
If the waveguide lens has a radius Rl λ, where λ is the wavelength, |∂h1/∂y| 1 and assuming in this case that the electromagnetic field varies slowly along y, we introduce a small parameter defined as δ = max { |∂Eα/∂y|, |∂Hα/∂y|, α = x, y, z }
There is no TM-mode in the incident radiation, which leads us in the zeroth order approximation to Hy(0) = E(x0) = Ez(0) ≡ 0, the reflection and transmission coefficients of the components E(x0) and Ez(0) are zeros

Summary

Zeroth order approximation

∂2/∂z2, and are reflection and transmission coefficients of the component Ey (complex values, as in [4]), A (y) determines the amplitude of the waveguide mode incident on the lens, Rl is radius of the waveguide lens. There is no TM-mode in the incident radiation, which leads us in the zeroth order approximation to Hy(0) = E(x0) = Ez(0) ≡ 0, the reflection and transmission coefficients of the components E(x0) and Ez(0) are zeros. As a result we obtain the mixed boundary value problem with respect to the desired Kantorovich coefficient functions V j (y, z) [3, 5, 6]: vzz + Q (y, z) v = 0, vz + ik0Dv z=−Rl = 2ik0Dan0 , vz − ik0Dv z=Rl = 0. The zeroth order approximation, does not describe the process of hybridization of modes and we proceed to the first order approximation

First order approximation

Numerical experiment

Conclusion