PhysData.jl

Avogadro constant

Amagat (Loschmidt constant)

Pressure in Pascal at standard conditions (atmospheric pressure)

Atomic unit of electric field

Atomic unit of energy

Atomic unit of electric polarisability

Atomic unit of time

Pressure in Pascal of 1 bar

Speed of light

Ratio of electron charge squared to electron mass (for plasma)

Electron charge

Boltzmann constant

Electron mass

Atomic mass unit

Room temperature in Kelvin (ca 20 deg C)

Reduced Planck's constant

Permittivity of vacuum

Permeability of vacuum

Cnl_ADK(material)

Return the value of Cₙₗ from the ADK paper for the material. For materialS other than noble gases, this returns missing.

Reference: Ammosov, M. V., Delone, N. B. & Krainov, V. P. Tunnel Ionization Of Complex Atoms And Atomic Ions In Electromagnetic Field. Soviet Physics JETP 64, 1191–1194 (1986).

Lookup tables for complex refractive indices of metals.

density(material::Symbol, P=1.0, T=roomtemp)

For a gas material, return the number density [m^-3] at pressure P [bar] and temperature T [K]. For a glass, this simply returns 1.0.

densityspline(gas; Pmax, Pmin=0, N=2^10, T=roomtemp)

Create a CSpline interpolant for the density of the gas between pressures Pmin and Pmax at temperature T. The spline is created using N samples.

dispersion(order, material, λ, P=1.0, T=roomtemp; lookup=nothing)

Calculate the dispersion of order order of a given material at a wavelength λ.

For gases the pressure P (default:atmosphere) and the temperature T (default: room temp) can also be specified. lookup::Bool determines whether a lookup table or a Sellmeier expansion is used for the refractive index (default is material dependent).

Examples

julia> dispersion(2, :BK7, 400e-9) * 1e30 * 1e-3 # convert to fs^2/mm
122.03632107303108

dispersion_func(order, material, P=1, T=roomtemp; lookup=nothing)

Get a function to calculate dispersion. Arguments are the same as for dispersion.

dispersion_func(order, n)

Get a function that calculates dispersion of order order for a refractive index given by n(λ).

fresnel(n2, θi; n1=1.0)

Calcualte reflection coefficients from Fresnel's equations.

ionisation_potential(material; unit=:SI)

Return the first ionisation potential of the material in a specific unit (default: SI). Possible units are :SI, :atomic and :eV.

lookup_glass(material::Symbol)

Create a CSpline interpolant for look-up-table values of the refractive index.

lookup_metal(material::Symbol)

Create a CSpline interpolant for look-up-table values of the refractive index.

lookup_mirror(type)

Create a CSpline interpolant for the complex-valued reflectivity of a mirror of type.

polarisability_difference(material; unit=:SI)

Return the difference in polarisability between the ground state and the ion for the material. unit can be :SI or :atomic

Reference: Wang, K. et al. Static dipole polarizabilities of atoms and ions from Z=1 to 20 calculated within a single theoretical scheme. Eur. Phys. J. D 75, 46 (2021).

pressure(gas, density, T=roomtemp)

Calculate the pressure in bar of the gas at number density density and temperature T.

process_mirror_data(λR, R, λGDD, GDD, λ0, λmin, λmax; fitorder=5, windowwidth=20e-9)

Process reflectivity and group-delay dispersion data for a mirror and create a transfer function for a frequency-domain electric field representing the mirror.

Arguments:

• λR: wavelength samples for reflectivity in SI units (m)
• R: mirror reflectivity (between 0 and 1)
• λGDD: wavelength samples for GDD in SI units (m)
• GDD: GDD in SI units (s²)
• λ0: central wavelength (used to remove any overall group delay)
• λmin, λmax: bounds of the wavelength region to apply the transfer function over

Keyword arguments

• fitorder: order of polynomial fit to use in removing overall group delay (default: 5)
• windowwidth: wavelength width of the smoothing region outside (λmin, λmax) for the window in SI units (default: 20e-9, i.e. 20 nm)

quantum_numbers(material)

Return the quantum numbers of the material for use in the PPT ionisation rate.

raman_parameters(material)

Get the Raman parameters for material.

Fields

Fields in the returned named tuple must include:

• kind::Symbol: one of :molecular or :intermediate or :normedsdo

If kind == :molecular then the following must also be specified:

• rotation::Symbol: only :nonrigid or :none supported at present.
• vibration::Symbol: only :sdo or :none supported at present.

If rotation == :nonrigid then the following must also be specified:

• B::Real: the rotational constant [1/m]
• Δα::Real: molecular polarizability anisotropy [m^3]
• qJodd::Integer: nuclear spin parameter for odd J
• qJeven::Integer: nuclear spin parameter for even J
• D::Real=0.0: centrifugal constant [1/m]

Along with one of:

• τ2r::Real: coherence time [s]
• Bρr::Real : density dependent broadening coefficient [Hz/amagat]

If both τ2r and Bρr are specified, then Bρr takes precedence. If Bρr is specified then we also need:

• Aρr::Real : self diffusion coefficient [Hz amagat]

If vibration == :sdo then the following must also be specified:

• Ωv::Real: vibrational frequency [rad/s]
• dαdQ::Real: isotropic averaged polarizability derivative [m^2]
• μ::Real: reduced molecular mass [kg]

Along with one of:

• τ2v::Real: coherence time [s]
• Bρv::Real : density dependent broadening coefficient [Hz/amagat]

If both τ2v and Bρv are specified, then Bρv takes precedence. If Bρv is specified then we also need:

• Aρv::Real : self diffusion coefficient [Hz amagat]

And can also add (if necessary) a constant offset:

• Cv::Real : constant linewidth offset [Hz]

If kind == :intermediate then the following must be specified

• ωi::Vector{Real} [rad/s], central angular freqencies
• Ai::Vector{Real}, amplitudes
• Γi::Vector{Real} [rad/s], Gaussian widths
• γi::Vector{Real} [rad/s], Lorentzian widths

References

[1] Phys. Rev. A, 94, 023816 (2016) [2] Phys. Rev. A, 85, 043820 (2012) [3] Phys. Rev. A, 92, 063828 (2015) [4] Journal of Raman Spectroscopy 2, 133 (1974) [5] J. Phys. Chem., 91, 41 (1987) [6] Applied Spectroscopy 23, 211 (1969) [7] Phys. Rev. A, 34, 3, 1944 (1986) [8] Can. J. Phys., 44, 4, 797 (1966) [9] G. V. MIKHAtLOV, SOVIET PHYSICS JETP, vol. 36, no. 9, (1959). [10] Phys. Rev. A, 33, 5, 3113 (1986) [11] IEEE Journal of Quantum Electronics 1986, 22 (2), 332–336. https://doi.org/10.1109/JQE.1986.1072945. [12] Phys. Rev. Lett. 1998, 81 (6), 1215–1218. https://doi.org/10.1103/PhysRevLett.81.1215. [13] Optics Communications 1987, 64 (4), 393–397. https://doi.org/10.1016/0030-4018(87)90258-6. [14] Science Advances 2020, 6 (34), eabb5375. https://doi.org/10.1126/sciadv.abb5375. [15] Long, The Raman Effect; John Wiley & Sons, Ltd, 2002; [16] IEEE Journal of Quantum Electronics, vol. 24, no. 10, pp. 2076–2080, Oct. 1988, doi: 10.1109/3.8545. [17] Journal of Raman Spectroscopy, vol. 22, no. 11, pp. 607–611, 1991, doi: 10.1002/jrs.1250221103. [18] Hollenbeck and Cantrell, JOSA B 19, 2886-2892 (2002). https://doi.org/10.1364/JOSAB.19.002886

ref_index(material, λ, P=1.0, T=roomtemp; lookup=nothing)

Get refractive index for any material at wavelength given in SI units.

ref_index_fun(material::Symbol, P=1.0, T=roomtemp; lookup=nothing)

Get function which returns refractive index.

ref_index_fun(gases, T=roomtemp)

Get function which returns ref index for mixture as function of wavelength and densities.

ref_index_fun(gases, P, T=roomtemp; lookup=nothing)

Get function which returns refractive index for gas mixture. gases is a Tuple of gas identifiers (Symbols) and P is a Tuple of equal length containing pressures.

sellmeier_crystal(material, axis)

Sellmeier for crystals. Returns function of wavelength in μm which in turn returns the refractive index directly. Possible values for axis depend on the type of crystal.

sellmeier_gas(material::Symbol)

Return function for linear polarisability γ, i.e. susceptibility of a single particle, calculated from Sellmeier expansions.

sellmeier_glass(material::Symbol)

Sellmeier for glasses. Returns function of wavelength in μm which in turn returns the refractive index directly

wlfreq(ωλ)

Change from ω (angular frequency) to λ (wavelength) and vice versa

ΔλΔω(Δλ, λ)

Convert Δλ (wavelength bandwidth) at λ (central wavelength) to Δω (angular frequency bandwidth)

γ3_gas(material::Symbol; source=nothing)

Calculate single-molecule third-order hyperpolarisability of a gas at given wavelength(s) and at room temperature. If source == :Bishop: Uses reference values to calculate γ If source == :Lehmeier (default): Uses scaling factors to calculate χ3 at 1 bar and scales by density to get to a single molecule i.e. the hyperpolarisability

References: [1] Journal of Chemical Physics, AIP, 91, 3549-3551 (1989) [2] Chemical Reviews, 94, 3-29 (1994) [3] Optics Communications, 56(1), 67–72 (1985) [4] Phys. Rev. A, vol. 42, 2578 (1990) [5] Optics Letters Vol. 40, No. 24 (2015)) [6] Phys. Rev. A 2012, 85 (4), 043820. https://doi.org/10.1103/PhysRevA.85.043820. [7] Phys. Rev. A, 32, no. 6, 3454, (1985), doi: 10.1103/PhysRevA.32.3454.

γ_Börzsönyi(B1, C1, B2, C2)

Sellmeier expansion for linear susceptibility from Applied Optics 47, 27, 4856 (2008) at room temperature and atmospheric pressure

γ_JCT(B1, C1, B2, C2, B3, C3)

Adapted Sellmeier expansion for helium made to fit high frequency data Phys. Rev. A 92, 033821 (2015)

γ_Peck(B1, C1, B2, C2, dens)

Sellmeier expansion for linear susceptibility from J. Opt. Soc. Am. 67, 1550 (1977)

γ_QuanfuHe(A, B, C, dens)

Sellmeier expansion for CH4, SF6 and N2O from Atmospheric Chemistry and Physics 2021, 21 (19), 14927–14940. https://doi.org/10.5194/acp-21-14927-2021.

γ_Zhang(A, B, C, dens)

Sellmeier expansion for Oxygen from Applied Optics 50, 35, 6484 (2011)

χ1(gas::Symbol, λ, P=1.0, T=roomtemp)

Calculate χ1 at wavelength λ in SI units, pressure P in bar and temperature T in Kelvin. Gases only.

χ1_fun(gas::Symbol)

Get function to return χ1 (linear susceptibility) for gases as a function of wavelength in SI units, pressure in bar, and temperature in Kelvin.