Self-modulation oscillations and Q-switched mode-locking of Vortex Laser Formed by Coherent Superposition of Off-axis Traveling Waves

Yuan-Yao Lin^1*, Chen-Yu Hsieh¹, Chih Nan Chen¹

¹Department of Photonics, National Sun Yat-sen University, Kaohsiung, Taiwan

* Presenter:Yuan-Yao Lin, email:yuyalin@mail.nsysu.edu.tw

Recently laser community pays great attentions to the coherent radiation with structured phase pattern, which are useful in improving the capability of applications such as high capacity communication system, super resolution microscopy. Dedications are made to generate structured light by conversion optics or direct emission from laser resonator. In 2018, we demonstrated the first optical vortex laser formed by the coherent superposition of off-axis multiple pass transverse mode in an azimuthal symmetry breaking laser resonator of hemi-spherical configuration [1]. Nonlinear bifurcation and chaotic laser dynamics were also shown when passive Q-switched laser was built based on the same structure [2]. The off-axis resonator design makes a flexible platform to construct structure light. In this work we generated optical vortex laser with self-modulation oscillation and Q-switched mode-locked vortex lasers in the proposed azimuthal symmetry breaking ring resonator.
A 39-cm-long laser resonator is formed by an a-cut Nd:YVO₄ crystal with a high reflectivity (HR) coated planar end facet and a planar output coupler (OC) of 5% transmission. At the center are placed a focusing lens of 10-cm-focal-length and a spiral phase plate (SPP) carrying a topological charge of positive one. Because the azimuthal symmetry is broken by the intra-cavity SPP, lights can only travel off-axis along a ring trajectory in either clockwise or counterclockwise manner. When the resonator was pumped by a diode laser above 1.3 W at the wavelength of 808 nm, laser with a doughnut-shaped intensity profile was emitted at the wavelength of 1064 nm. It was linearly polarized and carried spiral phase which was identified to have a positive unit topological charge by a Mach-Zehnder interferometer. The clear phase pattern indicated that the laser was formed by the coherent superposition of the off-axis traveling waves excited simultaneously.
In this multi-mode laser system, instability may occur and we thus examine the temporal evolution of the laser power with fast InGaAs photodiodes and record the waveform by oscilloscope with a sampling frequency of 5G Hz. Without any intracavity modulating elements, vortex laser output experiences large fluctuations. By taking the RF spectrum of the laser power of time, one perceived a few harmonics of 82.5 kHz with spectral power over 30 dB compared to the noise level. The oscillations were identified as self-modulation oscillation mainly due to the nonlinear interactions of non-reciprocal cavity modes in the laser gain media that couples the ring modes circulating in opposite directions. It resulted in modulation of laser output at a frequency of few tens of kHz [3]. At pumping power of 1.6 W, 1.81 W and 2.72W, respectively, self-modulation oscillation could interact with the conventional power dependent relaxation oscillation to cause periodic oscillations at the harmonic frequencies of 82.5 kHz, 165 kHz and 330 kHz accordingly. Notably the transient dynamics was synchronized among all the off-axis traveling wave modes that constituted the vortex. It indicated the high spatial-temporal coherence in the vortex laser formed by the coherent superposition of off-axis traveling waves in the proposed azimuthal symmetry breaking laser resonator.
We also study the laser mode-locking in this vortex laser by inserting an acousto-optic modulator (AOM) into the laser resonator. The cavity loss is modulated by the AOM driven by 40M Hz RF source externally gated at 1 kHz. During the time interval when AOM was switched on, the cavity loss increased and the laser oscillation stopped. The population inversion in gain media accumulated and at the same time the cavity experience index modulation at a frequency of 40M Hz close to one ninth of the free spectral range (FSR) of the laser ring cavity. Although the modulation was weak, signature of laser mode-locking was observed within the Q-switched envelope. By taking the Fourier spectrum of each one of the Q-switched envelope, up to 6 harmonics of 358 MHz could be retrieved. Mode-locked pulse of duration below 600 ps was experimentally measured. The off-axis traveling wave modes that formed the mode-locked vortex pulses were synchronized and their correlations were above 0.96 at low pump power and 0.92 at high pump power.
[1]Yuan-Yao Lin , Chia-Chi Yeh, Hsien-Che Lee, Shang-Lin Yang, Jhih-He Tu and Chun-Po Tang, ”Optical vortex lasers by the coherent superposition of off-axis multiple-pass transverse modes in an azimuthal symmetry breaking laser resonator,” J. Opt. 20, 075203 (2018).
[2] Yuan-Yao Lin , Jhih-He Tu, Hsien-Che Lee, Shang-Lin Yang and Chun-Po Tang, ”Bifurcation and nonlinear dynamics in passive Q-switched optical vortex lasers,” J. Opt. 21, 085201 (2019).
[3] N.V. Kravstov and E.G. Lariontsev, Self-modulation oscillations and relaxation processes in solid-state ring lasers, Quantum electon. 24, 841-856 (1994).

Keywords: Q-switched, mode locking, optical vortex, laser dynamics