A theoretical study of the mutual coherence function associated with the fields generated within a laser cavity

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1970

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Abstract

This dissertation is concerned with examining the coherence of the fields generated by a laser resonator. The resonator is assumed to be of the Fabry-Perot type, and the active media is assumed to be homogeneous and isotropic. The problem is formulated in terms of the mutual coherence function associated with these fields. After determining the propagation of the mutual coherence function from a plane aperture using a Fourier transform technique, this expression is applied to the problem of determining the modes of the resonator. In general this problem is very complex but rather than assume that the field is quasimonochromatic we wish to examine the effects of the frequency distributed gain of the active media. This is accomplished by assuming that the field is cross- spectrally pure and utilizing our knowledge of the spectral distribution of a laser resonator. The problem is still extremely complex and thus we simply examine the conditions under which the integral equation reduces to one already considered. We assume these conditions to be satisfied and apply the propagation law and the concept of cross-spectral purity to the problem of obtaining the mutual coherence function propagating from a laser resonator. One or more longitudinal modes are assumed to exist and two cases are considered, the first of which is a Gaussian line shape. In the second case the longitudinal modes are assumed to have a Lorentzian line shape. The solution which we obtain applies to the nearfield as well as the far-field. As such it includes the effects of the size of the aperture which is important for small Fresnel numbers. These effects are particularly important in examining the intensity distribution of the resonator. Numerical results are also presented for the intensity pattern.

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