Quantifying the emergence of structured laser beams relevant to Lissajous parametric surfaces

Chen, Yung-Fu; Zheng, X. L.; Hsieh, M. X.

doi:10.1364/ol.461163

Cited by 6 publications

(5 citation statements)

References 28 publications

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“…In the degenerate cavity, there is a linear relationship between cavity length and 3D Lissajous-like structural laser modes [13], and the slope of the line can be confirmed as the effective cavity length difference,…”

Section: The Emergence and Distortion Of Lissajous-like Structural La...mentioning

confidence: 85%

“…where M is a positive integer [13], 𝑁 and 𝑁 are the transverse order in x and y directions, w 𝑧 and 𝑤 𝑧 indicate the variation of laser beam size in the z direction,…”

Section: Geometric Optics In Concave Mirror and Birefringence Crystalmentioning

confidence: 99%

“…prime, showing the trajectory behavior [13]. We extend the ray tracing model into a 3D situation in the next section and discuss how the 3D Lissajous-like structures appear and vary in the laser cavity.…”

Section: Geometric Optics In Concave Mirror and Birefringence Crystalmentioning

confidence: 99%

“…where M is a positive integer [13], √ N x and N y are the transverse order in x and y directions, w x (z) aNd w y (z) indicate the variation of laser beam size in the z direction, θ x (L) = θ q,s = θ s (1 − q/M), and θ y (L) = θ p,s = θ s (1 + p/M), where…”

Section: Ray Tracing Model In Spherical Plano Cavitymentioning

confidence: 99%

“…And the superposition of these eigen modes forms the geometric mode [9][10][11] and the non-planar geometric mode [12]. In the two-dimensional case (x-y-z cube), due to the birefringent crystal, Nd:YVO 4 , there is a cavity length difference between the x direction and the y direction [13], which causes the transverse mode spacing difference between the x direction and the y direction. Then, more refined degenerate superposition modes (Lissajous-like structural laser modes) appear [14,15].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Exploring the Origin of Lissajous Geometric Modes from the Ray Tracing Model

Zheng,

Fang,

Chung

et al. 2024

Photonics

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In this paper, we use the geometric optics and discuss the path of laser beam in a simple laser (concave-plano) cavity with the birefringence crystal. In specific lengths of the laser cavity, we can observe various types of Lissajous-like structural laser modes that can be simulated using our ray tracing model. At the end of this paper, we provide an adjusted ABCD matrix. With the adjusted ABCD matrix and iterative calculation, we can obtain the 3D trajectories which are similar to the experimental results. These structural laser modes can be realized by a Nd:YVO4 solid-state laser with off-axis pumping. From the comparison between the experimental data and the numerical data, we clarify the relationship between the 3D Lissajous-like structural laser modes and ray trajectory in the laser cavity.

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Section: The Emergence and Distortion Of Lissajous-like Structural La...mentioning

confidence: 85%

“…where M is a positive integer [13], 𝑁 and 𝑁 are the transverse order in x and y directions, w 𝑧 and 𝑤 𝑧 indicate the variation of laser beam size in the z direction,…”

Section: Geometric Optics In Concave Mirror and Birefringence Crystalmentioning

confidence: 99%

Section: Geometric Optics In Concave Mirror and Birefringence Crystalmentioning

confidence: 99%

Section: Ray Tracing Model In Spherical Plano Cavitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exploring the Origin of Lissajous Geometric Modes from the Ray Tracing Model

Zheng,

Fang,

Chung

et al. 2024

Photonics

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The frequency degeneracy range of transverse mode in an off-axis end-pumped solid-state lasers

Li,

Song,

Huang

et al. 2024

Appl. Phys. B

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The degenerate phenomena of transverse modal frequency in an off-axis end-pumped solidstate lasers was researched based on a semi-confocal cavity. Experimental results showed that at the large off-axis distance the transverse mode pattern changed from the Hermite-Gaussian mode to the geometric mode and finally back to the Hermite-Gaussian mode as cavity length varied. At the large off-axis distance, the degeneracy range of transverse mode patterns was a cavity length to mirrors radius ratio from 0.4958 to 0.5092 and the frequency degeneracy range was a cavity length to mirrors radius ratio from 0.4974 to 0.5025. The degeneracy range by observing beating frequency changes was more accurate and more useful than the method by comparing the transverse pattern changes. Furthermore, it was found that the off-axis pumping did not significantly alter the degeneracy position and range. 1.IntroductionUnder the principle of paraxial approximation, laser transverse modes in spherical cavities exhibit various eigenmodes, such as Hermite-Gaussian (HG) modes in cartesian coordinate and Laguerre-Gaussian (LG) modes in cylindrical coordinate [1,2]. Theoretical frameworks and experimental evidence suggested that structured light, according to specific requirements, can be synthesized within the spherical resonator [3][4][5]. Innumerable effort has been devoted to researching the degenerate phenomena of transverse modes in recently two decades [6][7][8][9][10][11][12][13]. By utilizing the degenerate method of transverse modes, people might obtain different structured lights. These structured lights could be applied in many fields, such as trapping nanoparticles[14], optical communication and optical device [15]. The method of transverse modes so far was mainly focused on frequency degenerating of transverse modes [10][11][12]16], it might also result from phase locking of modes [17]. As for the frequency degenerating of transverse modes, theory and results of it had been researched substantially [11,12,16,18,19]. But there were few researches on how wide the stable degenerate region was, to our knowledge. If there were some methods to analyze the detailed degeneracy process in the resonator, it will greatly promote the practical applications of the transverse modal degeneracy. It could help to judge whether the degenerate phenomena occurred or not. And the stable degenerate region was

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Superposition and interference of Gaussian wave packets for laser transverse modes

Liu,

Wang

2024

Laser Phys.

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We interpret the intrinsic mechanism of the transition from geometric modes to eigenmodes in the Gaussian wave-packet representation based on numerical simulation. We then construct multiaxial super-geometric modes and polygonal vortex modes based on Gaussian wave packets. We highlight that the superposition of Gaussian wave packets can build the geometric modes described by Hermite polynomials and that the eigenmodes are the result of the interference of Gaussian wave packets. We conclude that Gaussian wave packets might serve as a complete basis for constructing structured light generated in solid-state laser cavities. Our study may provide meaningful insight into Gaussian wave packets for laser transverse modes.

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Quantifying the emergence of structured laser beams relevant to Lissajous parametric surfaces

Cited by 6 publications

References 28 publications

Exploring the Origin of Lissajous Geometric Modes from the Ray Tracing Model

Exploring the Origin of Lissajous Geometric Modes from the Ray Tracing Model

The frequency degeneracy range of transverse mode in an off-axis end-pumped solid-state lasers

Superposition and interference of Gaussian wave packets for laser transverse modes

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