The generation and characterization of ultrafast optical waveforms having complex structure is of growing importance. Ultrafast-resolution measurement techniques are required to measure these waveforms. One of these techniques, temporal imaging, allows an arbitrarily shaped ultrafast waveform to be stretched or compressed in time while maintaining the shape of its envelope profile, thereby improving the temporal resolution of an existing measurement system. The function of a time lens in a temporal imaging system is to impart broad-band quadratic temporal phase onto an input signal. This operation cab be accomplished by generating a pump pulse with the required quadratic phase and imparting its phase on the input signal via mixing in a nonlinear optical device, such as an aperiodically poled lithium niobate (A-PPLN) waveguide device. Analogously to a spatial lens, the temporal lens may exhibit aberrations that distort the output image and therefore limit the performance of the imaging system. It is important to understand, measure, and minimize the effects of these aberrations.
Aberrations in spatial imaging systems have been studied extensively and many techniques have been developed to analyze them. In place of the well-known Zernike circle polynomials used to analyze such aberrations, we applied Hermite polynomials to represents aberrations in a temporal imaging system. Hermite polynomials share similar properties as their spatial counterpart, Zernike circle polynomials, making them a powerful tool for analysis. We further developed a simple expression describing the effect of phase aberrations on the resolution of the system. This expression could be used to understand the degree to which different types of aberrations contribute to the total aberration.
Some of the aberrations came from our linearly chirped A-PPLN waveguide device. We presented a new technique to measure both the magnitude and phase response of the nonlinear device. This technique utilized frequency resolved optical gating (FROG) to measure the magnitude and phase of both an input pulse and output pulse. By taking the ratio of the spectrum of the output to the spectrum of the square of the input, we were able to measure the complex transfer function (CTF). Furthermore, we developed a formulation to take the measured CTF and compute the spatial distribution of the nonlinear coefficient and the phasematching profile. This information allowed us to identify sources of spectral distortion in the A-PPLN device. We found that the dominant source of distortion in our devices was errors in the waveguide lithography process, which was confirmed by atomic force microscope (AFM) measurements of an actual SiO2 mask.
One particular source of distortion that we observed in our A-PPLN devices were localized fields generated nonlinearly by highly phase-mismatched interactions. Using multiple scale analysis, we derived an expression that described this phenomenon. From there, we presented a theoretical framework in which to understand how the spatial extent and energy of the localized field depended on parameters such as pulse bandwidth, pulse chirp rate, grating chirp rate, and quasi-phasematching (QPM) grating length. We then measured the spatial profile of the localized field as we changed the center wavelength and power of the input pulse. In order to minimize the effects of photorefractive damage (PRD) due to localized fields, we designed a grating with a 33% duty cycle as opposed to the original 50% duty cycle. A device fabricated according to this design showed a 90% reduction of the total power, thereby minimizing the effect of localized fields on device performance.