Direct observation of bulk second-harmonic generation inside a glass slide with tightly focused optical fields

Abstract

Bulk second-harmonic generation (SHG) inside glass slides is directly detected unambiguously without interference from surface contributions. This is enabled by tightly focused and highly localized ultrashort laser pulses. The theoretical calculations based on vector diffraction theory and the phenomenological model of SHG inside centrosymmetric materials agree well with the measured far-field SHG radiation patterns for different polarization states of the fundamental beam. The results indicate that the observed bulk SHG is predominantly related to the bulk parameter δ and originates from the three-dimensional field gradient in the focal region. DOI: 10.1103/PhysRevB.93.161109 Under the electric dipole approximation of light-matter interaction, second-harmonic generation (SHG) is usually considered forbidden in bulk centrosymmetric materials. Dipolar SHG is allowed through a surface contribution arising at the interface between centrosymmetric materials where centrosymmetry is broken [1,2]. However, when higher-order multipole interactions [3,4], such as magnetic-dipole and electric-quadrupole interactions, are taken into account, SHG can occur even inside bulk centrosymmetric materials, which was observed in several experiments [5][6][7][8]. When SHG is used as a surface or interface probe, it is essential to separate bulk contributions from the measured SH signal and verify that such multipolar contributions are actually negligible [9]. In addition, as suggested recently, strong multipole interactions may bypass the noncentrosymmetry requirement and promote applications of new nonlinear materials [10,11]. Therefore, a thorough understanding of the physical mechanisms behind bulk SHG from bulk centrosymmetric materials is fundamental for many practical applications utilizing SHG [12].Various attempts have been made to characterize surface and bulk contributions to SHG [7,8,13,14]. For example, the SHG based on two noncollinear fundamental beams [7,8] has been widely used to study surface and bulk contributions in a quantitative way. However, up to now, the separation of surface and bulk contributions is still known to be a fundamental difficulty in the field of SHG from centrosymmetric materials. Since two-beam overlap in a spatial region is usually several millimeters long [8], the excitation field is not highly localized. Furthermore, as the SH signal is often too weak to detect when the interaction volume is deep inside the bulk material, the excitation region is often chosen to be near the surface in order to maximize signal intensity [15]. Thus the surface dipolar response cannot be completely avoided, which often perturbs the bulk response. This contributes to the wide variation of results reported in the literature. So far, the mechanism of bulk SHG inside centrosymmetric materials still remains unclear.Bulk SHG has been previously observed in centrosymmetric gaseous materials [16,17] with focused laser pulses, where * Corresponding author: rhui@ku.edu SHG was attributed to the ponderomotive force cau...

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“…Both bulk and surface SHG excited by tightly focused laser beams have been earlier studied theoretically and experimentally in different media, including isolated centrosymmetric nanospheres 40,41 , metal nano-objects 42 , glass slides 43,44 and silicon nanowires 45 . The obtained results in particular have shown that analysis of SHG radiation patterns enables separating the second-harmonic response stemming from different elements of the surface nonlinear tensor 40,41,45 , different contributing terms in the bulk quadrupolar response 40,41,43 or distinguishing the surface and bulk signals 40,44 . However, it is important to emphasize here that all aforementioned works dealt with SHG from centrosymmetric materials only.…”