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Modified Frantz-Nodvik equation and numerical simulation of a high-power Innoslab picosecond laser amplifier

Bingnan Shi, Jiatong Li, Shuai Ye, Hongkun Nie, Kejian Yang, Jingliang He, Tao Li, and Baitao Zhang

Open Access Open Access

Abstract

A modified Frantz-Nodvik (F-N) equation and a simple one-dimensional unfolded slicing model for numerically simulating high-power Innoslab picosecond amplifier are developed for the first time. The anisotropic stimulated emission cross-section of laser crystal, the influence of the tilted optical path, the spatial overlap of the seed and pump laser, as well as the pump absorption saturation effect are considered. Based on the as-developed model, 4-, 6- and 8-pass schemes high-power Nd:YVO4 Innoslab picosecond amplifiers are designed with output powers of 76.2 W, 81.4 W, and 85.5 W, respectively. The experimental results agree well with that of numerical simulation, indicating that our model is a powerful tool and paves a new way for designing and optimizing high-power Innoslab picosecond laser amplifier.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (5)
Fig. 1.
Fig. 1. (a) The schematic of Innoslab amplifier. (b) The slice model of the Innoslab amplifier and on the right is the magnified view.

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Fig. 2.
Fig. 2. (a) The coordinate system for slab crystal. (b) Top view of 4-pass Innoslab amplifier (in y = 0 plane) (c) The unfolded 4-pass Innoslab amplifier.

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Fig. 3.
Fig. 3. (a) Setup of the Nd:YVO4 Innoslab picosecond laser amplifier (the subpicture is the stereoscopic view of fx1 and fy1). The c-axis of the crystals is parallel to the ground. λ/2: half-wave plates at 1064 nm; fx1, fx2: plano-convex cylindrical lenses (horizontal direction); fx3: plano-concave cylindrical lens (horizontal direction); fy1, fy2: plano-convex cylindrical lenses (vertical direction); M1, M2: dichroic mirrors (HR 1064 nm and HT 808 nm at 0°); HM: 45° high reflectivity mirrors at 1064 nm. (b) Single-pass amplification of seed laser at different incident angles. BHM: Broadband high reflectivity mirror.

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Fig. 4.
Fig. 4. (a) The simulation (with or without using anisotropic σe) and experiment data of the output power vs. the angle β in the single-pass amplification at the maximum pump power of LDA. (b) The simulated and experimental output powers of the 4-, 6- and 8-pass structure.

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Fig. 5.
Fig. 5. (a) The spectrum of the fiber seed laser in the home-made picosecond MOPA system and the output spectrum of 8-pass Nd:YVO4 Innoslab amplifier. (b) Intensity autocorrelation traces of the fiber seed laser and amplified output. And the solid curves represent Gaussian fit values. (c) The beam quality of the 8-pass Innoslab amplifier.

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Tables (1)

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Table 1. Parameters in the simulation

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Equations (21)

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σ e ( θ ) = σ e , σ sin 2 θ + σ e , π cos 2 θ
∂ ϕ ∂ t + c ∂ ϕ ∂ z cos ⁡ θ = c n σ e ( θ ) ϕ
∂ n ∂ t = − c n σ e ( θ ) ϕ
J out = J s ln ⁡ { 1 + [ exp ⁡ ( J i n J s ) − 1 ] exp ⁡ ( n σ e ( θ ) D z cos ⁡ ( θ ) ) }
J s = h v σ e ( θ )
r k ( x , y ) = 2 2 π π C W ω p y ( k ) exp ⁡ { − 2 [ 2 x W ] S G − 2 [ y ω p y ( k ) ] 2 }
C = 2 1 − 1 / S G Γ ( 1 + 1 / S G )
ω p y ( k ) = [ ω p y 0 2 + ( ( k D z − z y 0 ) θ y ) 2 ] ,     D z = L / m ,   z = k D z ,   0 ≤ k ≤ m
N k ( x , y ) = W k n t o t W k + 1 / τ f
W k = P k a σ a a + P k c σ a c h ν p r k ( x , y )
α k h ( x , y ) = σ a h [ n t o t − N k ( x , y ) ] , h = a o r c
P k + 1 h = ∫ ∫ P k h r k ( x , y ) exp ⁡ [ − α k h ( x , y ) D z ] d x d y , h = a  or  c , D z = L / m ,   z = k D z ,   0 ≤ k ≤ m
s n , k ( x , y ) = 2 π ω l x ( n , k ) ω l y exp ⁡ { − 2 x 2 [ ω l x ( n , k ) ] 2 − 2 y 2 ω l y 2 }
ω l x ( n , k ) = ω l x 0 { 1 + [ M l 2 λ l π ω l x 0 2 ( k D z n l cos ⁡ β + n ( L n l cos ⁡ β + 2 D cos ⁡ α ) − z 0 cos ⁡ α ) ] 2 } 1 / 2 , n ≤ 3
N n , k e f f = ∫ ∫ s n , k ( x , y ) N n , k ( x , y ) d x d y
g n , k i = g n , k ∞ − ( g n , k ∞ − g n , k f ) exp ⁡ ( − 1 f τ f )
g n , k ∞ = σ e ( β ) N n , k e f f D z cos ⁡ β
J n , k i n = E n , k i n π ω l x ( n , k ) ω l y
J n , k o u t = J s ln ⁡ { 1 + [ exp ⁡ ( J n , k i n J s ) − 1 ] exp ⁡ ( g n , k i ) }
g n , k i − g n , k f = J n , k o u t − J n , k i n J s
E n , k + 1 i n = J n , k o u t π ω l x ( n , k ) ω l y
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