cavcalc is a program for computing optical cavity parameters.

## Project description

A command line program and python module for computing parameters (and plots of these parameters) associated with linear, Fabry-Perot optical cavities.

## Installing the release version

To install the latest release version of cavcalc:

## Example usage

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

Some examples follow on how to use cavcalc.

### 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 (g) with:

cavcalc w -L 4000 -g 0.83

This would result in an output of:

Given [SYMMETRIC CAVITY]:
Cavity length = 4000.0 m
Wavelength of beam = 1064 nm
Stability g-factor of cavity = 0.83

Computed:
Radius of beam at mirrors = 5.732098477230927 cm

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 [SYMMETRIC CAVITY]:
Cavity length = 10.0 km
Wavelength of beam = 1064 nm
Round-trip Gouy phase = 145.0 deg

Computed:
Radius of beam at mirrors = 59.59174828941794 mm

### 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 aLIGO parameters,

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

gives the following output:

Given [ASYMMETRIC CAVITY]:
Cavity length = 4.0 km
Wavelength of beam = 1064 nm
Reflectivity of ITM = 0.9859625
Reflectivity of ETM = 0.9999574999999999
Radius of curvature of ITM = 1934.0 m
Radius of curvature of ETM = 2245.0 m

Computed:
FSR = 37474.05725 Hz
Finesse = 443.11699254426594
FWHM = 84.56921734107604 Hz
Pole frequency = 42.28460867053802 Hz
Eigenmode = (-1837.2153886417173+421.68018375440016j)
Radius of beam at ITM = 5.342106643304925 cm
Radius of beam at ETM = 6.244807988323089 cm
Radius of beam at waist = 1.1950538458990878 cm
Position of beam waist (from first cavity mirror) = 1837.2153886417168 m
Round-trip Gouy phase = 312.0813565565169 degrees
Stability g-factor of ITM = -1.0682523267838677
Stability g-factor of ETM = -0.7817371937639199
Stability g-factor of cavity = 0.8350925761717987
Mode separation frequency = 4988.072188176179 Hz

### 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. ~/.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, if that fails then
• next it tries to read from \$XDG_CONFIG_HOME/.cavcalc/ (or %APPDATA%/cavcalc/ on Windows), if that also fails then
• the final read attempt is from the within the source of the package directory itself.

If a successful read occurs at any of these steps then cavcalc will use the configuration defined by that file for the rest of the session - it will not try to read from any of the subsequent locations as well.

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

#### Evaluating parameters over data ranges

Parameters can be computed over ranges of data using:

• the data range syntax:
• -<param_name> "linspace(start, stop, num) [<units>]",
• -<param_name> "range(start, stop, stepsize) [<units>]",
• -<param_name> "start stop num [<units>]" (a shorthand version of the linspace command),
• or data from an input file with -<param_name> file.dat.

An example of using a range could be:

cavcalc w -L "1 10 100 km" -g 0.9 --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 1km to 10km with 100 data points, with a fixed cavity stability factor g = 0.9.

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

cavcalc gouy -L 10km -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 10km 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.

#### Image/density plots

Two arguments can be specified as data ranges (or files of data) in order to produce density plots of the target parameter. For example:

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

computes the radius of the beam on the mirrors of a symmetric cavity, against both the cavity length and round-trip Gouy phase. This results in the plot shown below.

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 w0 -L 10km -g1 "-2 2 200" -g2 "-2 2 200" --plot --cmap nipy_spectral

#### Finding conditions in a data range

Using the --find <condition> argument one can prompt cavcalc to spit out the value(s) at which the given condition is satisfied when doing a data range computation. Taking an example above, we can find the closest value of the Round-trip Gouy phase when the radius of the beam is 11 cm. The result is printed to the terminal and given on the plot (see below). The command to perform such a computation is:

cavcalc gouy -L 10km -w "5.8 15 1000 cm" --plot --find "x=11"

## 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.

## Using cavcalc programmatically

Whilst cavcalc is primarily a command line tool, it can also be used just as easily from within Python in a more "programmatic" way. The recommended method for doing this is to use the single function interface provided via cavcalc.calculate. This function works similarly to the command line interface, where a target can be specified along with a variable number of keyword arguments corresponding to physical parameters. It then returns a cavcalc.Output object which has a number of properties and methods for accessing the results and plotting them against the parameters provided.

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

import cavcalc as cc

# target = "all" is default behaviour
# parameters can be given as single values, an array of values or a tuple
# where the first element is as before and the second element is a valid
# string representing the units of the parameter
out = cc.calculate(L=(4, 'km'), Rc1=1934, Rc2=2245)

# we can get a dictionary of all the computed results...
computed = out.get()

# ... or just a single one if we want
w0 = out['w0']

# out can also be printed displaying results in the same way as the command line tool
print(out)