B Integral Laser – Cancellation Of B

Definition: a measure of the nonlinear phase shift of light, e.g. in an amplifier

German: B-Integral

Category: nonlinear optics

How to cite the article; suggest additional literature

Author: Dr. Rüdiger Paschotta

URL: https://www.wnyrails.org/b_integral.html

The B integral is frequently used in the context of ultrafast amplifiers, e.g. for optical components such as the Pockels cell of a regenerative amplifier.It is defined as


where I(z) is the optical intensity along the beam axis (assumed to be highest intensity in the transverse direction, e.g. for a Gaussian beam), z the position in beam direction, and n2 the nonlinear index quantifying the Kerr nonlinearity.As n2 I is the nonlinear change in the refractive index, one easily recognizes the B integral to be the total on-axis nonlinear phase shift accumulated in a passage through the device.

Đang xem: B integral laser

Importance for Self-focusing

For high optical intensities, as often occur when ultrashort pulses are amplified e.g. in a regenerative amplifier, the B integral can become larger than 1.For values above ≈ 3–5, there is a risk that self-focusing may occur: the nonlinear lensing (focusing) effect can become so strong that the beam collapses to a very small radius, so that the optical intensities are strongly further increased and easily exceed the damage threshold.A single pulse in this regime may be sufficient for destroying the amplifier gain medium or some other component.Other possible effects in this regime are strong spectral broadening and even the breakup of the amplified pulse, a reduction in the achievable gain, and a severely reduced beam quality.

See also  Integral Hybrid Scope - Optics And Attachments

The threshold for self-focusing in terms of the B integral actually depends on the conditions.The approximate value given above is based on the assumption that this value is acquired in a length below the Rayleigh length, so that diffraction effects will not be strong enough to stabilize the beam radius.In a regenerative amplifier, the total B integral for multiple passes through the gain medium may sometimes be well above 5 without causing self-focusing.Similarly, it does not matter that the accumulated B integral for an ultrashort pulse circulating in a mode-locked laser easily becomes greater than 10 within a single microsecond.

Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.

Xem thêm: Amazon Prime Free Trial For Student 6 Month Free Prime Student: Free 6

Please do not enter personal data here; we would otherwise delete it soon. (See also our privacy declaration.) If you wish to receive personal feedback or consultancy from the author, please contact him e.g. via e-mail.

Your question or comment:

Spam check:

(Please enter the sum of thirteen and three in the form of digits!)

See also  Int E Integral Calculator : E, Integral Calculator: Integrate With Wolfram

By submitting the information, you give your consent to the potential publication of your inputs on our website according to our rules. (If you later retract your consent, we will delete those inputs.) As your inputs are first reviewed by the author, they may be published with some delay.

Xem thêm: Integral Knife Handle Knives, Are Integral Knives Stronger Than Standard Knives

See also: focus, Kerr effect, nonlinear index, optical amplifiers, self-focusing, laser-induced damageand other articles in the category nonlinear optics

If you like this page, please share the link with your friends and colleagues, e.g. via social media:


These sharing buttons are implemented in a privacy-friendly way!

If you want to place a link to this article in some other resource (e.g. your website, social media, a discussion forum, Wikipedia), you can get the required code here.

HTML link on this article:

Article on B Integralin the RP Photonics EncyclopediaWith preview image (see the box just above):


© RP Photonics Consulting GmbH All rights reserved worldwide Contact and legal info, declaration of data privacy

Field Guide on Fiber Optics

A quick introduction to fiber optics:

basics of optical fibersfiber nonlinearities and their effectspassive fibers for data transmissionphotonic crystal fiberslarge mode area fiberspassive fiber-optic componentsactive fiber devices: fiber amplifiers and lasers


See more articles in category: Integral

Leave a Reply

Back to top button