{ "cells": [ { "cell_type": "markdown", "id": "5a3ba2b9", "metadata": {}, "source": [ "MIT Licence\n", "\n", "© Alexey A. Shcherbakov, 2024" ] }, { "cell_type": "markdown", "id": "00ffec2d", "metadata": {}, "source": [ "# Lecture 2.1. Photonic crystals. Properties and applications" ] }, { "cell_type": "code", "execution_count": 4, "id": "690a1b03", "metadata": {}, "outputs": [], "source": [ "from pathlib import Path\n", "import sys\n", "import os\n", "path_root = os.path.dirname(os.path.dirname(os.path.abspath('')))\n", "sys.path.append(str(path_root))\n", "import ANMOP.code.PhC1D_band_diagram as bd1\n", "import ANMOP.code.PhC2D_empty_lattice as ela" ] }, { "cell_type": "markdown", "id": "ab869914", "metadata": {}, "source": [ "## Photonic crystals\n", "\n", "A photonic crystal is a periodic structure in one, two, or three dimensions in which the material parameters relating the fields in the material equations for the electromagnetic field change periodically. In the theoretical description of photonic crystals, one usually starts by considering an infinite periodic structure that fills the entire space. In practice, examples of photonic crystals include periodic multilayers - Bragg gratings (one-dimensional), - etched long cylindrical cavities or periodically arranged cylinders on a substrate (two-dimensional), and artificial opals (three-dimensional). Profiled one-dimensional and two-dimensional diffraction gratings whose material distribution is invariant along the depth can also be considered as layers of corresponding photonic crystals.\n", "\n", "<figure>\n", " <center>\n", " <img src=\"../pic/2-1_PhC.png\" height=200>\n", " <figcaption>Illustration of a cut cube from an infinite one-, two-, and three-dimensional-periodic medium - photonic crystal.</figcaption>\n", " </center>\n", "</figure>\n", "\n", "The terminology of photonic crystals has arisen from analogy with the terminology of a branch of the solid state physics where periodic potentials are considered. Electrons in solid crystalline solids can be described using the zone theory. Such concepts as inverse lattice, Brillouin zones, forbidden zone appear in the optics of periodic media as well. Thus, for example, in photonic crystals it is possible to find frequency intervals in which there are no propagating eigen solutions, in other words, all waves excited within these intervals will be evanescent. Such intervals are called band gaps. The possibility of formation of band gaps for all possible electromagnetic waves in a crystal shows its essential difference from free isotropic or anisotropic space. Therefore, one can expect a significant change in the characteristics of various sources of electromagnetic radiation placed inside or near photonic-crystal structures. Another direction of application of the special properties of photonic crystals is the creation of high-frequency resonators and waveguides by introducing defects into the ideal lattice. In this case, if all optical materials of which the photonic crystal consists are dielectric, the quality factor of such resonators can be very high." ] }, { "cell_type": "markdown", "id": "007de6c3", "metadata": {}, "source": [ "## Band gap\n", "\n", "Let us consider some general electromagnetic properties of photonic crystals. In the simplest one-dimensional case of nonmagnetic media, the eigen equation in the crystal is the scalar Helmholtz equation\n", "\\begin{equation}\\tag{1}\n", " \\left[\\frac{d^2}{dz^2} + \\omega^2\\varepsilon(z)\\mu_0\\right] E(z) = 0\n", "\\end{equation}\n", "with the periodic function $\\varepsilon(z+n\\Lambda) = \\varepsilon(z)$, where $\\Lambda$ is the crystal period. According to the Floquet-Bloch's theorem, the field in a periodic potential is represented as a product of the Floquet-Bloch exponent by a periodic function. Let us decompose the latter into its Fourier series, so that\n", "\\begin{equation}\\tag{2}\n", " E(z) = e^{ik_0z} u(z) = e^{ik_0z} \\sum_{m=-\\infty}^{\\infty} u_m \\exp(2\\pi im z/\\Lambda).\n", "\\end{equation}\n", "The set of points $mK = 2\\pi im/\\Lambda$ defines a grid in the reciprocal space, where the region $-K/2\\leq k\\leq K/2$ is called the first Brillouin zone. Let us multiply equation (1) by the inverse dielectric permittivity function and decompose this function into its Fourier series. For simplicity, we assume that the first three terms make the main contribution to the series, so that\n", "\\begin{equation}\\tag{3}\n", " \\varepsilon^{-1}(z) = \\sum_{m=-\\infty}^{\\infty} \\zeta_m \\exp(2\\pi im z/\\Lambda) \\approx \\zeta_0 + \\zeta_1 e^{2\\pi i z/\\Lambda} + \\zeta_{-1} e^{-2\\pi i z/\\Lambda}.\n", "\\end{equation}\n", "Substituting (2) and (3) into (1) and using the orthogonality of exponential functions, we obtain a system of coupled equations\n", "\\begin{equation}\\tag{4}\n", " \\zeta_1 \\left[ k_0 + \\frac{2\\pi}{\\Lambda}(m-1) \\right]^2 u_{m-1} + \\zeta_{-1} \\left[ k_0 + \\frac{2\\pi}{\\Lambda}(m+1) \\right]^2 u_{m+1} \\approx \\left[ \\omega^2\\mu_0 - \\zeta_0 \\left(k_0 + \\frac{2\\pi}{\\Lambda}m\\right)^2 \\right] u_{m}\n", "\\end{equation}\n", "Let us write the equations for $m=0,\\pm1$ and consider the values of the Bloch vector at the edge of the first Brillouin zone $k_0\\approx K/2$. If the the dielectric permittivity is close to a one of a free isotropic space, we can also assume that at most points of k-space the dispersion is not very different from the dispersion of the free space $\\omega^2\\mu_0\\approx \\zeta_0 k_0^2$. Under these conditions, it can be shown that the main contribution to the field is made by the summands with $m=0,1$. Neglecting all other terms in (4), we obtain a system of two equations\n", "\\begin{equation*}\n", " \\begin{array}{c}\n", " \\left( \\omega^2\\mu_0 - \\zeta_0 k_0^2 \\right) u_{0} - \\zeta_1 \\left( k_0 - \\frac{2\\pi}{\\Lambda} \\right)^2 u_{-1} \\approx 0 \\\\\n", " -\\zeta_{-1} k_0^2 u_{0} + \\left[ \\omega^2\\mu_0 - \\zeta_0 \\left(k_0 - \\frac{2\\pi}{\\Lambda}\\right)^2 \\right] u_{-1} \\approx 0\n", " \\end{array}\n", "\\end{equation*}\n", "We denote $\\Delta k = k-\\pi/\\Lambda$, so that $|\\Delta k|\\ll \\pi/\\Lambda$. Equating the determinant of the system to zero and solving with respect to the eigne frequency, we find two solutions\n", "\\begin{equation*}\n", " \\omega_{\\pm} \\approx \\frac{K}{2} \\sqrt{\\zeta_0\\pm|\\zeta_1|} \\pm \\frac{1}{\\sqrt{\\zeta_0}|\\zeta_1|} \\frac{(\\Delta k)^2}{K/2} \\left( \\zeta_0^2 -\\frac{\\zeta_1^2}{4} \\right) \n", "\\end{equation*}\n", "The band gap excists in the frequency range $(K/2)\\sqrt{\\zeta_0-|\\zeta_1|} < \\omega < (K/2)\\sqrt{\\zeta_0+|\\zeta_1|}$.\n", "\n", "In the absence of modulation $\\zeta_m=0$ for all $m\\neq0$ and the forbidden zone vanishes - the so-called empty lattice approximation is obtained. At non-zero modulation there is an infinite number of band gaps - the estimate for the lowest one is given above. Pairs of coincident solutions corresponding to intersections of dispersion lines in the empty lattice approach are split. Since, in the presence of periodicity, the solutions differing by $K=2\\pi/\\Lambda$ are equivalent, the solutions at the edges of the Brillouin zones correspond to the interference of waves propagating in opposite directions, which leads to the formation of standing waves whose group velocity $v_g = d\\omega/dk_0$ is zero, and, therefore, the tangent to the dispersion curve $\\omega(k_0)$ at the boundaries has a zero angle of inclination." ] }, { "cell_type": "code", "execution_count": 6, "id": "2e090a94", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# The first Brillouin zone of a one-dimensional photonic crystal and the empty lattice approximation\n", "bd1.plot_1D_PhC_dispersion(eps1=1, eps2=2.5, d1=0.1, d2=0.2, n=5, nb=4)" ] }, { "cell_type": "markdown", "id": "42033768", "metadata": {}, "source": [ "## Group velocity anomaly\n", "\n", "In the case of two-dimensional crystals, there are two noncollinear periodicity directions and, accordingly, two basis vectors of the reciprocal lattice. The first Brillouin zone is a two-dimensional Wigner-Seitz cell in reciprocal space. The high symmetry points of this zone are usually denoted by capitalized Greek letters. The center of the first Brillouin zone is called the $\\Gamma$-point. Dispersion diagrams are often shown with with lines corresponding to direct trajectories connecting the points of high symmetry.\n", "\n", "<figure>\n", " <center>\n", " <img src=\"../pic/2-1_2D_PhC.png\" height=400>\n", " <figcaption>First Brillouin zone of two-dimensional crystals with square and hexagonal lattice.</figcaption>\n", " </center>\n", "</figure>\n", "\n", "In the empty lattice approximation the disperion is defined by the equation\n", "\\begin{equation}\\tag{5}\n", " \\left(k_x + mK_x\\right)^2 + \\left(k_y + nK_y\\right)^2 = \\omega^2\\varepsilon\\mu_0 \n", "\\end{equation}\n", "For example, for a square lattice, the two periods are given by the vectors $\\boldsymbol{p}_1 = (\\Lambda,0)^T$ and $\\boldsymbol{p}_2 = (0,\\Lambda)^T$. Corresponding reciprocal lattice vectors are $\\boldsymbol{K}_1 = (2\\pi/\\Lambda,0)^T$ and $\\boldsymbol{K}_2 = (0,2\\pi/\\Lambda)^T$. The trajectory $\\Gamma X$ is given by changing the vector $\\boldsymbol{k} = (k_x,0)^T$. For the third zone with $m=2$, it can be seen that along the entire trajectory the slope of the dispersion curve remains small, which corresponds to the small group velocity of the waves. This effect is called the group velocity anomaly. Some research have demonstrated the structures of photonic crystals that allow the appearance of dispersion bands with almost zero group velocity." ] }, { "cell_type": "code", "execution_count": 3, "id": "d7e5324b", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "<Figure size 1440x720 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ela.plot_empty_lattice_dispersion()" ] }, { "cell_type": "markdown", "id": "f6264f4c", "metadata": {}, "source": [ "## Scaling and time reversal symmetry\n", "\n", "If we normalize the wavevectors by the modulus of the inverse lattice vector $\\boldsymbol{k}\\rightarrow (1/K) \\boldsymbol{k} = (\\Lambda/2\\pi) \\boldsymbol{k}$, and the frequency is measured in units of $2\\pi c/\\Lambda$, the electromagnetic properties of photonic crystals as solutions of Maxwell's equations will remain the same under the condition that the values of material parameters are not changed. This follows from the substitution into the equations of the coordinates and time normalized by the period and $\\Lambda/c$, respectively. This property is called scaling.\n", "\n", "The wave equation is independent of the time sign change $t'=-t$, therefore, the solution $\\tilde{\\boldsymbol{E}}(\\boldsymbol{r},t') = \\boldsymbol{E}(\\boldsymbol{r},-t)$ also satisfies this equation. Consequently, the eigenfrequencies of $\\omega_{\\boldsymbol{k}n}$, which the solutions to the eigenvalue problem, remain the same. Then,\n", "\\begin{equation*}\n", " \\tilde{\\boldsymbol{E}}(\\boldsymbol{r},t') = \\boldsymbol{u}_{\\boldsymbol{k}n}(\\boldsymbol{r}) \\exp[i(\\boldsymbol{k}\\boldsymbol{r} - \\omega_{\\boldsymbol{k}n}t')]\n", "\\end{equation*}\n", "Inverse transformation gives\n", "\\begin{equation*}\n", " \\boldsymbol{E}(\\boldsymbol{r},t) = \\left( \\boldsymbol{u}^*_{\\boldsymbol{k}n}(\\boldsymbol{r}) \\exp[i(-\\boldsymbol{k}\\boldsymbol{r} - \\omega_{\\boldsymbol{k}n}t)] \\right)^*\n", "\\end{equation*}\n", "Since the measured field is the real part of a complex-valued solution, it can be seen that\n", "\\begin{equation}\\tag{6}\n", " \\begin{array}{c}\n", " \\omega_{-\\boldsymbol{k}n} = \\omega_{\\boldsymbol{k}n}, \\\\\n", " \\boldsymbol{u}_{-\\boldsymbol{k}n} = \\boldsymbol{u}^*_{\\boldsymbol{k}n}\n", " \\end{array}\n", "\\end{equation}\n", "This implies the symmetry of the dispersion diagrams with respect to the inversion in the reciprocal space." ] }, { "cell_type": "markdown", "id": "210e73b8", "metadata": {}, "source": [ "### References\n", "\n", "1. K. Sakoda, [Optical Properties of Photonic Crystals](https://materias.df.uba.ar/introNanoFot2014/files/2012/07/Optical-Properties-of-Photonic-Crystals_sakoda.pdf), Springer Science & Business Media (2004)\n", "2. J.D. Joannopoulos, S.G. Johnson, J.N. Winn, and R.D. Meade, [Photonic Crystals. Molding the Flow of Light (Second Edition)](), Princeton University Press (2011)" ] } ], "metadata": { "kernelspec": { "display_name": "base", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.8" } }, "nbformat": 4, "nbformat_minor": 5 }