Role of undoped cap in the scaling of thin-disk lasers

Dmitrii Kouznetsov; Jean-François Bisson

doi:10.1364/JOSAB.25.000338

Role of undoped cap in the scaling of thin-disk lasers

Dmitrii Kouznetsov and Jean-François Bisson

Journal of the Optical Society of America B
Vol. 25,
Issue 3,
pp. 338-345
(2008)
•https://doi.org/10.1364/JOSAB.25.000338

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Dmitrii Kouznetsov and Jean-François Bisson, "Role of undoped cap in the scaling of thin-disk lasers," J. Opt. Soc. Am. B 25, 338-345 (2008)

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Table of Contents Category
- Lasers and Laser Optics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Lasers, solid-state (140.3580)

About this Article
History
- Original Manuscript: July 25, 2007
- Revised Manuscript: November 14, 2007
- Manuscript Accepted: December 2, 2007
- Published: February 14, 2008

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Abstract

The optimum design of a powerful thin-disk laser implies a compromise between amplified spontaneous emission (ASE), overheating, and the round-trip losses. The power enhancement of a composite thin-disk laser made of an undoped layer bonded over a thin active layer to reduce ASE losses is estimated analytically. Scaling laws for the parameters of a disk laser are suggested for cases both with and without an anti-ASE cap. Predictions of the maximal power achievable for a given laser material are compared to the published experimental data. The anti-ASE cap allows an increase of the maximal output power proportional to the square of the logarithm of the round-trip loss.

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Cap	Yes	No	Yes	No
$β ∕ %$	1	1	0.1	0.1
$θ ∕ %$	1	0.3	1.3	0.4
$P_{s} ∕ kW$	225	26	435	390
$L ∕ mm$	200	130	100	120
$h ∕ μ m$	400	460	100	200

Material	h	$λ_{p}$	$λ_{s}$	R	Q	$η_{o}$	θ	$η_{a}$	$η_{s}$	$P_{s}$	Reference	$P_{d}$	β	s	Row Number
Unit	mm	nm	nm	$\frac{Watt}{mm}$	$\frac{kW}{{cm}^{2}}$	%	%	%	%	Watt		Watt	%
3% $Yb : {Lu}_{2} O_{3}$	0.25	976	1080	8	35	90.4	0.4	95	75	33	[22]	0.15	0.06	237	1
3% $Yb : {Lu}_{2} O_{3}$	0.25	976	1080	8	35	90.4	1.6	95	80	32	[22]	0.15	0.12	231	2
3% $Yb : {Lu}_{2} O_{3}$	0.25	976	1034	14	12	94.4	5.7	95	72	26	[22]	1.51	1.51	18	3
25% Yb:LSB	0.30	974	1040	3	36	94.0	1.0	99	48	40	[23]	0.03	1.38	1702	4
20% Yb:LSB	0.30	974	1040	3	36	94.0	1.0	96	38	36	[23]	0.03	0.94	1532	5
8% Yb:YAG	0.25	941	1030	20	5	91.2	1.0	95	56	480	[5]	0.68	0.2	66	6
9% Yb:YAG	0.25	941	1030	20	5	91.2	2.0	95	60	647	[5]	0.68	0.2	89	7
10% Yb:YAG	0.20	940	1030	20	5	91.4	3.0	95	56	520	[24]	0.68	1.10	71	8
Yb:YAG	0.1	940	1030	20	5	91.4	3.0	95	70	5000	[25, 26]	0.68	0.75	720	9


ASE	Amplified spontaneous emission
G	Gain [12]
$g = 2 G h$	Round-trip gain [12]
h	Thickness of the disk, Fig. 1
L	Size of the disk, Fig. 1
$P_{d} = \frac{R^{2}}{Q}$ $(\sim 0.5 W)$	Power scale [12]
$P_{k} = \frac{R^{2} η_{o}}{(Q β^{3})}$	Key parameter [12]
$P_{p}$	Absorbed pump power (A6)
$P_{s}$	Output power (A1)
$P_{th} = \frac{ℏ ω_{p} L^{2}}{2 σ_{e} τ} g$	Threshold power (A2) [12, 21]
$P_{s} = η_{o} (1 - β ∕ g) (P_{p} - P_{th})$	Signal power (2) (output power)
$p = P_{p} ∕ P_{d}$	Normalized pump power (3)
$Q = ℏ ω_{p} ∕ (2 τ_{o} σ_{se})$	Saturation parameter [12]
$R = \min {\begin{matrix} 3 R_{T} ∕ η_{h} \\ 2 k Δ T_{\max} ∕ η_{h} \end{matrix}$	Thermal loading [12]
$r_{o} = P ∕ Q$	Scale of size [12]
$s = P_{s} ∕ (η_{o} P_{d})$	Normalized output power (3)
$u = G L$	Transverse-trip gain [12]
β	Background surface loss (2)
$ε = 1 ∕ \ln \frac{3}{β}$	Small parameter (9)
$η_{h} = 1 - η_{o}$	Heat generation parameter
$η_{o} = ω_{s} ∕ ω_{p}$	Quantum limit of efficiency [12]
$τ = τ_{o} \exp (- G L)$	Effective lifetime [12]
$τ = {(\frac{1}{τ_{o}} + \frac{2 h}{L} \exp (- G L))}^{- 1}$	Effective lifetime (1)
$τ_{o}$	Lifetime of the upper manifold (1)
$σ_{e}$	Emission cross section (A2)
$ω_{p}$ , $ω_{s}$	Frequencies of pump and signal (A2)

Cap	Yes	No	Yes	No
$β ∕ %$	1	1	0.1	0.1
$θ ∕ %$	1	0.3	1.3	0.4
$P_{s} ∕ kW$	225	26	435	390
$L ∕ mm$	200	130	100	120
$h ∕ μ m$	400	460	100	200

Material	h	$λ_{p}$	$λ_{s}$	R	Q	$η_{o}$	θ	$η_{a}$	$η_{s}$	$P_{s}$	Reference	$P_{d}$	β	s	Row Number
Unit	mm	nm	nm	$\frac{Watt}{mm}$	$\frac{kW}{{cm}^{2}}$	%	%	%	%	Watt		Watt	%
3% $Yb : {Lu}_{2} O_{3}$	0.25	976	1080	8	35	90.4	0.4	95	75	33	[22]	0.15	0.06	237	1
3% $Yb : {Lu}_{2} O_{3}$	0.25	976	1080	8	35	90.4	1.6	95	80	32	[22]	0.15	0.12	231	2
3% $Yb : {Lu}_{2} O_{3}$	0.25	976	1034	14	12	94.4	5.7	95	72	26	[22]	1.51	1.51	18	3
25% Yb:LSB	0.30	974	1040	3	36	94.0	1.0	99	48	40	[23]	0.03	1.38	1702	4
20% Yb:LSB	0.30	974	1040	3	36	94.0	1.0	96	38	36	[23]	0.03	0.94	1532	5
8% Yb:YAG	0.25	941	1030	20	5	91.2	1.0	95	56	480	[5]	0.68	0.2	66	6
9% Yb:YAG	0.25	941	1030	20	5	91.2	2.0	95	60	647	[5]	0.68	0.2	89	7
10% Yb:YAG	0.20	940	1030	20	5	91.4	3.0	95	56	520	[24]	0.68	1.10	71	8
Yb:YAG	0.1	940	1030	20	5	91.4	3.0	95	70	5000	[25, 26]	0.68	0.75	720	9

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