Third-dimensional finite element computation of laser cavity eigenmodes

Altmann, Konrad; Pflaum, Christoph; Seider, David

doi:10.1364/ao.43.001892

Cited by 13 publications

(11 citation statements)

References 5 publications

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“…Finally, Figure 12 shows the TEM profile in an arbitrary cross section with´D 0:6 mm. The RPIM solutions of these 2D simulations of TEM mode are in good agreement with measurement results in [16] as seen in Figure 13 for cross sectioń D 0:6 mm and y D 0. This agreement reveals the fact that these simulations accurately illustrate the real thermal lensing effect.…”

Section: The Eigenvalue Problem Of Laser Open Cavitysupporting

confidence: 83%

“…If the temperature of any point in Nd:YAG cross section is T with the corresponding refractive index r , and the coolest temperature is T 0 , associated with the refractive index r 0 , the variations of refractive index is calculated according to the following ordinary differential equation ;

\frac{dr}{dT} = \frac{r_{0}^{2} - 1}{2 r_{0}} ((), d_{0} + 2 d_{1} △ T + 3 d_{2} {(△ T)}^{2} + \frac{c_{0} + 2 c_{1} △ T}{λ^{2} - λ_{0}^{2}}),

where c 0 , c 1 , d 0 , d 1 , d 2 are crystal coefficients, △ T = T − T 0 , λ 0 and λ are the wavelengths in free space and crystal, respectively .…”

Section: The Thermal Lensing Effect In End‐pumped Nd:yag Lasersmentioning

confidence: 99%

“…If the temperature of any point in Nd:YAG cross section is T with the corresponding refractive index r, and the coolest temperature is T 0 , associated with the refractive index r 0 , the variations of refractive index is calculated according to the following ordinary differential equation [16]; Figure 3 shows the solution of (6). As seen, variations of refractive index along the cross section is noticeable.…”

Section: Heat Equation and Refractive Indexmentioning

confidence: 99%

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3D meshless simulation of laser ray deviation under thermal lensing effect

Afsari

Heidari

Movahhedi

2015

Int J Numerical Modelling

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Summary In this study, one of the most important destructive effects in end‐pumped Nd:YAG laser, that is, thermal lensing is analyzed. Different partial differential equations, supplemented by suitable boundary conditions, are solved and joined to illustrate the fluctuations in laser Transverse Electromagnetic (TEM) mode. Because of no analytic demonstration of this effect, an efficient meshless method known as radial point interpolation meshless method (RPIM) is used to simulate the problem divided into two two‐dimensional cases, that is, xz and yz planes so as to be graphically understandable. The results are in good agreement with measurement reports, and the RPIM shows better accuracy than FEM. Copyright © 2015 John Wiley & Sons, Ltd.

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Section: The Eigenvalue Problem Of Laser Open Cavitysupporting

confidence: 83%

\frac{dr}{dT} = \frac{r_{0}^{2} - 1}{2 r_{0}} ((), d_{0} + 2 d_{1} △ T + 3 d_{2} {(△ T)}^{2} + \frac{c_{0} + 2 c_{1} △ T}{λ^{2} - λ_{0}^{2}}),

where c 0 , c 1 , d 0 , d 1 , d 2 are crystal coefficients, △ T = T − T 0 , λ 0 and λ are the wavelengths in free space and crystal, respectively .…”

Section: The Thermal Lensing Effect In End‐pumped Nd:yag Lasersmentioning

confidence: 99%

“…If the temperature of any point in Nd:YAG cross section is T with the corresponding refractive index r, and the coolest temperature is T 0 , associated with the refractive index r 0 , the variations of refractive index is calculated according to the following ordinary differential equation [16]; Figure 3 shows the solution of (6). As seen, variations of refractive index along the cross section is noticeable.…”

Section: Heat Equation and Refractive Indexmentioning

confidence: 99%

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3D meshless simulation of laser ray deviation under thermal lensing effect

Afsari

Heidari

Movahhedi

2015

Int J Numerical Modelling

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“…So in addition to the calculation of the dominant transversal resonator mode, we can use the vectorial operator equations given by Eq. (7) to check if the angular frequency ω 0 of the vectorial harmonic field V R x; y; z 0 ; t is an axial resonator mode. It will be an axial mode if there is a 2π modulo phase shift, so that Γ l 0.…”

Section: Zzmentioning

confidence: 99%

“…Rigorous techniques are based on the discretization of the wave equation or of the original Maxwell's equations directly by applying, for example, the finite element method [7,8] or the finite difference time domain method [9]. In principle, any type of resonator component can be included in these fully vectorial modeling approaches.…”

Section: Introductionmentioning

confidence: 99%

Laser resonator modeling by field tracing: a flexible approach for fully vectorial transversal eigenmode calculation

et al. 2014

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In this work we generalize the scalar Fox and Li algorithm for the dominant transversal resonator eigenmode calculation to a fully vectorial field tracing concept. Therefore we reformulate Fox and Li's scalar integral equation to a set of coupled operator equations. The introduction of a field tracing round trip operator concept shows that, in principle, any modeling technique which can be formulated to operate for electromagnetic fields can be used to simulate light propagation through the different subdomains of the resonator. This allows a flexible, fast, and accurate simulation of the fully vectorial dominant transversal resonator eigenmode. An example is presented to demonstrate the flexibility and accuracy of the field tracing approach.

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Lasers

Photonics

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The LASER light source, whose name is based on "Light Amplification by Stimulated Emission of Radiation", is the most important device in almost all photonic applications. First built in 1960 [6.1-6.5] it allows the generation of light with properties not available from natural light sources. Modern commercially available laser systems allow output powers of up to 10 20 W for short times with good beam quality and of several kW in continuos operation, usually with less good beam quality. Very short pulses with durations smaller than 5 · 10 −15 s, wavelengths from a few nm in the XUV to the far IR with several 10 µm, pulse energies of up to 10 4 J and frequency stability's and resolutions of better 10 −13 can be generated. The laser prices range from $ 1 to many millions of dollars and their size from less than a cubic mm to the dimensions of large buildings.The good coherence and beam quality of laser light in combination with high powers and short pulses are the basis for many nonlinear interactions, but the laser is a highly nonlinear optical device itself, using nonlinear properties of materials as described in the previous chapters. Therefore, the fundamental laws treated in Chap. 2 for the description of light as well as the description of linear and nonlinear interactions of light with matter in Chaps. 3, 4 and 5 are the basis for the analysis of laser operation and its light properties. Therefore, the theoretical description of laser devices represents an application of these laws and can be presented in this chapter in a compact form. For details the related sections of the previous chapters should be consulted. The different lasers and their constructions, as well as the resulting relevant light and operation parameters, are described and the consequences for photonic applications are discussed. Finally, possible classifications are given and safety aspects are mentioned. For further reading see [M6, M16, M17, M23-M25, M27, M28, M30, M33, M43, M44, M49, M50, M58-M65].

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Third-dimensional finite element computation of laser cavity eigenmodes

Cited by 13 publications

References 5 publications

3D meshless simulation of laser ray deviation under thermal lensing effect

3D meshless simulation of laser ray deviation under thermal lensing effect

Laser resonator modeling by field tracing: a flexible approach for fully vectorial transversal eigenmode calculation

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