M2factor of nonparaxial vector beams

Qing Cao; Ximing Deng

doi:10.1117/12.259903

20 November 1996 M² factor of nonparaxial vector beams

Qing Cao, Ximing Deng

Proceedings Volume 2870, Third International Workshop on Laser Beam and Optics Characterization; (1996) https://doi.org/10.1117/12.259903
Event: Third International Workshop on Laser Beam and Optics Characterization, 1996, Quebec City, Canada

Abstract

By taking the vectorial property of the (time average) energy flow density into account, the first and the second intensity moments of the nonparaxial vector beams are defined. The parabolic propagation law of the second intensity moment in free space is deduced by employing the Maxwell's equations. And then, as an extension of the M² factor of the paraxial scalar beams, the M² factor of the nonparaxial vector beams is introduced. In the condition that the beam width is greater than a few wavelength, the relation M² greater than 1 is proven by using the Schwarz inequality. Finally, the intensity moment theory is generalized for the propagation of general polychromatic and nonparaxial pulsed vector beams in free space except that the M² factor of the static beams is replaced by the characterization width W_c which is defined as the product of the minimum beam width in the near field and the divergence in the far field.

Citation Download Citation

Qing Cao and Ximing Deng "M² factor of nonparaxial vector beams", Proc. SPIE 2870, Third International Workshop on Laser Beam and Optics Characterization, (20 November 1996); https://doi.org/10.1117/12.259903

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available