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        "description": "# Simple ABCD matrix propagator.\n\nMain file in this directory is tracer.py.  \n\n# Installation\n\nYou can install using `pip` at https://pypi.org/project/beamtrace/ \n```\npip install beamtrace\n```\nthen in a python scipy or ipython terminal, import the BeamTrace class by running\n```python\nimport beamtrace\nfrom beamtrace.tracer import BeamTrace\n```\n\nor if you have LIGO credentials you can git clone the directory at https://git.ligo.org/craig-cahillane/beamtrace\nand run\n```python\nimport sys\nsys.path.addpath('path/to/this/directory')\nfrom beamtrace.tracer import BeamTrace\n```\n\n# Docstring\n\nFrom beamtrace/tracer.py, the main class BeamTrace docstring;\n\n```python\nClass BeamTrace\nFor very simple beam waist and gouy phase calculations in python.\nNo fancy optimization like alamode, no nice GUI like jammt.\nJust mirrors, lenses, and lengths added in sequence.\n\n### Better options:\nMATLAB alamode: https://github.com/nicolassmith/alm\nJAMMT: http://www.sr.bham.ac.uk/dokuwiki/doku.php?id=geosim:jammt\nFinesse + pykat: https://git.ligo.org/finesse/pykat\n\n\n### Process:\nUser adds in mirrors, lenses, and spaces *in sequential order*.\nUser computes the cavity ABCD matrix from the components added using calculate_cavity_ABCD().\nIf cavity is stable, find the fundamental eigenmode for the beam (q-parameter)\nSet this q-parameter as q_input beam.\nScan the cavity beam parmater using scan_cavity().\n\n### Examples:\n# Simple resonator\nimport numpy as np\n\nmy_cav = BeamTrace()        # initializes ABCD class\nmy_cav.add_mirror(1.0) # adds mirror with 1.0 meter radius of curvature at z=0.0 meters\nmy_cav.add_space(0.5)  # adds 0.5 meters of space to cavity\nmy_cav.add_mirror(1.0) # adds mirror with 1.0 meter radius of curvature at z=0.5 meters\nmy_cav.calculate_cavity_ABCD() # Finds the cavity round-trip ABCD matrix, tells you if it's stable.  If it is stable, populates the my_cav.q_input parameter\nzz, ww, gouy, qq = my_cav.scan_cavity(round_trip=True) # Returns propagation distance, beam radius, accumulated gouy phase, and beam q-parameter for the entire cavity, plus the round-trip\n\nimport matplotlib.pyplot as plt\nfig = my_cav.plot_cavity_scan(round_trip=True, label='Simple Cavity')\nplt.show()\n\n# LIGO arm cavity\nR1 = 1934. # m\nR2 = 2245. # m\nL = 3994.469 # m\narm_cav = BeamTrace()\n\narm_cav.add_mirror(R1, name='ITMY')\narm_cav.add_space(L)\narm_cav.add_mirror(R2, name='ETMY')\n\nfig = arm_cav.plot_cavity_scan(round_trip=True)\nplt.show()\n```\n\n# Simple ABCD matrix calculations\n\nSpace matrix, $`L`$ is the length of the space\n\n$`S(L) = \\begin{bmatrix}\n1 & L \\\\\n0 & 1\n\\end{bmatrix}\n`$\n\nLens, $`f`$ is the focal length\n\n$`L(f) = \\begin{bmatrix}\n1 & 0 \\\\\n-\\frac{1}{f} & 1\n\\end{bmatrix}\n`$\n\nMirror, $`R`$ is the radius of curvature with index of refraction $`n`$, same as lens with $`f = RoC/2`$\n\n$`M(R) = \\begin{bmatrix}\n1 & 0 \\\\\n-\\frac{2 n}{R} & 1\n\\end{bmatrix}\n`$\n\nRefraction through a surface with radius of curvature $`R`$, initial index of refraction $`n1`$, and final index of refraction $`n2`$:\n\n$`F(R, n1, n2) = \\begin{bmatrix}\n1 & 0 \\\\\n\\frac{n2 - n1}{n2 R} & \\frac{n1}{n2}\n\\end{bmatrix}\n`$\n\n# Other Options:\n[Finesse + pykat](https://git.ligo.org/finesse/pykat)\n\n[MATLAB alamode](https://github.com/nicolassmith/alm)\n\n[JAMMT](http://www.sr.bham.ac.uk/dokuwiki/doku.php?id=geosim:jammt)\n\n# References:\n\n[Kogelnik and Li](https://www.osapublishing.org/ao/abstract.cfm?URI=ao-5-10-1550)\n\n[Koji Arai on beam prop](https://dcc.ligo.org/public/0102/T1300189/001/T1300189_v1_cavity_gouy_phase.pdf)\n\n[Wikipedia with ABCD matrices](https://en.wikipedia.org/wiki/Ray_transfer_matrix_analysis)\n\n[Stefan SRC gouy phase meas](https://alog.ligo-wa.caltech.edu/aLOG/index.php?callRep=52504)\n\n\n",
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