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Inconsistent Unit in Drude- Lorentz model

Posted 25 giu 2020, 09:55 GMT-4 3 Replies

Noor Nabi Afnan
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Hi,

I am facing inconsistent unit problem while applying Drude- Lorentz model equation for dielectric constant, E - (m^2/(w^2 + i * w * h)) - (f * g^2/((w^2-g^2)+i * k * w)) where E = 5.9673,

w=(2 * 3.1416 * c)/l,

l = 680[nm],

m = 0.022574495298995342[um],

h = 2.9970254723582923[um],

f = 1.09,

g = 0.07339741070532327[um],

k = 0.4550169353125095[um],

c = 3* 10^8 [m/s]

I have converted the unit eV to [um]. Can someone help me out please. Thank You

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3 Replies Last Post 27 giu 2020, 06:19 GMT-4
Alexis Prel
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Posted: 4 years ago 25 giu 2020, 11:12 GMT-4

Hi Noor,

The build-ins constants pi and c_const are available in COMSOL, so you don't have to type approximative values. ;-)

From your file it looks like you applied the following name convention :

m

w

h

f

g

k

But with the expression you put in COMSOl, (m) has the dimension of a frequency, whereas your other variables have the dimension of lengths.

Hi Noor, The build-ins constants `pi` and `c_const` are available in COMSOL, so you don't have to type approximative values. ;-) From your file it looks like you applied the following name convention : \omega_D \to `m` \omega \to `w` \lambda_D \to `h` \Delta\epsilon \to `f` \Omega_L \to `g` \tau_L \to `k` But with the expression you put in COMSOl, \omega_D (`m`) has the dimension of a frequency, whereas your other variables have the dimension of lengths.
Noor Nabi Afnan
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Posted: 4 years ago 26 giu 2020, 08:07 GMT-4

Thanks Alexis for your response. I have converted all the value to Hz now. But still comsol is showing the inconsistent unit problem :(

E - (m^2/(w^2 + i * w * h)) - (f * g^2/((w^2-g^2)+i * k * w)) where

E = 5.9673,

f = 1.09,

w = (2 * pi * c)/l [Hz],

m = 2113.6 * 2 * pi * 10^12 [Hz],

h = 15.92 * 2 * pi * 10^12 [Hz],

g = 650.07 * 2 * pi * 10^12 [Hz],

k = 104.86 * 2 * pi * 10^12 [Hz]

Have I done any mistake in writing the equation in comsol?

Thanks Alexis for your response. I have converted all the value to Hz now. But still comsol is showing the inconsistent unit problem :( E - (m^2/(w^2 + i * w * h)) - (f * g^2/((w^2-g^2)+i * k * w)) where E = 5.9673, f = 1.09, w = (2 * pi * c)/l [Hz], m = 2113.6 * 2 * pi * 10^12 [Hz], h = 15.92 * 2 * pi * 10^12 [Hz], g = 650.07 * 2 * pi * 10^12 [Hz], k = 104.86 * 2 * pi * 10^12 [Hz] Have I done any mistake in writing the equation in comsol?

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Alexis Prel
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Posted: 4 years ago 27 giu 2020, 06:19 GMT-4
Updated: 4 years ago 27 giu 2020, 06:24 GMT-4

Hi Noor, The problem you have now is with the expression of w. When you enter a value directly as for the other parameters you must specify the units, but when the expression is computed from other quantities, the unit will be computed automatically, so you must not put it again. Here the effect of the [Hz] at the end of your expression for w is to multiply l by 1[Hz] in the expression.

If I remove it, I get no unit error from COMSOL. The attached file is exported from the COMSOL interface, you can import it in your model.

Besides the image you attached as an error in the formula, it should read , instead of . Or maybe it is

Hi Noor, The problem you have now is with the expression of `w`. When you enter a value directly as for the other parameters you must specify the units, but when the expression is computed from other quantities, the unit will be computed automatically, so you must not put it again. Here the effect of the `[Hz]` at the end of your expression for `w` is to multiply `l` by 1[Hz] in the expression. If I remove it, I get no unit error from COMSOL. The attached file is exported from the COMSOL interface, you can import it in your model. Besides the image you attached as an error in the formula, it should read \Gamma_L^2, instead of \Gamma_L^{\omega}. Or maybe it is \Gamma_L \cdot \omega

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