May 15 2014
B-Integral is defined as the measure of the non-linear phase shift of light in devices such as amplifiers. B-Integral is a term that is specific to non-linear optics. The non-linear shift of the laser system along the optical axis is equal to the B-Integral of the laser beam.
B-Integral is often used in the context of ultra-fast and regenerative amplifiers to describe the optical components, such as Pockels cell, Kerr non-linearity, etc. The value of B-Integral is used to quantify the self-focusing ability of ultra-short pulses that are fed to regenerative amplifiers.
Calculation of B-Integral
The formula for calculating the value of B-Integral is given below:
B = 2π/λ ∫ n2I(z) dz
I(z) is the optical intensity of the beam, z is the position in beam direction, and n2 is the non-linear index, quantifying the Kerr non-linearity. The value of B-Integral quantifies the exponential growth of the least stable spatial frequency of a laser beam.
Significance of B-Integral
At high optical intensities in regenerative amplifiers, the B-Integral value tends to be larger than 1. When the value of B-Integral varies between 3 and 5, there is a risk of self-focusing of the laser beam.
Due to the self-focusing, the lensing effect on the beam intensifies and, hence, the beam collapses to a very small radius. At this point, the risk of exceeding the damage threshold increases.
An increase in the value of B-Integral may cause spectral broadening, and even break-up, of the amplified beam. Hence, it is important to monitor its value from time to time.
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