Difference Frequency Generation Calculator

Compute difference-frequency output from two optical pumps. Explore wavelength, frequency, energy, and coherence length tools. Export results quickly using clean tables and instant downloads.

Calculator
Enter either wavelengths or frequencies. Optional fields refine phase matching checks.
Choose one method; the calculator converts both.
Controls displayed wavelengths in results.
Controls displayed frequencies in results.
Often the higher frequency input.
The second optical input for mixing.
Use the same units for easy comparison.
DFG output uses |f1 − f2|.
Used for wavevector k1 = 2πn1/λ1.
Used for wavevector k2 = 2πn2/λ2.
Use the output index at λ3.
If set, applies first-order QPM correction.
Used in sinc² buildup factor.
Formula Used

Difference frequency generation produces an output whose frequency equals the absolute frequency difference between two optical inputs.

How to Use This Calculator
  1. Select an input mode and enter two laser values.
  2. Choose units for displayed wavelength and frequency outputs.
  3. Enter refractive indices to evaluate phase mismatch in a medium.
  4. Set the interaction length to estimate the relative buildup factor.
  5. Optionally enter a poling period to check quasi-phase matching.
  6. Press Calculate to show results above the form.
  7. Use CSV or PDF buttons to save the computed report.
Example Data Table
λ1 (nm) λ2 (nm) DFG λ3 (nm) Notes
1064 1550 3393.416 Common near-IR mixing producing mid-IR output.
1030 1565 3015.673 Useful for fiber-laser systems and tunable sources.
780 1064 2908.801 Wide spacing increases output wavelength into mid-IR.
Values use vacuum conversion and absolute frequency difference.
Difference Frequency Generation Guide

1) What DFG Produces

Difference frequency generation (DFG) is nonlinear mixing that creates a third wave at the absolute frequency difference of two inputs. The core relation is f3 = |f1 - f2|. Because small pump adjustments can shift f3 strongly, DFG is widely used for tunable mid-infrared outputs.

2) Converting Wavelengths and Frequencies

The calculator converts between views using f = c/λ and λ3 = c/f3. You can enter either wavelengths or frequencies, then read both in your chosen units. As a quick reference, pumps near 1064 nm and 1550 nm generate an output near 3.39 μm.

3) Photon Energy for Planning

Photon energy is reported with E = hf in electron-volts. This helps you compare outputs to detector sensitivity bands, absorption lines, and filter windows, especially when you are working across near-IR pumps and mid-IR targets.

4) Why Refractive Index Inputs Matter

Inside a material, dispersion changes the phase velocity and therefore the wavevector. The tool estimates each wavevector using k = 2πn/λ0 (vacuum wavelength λ0) with your n1, n2, n3. Using realistic indices (from dispersion data) improves the phase-matching diagnostics.

5) Phase Mismatch and Coherence Length

Efficient buildup requires the interacting waves to stay in phase. The calculator evaluates Δk = k1 - k2 - k3 and the coherence length Lc = π/|Δk|. It also reports a normalized factor sinc²(Δk·L/2), which approaches 1 when phase matching is near ideal.

6) Quasi-Phase Matching with Poling

If you enter a poling period Λ, the tool applies first-order quasi-phase matching via Δk_QPM = Δk - 2π/Λ. This is useful for scanning candidate poling periods and checking whether QPM can recover strong buildup over your chosen interaction length.

7) Bandwidth, Tuning, and Practical Limits

Real systems deviate from ideal assumptions due to pump linewidth, temperature drift, and group-velocity mismatch. In general, shorter crystals increase acceptance bandwidth, while longer crystals can improve peak conversion when matching is achieved. Also consider focusing, mode overlap, and absorption, which can dominate even when phase matching looks excellent. Use the length and index inputs to explore these tradeoffs quickly, then export CSV or print a PDF report for documentation.

8) A Practical Workflow

Start by selecting a target output wavelength or frequency, then try pump pairs that bracket the desired difference. Next, enter approximate indices and length to evaluate Δk, Lc, and the sinc² factor. Finally, export CSV or a print-ready PDF report for documentation and review.

FAQs

1) Why does the calculator use an absolute frequency difference?

DFG produces a real, positive output frequency, so the magnitude |f1 − f2| is used. Swapping the two inputs does not change the generated frequency or wavelength.

2) Can I enter wavelengths and still see frequencies?

Yes. In wavelength mode, the tool converts both inputs to frequency using f = c/λ, then computes f3 and converts back to λ3 in your chosen units.

3) What refractive index values should I use?

Use indices at each relevant wavelength in your material, ideally from dispersion data or Sellmeier fits. n1 and n2 are for the pumps, and n3 is for the generated output.

4) What does the sinc² factor represent?

It is a normalized indicator of phase‑matching build‑up: sinc²(Δk·L/2). A value near 1 suggests strong constructive growth, while smaller values indicate dephasing over the chosen interaction length.

5) When should I use the poling period input?

Enter a poling period when your medium supports periodic poling and you want a first‑order quasi‑phase‑matching estimate. The tool then reports Δk_QPM and a QPM coherence length.

6) Does this calculator predict absolute output power?

No. It provides spectral conversion, mismatch diagnostics, and a relative phase‑matching factor. Absolute power requires nonlinear coefficient, pump intensities, focusing, losses, and coupling details.

7) Why might my lab result differ from the estimate?

Differences come from dispersion errors, temperature dependence, finite pump bandwidth, spatial overlap, absorption, and group‑velocity mismatch. Use measured indices and realistic lengths, then refine with experiment‑specific parameters.