We have conducted studies of basic nonlinear optical processes. Traditionally, nonlinear optical processes have been studied using focused laser beams. The illumination of the interaction region usually comes from a solid angle W much smaller than 2p steradians, the solid angle subtended by a hemisphere. Most theoretical treatments of nonlinear optics consequently treat the nonlinear interaction through use of the paraxial approximation. In our study, we have for the first time studied the opposite limiting case, where the sample is excited coherently from all directions by an incoming spherical wave that subtends a solid angle of 4p steradians. Nonlinear optical processes behave very differently in this limit. There is no phase-matching requirement, because the nonlinear signal comes primarily from the focal region, which in this case has a size of approximately the wavelength of light. We find that nonlinear processes consequently become very efficient in this limit .
We have studied the process of adiabatic wavelength conversion  in a highly nonlinear material, indium tin oxide excited at a wavelength where the real part of its dielectric permittivity vanishes, the so-called epsilon-near-zero (ENZ) condition. We find that the wavelength range over which the output wave can be tuned is much larger for ENZ regions than had previously been studied under non-ENZ conditions. We have also performed a theoretical study of the nonlinear propagation of THz pulses . THz propagation shows effect qualitatively different from the propagation of visible light because the wavelength of THz waves is so large the diffraction effects are dominant and the paraxial is not valid. Moreover, THz nonlinearities tend to be very much stronger than nonlinearities at optical frequencies. We have also studied the nonlinear propagation of few-cycle optical pulses . A key finding is that self-focusing effects tend to be strongly suppressed in this circumstance, as a result of pulse broadening through the process of group velocity dispersion.
- Nonlinear optics with full three-dimensional illumination, R. Penjweini, M. Weber, M. Sondermann, R. W. Boyd, and G. Leuchs, Optica 6, 878-883 (2019).
- Broadband frequency translation through time refraction in an epsilon-near-zero material, Y. Zhou, M. Z. Alam, M. Karimi, J. Upham, O. Reshef, C. Liu, A. E. Willner and R. W. Boyd, Nature Communications 11, 2180 (2020).
- Propagation of broadband THz pulses: effects of dispersion, diffraction and time-varying nonlinear refraction, P. Rasekh, M. Saliminabi, M. Yildirim, R. W. Boyd, J-M. Ménard, and K. Dolgaleva, Optics Express 28, 3237-3248 (2020).
4. Suppression of self-focusing for few-cycle pulses, S. A. Kozlov, A. A. Drozdov, S. Choudhary, M. A. Kniazev, and R. W. Boyd, Journal of the Optical Society of America B 36, G68-G77 (2019).