The design of an optical slot waveguide typically aims to achieve an intensity of a x-component of the E-field that is much higher than the other components, leading to a quasi TE-condition. In most of publications, when optimizing the optical field confinement factor (Gamma) into the slot, the power term, i.e. the Poynting vector, is often approximated in terms of integral of Ex2/Z, being Z the wave impedance of the mode. Nevertheless, the approximation of Z as Z0/n, being n the real refractive index of the slot material, is valid only for TEM modes, whereas for TE and TM modes Z is not depending only on material properties, leading to a surface distribution.
Therefore, using the approximation in COMSOL Multiphysics (Wave Optics) leads to meaningless values of the Gamma factor, with respect to what achieved using the Poynting vector expression.
Anyway, I guess that for my application of a slot waveguide photonic modulator, the estimation using the Ex-field leads to a more useful Gamma, as it is referred to the same direction of the TE RF field whose overlap to the optical field must be optimized. I expect that in such a way a proper estimation of Gamma can be achieved, even if slightly lower than what achieved using the Poynting vector.
Unfortunately, I saw that the wave impedance is not included among the variables of Wave Optics. From what read in Classic Electrodynamics books, maybe the surface distribution of the wave vector can be used to derive the wave impedance, but not even the wave vector is included as a variable in COMSOL.
Has anyone any suggestions to solve this ?
I attached a slide trying to resume this.
Hi Stefano,
I'm not totally familiar with the module of COMSOL that you're using, but, if you can obtain the solution for the transverse components of both the electric and magnetic fields (Ex,Ey,Hx,Hy) then you can compute the z-component of the Poynting vector directly.
Alternatively, if you know both transverse components of the electric field (Ex and Ey), then you can compute the plane-wave spectrum of each of these components (using a Fourier transform). You can then compute all the other magnetic and electric field components from these two plane-wave spectra by invoking Maxwell's equations. The Poynting vector can then be computed. In fact, I think you may be able to get the Poynting vector directly from the squared modulus of the plane-wave spectra via Parseval's Theorem.
Hope this helps:)
Ray
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