Kerr Effect Index Calculator

Calculator

Linear refractive index n₀ (unitless)

Typical dielectrics: 1.3–2.2.

Nonlinear index n₂ (m²/W)

Can be negative for some materials.

Intensity input method Use intensity I directly Use optical power and beam radius Use electric field amplitude

Pick what you measure most reliably.

Intensity I (W/m²)

Example: 1.0e12 W/m².

Optical power P (W)

Used with radius to estimate intensity.

Beam radius w (m)

Area A = πw² assumes circular beam.

Electric field amplitude E (V/m)

Intensity uses 0.5·n₀·ε₀·c·E².

Wavelength λ (m)

Example: 1.55e-6 m for 1550 nm.

Interaction length L (m)

For waveguides, use physical path length.

Calculate Reset

Formula used

The optical Kerr effect links refractive index to intensity:

• Δn = n₂ · I
• n_eff = n₀ + Δn
• Δφ = (2π/λ) · Δn · L

If you input electric field amplitude, the calculator estimates intensity using I = 0.5 · n₀ · ε₀ · c · E² with ε₀ and c in SI units.

How to use this calculator

1. Enter n₀ and n₂ for your material at the chosen wavelength.
2. Select the intensity method matching your measurement setup.
3. Provide intensity, or power and beam radius, or field amplitude.
4. Set wavelength λ and interaction length L for phase calculations.
5. Press Calculate to view Δn, n_eff, and Δφ above.

Example data table

Article

Overview of the Kerr index

The optical Kerr effect describes how a material's refractive index changes with optical intensity. In many transparent dielectrics the response is fast and approximately proportional, so an effective index can be modeled as n_eff = n₀ + n₂I. This calculator translates measured conditions into an index shift you can use for design and comparison.

Understanding n₀ and n₂

The linear index n₀ sets the baseline phase velocity at a given wavelength, while the nonlinear index n₂ captures the third-order nonlinearity in the common intensity form. Typical n₂ values are small, so even large intensities often produce Delta n in the 1e-9 to 1e-5 range depending on material and confinement.

Choosing an intensity pathway

In practice, intensity is not always measured directly. If you know optical power and an approximate beam radius, the tool estimates I = P/(pi w^2) for a circular beam. If you know the electric field amplitude, it estimates intensity with I = 0.5 n₀ epsilon₀ c E^2 using SI constants.

Units and scaling checks

Because Delta n scales linearly with intensity, unit mistakes are the most common failure mode. Keep power in watts, radius in meters, wavelength in meters, and field in volts per meter. The results panel includes warnings when computed intensities or index shifts look unusually large.

Effective index implications

Once Delta n is computed, the calculator reports n_eff. This is useful for predicting self-focusing trends, index-guided confinement changes, and propagation constant shifts. Negative n₂ produces a negative Delta n and can reduce the index under high intensity, which may broaden beams in bulk media.

Nonlinear phase shift prediction

For interferometric or waveguide devices, phase is often the key observable. The calculator uses Delta phi = (2pi/lambda) Delta n L to estimate the Kerr-induced phase shift over an interaction length L. Even modest index change can accumulate measurable phase in long fibers or high-Q resonators.

Data interpretation tips

If your setup is pulsed, use peak intensity rather than average intensity when modeling instantaneous Kerr response. For guided modes, an effective area may be more appropriate than a geometric radius; you can convert using I = P/A_eff by selecting the power-and-radius method with an equivalent radius.

Where this calculator fits

Engineers use Kerr index estimates to size nonlinear phase shifters, evaluate self-phase modulation thresholds, and compare candidate materials for all-optical switching. By exporting CSV or PDF, you can document assumptions and track sensitivity to power, wavelength, and interaction length.

FAQs

1) What does the calculator output?

It outputs intensity I, Kerr index change Delta n, effective index n_eff, and nonlinear phase shift Delta phi for a chosen wavelength and interaction length, along with unit-reasonableness warnings.

2) How do I choose n₂?

Use n₂ measured for your material at the same wavelength and polarization when possible. Values depend on composition, temperature, and wavelength. If you only have chi(3), convert to n₂ before using this tool.

3) Is intensity based on peak or average power?

For continuous-wave sources, average and peak are the same. For pulsed lasers, Kerr response follows the instantaneous field, so use peak power or peak intensity that matches your pulse shape and repetition rate.

4) Why is my Delta n negative?

Delta n inherits the sign of n₂. Some media or wavelength regions can have negative n₂, producing a negative index change at high intensity. Confirm your reference data and ensure intensity is positive.

5) Can I use this for waveguides?

Yes, but intensity should reflect modal confinement. Replace beam radius with an equivalent radius derived from effective area A_eff, or compute I = P/A_eff externally and use the direct-intensity option.

6) What length L should I enter?

Enter the physical interaction length where the optical field overlaps the nonlinear medium. For resonators, L can represent the round-trip path or an effective length tied to the number of passes.

7) How accurate is the power-and-radius estimate?

It assumes a circular, uniform intensity distribution using A = pi w^2. Real beams are often Gaussian, so peak intensity can be about twice the average over that area. Use measured spot size conventions for best results.