Abstract
Nonlinear frequency conversion of structured beams has been of great interest recently. We present an intracavity second harmonic generation (SHG) of laser beams in transverse mode locking (TML) states with a specially designed sandwich such as a microchip laser. The intracavity nonlinear frequency conversion process of a laser beam in a TML state to its second harmonic is theoretically and experimentally investigated, considering different relative phase and weight parameters between the basic modes in the TML beam. Comparison between the far-field SHG beam patterns of fundamental frequency transverse modes in coherently locked and incoherently superposed states demonstrates that the SHG of TML beams can carry more information. Various rarely observed far-field SHG beam patterns are obtained, and they are consistent with the theoretical analysis and numerical simulations. With the obtained SHG beams, the characteristics of the structured fundamental frequency beams can also be conversely investigated or predicted. This work may have important applications in optical 3D printing, optical trapping of particles, and free-space optical communication areas.
Highlights
The transverse mode locking (TML) effect has been attracting increasing attention, due to its possible use to generate various beam patterns possessing optical vortices
With the designed sandwich-like microchip cavity laser system, the second harmonic generation (SHG) of various beams formed by the TML state of LG or HG modes has been successfully achieved
Three cases are shown here, and the LG modes in the TML states have the azimuthal index l be 2, 3, and 4, Fig. 7 The experimental and simulated results for the SHG of TML beams that are composed of LG0;1 þ LG0;−l modes. (a)–(c) The combinations are LG0;2 þ LG0;−2, LG0;3 þ LG0;−3, and LG0;4 þ LG0;−4, respectively. (a1)–(c1) and (a4)–(c4) Experimentally measured far-field beam patterns of TML beams and SHG beams. (a2)–(c2), (a3)–(c3) and (a5)–(c5), (a6)–(c6) are the corresponding simulated far-field patterns and phases
Summary
The transverse mode locking (TML) effect has been attracting increasing attention, due to its possible use to generate various beam patterns possessing optical vortices. For SHG of two photons with angular frequency ω and single OAM, respectively, if the OAMs are equal, the OAM variation has l2ω 1⁄4 2lω or it has l2ω 1⁄4 l0ω þ l0ω0 .23–25 All these above studies on nonlinear processes were explored based on external-cavity structured mode generation. Different from the traditional study on the nonlinear frequency conversion of a longitudinal mode-locked ultrafast laser beam, the variation of spatial structure information is focused on nonlinear frequency conversion of a TML beam. Pairs of a fundamental frequency beam and its SHG beam are obtained with a temporal pulse duration of 2 ns and a repetition rate of tens of kilohertz The generation of these TML laser modes, especially for their frequency converted ones, opens up intriguing new avenues for obtaining various structured beams with the intracavity method. We believe that this work will be helpful to promote the applications of structured beams in optical 3D printing,[29,30] optical trapping of particles, and free-space optical communication areas in the future
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