Field properties
ElectricFields.wavelength — Functionwavelength(f)Return the carrier wavelength $\lambda$ of f.
ElectricFields.period — Functionperiod(f)Return the carrier period time $T$ of f.
ElectricFields.frequency — Functionfrequency(f)Return the carrier frequency $f$ of the field f.
ElectricFields.max_frequency — Functionmax_frequency(f)Return the maximum carrier frequency $f$ in case of a composite field f.
ElectricFields.wavenumber — Functionwavenumber(f)Return the carrier wavenumber $\nu$ of the field f.
ElectricFields.photon_energy — Functionphoton_energy(f)Return the carrier photon energy $\hbar\omega$ of the field f.
ElectricFields.duration — Functionduration(f)Return the pulse duration $\tau$ of the field f.
ElectricFields.time_bandwidth_product — Functiontime_bandwidth_product(f)Return the time–bandwidth product of the field f.
ElectricFields.continuity — Functioncontinuity(f)Return the pulse continuity, i.e. differentiability, of the field f.
ElectricFields.fluence — Functionfluence(f)Compute the fluence of the field f, i.e.
\[\frac{1}{\hbar\omega} \int\diff{t} I(t),\]
where $I(t)$ is the intensity envelope of the pulse.
ElectricFields.intensity — Functionintensity(f)Return the peak intensity of the field f.
ElectricFields.amplitude — Functionamplitude(f)Return the peak amplitude of the field f.
ElectricFields.carrier — Functioncarrier(f)Return the carrier of the field f.
ElectricFields.envelope — Functionenvelope(f)Return the envelope of the field f.
ElectricFields.phase — Functionphase(c)Return the phase of the carrier c.
ElectricFields.dimensions — Functiondimensions(f)Return the number of dimensions of the field f. See also polarization.
Examples
julia> @field(F) do
I₀ = 2.0
T = 2.0
σ = 3.0
Tmax = 3.0
end
Linearly polarized field with
- I₀ = 2.0000e+00 au = 7.0188904e16 W cm^-2 =>
- E₀ = 1.4142e+00 au = 727.2178 GV m^-1
- A₀ = 0.4502 au
– a Fixed carrier @ λ = 14.5033 nm (T = 48.3777 as, ω = 3.1416 Ha = 85.4871 eV, f = 20.6707 PHz)
– and a Gaussian envelope of duration 170.8811 as (intensity FWHM; ±2.00σ)
– and a bandwidth of 0.3925 Ha = 10.6797 eV ⟺ 2.5823 PHz ⟺ 34.2390 Bohr = 1.8119 nm
– Uₚ = 0.0507 Ha = 1.3785 eV => α = 0.1433 Bohr = 7.5826 pm
julia> dimensions(F)
1
julia> @field(F) do
I₀ = 2.0
T = 2.0
σ = 3.0
Tmax = 3.0
ξ = 1.0
end
Transversely polarized field with
- I₀ = 2.0000e+00 au = 7.0188904e16 W cm^-2 =>
- E₀ = 1.4142e+00 au = 727.2178 GV m^-1
- A₀ = 0.4502 au
– a Elliptical carrier with ξ = 1.00 (RCP) @ λ = 14.5033 nm (T = 48.3777 as, ω = 3.1416 Ha = 85.4871 eV, f = 20.6707 PHz)
– and a Gaussian envelope of duration 170.8811 as (intensity FWHM; ±2.00σ)
– and a bandwidth of 0.3925 Ha = 10.6797 eV ⟺ 2.5823 PHz ⟺ 34.2390 Bohr = 1.8119 nm
– Uₚ = 0.0507 Ha = 1.3785 eV => α = 0.1433 Bohr = 7.5826 pm
julia> dimensions(F)
3ElectricFields.polarization — Functionpolarization(f)Return the polarization kind of the field f. See also dimensions.
Examples
julia> @field(F) do
I₀ = 2.0
T = 2.0
σ = 3.0
Tmax = 3.0
end
Linearly polarized field with
- I₀ = 2.0000e+00 au = 7.0188904e16 W cm^-2 =>
- E₀ = 1.4142e+00 au = 727.2178 GV m^-1
- A₀ = 0.4502 au
– a Fixed carrier @ λ = 14.5033 nm (T = 48.3777 as, ω = 3.1416 Ha = 85.4871 eV, f = 20.6707 PHz)
– and a Gaussian envelope of duration 170.8811 as (intensity FWHM; ±2.00σ)
– and a bandwidth of 0.3925 Ha = 10.6797 eV ⟺ 2.5823 PHz ⟺ 34.2390 Bohr = 1.8119 nm
– Uₚ = 0.0507 Ha = 1.3785 eV => α = 0.1433 Bohr = 7.5826 pm
julia> polarization(F)
LinearPolarization()
julia> @field(F) do
I₀ = 2.0
T = 2.0
σ = 3.0
Tmax = 3.0
ξ = 1.0
end
Transversely polarized field with
- I₀ = 2.0000e+00 au = 7.0188904e16 W cm^-2 =>
- E₀ = 1.4142e+00 au = 727.2178 GV m^-1
- A₀ = 0.4502 au
– a Elliptical carrier with ξ = 1.00 (RCP) @ λ = 14.5033 nm (T = 48.3777 as, ω = 3.1416 Ha = 85.4871 eV, f = 20.6707 PHz)
– and a Gaussian envelope of duration 170.8811 as (intensity FWHM; ±2.00σ)
– and a bandwidth of 0.3925 Ha = 10.6797 eV ⟺ 2.5823 PHz ⟺ 34.2390 Bohr = 1.8119 nm
– Uₚ = 0.0507 Ha = 1.3785 eV => α = 0.1433 Bohr = 7.5826 pm
julia> polarization(F)
ArbitraryPolarization()Strong-field properties
ElectricFields.ponderomotive_potential — Functionponderomotive_potential(f)Return the ponderomotive potential $U_p$, which is the cycle-average quiver energy of a free electron in an electromagnetic field f. It is given by
\[U_p = \frac{e^2E_0^2}{4m\omega^2}=\frac{2e^2}{c\varepsilon_0m}\times\frac{I}{4\omega^2},\]
or, in atomic units,
\[U_p = \frac{I}{4\omega^2}.\]
ElectricFields.keldysh — Functionkeldysh(f, Iₚ)The Keldysh parameter relates the strength of a dynamic electric field to that of the binding potential of an atom. It is given by
\[\gamma = \sqrt{\frac{I_p}{2U_p}},\]
where $I_p$ is the ionization potential of the atom and $U_p$ is the ponderomotive potential of the dynamic field.
ElectricFields.free_oscillation_amplitude — Functionfree_oscillation_amplitude(F)Compute the free oscillation amplitude of an electric field F, i.e. the mean excursion length during one cycle of the field, defined as
\[\alpha \defd \frac{F}{\omega^2}\]
where F is the peak amplitude, i.e. this is defined for one cycle of a monochrome field.