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https://github.com/jagot/sellmeier.jl

Last synced: 6 days ago
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Host: GitHub
URL: https://github.com/jagot/sellmeier.jl
Owner: jagot
License: other
Created: 2016-03-31T14:51:10.000Z (almost 9 years ago)
Default Branch: master
Last Pushed: 2018-10-08T19:05:45.000Z (over 6 years ago)
Last Synced: 2024-11-15T18:34:54.898Z (2 months ago)
Language: Julia
Size: 74.2 KB
Stars: 0
Watchers: 2
Forks: 1
Open Issues: 0
Metadata Files:
- Readme: README.org
- License: LICENSE.md

Awesome Lists containing this project

README

        #+TITLE: Sellmeier.jl

#+AUTHOR: Stefanos Carlström

#+EMAIL: [email protected]

[[https://travis-ci.org/jagot/Sellmeier.jl][https://travis-ci.org/jagot/Sellmeier.jl.svg?branch=master]]

[[https://coveralls.io/github/jagot/Sellmeier.jl?branch=master][https://coveralls.io/repos/github/jagot/Sellmeier.jl/badge.svg?branch=master]]

[[http://codecov.io/gh/jagot/Sellmeier.jl][http://codecov.io/gh/jagot/Sellmeier.jl/branch/master/graph/badge.svg]]

#+PROPERTY: header-args:julia :session *julia-README*

Small library for the [[https://en.wikipedia.org/wiki/Sellmeier_equation][Sellmeier equation]], used to model the refractive

index of transparent media, as a function of wavelength.

This is a [[https://github.com/jagot/LiterateOrg.jl][LiterateOrg.jl]] project. The documentation is found [[file:src/Sellmeier.org][within the code]].

* Usage

  It is very simple to calculate the refractive index of e.g. BK7

  glass at a specific wavelength, or a specific frequency:

  #+BEGIN_SRC julia :exports both :results verbatim

    using Sellmeier

    using Unitful

    BK7(800u"nm"), BK7(2u"THz")

  #+END_SRC

  #+RESULTS:

  : (1.5107762314198745, 1.812885348989345)

  It is equally easy to evaluate the refractive index over a range of

  wavelengths:

  #+BEGIN_SRC julia :exports code

    λ = linspace(200u"nm",6.0u"μm", 1000)

    n = [BK7.(λ) SiO2.(λ)]

  #+END_SRC

  #+RESULTS:

  #+BEGIN_SRC julia :exports none

    using PyPlot

    PyPlot.svg(true)

    function savefig_f(filename)

        mkpath(dirname(filename))

        savefig(filename, transparent=true)

        filename

    end

    no_units(x::Quantity, u) = x/u |> NoUnits

  #+END_SRC

  #+RESULTS:

  : no_units (generic function with 1 method)

  #+BEGIN_SRC julia :exports results :results file

    figure("BK7 & SiO2")

    clf()

    plot(no_units.(λ, u"nm"), n)

    xlabel(L"$\lambda$ [nm]")

    ylabel(L"$n(\lambda)$")

    legend(["BK7", L"SiO$_2$"])

    title("Refractive index")

    tight_layout()

    savefig_f("figures/refractive-index.svg")

  #+END_SRC

  #+RESULTS:

  [[file:figures/refractive-index.svg]]

** Dispersion through glass

   #+BEGIN_SRC julia :exports code

     λ = 500.0u"nm"

     f₀ = u"c"/λ |> u"THz"

     ω₀ = 2π*f₀

     τ = 6.2u"fs" # Pulse duration, intensity FWHM

     γ = τ^2/8log(2)

     f = linspace(0,30,2000)*f₀

     ω = 2π*f

     Ê = exp.(-(ω-ω₀).^2*γ)

     # We propagate the pulse through 200 μm of BK7. We also remove

     # dispersion at the central frequency, to keep the pulse centred in

     # the time window.

     Ê′ = Ê.*dispersion(BK7, 200u"μm", f, f₀)

   #+END_SRC

   #+RESULTS:

   #+BEGIN_SRC julia :exports results :results file

     time_domain(spectrum) = real(fftshift(ifft(spectrum)*√(length(spectrum))))

     E = time_domain(Ê)

     E′ = time_domain(Ê′)

     using DSP

     t = fftshift(fftfreq(length(f), ustrip(1.0/(f[2]-f[1]) .|> u"s")))*u"s"

     t_ax = no_units.(t, u"fs")

     f_ax = no_units.(ω, (2π*u"THz"))

     sel = f_ax .< 2500

     figure("pulse")

     clf()

     subplot(311)

     plot(t_ax, E)

     plot(t_ax, E′)

     xlabel(L"$t$ [fs]")

     ylabel(L"$E(t)$ [arb.u.]")

     gca()[:xaxis][:tick_top]()

     gca()[:xaxis][:set_label_position]("top")

     margins(0,0.1)

     subplot(312)

     plot(f_ax[sel], abs2.(Ê[sel]))

     plot(f_ax[sel], abs2.(Ê′[sel]))

     ylabel(L"$|\hat{E}(f)|^2$ [arb.u.]")

     margins(0,0.1)

     ax = gca()[:twinx]()

     ax[:plot](f_ax[sel], BK7.(f)[sel], "k--")

     ylabel(L"n(f)")

     margins(0,0.1)

     gca()[:set_xticklabels]([])

     subplot(313)

     plot(f_ax[sel], unwrap(angle.(Ê[sel])))

     plot(f_ax[sel], unwrap(angle.(Ê′[sel])))

     xlabel(L"$f$ [THz]")

     ylabel(L"$\arg\{\hat{E}(f)\}$ [rad]")

     margins(0,0.1)

     tight_layout()

     savefig_f("figures/dispersed-pulse.svg")

   #+END_SRC

   #+RESULTS:

   [[file:figures/dispersed-pulse.svg]]