{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Gaussopt Example\n", "\n", "The ``GaussOpt`` package can be used to analyze quasioptical systems using Gaussian beam analysis. \n", "\n", "This simple example will walk through the basics of setting up a Gaussian beam telescope." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "from gaussopt import *\n", "\n", "import matplotlib.pyplot as plt \n", "from IPython.display import Image" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Gaussian beam telescopes** use two mirrors to couple energy between two horn antennas. If the mirrors have focal lengths $f$, then the mirrors should be separated by $2\\,f$ and the distance between each horn's beam waist and its respective mirror should be $f$.\n", "\n", "![](misc/GaussianBeamTelescope.jpg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define frequency sweep\n", "\n", "Here we will define a frequency sweep from 150 GHz to 300 GHz using the ``gaussopt.Frequency`` class. \n", "\n", "Note that this class assumes units of GHz unless a different unit is provided." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Frequency sweep:\n", "\tf = 150.0 to 300.0 GHz, 301 pts\n", "\n" ] } ], "source": [ "freq = Frequency(150, 300)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define horns\n", "\n", "As seen in the figure below, horn antennas are defined by their slant length, aperture radius and horn factor. See \"Quasioptical Systems\" by Paul Goldsmith for more information. We will use the ``gaussopt.Horn`` class to generate the transmitting horn (``horn_tx``) and then copy this horn to generate the receiving horn (``horn_rx``).\n", "\n", "![title](misc/Horn.jpg)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Horn: Trasmitting\n", "\tslen = 22.64 mm\n", "\tarad = 3.60 mm\n", "\thf = 0.59\n", "\n", "Horn: Receiving\n", "\tslen = 22.64 mm\n", "\tarad = 3.60 mm\n", "\thf = 0.59\n", "\n" ] } ], "source": [ "slen = 22.64 # slant length (in mm)\n", "arad = 3.6 # aperture radius (in mm)\n", "hfac = 0.59 # horn factor\n", "\n", "horn_tx = Horn(freq, slen, arad, hfac, comment='Trasmitting')\n", "horn_rx = horn_tx.copy(comment='Receiving')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define optical components\n", "\n", "Now it is time to build the rest of the circuit, i.e., everything between the transmitting and receiving horns. We can define empty space using the ``gaussopt.Freespace`` class and mirrors using the ``gaussopt.Mirror`` class." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Freespace: \n", "\td = 160.0 mm\n", "\n", "Mirror: M1\n", "\tf = 16.0 cm\n", "\n", "Mirror: M2\n", "\tf = 16.0 cm\n", "\n" ] } ], "source": [ "d = Freespace(160)\n", "m1 = Mirror(16, units='cm', radius=8, comment='M1')\n", "m2 = Mirror(16, units='cm', radius=8, comment='M2')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the distance between a horn and a mirror needs to be reduced because the actual beam waist will be behind the horn aperture." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Freespace: reduced\n", "\td = 155.8 mm\n", "\n" ] } ], "source": [ "z_offset = horn_tx.z_offset(units='mm')[freq.idx(230)]\n", "d_red = Freespace(160 - z_offset, comment='reduced')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Build Optical System\n", "\n", "We can now combine all of the individual optical components to build our optical system. This is normally done by creating a list of optical components (``component_list`` below), starting from the transmitting horn and then listing each component to the receiving horn.\n", "\n", "The component list is then passed to the ``gaussopt.System`` class, along with the two horns, to calculate the system properties." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "System: \n", "[[-1. 0.00848684]\n", " [ 0. -1. ]]\n" ] } ], "source": [ "component_list = (d_red, m1, d, d, m2, d_red)\n", "\n", "system = System(horn_rx, component_list, horn_tx)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot Coupling\n", "\n", "The coupling between the two horns can be plotted using the ``plot_coupling`` method. There should be perfect coupling at the center frequency." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best coupling: 100.0 % at 230.0 GHz\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "system.plot_coupling()\n", "system.print_best_coupling()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot Beam Propagation\n", "\n", "The beam waist can be plotted through the entire chain using the ``plot_system`` command. This method will also plot the aperture of each component to ensure that there isn't too much edge taper anywhere in the system." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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