Direct focusing modifications of elliptical Gaussian beam by non-circular apertures

Abstract

For focusing the elliptical Gaussian beam directly, the e ects of a non-circular aperture on the focusing properties are studied. The focusing properties for di erent shapes of apertures, which include a circle, an ellipse and a rectangle, are calculated and compared. Moreover, for di erent elliptical Gaussian beams, an empirical aperture selection rule that can be used to circularize the focusing spot is proposed. The energy transmission ratios are also considered in this paper. Gaussian beams. In practical applications, there are two methods of focusing elliptical Gaussian beams. The ®rst method, which is most often used, is to use prisms or cylindrical lenses [1] to obtain a circular beam before focusing. Because of misalignment and defects of the optical elements this approach may cause unavoidable throughput losses and increase the system cost. The other method is the so-called direct focusing method, which utilizes the aperture to truncate the incident beam to get the desired characteristics of the focusing spot. Marchant [2] studied the direct focusing properties of the elliptical Gaussian beams by using the central irradiance and the line spread function. With considerations of system cost and power increase of the laser diode, Kondo [3] has used this approach for the optical heads. However, when the elliptical beam can be focused through a circular objective lens, the focusing spot will also be non-circular, and the ellipticity of the focusing spot depends on the beam ellipticity and the apodization values [2]. Kondo [3] showed that the orientation of the major or minor axis of the elliptical Gaussian beam can a ect the signal level, the spatial frequency characteristics and the cross-talk level. In some other applications, for instance the laser printer, a non-circular focusing spot is an annoying problem.According to the di raction theory, the shape of the aperture can a ect the di raction pattern in the image plane of an optical system [4±6]. The di raction of an elliptical Gaussian beam truncated by an elliptical aperture has been calculated numerically by Kathuria [7], who found that the beam ellipticity, which is not equal to the ellipticity of the aperture, can be changed in the far ®eld. In this paper, the aperture di raction method is put forward to modify the characteristics of the elliptical focusing spot. The e ects of rectangular and elliptical apertures on the