Field of a Truncated Gaussian Beam as Given by the Boundary-Diffraction-Wave Theory

Abstract

The field of an incident wave with a Gaussian irradiance distribution diffracted by a circular aperture has been evaluated by using the boundary-diffraction-wave theory. Numerical results of the irradiance distributions, both along the axis and in transverse planes, are compared with those given by the Kirchhoff integral. Good agreement is obtained in all cases over wide regions of the diffracted field.La theorie des ondes de bord est appliquee au calcul de la diffraction d'un faisceau Gaussien par une ouverture circulaire. On compare les resultats numeriques obtenus de cette favon, pour des distributions d'intensite axiales et transverses, avec les resultats obtenus a I'aide de l'integrale de Kirchhoff. Ces deux theories sont en accord pour une grande rCgion du champ diffracte.

Diffraction of Focused Laser Beams

“…UQ =d/zo exp (-ikzo -r' 2 /w 2 ), (1) where w is the spot radius of the beam at the edge (i .e . half-width of i/e points of amplitude profile) and z o the radius of curvature of the incident beam phase front ; the equivalent peak amplitude Q/zo = \/(2p/aw2 ) with p being the beam power (milliwatts, say) and k = 27r/A with A the light wavelength ; w and z0, in turn given by the propagation laws [5] for Gaussian beam, which contracts to a minimum spot radius coo at the beam waist (z=0), prior to spreading : By symmetry, as the fringes are parallel to the edge, we can ignore the steady field variation along the x axis ; under these circumstances, the intensity at a point P(y) in the illuminated region of the pattern (distant z1 from the edge) can be shown to be (avoiding details)…”

“…This behaviour is also true generally for laser diffraction by opaque obstacles, and apparently no such restriction exists for ordinary light diffraction . So far no theoretical explanation of this effect has been advanced, although several authors [1][2][3] have extensively investigated laser diffraction, obtaining very cumbrous expressions for the intensity profile, and plotted the results for a few specific beam sizes (significantly for the straight edge, the work of Yariv and collaborators [3], Caltech ., U .S .A.) .…”