Computational Simulation Of The Transmission Characteristics Of A Pulsed Beam With A Flat Top Section

Along with the development of the laser, the emergence of ultrashort ultra-intense laser pulse for all areas of study provides advanced technical conditions and extreme physical conditions, and the development of various fields of laser requirements also more and more diversified, for example, inertial confinement fusion, laser material processing, laser cosmetic etc, in order to ensure to get the desired effect, usually requires uniform beam as the light intensity distribution of flattened beams. Therefore, flat-topped beams in free space, dispersion medium, the optical fiber and aperture optical system in the transmission characteristics of space and time, the research of the light intensity and spectral characteristic of laser pulse and the corresponding appliance design and application have important practical significance.Simply introduced the spectral abnormal behavior; In detail elaborated commonly used research methods, pulse beam related basic concepts(including pulse width, center frequency, carrier frequency and the beam waist width, etc.) in the laser optical, two mathematical physics model of flattened beam-flat-topped Gaussian beam and Super Gaussian beam. Based on the basic theory and analysis method, and ultrashort flat-topped Gaussian beams and ultrashort pulsed Super Gaussian beam as the research object, the transmission characteristics and spectral behavior of the ultrashort pulse flat-topped Gaussian beams after a circular aperture or a ring aperture and the transmission characteristics and spectral behavior of the ultrashort pulse Super Gaussian beams after a circular aperture or a ring aperture have been studied. The main conclusions are the following:Based on Collins integral formula and complex Gaussian function expansion method, the light field analytical expression in the frequency domain of the ultrashort pulse flat-topped Gaussian beams after a circular aperture was obtained. And the influence for light intensity distribution and the spectral changes of the change of transmission distance, truncation parameter and pulse width were studied. The result shows that the ultrashort pulse flat-topped Gaussian beams after a circular aperture intensity distribution no more remain flat distribution, present a concave and convex distribution, and with the increase of transmission distance, light intensity distribution of concave and convex more evident, and the concave and convex degree at the edge is bigger than that in the middle section; At critical transmission distance, spectral switch is appears, when the transmission distance is less than the critical transmission distance, spectral blue-shift, when the transmission distance is greater than the critical transmission distance, spectral red-shift. For the same truncation parameter, with the increase of transmission distance, spectral blue-shift, at the first critical transmission distance, spectral jump from blue-shift to the red-shift, which is called first-order spectral switch; then with the increase of transmission distance, spectral shift changes from red-shift to blue-shift, at the second critical transmission distance, spectral shift jump from blue-shift to red-shift quickly, where the second-order spectral switch appears. With the increase of the truncation parameter, relative spectral shift reduced significantly and the orders of the spectral switch reduced. With the increase of pulse width, the relative spectral shift decreased significantly, but the spectral switch location and the orders of the spectral shift have not changed.Based on Collins integral formula and complex Gaussian function expansion method, the light field analytical expression in the frequency domain of the ultrashort pulse flat-topped Gaussian beams after a circle ring was obtained. And the influence for light intensity distribution and the spectral changes of the change of transmission distance, truncation parameter and pulse width were studied. The result shows that the light intensity distribution of the ultrashort pulse flat-topped Gaussian beams after a circle ring becomes variation, and with the increases of transmission distance, light intensity distribution gradually focused on the optical axis. Near the spectral switch, spectrum split into two peaks incomplete, with the increase of transmission distance, spectral blue-shift first and then red-shift; with the increase of the size of the size of the circle ring, the extreme of relative spectral shift remain unchanged, but the orders of spectral switch change, and with the increase of transmission distance, relative change regularly, spectral blue-shift and tends to a constant value finally.Based on Rayleigh Sommerfeld diffraction integral formula and complex Gaussian function expansion method, the light field in the spatial frequency domain of the ultrashort pulse Super Gaussian beams after a circular aperture was studied. The analytic expression of the ultrashort pulsed Super Gaussian beams after a circular aperture at N=2 is given. The spectral shift and spectral switch of ultrashort pulsed Super Gaussian beam at N=2 have been numerical calculated and analyzed. The article did not make the paraxial approximation, nor on the far field approximation; the research result with a general. Research result shows that the spectral switch appears near the critical Angle and spectrum splits into two equal peaks; when the diffraction Angle is less than the critical Angle, the spectral red-shift, and when the diffraction Angle is greater than the critical Angle, the spectrum blue-shift. With the increases of the pulse width, the angular frequency interval between two equivalent peaks of spectral switch decreases, and the line-width decreases, and the relative spectral shift decrease significantly.Based on Rayleigh Sommerfeld diffraction integral formula and complex Gaussian function expansion method, the light field in the spatial frequency domain of the ultrashort pulse Super Gaussian beams after a circle ring was studied. The analytic expression of the ultrashort pulsed Super Gaussian beams after a circle ring at N=2,3 is given. The spectral shift and spectral switch of ultrashort pulsed Super Gaussian beam at N=2 have been numerical calculated and analyzed. The research result shows that the spectral switch appears near the critical Angle and spectrum splits into two equal peaks; when the diffraction angle is less than the critical angle, the spectral red-shift, and when the diffraction angle is greater than the critical angle, the spectrum blue-shift. With the increases of the pulse width, the angular frequency interval between two equivalent peaks of spectral switch decreases, and the line-width decreases.Based on Fresnel diffraction integral formula, the propagation properties of ultrashort pulse flat-topped Gaussian beams in the dispersion medium was studied. The results show that with the increase of transmission distance, pulse broadening; The relative spectral shift increases first and then decreases and then increases again and tends to a constant value finally; with the increase of transmission distance, the light intensity on the axis increases first and then decreases and then increases and reduced gradually finally.