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QEDfields

Documentation for QEDfields.

QEDfields.AbstractPulsedPlaneWaveField — Type

Abstract base type for pulsed plane-wave fields.

Pulsed field interface

For every subtype, the following functions need to be implemented.


reference_momentum(::AbstractPulsedPlaneWaveField)
domain(::AbstractPulsedPlaneWaveField)
pulse_length(::AbstractPulsedPlaneWaveField)
envelope(::AbstractPulsedPlaneWaveField,x::Real)
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QEDfields.CosSquarePulse — Type
CosSquarePulse(mom::M,pulse_length::T) where {M<:QEDbase.AbstractFourMomentum,T<:Real}

Concrete implementation of an AbstractPulsedPlaneWaveField for cos-square pulses.

Pulse shape

The pulse envelope of a cos-square pulse is defined as

\[g(\phi) = \cos^2(\frac{\pi\phi}{2\Delta\phi})\]

for $\phi\in (-\Delta\phi,\Delta\phi)$, where $\Delta\phi$ denotes the pulse_length, and zero otherwise.

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QEDfields.GaussianPulse — Type
GaussianPulse(mom::M,pulse_length::T) where {M<:QEDbase.AbstractFourMomentum,T<:Real}

Concrete implementation of an AbstractPulsedPlaneWaveField for Gaussian pulses.

Propagates along the direction given by the space-like components of the reference momentum vector kmu = (omega/speedoflight, kx, ky, kz), and omega = 2pispeedoflight/wavelength.

The time-like coordinate omega/speedofligth of k_mu defines the field's oscillation frequency.

In order to fulfill the vacuum dispersion relation, k_mu*k^mu=0 is required.

Pulse shape

The longitudinal envelope of a Gaussian pulse is defined as

\[g(\phi) = \exp(-\frac{\phi^2}{2\Delta\phi^2})\]

for $\phi\in (-\infty, \infty) and $\Delta\phi`$ denotes the pulse_length.

There is no envelope in the transverse directions.

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QEDfields._envelope — Function
_envelope(::AbstractPulsedPlaneWaveField, phi::Real)

Interface function for AbstractPulsedPlaneWaveField, which returns the value of the phase envelope function (also referred to as pulse envelope) for a given phase variable.

Single point implementation

The interface function can be implemented for just one phase point as input. With that, evaluation on a vector of inputs is generically implemented by broadcasting. However, if there is a better custom implementation for vectors in input values, consider implementing


    _envelope(::AbstractPulsedPlaneWaveField, phi::AbstractVector{T<:Real})
unsafe implementation

This is the unsafe version of the phase envelope function, i.e. this should be implement without input checks like the domain check. In the safe version envelope, a domain check is performed, i.e. it returns the value of _envelope if the passed in phi is in the domain of the field, and zero otherwise.

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QEDfields._unsafe_gaussian_envelope — Method
_unsafe_gaussian_envelope(phi::Real, dphi::Real)

The envelope of the Gaussian background field is defined according to the standard Gaussian distribution with dphi representing the distribution's standard deviation.

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QEDfields.amplitude — Method
amplitude(field::AbstractPulsedPlaneWaveField, pol::AbstractDefinitePolarization, phi)

Returns the value of the amplitude for a given polarization direction and phase variable phi.

Conventions

There are two directions supported:

pol::PolX # -> return envelope(phi)*cos(phi)
pol::PolY # -> return envelope(phi)*sin(phi)
Safe implementation

In this function, a domain check is performed, i.e. if phi is in the domain of the field, the value of the amplitude is returned, and zero otherwise.

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QEDfields.envelope — Method
envelope(pulsed_field::AbstractPulsedPlaneWaveField, phi::Real)

Return the value of the phase envelope function (also referred to as pulse envelope or pulse shape) for given pulsed_field and phase phi. Performs domain check on phi before calling _envelope; returns zero if phi is not in the domain returned by [domain](@ref).

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QEDfields.generic_spectrum — Method
generic_spectrum(field::AbstractPulsedPlaneWaveField, pol::AbstractDefinitePolarization, pnum)

Return the generic spectrum of the given field, for the given polarization direction pol and a given photon number parameter pnum.

Convention

The generic spectrum is defined as the Fourier transform of the respective amplitude function for the given polarization direction:

\[\begin{align*} x-\mathrm{pol} &\to \int_{-\infty}^{\infty} g(\phi) \cos(\phi) \exp(il\phi)\\ y-\mathrm{pol} &\to \int_{-\infty}^{\infty} g(\phi) \sin(\phi) \exp(il\phi) \end{align*}\]

where $g(\phi)$ is the envelope and $l$ the photon number parameter.

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QEDfields.oscillator — Function
oscillator(pol::AbstractPolarizaion, phi::Real)

Return the value of the base oscillator associated with a given polarization pol at a given point phi.

Convention

The current default implementation are

PolX() -> cos(phi)
PolY() -> sin(phi)
AllPol() -> (cos(phi), sin(phi))
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QEDfields.polarization_vector — Method
polarization_vector(pol::AbstractPolarization, mom::QEDbase.AbstractFourMomentum)

Return the polarization vector for a given polarization and four-momentum mom. For a definite polarization, the respective LorentzVector is returned, where as for an indefinite polarization, a tuple of polarization vectors is returned.

Convention

In the current implementation, we use the base_state function for Photon provided by QEDcore.jl.

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QEDfields.pulse_length — Function
pulse_length(::AbstractPulsedPlaneWaveField)

Interface function for AbstractPulsedPlaneWaveField, which returns a dimensionless representative number for the duration of the background field, i.e. a half-width or standard deviation in units of phase periods.

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