Calculators for Gaussian beam propagation and ABCD matrix ray tracing.
37 calculators
Rayleigh range, divergence, beam radius, wavefront curvature and Gouy phase of a Gaussian beam at any distance from its waist.
Build an optical system from sequential elements and compute the ray transfer matrix.
High-harmonic generation in a gas: ponderomotive energy, cutoff photon energy I_p + 3.17 U_p, last odd harmonic, barrier-suppression intensity and the Fourier-limited attosecond pulse of the selected band.
M² = (π w₀ θ)/λ. M² = 1 for ideal Gaussian, higher for multimode beams.
Core radius, FWHM and non-diffracting range of a Bessel beam from its cone angle and input beam radius, with J₀ and J₁ profiles.
Two-mirror resonator: g-parameters and stability diagram, free spectral range, transverse mode spacing, TEM₀₀ waist size and position, and spot sizes on the mirrors.
Cavity-dumped laser: round-trip pulse length 2L/c, peak and circulating power, average power and the highest possible dump rate.
Chirped pulse amplification: transform-limited duration of a bandwidth, stretcher GDD for a stretch ratio, Treacy grating-compressor separation, recompressed duration against a separation error, and peak powers.
Idler power, wavelength and quasi-phase-matching period of χ⁽²⁾ difference-frequency generation (ωp − ωs → ωi) from pump and signal powers, beam radius, d_eff, indices and phase mismatch.
Fresnel diffraction pattern of a circular aperture or slit at any distance, with the Fresnel number, on-axis intensity and the far-field Fraunhofer limit.
Fabry–Pérot diode laser: threshold modal gain, carrier density and current, differential and slope efficiency, front-facet share, far-field divergence and mode spacing.
CW dye jet laser in a two-mirror cavity: TEM₀₀ waist, triplet loss versus flow speed, threshold pump power, small-signal gain, output power and slope efficiency.
Where a femtosecond filament starts: critical power for self-focusing, peak power against it, and the Marburger collapse distance of a collimated or lens-focused Gaussian beam.
Degenerate four-wave mixing in a fiber (2ωp = ωs + ωi): parametric signal gain, idler wavelength and power, phase mismatch κ = Δβ + 2γP, gain spectrum and peak-gain detuning from pump power, n₂, A_eff, length, β₂ and β₄.
SASE free-electron laser: resonance wavelength, Pierce parameter ρ with the beam size, 3D gain length from Ming Xie's fit, saturation power and length, and the power along the undulator.
Stability g₁g₂, TEM₀₀ waist and spot sizes against the bore, Fresnel number, threshold gain, output power and the optimum output coupler of a HeNe, Ar⁺ or CO₂ laser.
Dispersion control via a GTI — constant reflectivity with tunable group delay dispersion.
Intensity of TEMmn and LGpl modes at any distance, with second-moment radius, M², Gouy phase, peak intensity and orbital angular momentum.
Locking range of an injection-locked laser from the injection ratio, coupling rate and linewidth enhancement factor α: Adler's symmetric range and the asymmetric semiconductor-laser range, with a locking map.
Thin Kerr lens of a Gaussian beam, f = πw⁴/(8n₂PL), with the on-axis nonlinear phase, the critical power for self-focusing and the Rayleigh range in the crystal.
The single lens, and its position, that couples one Gaussian beam waist into another, plus the best coupling of a lens you already have.
Mode-locked laser: cavity length for a repetition rate, transform-limited bandwidth of a sech² or Gaussian pulse, number of locked modes, pulse energy and peak power.
Optical frequency comb: tooth frequencies ν_n = n f_rep + f_ceo, the carrier-envelope phase slip per pulse, teeth in the spectrum, and the electric field of consecutive pulses.
Signal gain, idler output and gain bandwidth of an optical parametric amplifier from pump power and radius, d_eff, indices, phase mismatch and signal–idler group-velocity mismatch.
Parametric gain, walk-off-limited interaction length and singly-resonant OPO threshold from pump wavelength, d_eff, beam radius and cavity loss.
Symmetric slab waveguide: V-number, number of TE and TM modes, exact effective indices, core power fraction, b–V diagram and TE mode fields.
Q-switched laser: peak and average power and duty cycle of a pulse train, plus pulse energy, width and peak power from the Q-switch rate equations.
Ring laser cavity of N curved mirrors: free spectral range, finesse, linewidth, photon lifetime, stability and the astigmatic mode sizes from the tilted mirrors.
Self-phase modulation of a Gaussian or sech² pulse: peak nonlinear phase k₀n₂I₀L, largest frequency shift, rms broadening and the SPM spectrum by FFT, with a self-focusing check.
Slow light: group delay τ = n_gL/c, group velocity and delay-bandwidth product from a group index, or from a Lorentzian resonance (Brillouin gain, EIT window) whose delay is G/Γ.
Nd:YAG-type rod laser: two-mirror stability and TEM₀₀ mode with the crystal in the cavity, threshold pump power, small-signal gain, Rigrod output power and slope efficiency.
Fibre soliton order N, dispersion and nonlinear lengths, fundamental soliton power and soliton period, with a split-step Fourier simulation of a sech pulse along the fibre.
Focal spot, recommended pinhole diameter, throughput of any pinhole and the output beam profile of a lens–pinhole spatial filter.
Sum-frequency power, wavelength and quasi-phase-matching period of χ⁽²⁾ upconversion (ω1 + ω2 → ω3) from the input powers, beam radius, d_eff, indices and phase mismatch.
Length scales of supercontinuum generation in a photonic crystal fibre: soliton number, dispersion length, soliton fission length and the dispersive-wave wavelength from β₂ and β₃.
Yb:YAG thin-disk laser: quasi-three-level threshold inversion, multipass pump absorption with bleaching, threshold pump power, slope efficiency, output power and temperature rise through the disk.
Zigzag slab laser: bounce angle and total internal reflection, threshold and output power, slope efficiency, heat density, temperature profile and the thermal lens the zigzag cancels.