# Value of H is always very low in input source of ring resonator

#1
1. value of H is always very low in input mode source, even if we select TE or TM ? why, ?
2. due to low value of H, it am unable to obtain high strength H field in output, then how can one confirm about its output belongs to TE or TM?
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Measure the fresnel reflection coefficient off a rough surface
Far field 2d projection
#2

Dear @gauravb.sch

In our calculations, we assume that the amplitude of electric field is one. Then we can calculate the amplitude of H intensity from the electric field using the Maxwell’s equations.

For example, lets consider a simple case of plane wave propagation along the z-direction with electric field polarized in the x-direction:

E = Ex(z,t) = E0 *exp(ikz)*exp(-iwt)

where k is the wave number and w is the angular frequency. Using Maxwell’s equations, you can find the magnetic field (which propagates along the z-direction and is polarized in the y-direction):

H = Hy(z,t) = sqrt(ɛ0/μ0) *E0 *exp(ikz)*exp(-iwt)

where ɛ0 and μ0 are the free space permittivity and permeability, respectively, and we have

c= w/k=sqrt(1/ɛ0μ0)

This means that the amplitude of H-field will be sqrt(ɛ0/μ0) ~2.5 e-3 of electric field. This is why H-field has lower magnitude compared to E-field. You may obtain different ratios for more complex fields.

In our software, we define TE polarization fraction (Ex).

https://kb.lumerical.com/en/index.html?layout_analysis_eigensolver_mode_list_deck.html

In most cases, the modes with highest value are TE mode. However, please note that this is a convention in our tools, and you may need to check and make sure that you are using same convection i.e. the mode with biggest Ex component is TE. By comparing the field components you can identify the polarization of the modes. These links may be useful for your review: