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Study On Characteristics Of Optical Field In Off-axis Unstable-waveguide Hybrid Resonators

Posted on:2013-02-02Degree:DoctorType:Dissertation
Country:ChinaCandidate:G LiFull Text:PDF
GTID:1118330371980946Subject:Optical Engineering
Abstract/Summary:PDF Full Text Request
The high power diffusion-cool slab CO2 laser is widely used for industrial applications. The off-axis unstable-waveguide hybrid resonator is a core component of the laser. Characteristics of the field distribution in the resonator have been studied in this thesis. The transverse modes are analysed by the asymptotic theory, including the virtual source method for the lowest transverse mode and the eigen-function method for all order modes. The mode crossing and the excess noise are also discussed in detail. The main contents are classified as follows.(1) The transmission characteristics of both travelling waves along forward and backward direction have been studied. The approximate solutions for both waves are obtained with the spherical wave theory. The results show that the eigen-solution for forward travelling wave is TE mode or TM mode, the two modes can not exist simultaneously. The effect on transmission loss caused by the dielectric constant of waveguide materials is also discussed; alumina is the optimal material on the loss account. The characteristics of the field distribution along the narrow direction at the "hot spot" in the negative branch unstable resonator are analysed with the formula for the cylindrical wave. At the "hot spot", there is only one component which is along the waveguide direction. The effects on the filed amplitudes on the surface of the electrode caused by the dielectric constant of electrode material and the distance between the electrodes are studied.(2) The mathematic formula and physical meaning of the virtual source method are presented. The analysis shows that the errors are caused by three cases, the axial distance between the observation plane and the aperture, or the transverse distance between the aperture edge and the observation point is too small, the different width of the geometric shadow of the apertures are not considered, the effects on the fine structure of distribution caused by the geometric approximation of the virtual source location are ignored. The virtual source method is extended to the calculation of the lowest mode in the off-axis unstable resonators, the errors are also treated carefully, and the number of the apertures should be small as possible under the condition of the self-produce mode. The numerical result for the kilowatt diffusion-cool slab laser shows good agreement between the virtual source method and FFT.(3) A group of eigen functions have been found by the uniform asymptotic theory. The transverse modes are presented by the linear superposition of the functions. The mathematical validity of the self similar fractal method is proved and the analytic formula for the lowest mode is presented by the functions. To calculate high order modes, a polynomial about the scaled-eigenvalue is obtained.(4) The numerical results by the eigen-vector method show that the mode crossing between the lowest-and the next-lowest-loss modes occurs when the equivalent Fresnel number Neq is close to s+0.08 (s positive integer) for positive branch resonators and is close to s-0.125 for negative branch resonators, the lowest mode in positive branch is not the traditional even mode, the diffraction loss is much larger than the value predicted by the geometric optics. The degeneracy is also determined by the polynomial. The results show that the real part of Neq which is most close to the real axis is equal to about 78.4.(5) The relationship between the laser linewidth and the transverse distribution of the field is discussed. The statistical average of the Langevin noise that describes the spontaneous radiation noise coupling into a given mode is determined by the Biorthogonality of the transverses modes (K factor) and their eigenvalues. The values of K factor varying as a function of Neq are calculated numerically by the eigen-vector method with a fixed magnification. The profile shows discontinuity at mode crossing point instead of the peak. The hybrid-geometry method is modified to calculate the K factor of all order modes, and the magnitude error is corrected.
Keywords/Search Tags:Off-axis Unstable-waveguide resonator, Transverse mode, Uniform asymptotic, Excess noise, Mode Biorthogonality
PDF Full Text Request
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