B-Integral Calculator

Calculate cumulative B-integral and self-focusing critical power for ultrafast beam paths through optical elements.

Beam Parameters
Optical Elements
Element 1
Beam & Peak Power
Peak power (P\u209A\u2091\u2090\u2096)
E / (K \u00B7 \u03C4)
10.65MW
Beam area (A)
\u03C0w\u00B2
0.1257cm\u00B2
Peak intensity (I)
P\u209A\u2091\u2090\u2096 / A
8.471e+7W/cm\u00B2
Element 1: Fused Silica
B-integral
(2\u03C0/\u03BB) \u00B7 n\u2082 \u00B7 I \u00B7 L
9.115e-4rad
Critical power (P\u1D9C\u1D63)
3.77\u03BB\u00B2 / (8\u03C0n\u2080n\u2082)
2.411MW
Cumulative B-Integral
B\u209C\u2092\u209C\u2090\u2097
9.115e-4rad
LowB < π/4 — negligible self-phase modulation
Abridged Optics — B-Integral Calculator v1.0Assumes uniform plane-wave intensity across the beam. n\u2082 values at 800 nm. Critical power formula valid for CW; ultrafast pulses may self-focus at lower powers due to temporal profile effects.

All information, equations, and calculations have been compiled and verified to the best of our ability. For mission-critical applications, we recommend independent verification of all values. If you find an error, please let us know.