Combine two inputs to predict the generated wave. Switch between wavelength, frequency, or angular form. Model mismatch and coherence length for practical alignment.
f3 = f1 + f2ω3 = ω1 + ω21/λ3 = 1/λ1 + 1/λ2f = c/λ and ω = 2πfk = 2πn/λ using vacuum λΔk = k3 − k1 − k2Lc = π/|Δk|| Case | λ1 (nm) | λ2 (nm) | Predicted λ3 (nm) | Notes |
|---|---|---|---|---|
| Example A | 1064 | 532 | 355 | Common harmonic mixing combination. |
| Example B | 1550 | 1064 | 632.6 | Near visible output from telecom + Nd sources. |
| Example C | 800 | 1030 | 451.6 | Typical ultrafast mixing in nonlinear crystals. |
Sum frequency generation (SFG) is a second-order nonlinear process where two inputs at f1 and f2 create an output at f3 = f1 + f2. Because frequency increases, the output wavelength is shorter in vacuum. This supports tunable visible or UV generation, spectroscopy, and wavelength translation across laser bands.
The core design rule is frequency addition. In wavelength form (vacuum), the relation is 1/lambda3 = 1/lambda1 + 1/lambda2. Mixing 1064 nm and 532 nm predicts about 355 nm, a common reference point for quick sanity checks and reporting.
High efficiency also needs wavevector matching, often written dk = k3 - k1 - k2. When dk is near zero, the generated field adds constructively along the interaction length. The calculator estimates dk from user indices and reports coherence length Lc = pi/|dk| as a compact figure of merit.
Crystals are dispersive, so n changes with wavelength and polarization. Birefringent phase matching assigns polarizations to satisfy dk near zero, while quasi-phase matching uses periodic poling to compensate mismatch. Even approximate n1, n2, and n3 values are useful for early comparisons.
Common SFG platforms include BBO, LBO, KTP, and periodically poled materials such as PPLN. Effective nonlinear coefficients are typically a few to tens of pm/V depending on orientation and poling. Practical interaction lengths range from about 1 mm to several cm, limited by absorption and walk-off.
Collinear mixing is simplest, but noncollinear geometries can separate beams and reduce background. The calculator offers an approximate crossing-angle option. Tight focusing raises intensity, yet may reduce effective length through walk-off and confocal limits, so treat dk and Lc as screening metrics.
Confirm the predicted lambda3 lies within your detector and optics window, including coatings and filters. Then compare Lc to your planned crystal length. If Lc is much shorter, conversion will oscillate and average down unless you retune angle, temperature, polarization, or poling period.
Enter inputs in wavelength, frequency, or angular form and confirm the derived output. Add estimated indices for your material, evaluate dk and Lc for candidate geometries, and iterate wavelength pairs. Export CSV or PDF to track scenarios, share settings, and justify component selection in a lab log.
1) What is the main equation behind SFG?
SFG follows frequency addition: f3 = f1 + f2. In vacuum wavelength form, 1/lambda3 = 1/lambda1 + 1/lambda2. Real media add refractive-index and phase-matching constraints that control efficiency.
2) Why is the generated wavelength always shorter?
Because f3 is the sum of two positive frequencies, f3 is larger than f1 or f2. Since lambda = c/f in vacuum, higher frequency corresponds to a shorter wavelength, so lambda3 is smaller.
3) What does dk represent in the results?
dk is the phase mismatch between the generated wave and the two inputs. When dk is close to zero, the generated field builds up coherently. Large dk causes oscillatory growth and reduces net conversion.
4) How should I interpret the coherence length Lc?
Lc = pi/|dk| is the distance over which the generated field stays mostly in phase. If Lc is comparable to, or larger than, your crystal length, mismatch is less limiting. If it is much smaller, efficiency drops.
5) Do I need refractive indices to use the calculator?
No. You can compute the output wavelength and frequency without indices. Indices are only needed for the dk and Lc estimates. If you do not know them, keep n1 = n2 = n3 = 1 to focus on vacuum relations.
6) Why might my lab output differ from the predicted lambda3?
The predicted lambda3 is based on ideal energy conservation. Real systems can differ due to dispersion, tuning angle, temperature, poling period, and calibration. Efficiency limits can also make weak outputs hard to detect.
7) Is noncollinear mixing supported here?
Yes, an approximate noncollinear option is included. It projects the input wavevectors along the generated direction using a user-provided crossing angle. Use it for quick comparisons; detailed designs require full vector phase matching and beam geometry.
The Δk estimate here uses a compact model with user-supplied indices. Real systems often require dispersion, birefringence, polarization selection, temperature tuning, and crystal orientation constraints.
If Δk approaches zero, the coherence length becomes large, indicating stronger constructive buildup. If Δk is large, conversion oscillates and averages down over distance.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.