Propagation Of Light Beams Through Optical System With Hard-edge Aperture

Since the first laser invention, the laser has been the research subject about beams through the complex optical system's transmission and the transformation question that the scientific worker is interested in . Generally, the laser through the hard-edge aperture optical system's transmission and the transformation research, we often calculate from straightforward integral of the Collins formula. Optical elements that limit the beams through optical systems are called the aperture. It may be the optical element (for example lens,reflector and so on) itself, may also be the other establishment belt round hole airtight illuminant shield. The aperture center usually is located in the main axis, and the aperture surface and the main axis perpendicular .Generally optical system has many apertures, the limit function is biggest to the light beam, namely in fact decided that is called the aperture. To other simple lens without any apertures, the size of optical system is aperture . The aperture may curtain off the light beams that deviate paraxial, the object clarity, which has the immediate have an effect on the accuracy, brightness and the depth of field and so on. Therefore, numerical simulation of the transform of laser beams through the hard-edge aperture optical systems is an important research subject.The main contents of this thesis are summarized as follows:1. Introduces method of the complex Gaussian functions and its application in the laser through optical system with the hard-edge aperture.2. The definition and the nature of Fractional Fourier transform, their optical implementation. 3. Analysised the characteristic of the propagation properties of Hermit-Guassian beams through the hard-edge aperture optical systems. The approximate analytical propagation equation is derived by means of expansion of the hard-edge aperture function into a finite sum of complex Gaussian functions. Numerical calculation examples are given for the intensity of Hermit-Gaussian beams by a thin lens.4. By expanding the rectangular function into a finite sum of complex Gaussian functions, then making use of the ABCD matrix form of Gaussian aperture to reply Gaussian function, the approximation analytical expression for Fractional Fourier transforms of Elliptical Hermit-Gaussian beams passing through the hard aperture is derived. By using the derived formula, numerical calculation examples are given for the intensity of Elliptical Hermit-Gaussian beams. The influences of the fractional order, Hermit mode order and the sizes of the hard-edged apertures on the properties of Elliptical Hermit- Gaussian beams in the fractional Fourier plane are studied in details.5. By expanding the rectangular function into a finite sum of complex Gaussian functions, then making use of the ABCD matrix form of Gaussian aperture to reply Gaussian function, the approximation analytical expression for Fractional Fourier transforms of Flat-topped light beams passing through the hard aperture is derived. By using the derived formula, numerical calculation examples are given for the intensity of Flat-topped light beams. The influences of the order M,the fractional order and the size of the hard-edged apertures on the properties of Flat-topped light beams in the fractional Fourier plane are studied in details.