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GM3D/Reflection coefficient in Drude theory.ipynb

Last active September 8, 2021 06:12
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Reflection coefficient in Drude theory.ipynb
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Reflection coefficient in Drude theory.ipynb
{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": "$\\epsilon(\\omega)$ in Drude theory.\n\nformula (9.31) in the textbook. $\\omega_p \\tau_{tr}$ set to $10^2$, $x$ refers $\\omega\\tau_{tr}$."
},
{
"metadata": {
"trusted": true
},
"id": "499b618e",
"cell_type": "code",
"source": "ϵ(x) = 1 + im * 10^4 / (x * (1 - im * x))",
"execution_count": 1,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 1,
"data": {
"text/plain": "ϵ (generic function with 1 method)"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "define refraction rate $n$ and \"intrusion coefficient\" $1 - R(x)$, where $R(x)$ is the reflecton coefficient."
},
{
"metadata": {
"trusted": true
},
"id": "8a07342e",
"cell_type": "code",
"source": "n(x) = sqrt(ϵ(x))\nR1(x) = 1 - abs((1 - n(x))/(1 + n(x)))^2",
"execution_count": 2,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 2,
"data": {
"text/plain": "R1 (generic function with 1 method)"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Sanity check. all these quantities should be close to 1 at large $x$."
},
{
"metadata": {
"trusted": true
},
"id": "7868401e",
"cell_type": "code",
"source": "x0 = 1e10\nϵ(x0), n(x0), R1(x0)",
"execution_count": 3,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 3,
"data": {
"text/plain": "(0.9999999999999999 + 9.999999999999999e-27im, 0.9999999999999999 + 5.0e-27im, 1.0)"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "define function for log-log plot."
},
{
"metadata": {
"trusted": true
},
"id": "3549b3bb",
"cell_type": "code",
"source": "llR1(x) = log10(R1(exp10(x)))",
"execution_count": 5,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 5,
"data": {
"text/plain": "llR1 (generic function with 1 method)"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Calculate the function values in the same range with fig. 9.1 in the textbook."
},
{
"metadata": {
"trusted": true
},
"id": "5b6c4afd",
"cell_type": "code",
"source": "x = -2:0.1:3\ny = llR1.(x);",
"execution_count": 9,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"id": "3e1e5f67",
"cell_type": "code",
"source": "using Plots; gr()",
"execution_count": 10,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 10,
"data": {
"text/plain": "Plots.GRBackend()"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"id": "2d37c200",
"cell_type": "code",
"source": "plot(x, y, ylims=(-5, 4))",
"execution_count": 11,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 11,
"data": {
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