The Lens Effect Of Fresnel Binary Pulse Shaping And Its Application

Lens has the focusing and divergent effects for the beam and imaging function, so it is one of the most simple and important optical element. In Fourier optics, thin lens can also be used as a phase variator (impart or eliminate spatial quadratic phase)and have the properties of Fourier transform. We can prepare Fresnel zone plates with the function of lens-like based on the idea of Fresnel half-wave zone, thus making a Fresnel lens, which has been widely used in projected display, condenser and amplitude transformer, aviation and maritime, scientific and technological research, infrared detection, illumination optics, and smart home etc. By analogy with spatial effects in classical optics, we can extend these spatial effects to other associated physical processes in the time domain and frequency domain under certain conditions. A typical example of which is the spatial properties of the lens, including the focus of the beam divergence, phase transformation and its Fourier transform nature extended to associated physical processes in the time domain or frequency domain. The space-time (frequency) duality has been widely used in quantum focusing, spectral compression, temporal imaging, ultra high-speed optical signal processing etc.Based on the space-time (frequency) duality, we propose a pulse shaping scheme called as Fresnel-inspired binary pulse shaping and design a Fresnel lens-like in the frequency domain and time-domain with this scheme, which solves some related problems of lens-like effects. The range of wavelengths can be focused are broadened by using these Fresnel zone lenses, which is also used for focusing x-ray, slow protons, even atom. Therefore, it is very important and valuable to investigate Fresnel lens-like effect of the physical processes related with the space-time (frequency) duality. The content of making a Fresnel lens-like using Fresnel binary pulse shaping mentioned in the text is a general method for associated physical processes of dealing with or eliminating the quadratic phase factor.This work can be mainly divided into two parts, i.e., Fresnel lens-like effect in the frequency domain and in the time domain. Fresnel lens-like effects in the frequency domain involve two second-order nonlinear processes, i.e., two-photon absorption and second harmonic generation. Fresnel lens-like effects in the time domain involve two physical processes, i.e., compression of chirped biphotons and chirped optical pulse compression. Specified contents are shown as follows:1. Quantum focusing and coherent control of non-resonant two-photon process:(i) By analogy between two-photon process and Fresnel diffraction, we find that the evolution of the two-photon wave function in the frequency domain is similar to a wide-slit Fresnel diffraction behavior;(ii) The ratio between the real and imaginary parts of the wave function, i.e., the relationship between dispersion and absorption of atomic polarization process can be controlled by controlling the initial phase of the excitation pulse, thus manipulating the process of atomic polarization;(iii) We propose a new binary pulse tailoring scheme according to the extreme conditions of two-photon transition probability for the weaknesses of large background by Broers’method. This is equivalent to the production of the frequency-domain lens-like and obtain the focus signal with lower background and greater signal intensity in center frequency 2. Spectral compression and modulation of second harmonic generation:(i) Second harmonic generation (SHG) is studied using coherent control method of quantum mechanics, and a comparison is done between ultrashort-pulse SHG in thin and thick crystals. It is found that second harmonic generation in thick crystals can be controlled coherently by modulating various interference channels.(ii) We design a pulse tailoring scheme named as Fresnel-inspired binary pulse shaping. With this scheme, we obtain a perfect compressed second-harmonic spectrum with narrowband and low background by modulating the phase relationship between the different frequency components within fundamental pulse.(iii) Based on a analogy with the Fresnel single-slit diffraction, a multi-peak second-harmonic signal is generated by tailoring the fundamental pulse, realizing spectral modulation of SHG.3. Compression and shaping of chirped biphotons:(i) We introduce the generation method and physical mechanism of chirped biphotons and study the coherence properties and time correlation properties (entanglement properties) of chirped biphotons, and the influence of crystal length, chirp coefficient for these quantum properties.(ii) Based on the pulse-shaping technique, we propose a new method for compression of chirped biphotons in the time domain, which can overcome the weaknesses of the dispersion compensation scheme. It can eliminate quadratic phase factor by shaping biphoton spectrum with Fresnel binary pulse shaping, which is equivalent to making Fresnel lens in the frequency domain.(iii) With this method, we also obtain multi-peak temporal two-photon wave packet through appropriate shaping biphoton spectrum, realizing shaping of chirped biphotons.4. Chirped optical pulse compression:(i) We introduce the basic principles and methods of ultrashort pulse compression, ultrashort pulse spectral broadening, and ultrashort pulse dispersion compensation techniques.(ii) We propose a new method of chirped pulse compression using Fresnel-inspried binary phase modulation. The method is simple, compact and can be easy to operate due to overcoming the shortcomings of traditional dispersion compensation.