This calculator supports two approaches:
- Measured: \(\eta = P_{2\omega}/P_{\omega}\), with optional transmission correction.
- Model: Undepleted-pump estimate for second-harmonic power:
Here, ω = 2πc/λ, Aeff is a Gaussian-area approximation, and F is a user-supplied focusing factor. Absorption is included through Leff.
- Select Model-based estimate to predict output from crystal and beam parameters.
- Or select Measured efficiency to compute η from your measured powers.
- Keep units consistent, especially for beam waist and crystal length.
- Set Δk to zero for ideal phase matching, or enter your mismatch.
- Use transmissions to account for coupling and collection losses.
- Click Calculate to show results above the form.
- Use Download CSV or Download PDF to save results.
| Case | λ (nm) | Pω (W) | w0 (µm) | L (mm) | deff (pm/V) | n(ω) | n(2ω) | Δk (1/mm) | Predicted P2ω (W) | η (%) |
|---|---|---|---|---|---|---|---|---|---|---|
| A | 1064 | 1.00 | 30 | 10 | 2.0 | 1.65 | 1.70 | 0.0 | 0.00160627 | 0.160627 |
| B | 1550 | 0.50 | 25 | 20 | 1.2 | 2.10 | 2.20 | 0.2 | 0.00003869 | 0.007738 |
| C | 1030 | 2.00 | 40 | 5 | 3.0 | 1.80 | 1.85 | 0.0 | 0.00167507 | 0.083753 |
Second-harmonic generation in one pass
Second-harmonic generation (SHG) converts a fundamental wave at frequency ω into light at 2ω, often doubling 1064 nm to 532 nm. In the low-conversion regime, an undepleted-pump model captures the dominant scaling trends, which is what this calculator reports.
Efficiency definitions that engineers use
Two metrics are widely reported: conversion efficiency η = P2ω/Pω and normalized efficiency for comparing devices across different lengths. In model mode, P2ω scales roughly with Pω2, so η typically grows with power until depletion or heating matters.
Length scaling and effective interaction length
With good phase matching and low loss, SH power grows with L2. If absorption exists, the effective length Leff is smaller than the physical length and the quadratic scaling weakens. The model includes α and reports an absorption-corrected interaction length.
Phase mismatch, coherence length, and sinc² behavior
When Δk ≠ 0, SH contributions from different sections do not add perfectly in phase. The factor sinc²(Δk·L/2) captures this reduction. The coherence length Lc = π/|Δk| is a useful check: as L spans multiple coherence lengths, efficiency can oscillate.
Beam waist, effective area, and focusing
Nonlinear drive scales with intensity, so smaller waists increase conversion by reducing Aeff. Overly tight focusing can introduce walk-off and reduced overlap. The focusing factor lets you tune the estimate to match your focusing strategy.
Material parameters: deff and refractive indices
The coefficient deff appears squared in the scaling constant K, so effective nonlinearity strongly impacts predicted power. Refractive indices n(ω) and n(2ω) affect field normalization and phase velocity. For best accuracy, use indices for your temperature and polarization.
Losses and what “measured efficiency” really means
Measured SH power often includes losses from coupling optics, filters, and detectors. Measured mode supports a transmission correction to estimate the SH power at the source. In model mode, tin and tout help keep internal and external performance separated.
Using results for design comparison
Use η (%) for quick sanity checks, and use normalized efficiency to compare devices independent of length. If predicted P2ω is much higher than observed, investigate phase matching (Δk), beam quality, focusing, and losses. If measurements exceed the model, resonant enhancement may be present. Document your reference plane and calibration so comparisons between runs remain consistent, always for reproducible engineering decisions.
1) What does “second-harmonic efficiency” mean?
It is the fraction of fundamental optical power converted to the second harmonic, usually reported as η = P2ω/Pω. It can be quoted at the crystal output or after external optics, depending on your measurement reference plane.
2) Why does the model use P2ω ∝ Pω2?
In the undepleted-pump regime, the nonlinear polarization driving SHG is proportional to the square of the fundamental field. That makes second-harmonic power approximately quadratic in the input power until depletion, heating, or saturation effects appear.
3) What is the purpose of the sinc² phase-matching term?
sinc²(Δk·L/2) accounts for reduced constructive interference when the fundamental and second-harmonic waves are not perfectly phase matched. Even small Δk values can significantly lower conversion for long crystals, especially when L exceeds the coherence length.
4) How should I choose the focusing factor?
Start with 1.0 for a baseline estimate. Use values below 1.0 for loose focusing or poor overlap, and values above 1.0 for optimized focusing in a well-aligned setup. Keep adjustments modest unless you have experimental justification.
5) Why are transmission inputs included in model mode?
Transmission terms let you separate internal generation from external losses such as coupling, Fresnel reflections, filters, and collection optics. This helps you reconcile predicted internal power with what you actually measure at a detector.
6) What units should I use for Δk and α?
Enter Δk in 1/mm, 1/cm, or 1/m and α in 1/cm or 1/m, then select the matching unit in the dropdown. The calculator converts everything to SI internally so the phase-matching and effective-length terms remain consistent.
7) Why might my measured efficiency be lower than predicted?
Common causes include imperfect phase matching, wrong refractive indices, beam quality issues, suboptimal focusing, thermal effects, or unaccounted losses. Verify Δk and temperature first, then check alignment, waist location, and power calibration.