Tamblyn, Isaac

Spectral-focusing-based coherent anti-Stokes Raman scattering (SF-CARS) microscopy is a powerful imaging technique that involves temporally and spectrally stretching ultrashort laser pulses and controlling their frequency-time characteristics. However, a broader and more detailed understanding of the frequency-time characteristics of the laser pulses and signals involved, how they are related, and how they influence important aspects such as the spectral resolution is needed to understand the full potential of SF-CARS systems. In this work, I elucidate these relationships and discuss how they can be exploited to optimize SF-CARS microscopy setups. I present a theoretical analysis of the relationships between the spectral resolution, the degree of chirp-matching, and pulse bandwidth in SF-CARS. I find that, despite allowing better ultimate spectral resolution when chirp-matching is attained, the use of the broadest bandwidth pulses can significantly worsen the spectral resolution if the pulses are not chirp-matched. I demonstrate that the bandwidth of the detected anti-Stokes signal is minimized when the pump is twice as chirped as the Stokes, meaning that (perhaps counter-intuitively) a narrow anti-Stokes bandwidth does not imply good spectral resolution. I present approximate expressions that relate the bandwidths of the pump, Stokes, and anti-Stokes pulses to the degree of chirp-matching and outline how these could be used to estimate the amount of glass needed to attain chirp-matching.

I develop a spectral-focusing-based polarization-resolved (SFP-CARS) setup, by modifying our existing system, to explore the merits of integrating polarization-dependent detection as an add-on to existing SF-CARS setups. By using the system to study polarization-dependent features in the CARS spectrum of benzonitrile, I assess its capabilities and demonstrate its ability to accurately determine Raman depolarization ratios. Ultimately, the detected anti-Stokes signals are more elliptically polarized than desired, hindering a complete suppression of the non-resonant background. Nevertheless, I find that the SFP-CARS setup is a useful tool for studying polarization-dependent features in the CARS spectra of various samples and is worthy of further investigation. This work clarifies several technical aspects of SF-CARS microscopy and provides researchers with valuable information to consider when working with SF-CARS microscopy systems.

Author Keywords: coherent anti-Stokes Raman scattering, nonlinear microscopy, polarization, spectral focusing, spectroscopy

Many of the most interesting electronic behaviours currently being studied are associated with strong correlations. In addition, many of these materials are disordered either intrinsically or due to doping. Solving interacting systems exactly is extremely computationally expensive, and approximate techniques developed for strongly correlated systems are not easily adapted to include disorder. As a non-interacting disordered model, it makes sense to consider the Anderson model as a first step in developing an approximate method of solution to the interacting and disordered Anderson-Hubbard model. Our renormalization group (RG) approach is modeled on that proposed by Johri and Bhatt [23]. We found an error in their work which we have corrected in our procedure. After testing the execution of the RG, we benchmarked the density of states and inverse participation ratio results against exact diagonalization. Our approach is significantly faster than exact diagonalization and is most accurate in the limit of strong disorder.

Author Keywords: disorder, localization, real-space renormalization, strong correlations