cavcalc is a program for computing optical cavity parameters.
A command line program and python module for computing parameters (and plots of these 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
Installing the release version
To install the latest release version of
pip install --upgrade cavcalc
For details on available arguments run
cavcalc -h on the command line.
Some examples follow on how to use
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
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
%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
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.
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
--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
-g2such 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
-g1such that the overall cavity g-factor is then
g = g1 * g2.
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
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)
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