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J Opt Soc Am A Opt Image Sci Vis. 2006 Aug;23(8):2027-38.

Analytical calculation of the longitudinal electric field resulting from the tight focusing of an ultrafast transverse-magnetic laser beam.

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  • 1Centre d'Optique, Potonique et Laser, Université Laval, Québec, Canada.


A purely time-domain approach is proposed for the propagation of vectorial ultrafast beams in free space beyond the paraxial and the slowly varying envelope approximations. As an example of application of this method, we describe in detail the vectorial properties of an ultrafast tightly focused transverse-magnetic (TM(01)) beam, where special attention is given to the longitudinal electric field component. We show that for spot sizes at the waist comparable to the wavelength, the beam diverges more rapidly than expected from paraxial theory. A consequence of this phenomenon is a faster decrease of the amplitude of the longitudinal field away from the waist and a faster evolution of the axial Gouy phase shift in the vicinity of the focus. It has been observed that the phase of the beam has an overall variation of 2pi from z=-infinity to infinity, independent of the beam spot size at the waist and pulse duration.

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