Mixing Ince–Gaussian modes through sum-frequency generation

Abstract

We present a nonlinear mixing study of Ince–Gaussian (IG) beams in non-collinear sum-frequency generation, completing the fundamental analysis of all three families of paraxial wave equation solutions under this nonlinear process. Through theoretical and experimental results, we consider the nonlinear mixing of even and odd IG modes, and transition between the paraxial modes by controlling the eccentricity parameter ϵ and helical IG modes possessing arbitrary orbital angular momentum. Additionally, the selection rule of IG modes in the nonlinear mixing processes is determined. This work is important for optical communications and quantum protocols.

Towards higher-dimensional structured light

“…For instance, the “untwisting” of the azimuthal phase of an OAM LG mode, in turn, alters the radial index 196 , with the rules governing this interaction only recently unveiled 197 , and shown to be true for wave mixing processes of any order 198 . Similar processes have been observed with HG modes 199 , Ince-Gaussian 200 , 201 and Bessel-Gaussian modes 202 , confirming OAM conservation 87 and exploring the selection rules of these families.…”

Evolution on spatial patterns of structured laser beams: from spontaneous organization to multiple transformations

“…134 The generation of LG beams with higher radial orders and IG beams through a nonlinear wave mixing process was further investigated to obtain more complex beam patterns. 130,139,140 However, in the above studies, the characteristics of the frequency-doubled beam patterns during propagation have hardly been mentioned. Later, in the research of SHG modes through input LG beams with opposite OAMs, the near-and far-field patterns show different light field distributions, 137 as shown in Fig.…”

“…Combining nonlinear frequency conversion with the generation of structured laser beams, the beam patterns of harmonic waves are found to be endowed with much richer spatial information. Through nonlinear frequency conversion of structured laser beams, the beam pattern transformations in sum frequency generation (SFG), 127 – 130 second-harmonic generation (SHG), 131 – 140 four-wave mixing (FWM), 141 , 142 and other frequency upconversion 143 – 145 processes are carried out. Usually, these studies first generate structured beams with the help of modulation devices (such as SLM), and then carry out nonlinear conversion, which belongs to the external cavity nonlinear process of structured laser beams.…”

Nonlinear optics with structured light

“…Similar processes have been observed with Hermite-Gaussian (HG) modes. Here, their separable Cartesian form makes the interpretation of the selection rules far more straightforward, aided further by the fact that they are the natural solutions of the anisotropy of a biaxial crystal 56 , an important aspect in optical cavities. Since these seminal studies, wave mixing with structured light has included Ince-Gaussian 57,58 and Bessel-Gaussian 59−62 modes, confirming OAM conservation and exploring the selection rules of these families.…”

“…A thorough study on the influence of the geometrical properties of the OPO on the generated spatial modes can be seen in 116 and their applications in continuous variable entanglement in 117 . The structured output can be tailored by structuring the pump 56,118 , as can the geometry of the cavity itself 119 , making the cavity selective to specific modes.…”