cavcalc 1.2.0

A program for computing Fabry-Perot optical cavity parameters.

A command line program and Python module for computing parameters associated with linear, Fabry-Perot optical cavities.

• Find the documentation at: https://cavcalc.readthedocs.io/en/latest/
• Follow the latest changes: https://gitlab.com/sjrowlinson/cavcalc
• See the entry on PyPI: https://pypi.org/project/cavcalc/

Installation

To install cavcalc, simply run:

pip install cavcalc

Check that the installation was successful with:

cavcalc --version

if you see something along the lines of

cavcalc v1.2.0

then you should be ready to start using cavcalc!

Note: As is often recommended with the installation of Python packages (especially those with dependencies on packages such as numpy and matplotlib, as is the case here), you should prefer to install cavcalc in a suitable virtual environment. See the official documentation on Python virtual environments for details on how to set up these if you are unfamiliar with the topic.

Example usage via the CLI

For details on available arguments run cavcalc -h on the command line.

Some examples follow on how to use cavcalc. See the documentation on using cavcalc for more in-depth examples and guides.

Computing single parameters

You can ask for, e.g., the beam size on the mirrors of a symmetric cavity given its length and stability factor of the mirrors (gs) with:

cavcalc w -L 4000 -gs 0.91

This would result in an output of:

Given:
	Cavity length = 4000 m

	Stability g-factor of both mirrors = 0.91

	Wavelength of beam = 1064 nm

Computed:
	Radius of beam at mirrors = 57.16193267930482 mm

Units for both inputs and outputs can also be specified:

cavcalc w -u mm -L 10km -gouy 145deg

This requests the beam radius (in mm) on the mirrors of a symmetric cavity of length 10km given that the round-trip Gouy phase is 145 degrees; resulting in the following output:

Given:
	Cavity length = 10 km

	Round-trip Gouy phase = 145 deg

	Wavelength of beam = 1064 nm

Computed:
	Radius of beam at mirrors = 59.59174828941794 mm

Support for units is provided via the package Pint, so any units defined in the Pint unit-registry can be used in cavcalc.

Computing all available parameters

A compute target of all is the default choice which is used to calculate all parameters which can be determined from the arguments specified. For example, using approximate values of the Advanced LIGO arm cavity parameters,

cavcalc -L 4km -Rc1 1934 -Rc2 2245 -T1 0.014 -L1 37.5e-6 -T2 5e-6 -L2 L1

gives the following output:

Given:
	Loss of first mirror = 3.75e-05
	Loss of second mirror = 3.75e-05
	Transmission of first mirror = 0.014
	Transmission of second mirror = 5e-06

	Cavity length = 4 km

	Radius of curvature of first mirror = 1934 m
	Radius of curvature of second mirror = 2245 m

	Wavelength of beam = 1064 nm

Computed:
	FSR = 37474.05725 Hz
	FWHM = 84.56921734107604 Hz
	Mode separation frequency = 4988.072188176178 Hz
	Pole frequency = 42.28460867053802 Hz

	Finesse = 443.11699254426594
	Reflectivity of first mirror = 0.9859625
	Reflectivity of second mirror = 0.9999574999999999
	Internal resonance enhancement factor = 20036.317877295227
	External resonance enhancement factor = 281.2598122025325
	Fractional transmission intensity = 0.011953542018623487

	Position of beam waist (from first mirror) = 1837.2153886417168 m

	Radius of beam at first mirror = 53.421066433049255 mm
	Radius of beam at second mirror = 62.448079883230896 mm
	Radius of beam at waist = 11.950538458990879 mm

	Stability g-factor of cavity = 0.8350925761717987
	Stability g-factor of first mirror = -1.0682523267838677
	Stability g-factor of second mirror = -0.7817371937639199

	Round-trip Gouy phase = 312.0813565565169 deg

	Divergence angle = 0.0016237789746943276 deg

Units of output

The default behaviour for the output parameter units is to grab the relevant parameter type option under the [units] header of the cavcalc.ini configuration file. When installing cavcalc, this file is written to a new cavcalc/ directory within your config directory (i.e. typically ~/.config/cavcalc/cavcalc.ini under Unix systems). See the comments in this file for details on the options available for the output units of each parameter type.

cavcalc attempts to read a cavcalc.ini config file from several locations in this fixed order:

• Firstly from the current working directory, then
• from $XDG_CONFIG_HOME/cavcalc/ (or %APPDATA%/cavcalc/ on Windows), then
• the final read attempt is from the within the source of the package directory itself.

The config options from these read attempts are loaded in a standard way; that is, any options appearing first in the sequence defined above will take priority. If any of the above read attempts fails, then this will be a silent failure; the only situation where an error could occur would be when all of the above read attempts fail (which is very unlikely to happen).

Note that if you specify a -u argument when running cavcalc from the CLI, then this takes priority over the options in the config file (as we saw in an example above).

Evaluating, and plotting, parameters over data ranges

Parameters can be computed over ranges of data using:

• the data range syntax: -<param_name> "start stop num [<units>]",
• or data from an input file with -<param_name> <file>.

We can use data-ranges to compute, and plot, arrays of target values, e.g:

cavcalc w -L "1 10 100 km" -Rc 5.1km --plot

This results in a plot (see below) showing how the beam radius at the mirrors of a symmetric cavity varies from a cavity length of 1 km to 10 km with 100 data points, with the radii of curvature of both mirrors fixed at 5.1 km.

Alternatively one could use a file of data, e.g:

cavcalc gouy -L 5cm -w beam_radii.txt --plot --saveplot symmcav_gouy_vs_ws.png

This then computes the round-trip Gouy phase (in degrees) of a symmetric cavity of length 5cm using beam radii data stored in a file beam_radii.txt, and plots the results (see below). Note also that you can save the resulting figure using the --saveplot <filename> syntax as seen in the above command.

From the plot above you can also see that cavcalc supports automatically plotting of quantities which can be dual-valued. In this case, the Gouy phase can be one of two values for each beam radius; this is due to the nature of the equations which govern the Fabry-Perot cavity dynamics.

Image / density plots via --mesh

When multiple arguments are given as data-ranges, one can use the --mesh option to construct mesh-grids of these parameters. This allows cavcalc to automatically produce image plots. For example:

cavcalc w -L "1 10 100 km" -gouy "20 120 100 deg" --mesh true --plot

computes the radius of the beam on the mirrors of a symmetric cavity, against both the cavity length and round-trip Gouy phase on a grid. This results in the plot shown below. Note that we simply used --mesh true here, which automatically determines the ordering of the mesh-grid parameters based on the order in which these parameters were given. One could replace the above with, e.g., --mesh "gouy,L" to reverse the order of the mesh-grid; and thereby flip the parameter axes on any automated plots.

A matplotlib compliant colour-map can be specified when making an image plot using the --cmap <name> option. For example, the following command gives the plot shown below.

cavcalc gouy -g1 "-2 2 499" -g2 g1 --mesh true --plot --cmap Spectral_r

Note that here we also used the parameter-referencing feature of cavcalc, introduced in v1.2.0, to set the values of g1 to those of g2.

A note on g-factors

Stability (g) factors are split into four different parameters for implementation purposes and to hopefully make it clearer as to which argument is being used and whether the resulting cavity computations are for a symmetric or asymmetric cavity. These arguments are detailed here:

• -gs : The symmetric, singular stability factor. This represents the individual g-factors of both cavity mirrors. Use this to define a symmetric cavity where the overall cavity g-factor is then simply g = gs * gs.
• -g : The overall cavity stability factor. This is the product of the individual g-factors of the cavity mirrors. Use this to define a symmetric cavity where the individual g-factors of both mirrors are then gs = +/- sqrt(g).
• -g1 : The stability factor of the first cavity mirror. Use this to define an asymmetric cavity along with the argument -g2 such that the overall cavity g-factor is then g = g1 * g2.
• -g2 : The stability factor of the second cavity mirror. Use this to define an asymmetric cavity along with the argument -g1 such that the overall cavity g-factor is then g = g1 * g2.

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Using cavcalc programmatically

As well as providing a CLI, cavcalc has a full API which allows users to interact with this tool via Python. The recommended method for doing this is to use the single-function interface via cavcalc.calculate. This function works similarly to the CLI, where a target can be specified along with a variable number of keyword arguments corresponding to the physical parameters. This function then returns one of two output objects (SingleOutput if a target was given, MultiOutput otherwise); see cavcalc.output for details.

For example, the following script will compute all available targets from the cavity length and mirror radii of curvature provided:

import cavcalc as cc

# Specifying no target means all possible targets are computed
out = cc.calculate(L="4km", Rc1=1934, Rc2=2245)

# Printing the output object results in the same output as
# you would see when running via the CLI
print(out)

producing:

Given:
	Cavity length = 4 km

	Radius of curvature of first mirror = 1934 m
	Radius of curvature of second mirror = 2245 m

	Wavelength of beam = 1064 nm

Computed:
	FSR = 37474.05725 Hz
	Mode separation frequency = 4988.072188176178 Hz

	Position of beam waist (from first mirror) = 1837.2153886417168 m

	Radius of beam at first mirror = 53.421066433049255 mm
	Radius of beam at second mirror = 62.448079883230896 mm
	Radius of beam at waist = 11.950538458990879 mm

	Stability g-factor of cavity = 0.8350925761717987
	Stability g-factor of first mirror = -1.0682523267838677
	Stability g-factor of second mirror = -0.7817371937639199

	Round-trip Gouy phase = 312.0813565565169 deg

	Divergence angle = 0.0016237789746943276 deg

An extra feature of the API is the ability to use the cavcalc.configure function for overriding default behaviour. For example, in the script below we use this in a context-managed scope to temporarily use microns for any beam radius parameters, mm for distances, and GHz for any frequencies:

import cavcalc as cc

# Temporarily override units...
with cc.configure(beamsizes="um", distances="mm", frequencies="GHz"):
    out = cc.calculate(L=8, gouy=121)
    print(out)

# ... previous state (using loaded config options) will
# be restored on exit from the with block above

resulting in:

Given:
    Cavity length = 8 mm

    Round-trip Gouy phase = 121 deg

    Wavelength of beam = 1064 nm

Computed:
    FSR = 18.737028625 GHz
    Mode separation frequency = 6.297723510069445 GHz

    Position of beam waist (from first mirror) = 4.0 mm

    Radius of curvature of both mirrors = 0.01576117284251957 m

    Radius of beam at mirrors = 55.79464044247193 µm
    Radius of beam at waist = 48.19739141432035 µm

    Stability g-factor of cavity = 0.2424809625449729
    Stability g-factor of both mirrors = 0.4924235601034671

    Divergence angle = 0.40260921048107506 deg