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Defination about two parameters, gop.I and gop.normE, in the Ray Optics Module

Posted 29 mar 2018, 23:18 GMT-4 Ray Optics, Wave Optics 3 Replies

Haha Huang
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Hi everyone, I'm new to COMSOL Multiphysics and I am interested in the Ray Optics Module.

Recently, when I was conducting a simple model about the light refraction with p-polarization on an interface between two isotropic dielectric media, the defination of two exported parameters gop.I and gop.normE puzzles me.

It seems that, gop.I is calculated by Tp=n2/n1·cos(θ2)/cos(θ1)·tp^2. That is, I2=Tp·I1. However, gop.normE is not obtained according to the relationship between the electric field amplitude in the refracted light and incident light, tp=2n1cos(θ1)/[n2cos(θ1)+n1cos(θ2)].

It seem that gop.normE is actually calculated by E2=sqrt(cos(θ2)/cos(θ1))·tp·E1, rather than E2=tp·E1. Why did this happen? Is my knowledge wrong? Or the defination of gop.normE is not the electric field amplitude ??

3 Replies Last Post 19 apr 2018, 08:27 GMT-4
Haha Huang
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Posted: 7 years ago 17 apr 2018, 03:41 GMT-4

It seems that, the light intensity (unit:W/m2) of the refracted light should be calculated by, I2=n2/n1·tp^2·I1 rather than I2=n2/n1·cos(θ2)/cos(θ1)·tp^2·I1.

The latter one, which is actually used in COMSOL to calculate the light intensity (parameter: gop.I), should be the ray power.

It can be seen in wikipedia about the Fresnel Equations, https://en.wikipedia.org/wiki/Fresnel_equations

It seems that, the light intensity (unit:W/m2) of the refracted light should be calculated by, I2=n2/n1·tp^2·I1 rather than I2=n2/n1·cos(θ2)/cos(θ1)·tp^2·I1. The latter one, which is actually used in COMSOL to calculate the light intensity (parameter: **gop.I**), should be the ray power. It can be seen in wikipedia about the Fresnel Equations, https://en.wikipedia.org/wiki/Fresnel_equations
Christopher Boucher COMSOL Employee

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Posted: 7 years ago 18 apr 2018, 14:54 GMT-4

Hi,

The expression

I2=n2/n1·cos(θ2)/cos(θ1)·tp^2·I1

matches the expression given in the literature for the transmittance or transmissivity. For example, in the notation of Born and Wolf, Principles of Optics (7th ed.), pp.43,

where is the transmittance and is the transmission coefficient.

Best Regards, Chris

Hi, The expression I2=n2/n1·cos(θ2)/cos(θ1)·tp^2·I1 matches the expression given in the literature for the transmittance or transmissivity. For example, in the notation of Born and Wolf, Principles of Optics (7th ed.), pp.43, \mathcal{T} = \frac{J^{(t)}}{J^{(i)}} = \frac{n_2}{n_1}\frac{\cos\theta_t}{\cos\theta_i}\frac{\left|T\right|^2}{\left|A\right|^2} where \mathcal{T} is the transmittance and T is the transmission coefficient. Best Regards, Chris
Haha Huang
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Posted: 7 years ago 19 apr 2018, 08:27 GMT-4

Hi, Boucher, I am very glad to receive your reply!

I have consult the Principles of Optics (7th ed.) by Born and Wolf.

I have noticed the formula that you refered, T'=J(t)/J(i)=n2/n1·cos(θt)/cos(θi)·(T^2)/(A^2)

Actually, in the literature, J is regarded as the energy (or power) of the transmitted or the incident wave, whose unit is Joule or Watt. Thus the transmittance is the energy or power ratio between the two waves.

However,** the key of my question is that**, the parameter gop.I that calculated by the Ray Optics of COMSOL represents the light intensity and uses the unit of W/m2.

In fact, in your formula, the difference of the cross-sectional area between the refracted wave and the incident wave is included. So, in my opinion, it could not calculate the light intensity, but can be only used to calculate the ray energy or ray power.

Thanks!

Appendix

Hi,

The expression

I2=n2/n1·cos(θ2)/cos(θ1)·tp^2·I1

matches the expression given in the literature for the transmittance or transmissivity. For example, in the notation of Born and Wolf, Principles of Optics (7th ed.), pp.43,

\mathcal{T} = \frac{J^{(t)}}{J^{(i)}} = \frac{n_2}{n_1}\frac{\cos\theta_t}{\cos\theta_i}\frac{\left|T\right|^2}{\left|A\right|^2}

where \mathcal{T} is the transmittance and T is the transmission coefficient.

Best Regards, Chris

Hi, Boucher, I am very glad to receive your reply! I have consult the *Principles of Optics (7th ed.)* by Born and Wolf. I have noticed the formula that you refered, T'=J(t)/J(i)=n2/n1·cos(θt)/cos(θi)·(T^2)/(A^2) Actually, in the literature, **J** is regarded as the **energy (or power)** of the transmitted or the incident wave, whose unit is Joule or Watt. Thus the transmittance is the energy or power ratio between the two waves. However,** the key of my question is that**, the parameter **gop.I** that calculated by the Ray Optics of COMSOL represents the light intensity and uses the unit of W/m2. In fact, in your formula, the difference of the cross-sectional area between the refracted wave and the incident wave is included. So, in my opinion, it could not calculate the light intensity, but can be only used to calculate the ray energy or ray power. Thanks! **Appendix** >Hi, > >The expression > > I2=n2/n1·cos(θ2)/cos(θ1)·tp^2·I1 > >matches the expression given in the literature for the transmittance or transmissivity. For example, in the notation of Born and Wolf, Principles of Optics (7th ed.), pp.43, > > \mathcal{T} = \frac{J^{(t)}}{J^{(i)}} = \frac{n_2}{n_1}\frac{\cos\theta_t}{\cos\theta_i}\frac{\left|T\right|^2}{\left|A\right|^2} > > where \mathcal{T} is the transmittance and T is the transmission coefficient. > > Best Regards, > Chris

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