Quantify self phase modulation in fibers and waveguides. Pick parameters, losses, and pulse width options. See phase shift, chirp estimate, then export results instantly.
Self phase modulation arises from an intensity‑dependent refractive index. In a guided structure, the nonlinear phase accumulated over the effective interaction length is:
If the Gaussian pulse option is enabled, the instantaneous frequency shift follows Δω(t)=−d(Δφ(t))/dt. For P(t)=P0·exp(−(t/T0)²), the maximum shift is approximated by:
| Case | Mode | P0 (W) | L (m) | α (dB/km) | λ (nm) | Aeff (µm²) | n2 (m²/W) | Approx Δφ (rad) |
|---|---|---|---|---|---|---|---|---|
| Telecom fiber | Compute γ | 5 | 1000 | 0.2 | 1550 | 80 | 2.6e-20 | ≈ 6.5 |
| Short waveguide | Direct γ | 2 | 50 | 0 | — | — | — | ≈ γ·P0·L |
| Low power check | Compute γ | 0.2 | 500 | 0.2 | 1550 | 80 | 2.6e-20 | < 1 |
These examples are illustrative. Use your measured parameters for accurate design checks.
Self phase modulation (SPM) is a Kerr-effect process where optical intensity changes the refractive index, imprinting a time-varying phase on the waveform. That phase becomes chirp, which broadens the spectrum and can reshape pulses. In links it can distort phase; in labs it enables broad spectra.
The main quantity is the accumulated nonlinear phase shift Δφ = γ·P0·Leff. A common design checkpoint is Δφ ≈ 1 rad, where spectral changes become noticeable. Values above ~3–5 rad often indicate strong broadening, higher sensitivity to dispersion, and more stringent launch-power control.
If γ is computed, the calculator uses γ = 2πn2/(λAeff). For silica near 1550 nm, n2 is often around 2.6×10−20 m²/W. A smaller effective area increases γ, so compact waveguides can show large SPM at modest power compared with standard single-mode fiber.
Loss reduces the interaction, captured by Leff = (1−e−αL)/α. For low-loss fiber such as 0.2 dB/km, Leff approaches L for short spans but saturates over longer distances. This is why long links do not increase Δφ linearly once attenuation becomes significant.
For a Gaussian pulse, the peak chirp scales roughly with Δφ/T0, where T0 is derived from the pulse FWHM. Shorter pulses generate larger instantaneous frequency shifts for the same Δφ. This calculator reports an approximate maximum Δf and a symmetric peak-to-peak broadening estimate of about 2·Δfmax.
If your estimated broadening is comparable to instrument resolution, you should expect measurable changes. In time-domain systems, added chirp can interact with dispersion to stretch pulses. In coherent systems, SPM shifts phase and increases nonlinear interference at higher launch powers.
Use peak power P0 for pulsed sources; average power can understate SPM by large factors. When in doubt, compute peak power from pulse energy and duration. For waveguides, prefer measured γ and Aeff. Include realistic loss values so Leff reflects the actual nonlinear interaction region.
To reduce SPM, lower P0, increase Aeff, or shorten L. Dispersion management can limit pulse distortion by controlling chirp evolution. When SPM is desired, target a Δφ range and verify the broadened spectrum stays inside component bandwidth and safety limits.
The B-integral is the accumulated nonlinear phase in radians. In this tool it is equal to Δφ. It is widely used as a quick measure of Kerr nonlinearity strength in fibers and bulk optics.
Use peak power for pulsed operation because SPM depends on instantaneous intensity. If you only know average power, estimate peak power using repetition rate and pulse duration, or use measured peak values from your source specifications.
Loss reduces optical power along the path, so the nonlinear interaction is weaker than γ·P0·L. Leff accounts for this decay, providing a realistic interaction length when attenuation is nonzero.
Use direct γ when you have a datasheet or measured value for your exact fiber or waveguide. Computed γ is sensitive to Aeff, λ, and n2 assumptions, which can differ across designs and fabrication runs.
It is a common threshold where SPM-driven spectral changes become noticeable. Below that, broadening is often modest. Above that, chirp and spectrum growth are stronger, and dispersion or filtering effects become more important.
No. It is an engineering estimate for a Gaussian pulse, intended for quick sizing. Exact behavior depends on pulse shape, dispersion, higher-order nonlinearities, and any power evolution beyond simple loss.
That row illustrates the lossless limit. When α is zero, Leff equals L, so Δφ reduces to γ·P0·L. It is a useful sanity check for short, low-loss waveguides.
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.