CollinearPhaseMatch <: PhaseMatch

Encapsulates a full collinear phase-matching solution, including refractive data, geometric parameters, nonlinear efficiency, and bandwidths (fields refr_data, pm_data, eff_data, and bw_data, respectively). In addition, field access is forwarded to the internal fields of both refr_data and pm_data for convenience.

PMBandwidthData

Represents the phase-matching bandwidths of a collinear configuration, defined as the range of parameters over which the phase mismatch Δk remains within ±π / L for a given interaction length L.

The stored values are ΔX · L quantities (units of Hz·m, K·m, rad·m), which characterize the tolerance of the phase-matching condition to changes in each parameter X:

• omega_L_bw: Tuple of angular frequency bandwidths (Δω · L) for the three waves (r₁, r₂, b). Each entry is computed by holding that wave's frequency fixed while adjusting the other two to maintain the phase-matching condition (1/λr₁ + 1/λr₂ = 1/λ_b).
• temp_L_bw: Temperature bandwidth (ΔT · L) computed by evaluating how Δk varies with small temperature changes, with all wavelengths and geometry fixed.
• theta_L_bw: Angular bandwidth with respect to polar angle θ (Δθ · L), evaluated at fixed temperature and wavelengths.
• phi_L_bw: Angular bandwidth with respect to azimuthal angle ϕ (Δϕ · L), also at fixed conditions.

These values describe how sensitive the phase-matching is to deviations in each parameter. For example, a small theta_L_bw means tight angular alignment is needed, while a large temp_L_bw suggests thermally robust operation.

Bandwidths are calculated as:

\[ΔX · L = \frac{2π}{|∂Δk/∂X|}\]

where Δk is the phase mismatch, and X is one of frequency, temperature, or angle.

PMCollinearData

Represents the geometry and wavelengths of a collinear phase-matching configuration, including propagation angles theta_pm and phi_pm, crystal reference, temperature, and polarization type data (hi_or_lo_rrb and optional PMType classification).

This is the geometric input used to calculate CollinearPhaseMatch properties.

PMEfficiencyData

Stores the effective nonlinear coefficient d_eff (with and without Miller scaling) and the associated conversion factor S₀·L². Used to compare the efficiency of different phase-matching solutions based on geometry and polarization.

PMType

Describes the polarization type of a phase-matching configuration, including the principal plane (e.g. :XY or :UD for uniaxial crystals), the polarization of each wave (:o or :e), and a human-readable type classification like "I", "II/III", "IV", or "V".

Used for diagnostic purposes and auto-labeling of phase-match types.

calc_noncritical_pm_lines(principal_axis, hi_or_lo_rrb, cr; ...)

Computes the coordinates of Δk = 0 isolines in the λb-λr1 parameter space where noncritical phase-matching is achieved (i.e., phase matching occurs at fixed propagation direction, along the crystal's principal_axis).

Returns:

• segments_b: vector of λ_b curves (x-axis)
• segments_r: corresponding λ_r1 curves (y-axis)
• cb_intersections, cr_intersections: SHG symmetry intersection points (e.g., λb = λr / 2)

delta_k(theta_pm, phi_pm, hi_or_lo_rrb, cr; lambda_r1, lambda_r2, lambda_b, temp)

Computes the phase mismatch Δk = kr1 + kr2 - kb for a given configuration. Each `kiis calculated from2π * ni / λibased on the given crystalcr, propagation anglesthetapm,phipm, and the three polarization typeshiorlo_rrb`.

delta_k_with_shifting(theta_pm, phi_pm, hi_or_lo_rrb, cr; ...)

Same as delta_k, but allows small parameter perturbations (Δθ, Δϕ, ΔT, Δωr1, Δωr2, Δωb). The frequency shifts adjust the wavelengths while conserving energy (Δωr1 + Δωr2 = Δωb), enabling bandwidth estimation.

Used internally for computing how Δk varies with perturbations for calculating ΔX · L quantities in PMBandwidthData.

find_all_ncpm_over_lambda(pol_rrb, cr, temp; lambda_r1, lambda_r2, lambda_b, ...)

Finds all noncritical phase-matches (NCPM) by varying wavelength, while keeping the temperature fixed. You must specify exactly one of the three wavelengths (lambda_r1, lambda_r2, or lambda_b) and leave the others as nothing. The scan range is chosen automatically based on the crystal's validity domain. Returns a list of CollinearPhaseMatch solutions found within the allowed range. The return value can be an empty array if no solution is found.

find_all_ncpm_over_temp(pol_rrb, cr; lambda_r1, lambda_r2, lambda_b, temp_min, temp_max, ...)

Returns all noncritical phase-matching (NCPM) configurations where Δk = 0 can be achieved by tuning the temperature. You must specify at least two of the three wavelengths, and a temperature range [temp_min, temp_max]. The search is limited to propagation along principal axes. Returns an array of CollinearPhaseMatch solutions. The return value can be an empty array if no solution is found.

find_all_pms_along_dimension(pol_rrb, cr; ...)

Performs a one-dimensional search to find all collinear phase-matching solutions (Δk ≈ 0) for a given polarization tuple pol_rrb.

Depending on which parameters are held fixed (lambda_r1, lambda_r2, lambda_b, temp_min == temp_max, or angular constraints like theta_fixed), this scans over:

• Wavelength (λb or λr1)
• Temperature
• Angle (θ or ϕ)

This function is the main backend used by higher-level routines like find_nearest_pm_along_theta_phi or find_all_ncpm_over_temp.

Returns a list of CollinearPhaseMatch solutions found by detecting sign changes in Δk via a global search and refining them with bisection.

find_nearest_pm_along_lambda_r_b(pol_rrb, cr; lambda_r1, lambda_r2, lambda_b, ...)

Searches for the best phase-match for a given pair of red and blue wavelengths. You must specify exactly one of lambda_r1 or lambda_r2, plus lambda_b.

Scans along both the missing red wavelength and the blue wavelength, finds all matching configurations (via find_all_pms_along_dimension), and returns the one closest to the provided values.

Used to fine-tune a target wavelength combination to an actual valid phase-match geometry.

find_nearest_pm_along_theta_phi(theta_target, phi_target, pol_rrb, cr; ...)

Searches for the phase-matching configuration closest to a given direction (theta_target, phi_target) by scanning phase-matches at fixed θ or fixed ϕ, using find_all_pms_along_dimension.

The search returns the CollinearPhaseMatch whose propagation direction is most aligned (in dot product) with the target vector. Returns nothing if no solution is found.

plot_critical_pms(cr::NonlinearCrystal; kwargs...) -> Figure

Visualizes and compares critical phase-matching solutions for a given nonlinear crystal cr across all possible polarization configurations and propagation directions. This plot gives insight into how the phase-matching characteristics vary with angle for a fixed wavelength triplet (λr1, λr2, λ_b).

Each horizontal segment in the figure corresponds to a distinct type of phase-matching configuration, and the plot shows how key quantities vary along that solution contour (i.e., as a function of θ and ϕ for which Δk = 0).

Plotted Quantities per Phasematch

For each matched solution (Δk = 0), the following attributes are visualized:

• Refractive index
• Group index
• β₂ — group velocity dispersion, unit: fs²/mm
• Walkoff angle — spatial beam walkoff, unit: mrad
• ω BW × L — angular frequency bandwidth product (Δω·L), from group velocity mismatch
• T BW × L — temperature tolerance (ΔT·L), from thermal dispersion mismatch
• ϕ BW × L, θ BW × L — angular acceptance bandwidths
• |d_eff| — effective nonlinearity (with Miller scaling applied)
• ϕ, θ — propagation angles
• Type — phase-matching type and polarization roles (label only)

Optional Arguments

• hi_or_lo_rrb: One or more polarization configurations (e.g., (:hi, :hi, :lo))
• lambda_r1, lambda_r2, lambda_b: At least two must be specified, the third is inferred
• temp: Temperature at which to evaluate phase-matching
• n_points: Angular resolution
• size: Plot size as a tuple (width, height)

Output

Returns a vertically stacked GLMakie Figure containing multiple linked plots, each showing one of the quantities above. Each horizontal span corresponds to a continuous critical phase-matching curve (i.e., varying θ and ϕ for fixed λ and T).

plot_delta_k_map(hi_or_lo_rrb, cr; ...)

Plots a 2D or 3D map of the phasemismatch Δk over the angular domain (θ, ϕ) for a given polarization assignment (hi_or_lo_rrb) and wavelength triplet.

Depending on plot_type:

• :polar → Shows Mercator style projected θ–ϕ map with Δk color-coded and phase match contours overlaid
• :sphere → Visualizes Δk on the surface of a 3D unit sphere using ray direction vectors

plot_noncritical_pms(principal_axis, cr; ...)

Generates an interactive plot of all noncritical phase-matching lines (Δk = 0) in λb-λr1 space for a given crystal cr along the selected principal_axis.

Each plotted contour represents a set of wavelength triplets (λr1, λr2, λ_b) that satisfy phase-matching without angular adjustment. Supports both Type I (equal polarization) and Type II (cross-polarized) combinations.

You can control the polarization combination via hi_or_lo_rrb, limit the scan ranges, and adjust the resolution with ngrid.

Returns a GLMakie Figure.

pm_wavelengths(; lambda_r1=nothing, lambda_r2=nothing, lambda_b=nothing)

Given any two of the three wavelengths involved in a second-order three-wave interaction (λ_r1, λ_r2, λ_b), compute the third to satisfy energy conservation:

\[1 / λ_{b} = 1 / λ_{r,1} + 1 / λ_{r,2}\]

Returns the tuple (λr1, λr2, λ_b). Throws an error if the relation is not fulfilled or fewer than two inputs are provided.

setup_click_saver(ax; pick_filter, position_units=nothing, compute_pm)

Adds a left-click handler to the Makie axis ax that uses pick_filter to select a plot element, optionally transforms the clicked position via position_units, and computes a phase-match with compute_pm. If successful, the result is pushed to the global selected_pms array. Returns nothing.