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Discrepancy in phase change of Fresnel Equation model
Posted Oct 8, 2012, 9:47 AM EDT RF & Microwave Engineering Version 4.3 0 Replies
I'm investigating the phase change of a plane wave travellling through medium 1 (higher refractive index) and getting reflected at the interface of medium 1 and medium 2 when the incident angle is larger than the critical angle. I started from the Fresnel Equation model. Since in this model the refractive index of medium 1 (n=1; air) is smaller than that of medium 2 (n=1.5; slab). So I did some modification to the model listed as follows:
(1) The n_air is changed into 1.5;
(2) The n_slab is changed into 1;
So now the light is coming from a high n layer and bouncing back at the interface.
(3) The ka is changed into n_air*emw.k0 because n_air is no longer equal to 1.
(4) The length of the geometry is extended and re-scaled into visible wavelength scale. The wavelength is now 612 nm, the height for two parts is 300 nm and 1200 nm respectively.
The computed transmittance and reflectance are almost the same as the analytical results. However, when the incident angle is larger than critical angle, the phases do not agree with theory.
The theory I used for the analytical results of phase change is illustrated in the attachment file (Fig 'theory'). Plane wave travels in the first medium and gets reflected at the interface. If we look at point A, then the phase difference between the incident plane wave and reflected plane wave is 2*d*cos(theta) plus the phase change at the interface (fresnel's equation; phase change at the interface can be calculated by rewriting 't' or 'r' as an expression like A*exp(i*Phi), Phi is the phase change ). The analytical result of phase change is also attached (Fig 'analytical result').
My understanding is that the phase shift should be the sum of what happens at the interface between the materials (phase_interface) and what I get from the propagation to and from this interface to the port boundaries (phase_propagation). However, the results from COMSOL is the subtract rather than the sum of these two. COMSOL file is attached. (solution has been cleared because of size issue. The solution can be recovered just by simply recalculate the study again.)
Has anyone met this problem?
PS. the phase change I'm looking at is for S11 at TM polarisation. But same situation happens to S11 at TE polarisation as well.
Hello Shuyu Zhang
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