Amplification of a propagation invariant vector flat-top beam

2021 ◽  
Author(s):  
Justin Harrison ◽  
Andrew Forbes ◽  
Darryl Naidoo
Keyword(s):  
Invariant Vector ◽  
Flat Top Beam

scholarly journals Realizing Gaussian to flat-top beam shaping in traveling-wave amplification

2017 ◽  
Vol 25 (26) ◽  
pp. 33226 ◽  
Author(s):  
Tianzhuo Zhao ◽  
Zhongwei Fan ◽  
Hong Xiao ◽  
Ke Huang ◽  
Zhenao Bai ◽  
...  
Keyword(s):  
Traveling Wave ◽  
Beam Shaping ◽  
Wave Amplification ◽  
Flat Top Beam

Semilinear PDEs in the Heisenberg group: The role of the right invariant vector fields

2010 ◽  
Vol 72 (2) ◽  
pp. 987-997 ◽  
Author(s):  
Isabeau Birindelli ◽  
Fausto Ferrari ◽  
Enrico Valdinoci
Keyword(s):  
Heisenberg Group ◽  
Vector Fields ◽  
Invariant Vector ◽  
Semilinear Pdes ◽  
The Right ◽  
Invariant Vector Fields

Harmonicity of vector fields on a class of Lorentzian solvable Lie groups

2018 ◽  
Vol 18 (3) ◽  
pp. 337-344 ◽  
Author(s):  
Ju Tan ◽  
Shaoqiang Deng
Keyword(s):  
Vector Field ◽  
Lie Groups ◽  
Lie Algebras ◽  
Critical Points ◽  
Vector Fields ◽  
Energy Functional ◽  
Smooth Vector ◽  
Solvable Lie Groups ◽  
Invariant Vector ◽  
Invariant Vector Fields

AbstractIn this paper, we consider a special class of solvable Lie groups such that for any x, y in their Lie algebras, [x, y] is a linear combination of x and y. We investigate the harmonicity properties of invariant vector fields of this kind of Lorentzian Lie groups. It is shown that any invariant unit time-like vector field is spatially harmonic. Moreover, we determine all vector fields which are critical points of the energy functional restricted to the space of smooth vector fields.

scholarly journals Demonstration of flat-top beam illumination in widefield multiphoton microscopy

2019 ◽  
Vol 25 (01) ◽  
pp. 1
Author(s):  
Mohammad M. Kabir ◽  
Hemangg S. Rajput ◽  
Varun A. Kelkar ◽  
Adriana C. Salazar Coariti ◽  
Kimani C. Toussaint
Keyword(s):  
Multiphoton Microscopy ◽  
Flat Top Beam

Degenerate p-Laplacian Operators and Hardy Type Inequalities on H-Type Groups

2010 ◽  
Vol 62 (5) ◽  
pp. 1116-1130 ◽  
Author(s):  
Yongyang Jin ◽  
Genkai Zhang
Keyword(s):  
Vector Fields ◽  
Orthonormal Basis ◽  
Type Inequality ◽  
Laplacian Operator ◽  
Hardy Type Inequality ◽  
Invariant Vector ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Left Invariant Vector ◽  
Laplacian Operators

AbstractLet 𝔾 be a step-two nilpotent group of H-type with Lie algebra 𝔊 = V ⊕ t. We define a class of vector fields X = {Xj} on 𝔾 depending on a real parameter k ≥ 1, and we consider the corresponding p-Laplacian operator Lp,ku = divX(|∇Xu|p−2∇Xu). For k = 1 the vector fields X = {Xj} are the left invariant vector fields corresponding to an orthonormal basis of V; for 𝔾 being the Heisenberg group the vector fields are the Greiner fields. In this paper we obtain the fundamental solution for the operator Lp,k and as an application, we get a Hardy type inequality associated with X.

Fluidic Laser Beam Shaper by Using Thermal Lens Effect

2011 ◽  
Author(s):  
Hong Duc Doan ◽  
Yoshihiko Akamine ◽  
Kazuyoshi Fushinobu
Keyword(s):  
Refractive Index ◽  
Pump Power ◽  
Absorption Coefficient ◽  
Laser Beam ◽  
Probe Beam ◽  
Thermal Lens ◽  
Refractive Index Distribution ◽  
Index Distribution ◽  
Thermal Lens Effect ◽  
Flat Top Beam

Laser measurement and laser processing techniques have been gaining strong attention from various applications [1,2]. This research aims at the development of a fluidic laser beam shaper, and in order to fulfill the objective, characteristics of the thermal lens effect are studied. This phenomenon has the optical property of a concave lens since the refractive index distribution on the optical axis is formed when the liquid is irradiated. One reason for the refractive index distribution in the liquid is the temperature distribution in the liquid when it is irradiated. In this research, effects of the pump power and propagation distance of the probe beam to probe beam profile are investigated experimentally and theoretically, in order to develop fluidic laser beam shaper. It is indicated that, by controlling some parameters in thermal lens system as pump power (in the regime of linear optics) and absorption coefficient, input Gaussian beam can be converted into flat-top beam profile. The relationship among the distance to obtain a flat-top beam, pump power and absorption coefficient is investigated to show the flexibility of fluidic laser beam shaper in many fields of laser application.

Investigation of combining output a uniform flat-top beam of six solid state lasers by DOE

2017 ◽  
Author(s):  
Meng-zhen Zhu ◽  
Cheng Yong ◽  
Liu Xu ◽  
Tan Caoyong ◽  
Xia Chen ◽  
...  
Keyword(s):  
Solid State ◽  
Solid State Lasers ◽  
Flat Top Beam
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