Line Shapes

SpectraUtils.jl provides several callable types that model common spectral profiles. Each line shape can be constructed with either numeric values or functions that resolve parameters at evaluation time.

Analytic profiles

• LineShape
• Lorentzian
• Gaussian
• Voigt
• VoigtApprx
• DopplerFree
• Smith
• lorentzian
• gaussian
• voigt

Example

using SpectraUtils

shape = Voigt(0.01, 0.002)
shape(0.0)              # peak amplitude at line centre
shape(0.03)

Doppler-free composites

DopplerFree combines a broad envelope with a narrow saturation dip to model classic Doppler-free spectroscopy traces. Any callable line shape can serve as the envelope or dip, allowing flexible compositions such as a Lorentzian envelope with a Gaussian dip. For example:

using SpectraUtils

envelop = Lorentzian(0.5)
dip = Gaussian(0.05)

shape = DopplerFree(0.2, envelop, dip)
shape(0.0)         # central dip on top of the envelope
shape(0.1)

Smith line profile

The Smith profile models cross-relaxation broadening following the formulation of Smith et al. (Phys. Rev. Lett. 26, 740). It blends a Lorentzian envelope with a Doppler-broadened Gaussian core while enforcing unit normalization so that the total integrated area is one. The cross_relaxation parameter controls the relative weight of the Gaussian component, with cross_relaxation = 0 yielding the pure Lorentzian-derived term and cross_relaxation = 1 reducing to the Gaussian profile gaussian(x, sigma).