“Beam parameter product”的意思、由来-开放百科全书

In laser science, the beam parameter product (BPP) is the product of a laser beam's divergence angle (half-angle) and the radius of the beam at its narrowest point (the beam waist).^[1] The BPP quantifies the quality of a laser beam, and how well it can be focused to a small spot.

A Gaussian beam has the lowest possible BPP,

, where

is the wavelength of the light.^[1] The ratio of the BPP of an actual beam to that of an ideal Gaussian beam at the same wavelength is denoted M² ("M squared"). This parameter is a wavelength-independent measure of beam quality.

The quality of a beam is important for many applications. In fiber-optic communications beams with an M² close to 1 are required for coupling to single-mode optical fiber. Laser machine shops care a lot about the M² parameter of their lasers because the beams will focus to an area that is M⁴ times larger than that of a Gaussian beam with the same wavelength and D4σ waist width; in other words, the fluence scales as 1/M⁴. The rule of thumb is that M² increases as the laser power increases. It is difficult to obtain excellent beam quality and high average power (100 W to kWs) due to thermal lensing in the laser gain medium.

Measurement

There are several ways to define the width of a beam. When measuring the beam parameter product and M², one uses the D4σ or "second moment" width of the beam to determine both the radius of the beam's waist and the divergence in the far field.^[2]

The BPP can be easily measured by placing an array detector or scanning-slit profiler at multiple positions within the beam after focusing it with a lens of high optical quality and known focal length. To properly obtain the BPP and M² the following steps must be followed:^[3]

In principle, one could use a single measurement at the waist to obtain the waist diameter, a single measurement in the far field to obtain the divergence, and then use these to calculate the BPP. The procedure above gives a more accurate result in practice, however.

High-power lasers, such as those used in laser welding and cutting are typically measured by using a beamsplitter to sample the beam. The sampled beam has much lower intensity and can be measured by a scanning-slit or knife-edge profiler. Good beam quality is very important in laser welding and cutting operations.^[5]

See also

References

1. ^¹{{cite web |url=https://www.rp-photonics.com/beam_parameter_product.html |title=Beam parameter product |accessdate=2006-09-22 |work=Encyclopedia of Laser Physics and Technology | archiveurl= https://web.archive.org/web/20061018175856/http://www.rp-photonics.com/beam_parameter_product.html |publisher=RP Photonics |first=Rüdiger |last=Paschotta| archivedate= 18 October 2006 | deadurl= no}}
2. ^A. E. Siegman, "[https://web.archive.org/web/20110604095354/http://www.stanford.edu/~siegman/beams_and_resonators/beam_quality_tutorial_osa.pdf How to (Maybe) Measure Laser Beam Quality]," Tutorial presentation at the Optical Society of America Annual Meeting, Long Beach, California, October 1997.
3. ^ISO 11146-1:2005(E), "Lasers and laser-related equipment — Test methods for laser beam widths, divergence angles and beam propagation ratios — Part 1: Stigmatic and simple astigmatic beams."
4. ^A. E. Siegman, "[https://web.archive.org/web/20110604095354/http://www.stanford.edu/~siegman/beams_and_resonators/beam_quality_tutorial_osa.pdf How to (Maybe) Measure Laser Beam Quality]," Tutorial presentation at the Optical Society of America Annual MeetingLong Beach, California, October 1997, p.9. (Note that there is a typo in equation on page 3. Correct form comes from equations on page 9.)
5. ^{{cite paper |first=Oren |last=Aharon |url=http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1833855 |title=High power beam analysis |journal=Proc. SPIE |volume=8963 |date=February 20, 2014 |doi=10.1117/12.2036550}}

Measurement

See also

References

Further reading