Spectral fields and apodizing windows

Project.toml

@@ -1,26 +1,27 @@
 name = "ElectricFields"
 uuid = "2f84ce32-9bb1-11e8-0d9f-3dce90a4beca"
 authors = ["Stefanos Carlström <[email protected]>"]
-version = "0.2.2"
+version = "0.2.3"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"
 FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
-Formatting = "59287772-0a20-5a39-b81b-1366585eb4c0"
+Format = "1fa38f19-a742-5d3f-a2b9-30dd87b9d5f8"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Optim = "429524aa-4258-5aef-a3af-852621145aeb"
 Parameters = "d96e819e-fc66-5662-9728-84c9c7592b0a"
 Roots = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
+SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 UnitfulAtomic = "a7773ee8-282e-5fa2-be4e-bd808c38a91a"
 
 [compat]
 AbstractFFTs = "1.3"
 FFTW = "1.3"
-Formatting = "0.4"
+Format = "1.3"
 ForwardDiff = "0.10"
 IntervalSets = "0.7"
 Optim = "1.3"

docs/Project.toml

@@ -8,7 +8,7 @@ UnitfulAtomic = "a7773ee8-282e-5fa2-be4e-bd808c38a91a"
 
 [compat]
 CondaPkg = "0.2"
-Documenter = "0.27"
+Documenter = "1"
 FFTW = "1.3.0"
 PythonPlot = "1"
 Unitful = "1.7"

docs/make.jl

@@ -30,6 +30,7 @@ makedocs(;
     ),
     pages=[
         "Home" => "index.md",
+        "Interface" => "interface.md",
         "Field types" => "field_types.md",
         "Envelopes" => "envelopes.md",
         "Carriers" => "carriers.md",

docs/plots.jl

@@ -165,6 +165,78 @@ function index_spectrum_example()
     end
 end
 
+function apodized_field()
+    @field(F) do
+        ω = 1.0
+        I₀ = 1.0
+        ramp = 0.0
+        flat = 3.0
+        env = :tophat
+    end
+
+    t = timeaxis(F)
+    tplot = 24.2e-3t
+
+    tmin = 1.0
+    tmax = 14.0
+
+    Fw = ApodizedField(F, tmin, tmax, ElectricFields.Kaiser(3))
+
+    Fv = field_amplitude(F, t)
+    Av = vector_potential(F, t)
+
+    Fwv = field_amplitude(Fw, t)
+    Awv = vector_potential(Fw, t)
+
+    w = ElectricFields.window_value.(Fw.window, 1.0, 14.0, t)
+
+   savedfigure("apodized_field", figsize=(7,8)) do
+        csubplot(211, nox=true) do
+            plot(tplot, Fv)
+            plot(tplot, Fwv)
+            ylabel(L"F(t)")
+        end
+        csubplot(212) do
+            plot(tplot, Av, label="Original field")
+            plot(tplot, Awv, label="Windowed field")
+            plot(tplot, w, "--", label="Window")
+            legend(loc=1)
+            xlabel(L"$t$ [fs]")
+            ylabel(L"A(t)")
+        end
+    end
+end
+
+function apodizing_windows()
+    x = range(-0.55, stop=0.55, length=1001)
+
+    savedfigure("windows", figsize=(7,8)) do
+        ws = (ElectricFields.Hann(), ElectricFields.Hamming(),
+              ElectricFields.Blackman(),
+              ElectricFields.BlackmanExact(),
+              ElectricFields.Nuttall(),
+              ElectricFields.BlackmanNuttall(),
+              ElectricFields.BlackmanHarris(),
+              ElectricFields.Kaiser(3), ElectricFields.Kaiser(2),
+              ElectricFields.Rect())
+
+        csubplot(211, nox=true) do
+            for w in ws
+                plot(x, ElectricFields.window_value.(w, x), label=string(w))
+            end
+            ylabel(L"w(x)")
+        end
+        csubplot(212) do
+            for w in ws
+                plot(x, ElectricFields.window_derivative.(w, x), label=string(w))
+            end
+            legend(loc=1, ncol=2)
+            xlabel(L"$t$ [fs]")
+            ylabel(L"w'(x)")
+        end
+    end
+end
+
 macro echo(expr)
     println(expr)
     :(@time $expr)
@@ -176,3 +248,5 @@ mkpath(fig_dir)
 @echo index_example()
 @echo index_polarized_example()
 @echo index_spectrum_example()
+@echo apodized_field()
+@echo apodizing_windows()

docs/src/field_types.md

@@ -4,6 +4,7 @@
 ```@docs
 ElectricFields.LinearField
 ElectricFields.TransverseField
+ElectricFields.LinearTransverseField
 ElectricFields.ConstantField
 ElectricFields.Ramp
 ```
@@ -16,4 +17,87 @@ ElectricFields.NegatedField
 ElectricFields.DelayedField
 ElectricFields.PaddedField
 ElectricFields.WindowedField
+ElectricFields.phase_shift
+```
+
+## Apodizing Windows
+
+This is a generalization of [`ElectricFields.WindowedField`](@ref),
+where the field is multiplied by an [_apodizing
+window_](https://en.wikipedia.org/wiki/Window_function), that tapers
+of towards the boundaries, and typically (but not always) is zero at
+the boundaries. The window functions are non-zero on the interval
+``[-1/2,1/2]``, so if other intervals are desired, they will need to
+be rescaled. This happens automatically.
+
+Since the apodizing window is multiplied with the vector potential,
+the field amplitude gains an extra term due to the chain rule:
+```math
+\vec{A}_w(t) =
+W(t)\vec{A}(t)
+\implies
+\vec{F}_w(t) =
+-\partial_t
+\vec{A}_w(t) =
+W(t)\vec{F}(t) -
+W'(t)\vec{A}(t).
+```
+
+### Usage
+
+```julia-repl
+julia> @field(F) do
+           ω = 1.0
+           I₀ = 1.0
+           ramp = 0.0
+           flat = 3.0
+           env = :tophat
+       end
+Linearly polarized field with
+  - I₀ = 1.0000e+00 au = 3.5094452e16 W cm⁻² =>
+    - E₀ = 1.0000e+00 au = 514.2207 GV m⁻¹
+    - A₀ = 1.0000 au
+  – a Fixed carrier @ λ = 45.5634 nm (T = 151.9830 as, ω = 1.0000 Ha = 27.2114 eV, f = 6.5797 PHz)
+  – and a /0‾3‾0\ cycles trapezoidal envelope
+  – and a bandwidth of Inf Ha = Inf eV ⟺ Inf Hz ⟺ Inf Bohr = Inf m
+  – Uₚ = 0.2500 Ha = 6.8028 eV => α = 1.0000 Bohr = 52.9177 pm
+
+julia> Fw = ApodizedField(F, 1.0, 14.0, ElectricFields.Kaiser(3))
+Kaiser(α = 3) window from 1.0000 jiffies = 24.1888 as to 14.0000 jiffies = 338.6438 as of
+Linearly polarized field with
+  - I₀ = 1.0000e+00 au = 3.5094452e16 W cm⁻² =>
+    - E₀ = 1.0000e+00 au = 514.2207 GV m⁻¹
+    - A₀ = 1.0000 au
+  – a Fixed carrier @ λ = 45.5634 nm (T = 151.9830 as, ω = 1.0000 Ha = 27.2114 eV, f = 6.5797 PHz)
+  – and a /0‾3‾0\ cycles trapezoidal envelope
+  – and a bandwidth of Inf Ha = Inf eV ⟺ Inf Hz ⟺ Inf Bohr = Inf m
+  – Uₚ = 0.2500 Ha = 6.8028 eV => α = 1.0000 Bohr = 52.9177 pm
+```
+
+![Apodized field](figures/apodized_field.svg)
+
+```@docs
+ApodizedField
+span(::ApodizedField)
+```
+
+### Windows
+
+See the [Wikipedia page on apodizing
+windows](https://en.wikipedia.org/wiki/Window_function) for the formal
+definitions of the windows and their frequency responses.
+
+![Apodizing windows](figures/windows.svg)
+
+```@docs
+ElectricFields.AbstractWindow
+ElectricFields.Rect
+ElectricFields.Hann
+ElectricFields.Hamming
+ElectricFields.Blackman
+ElectricFields.BlackmanExact
+ElectricFields.Nuttall
+ElectricFields.BlackmanNuttall
+ElectricFields.BlackmanHarris
+ElectricFields.Kaiser
 ```

docs/src/index.md

@@ -86,13 +86,13 @@ Linearly polarized field with
   – Uₚ = 0.2196 Ha = 5.9759 eV => α = 16.4562 Bohr = 870.8242 pm
 
 julia> vector_potential(IR, 4.0)
-0.21160647961322301
+0.21160647961322293
 
 julia> field_amplitude(IR, 4.0), field_envelope(IR, 4.0)
-(-0.05194703530281701, 0.05336224984361336)
+(-0.05194703530281699, 0.05336224984361333)
 
 julia> instantaneous_intensity(IR, 4.0), intensity(IR, 4.0)
-(0.0026984944767521166, 0.002847529708372214)
+(0.0026984944767521144, 0.0028475297083722113)
 
 julia> span(IR)
 -661.9198939608042 .. 661.9198939608042

docs/src/interface.md

@@ -0,0 +1,33 @@
+# Interface
+
+## Creation
+
+```@docs
+ElectricFields.@field
+```
+
+## Time-dependent quantities
+
+```@docs
+ElectricFields.field_amplitude
+ElectricFields.vector_potential
+ElectricFields.instantaneous_intensity
+ElectricFields.intensity(::LinearPolarization, f, t::Number; kwargs...)
+ElectricFields.field_envelope
+ElectricFields.span
+ElectricFields.timeaxis
+ElectricFields.steps
+```
+
+## Spectra
+
+```@docs
+ElectricFields.spectrum
+ElectricFields.field_amplitude_spectrum
+ElectricFields.vector_potential_spectrum
+ElectricFields.AbstractFFTs.fft
+ElectricFields.nfft
+ElectricFields.fft_vector_potential
+ElectricFields.nfft_vector_potential
+ElectricFields.fftω
+```

docs/src/properties.md

@@ -8,6 +8,7 @@ max_frequency
 wavenumber
 photon_energy
 duration
+time_bandwidth_product
 continuity
 fluence
 intensity

docs/src/reference.md

@@ -1,8 +1,17 @@
 # Reference
 
-```@index
+## Internals
+
+```@docs
+ElectricFields.calc_params!
+ElectricFields.@namespace!
+ElectricFields.gaussian_common!
+ElectricFields.test_field_parameters
+ElectricFields.convolution
+ElectricFields.DiracComb
 ```
 
-```@autodocs
-Modules = [ElectricFields]
+## Index
+
+```@index
 ```

src/ElectricFields.jl

@@ -11,13 +11,14 @@ using FFTW
 using ForwardDiff
 using Optim
 using Roots
+using SpecialFunctions
 
 using IntervalSets
 
 using Parameters
 
 import Base: show
-using Formatting
+using Format
 
 abstract type AbstractField end