Detailed performance modeling of a pulsed high-power single-frequency Ti:sapphire laser

Gerd Wagner; Volker Wulfmeyer; Andreas Behrendt

doi:10.1364/AO.50.005921

Applied Optics
Vol. 50,
Issue 31,
pp. 5921-5937
(2011)
•https://doi.org/10.1364/AO.50.005921

Detailed performance modeling of a pulsed high-power single-frequency Ti:sapphire laser

Gerd Wagner, Volker Wulfmeyer, and Andreas Behrendt

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Gerd Wagner, Volker Wulfmeyer, and Andreas Behrendt, "Detailed performance modeling of a pulsed high-power single-frequency Ti:sapphire laser," Appl. Opt. 50, 5921-5937 (2011)

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Table of Contents Category
- Lasers and Laser Optics
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About this Article
History
- Original Manuscript: May 2, 2011
- Revised Manuscript: July 22, 2011
- Manuscript Accepted: July 23, 2011
- Published: October 25, 2011

Abstract

Differential absorption lidar (DIAL) is a unique technique for profiling water vapor from the ground up to the lower stratosphere. For accurate measurements, the DIAL laser transmitter has to meet stringent requirements. These include high average power (up to $10 W$ ) and high single-shot pulse energy, a spectral purity $> 99.9 %$ , a frequency instability $< 60 MHz rms$ , and narrow spectral bandwidth (single-mode, $< 160 MHz$ ). We describe extensive modeling efforts to optimize the resonator design of a Ti:sapphire ring laser in these respects. The simulations were made for the wavelength range of $820 nm$ , which is optimum for ground-based observations, and for both stable and unstable resonator configurations. The simulator consists of four modules: (1) a thermal module for determining the thermal lensing of the Brewster-cut Ti:sapphire crystal collinear pumped from both ends with a high-power, frequency-doubled Nd:YAG laser; (2) a module for calculating the in-cavity beam propagations for stable and unstable resonators; (3) a performance module for simulating the pumping efficiency and the laser pulse energy; and (4) a spectral module for simulating injection seeding and the spectral properties of the laser radiation including spectral impurity. Both a stable and an unstable Ti:sapphire laser resonator were designed for delivering an average power of $10 W$ at a pulse repetition frequency of $250 Hz$ with a pulse length of approximately $40 ns$ , satisfying all spectral requirements. Although the unstable resonator design is more complex to align and has a higher lasing threshold, it yields similar efficiency and higher spectral purity at higher overall mode volume, which is promising for long-term routine operations.

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System, References	Application Area	Transmitter Type	Specifications
LASE [7, 24, 37, 38]	airborne, troposphere	TISA laser	$λ = 813 - 818 nm$
			$E_{p} = 100 - 150 mJ$
			$f = 10 Hz$ , $P = 1 W$
LEANDRE [25, 39, 40, 41]	airborne, troposphere	alexandrite laser	$λ = 727 - 770 nm$
			$E_{p} = 50 mJ$
			$f = 10 Hz$ , $P = 0.5 W$
DLR WALES [26]	airborne, troposphere	KTP OPO	$λ = 935 nm$
			$E_{p} = 45 - 60 mJ$
			$f = 100 Hz$ , $P = 4.5 - 6 W$
MPI [22]	ground-based, troposphere	TISA laser	$λ = 820 nm$
			$E_{p} = 18.6 mJ$
			$f = 50 Hz$ , $P = 0.93 W$
IMK FZK [23]	ground-based, troposphere	OPO with TISA amplifier	$λ = 813 - 818 nm$
			$E_{p} = 250 mJ$
			$f = 20 Hz$ , $P = 5 W$
UHOH DIAL [34, 50]	ground-based, troposphere	TISA laser	$λ = 820 nm$
			$E_{p} = 16 - 27 mJ$
			$f = 250 Hz$ , $P = 4 - 6.75 W$
CODI [21]	ground-based, lower troposphere	amplified DFB diode laser	$λ = 823 nm$
			$E_{p} = 0.15 mJ$
			$f = 6 - 10 kHz$ , $P = 0.9 - 1.5 W$
Montana State Univ. [47, 48]	ground-based, lower troposphere	amplified ECDL diode laser	$λ = 824 - 841 nm$
			$E_{p} = 0.125 μJ$
			$f = 25 kHz$ , $P \approx 2.5 mW$ [47]
Univ. of Aidelaide [49]	ground-based, lower troposphere	amplified Fabry–Perot diode laser	$λ = 823 nm$
			$E_{p} \approx 500 nJ$
			$f = 1.5 kHz$ , $P = 0.75 mW$

Parameter	Requirement
Energy and efficiency
Average power	$> 10 W$
Pulse energy	10– $40 mJ$
Repetition rate	250– $1000 Hz$
Pulse duration	$< 200 ns$
Shot-to-shot energy instability	$< 4 % rms$
Conversion efficiency (opt.-opt.)	$> 20 %$
Depolarization ratio	$< 1 %$
Mode quality
$M^{2}$	$< 2$
Pointing instability	$< 15 μrad rms$
Spectral properties
Wavelength range (wavenumber)	815– $825 nm$ (12,270– $12, 121 {cm}^{- 1}$ ) or $720 nm$ ( $13, 889 {cm}^{- 1}$ ), 920– $945 nm$ (10,870– $10, 582 {cm}^{- 1}$ ), 1400– $1450 nm$ (7143– $6897 {cm}^{- 1}$ )
Spectral purity	$> 99.9 %$ (see [16])
Bandwidth	$< 160 MHz$
Frequency instability	$< 60 MHz rms$
Fine tuning range	$\pm 10 GHz$ around absorption lines
Coarse tuning range	1– $3 nm$ typically for reaching suitable absorption lines under different atmospheric conditions

Parameter, Unit	Value	Comment
TISA crystal
Crystal length l, mm	20
Diameter d, mm	7
Small-signal absorption coefficient α, ${cm}^{- 1}$	1.84
Heat conductivity k, $W / (m K)$	46	at $T = 300 K$ , $k (T)$ [93]
Heat capacity $C_{p}$ , $J / (kg K)$	779	at $T = 300 K$ , $C_{p} (T)$ [94]
Density ρ, $g / {cm}^{3}$	3.98
Thermal expansion coeff., $10^{- 6} K^{- 1}$	6
$n_{0}$ , dim.-less	1.76
$d n / d T$ , $10^{- 6} K^{- 1}$	13
Pump beam parameters
Single-side average pump power $P_{0}$ , W	25
$η_{h}$ , dim.-less.	0.35	see Eq. (3)
Beam radius $ω_{p}$ , mm	0.75
Boundary conditions
Heat transfer coeff. crystal-air, $W / (m^{2} K)$	10
Surrounding temperature, K	298.15
Heat transfer coeff. crystal-cooler, $W / (m^{2} K)$	15,000
Crystal cooler temperature, K	288.15

Parameter, Unit	Value	Comment
TISA crystal length l, mm	20
Ring resonator length $l^{'}$ , cm	150
Pump beam radius $ω_{p}$ , mm	0.75
Pump wavelength $λ_{p}$ , nm	532
Pump pulse length τ, ns	25
Pump pulse energy $E_{pump}$ , mJ	0–1000
Repetition rate, Hz	250	according to pump laser
Stored pump energy, %	48.5
Lasing wavelength $λ_{L}$ , nm	820
Stim. emission cross section $σ_{e}$ , ${cm}^{2}$	$2.85 \cdot 10^{- 19}$	at $820 nm$ for π polarization
Fluorescence lifetime $τ_{f}$ , $μs$	3.15	at $300 K$
Output coupler reflectivity R, %	58.6	$R_{opt}$ at $150 mJ$
Dissipative loss $L$ , %	2; 6
Inversion reduction factor γ, dim.-less	1

Pump Pulse Energy, mJ	Optimum OC, %	Output Pulse Energy, mJ
25	88.7 (93.8)	9.9 (7.4)
50	80.7 (88.9)	21.7 (17.3)
100	68.3 (81.1)	45.6 (37.9)
150	58.6 (74.5)	69.6 (58.8)
200	50.7 (68.9)	93.7 (79.8)
300	38.5 (59.3)	141.9 (121.9)
400	29.6 (51.4)	190.3 (164.2)
500	22.9 (44.9)	238.6 (206.5)

Parameter, Unit	Value	Comment
TISA crystal length l, mm	20
Ring resonator length $l^{'}$ , cm	98.5
Pump beam radius $ω_{p}$ , mm	0.75	top hat pump beam profile
Pump wavelength $λ_{p}$ , nm	532
Pump pulse length τ, ns	25
Pump pulse energy $E_{pump}$ , mJ	0–1000
Repetition rate, Hz	250	according to pump laser
Stored pump pulse energy, %	48.5
Lasing wavelength $λ_{L}$ , nm	820
Stim. emission cross section $σ_{e}$ , ${cm}^{2}$	$2.85 \cdot 10^{- 19}$	at $820 nm$ for π polarization
Fluorescence lifetime $τ_{f}$ , $μs$	3.15	at $300 K$
Center reflectivity $R_{0}$ of VRM, %	60
Magnification M, dim.-less	1–5	according to beam propagation
Output coupler reflectivity, %	$R_{0} / M^{2}$
Dissipative loss $L$ , %	2; 6
Inversion reduction factor γ, dim.-less	1

Parameter, Unit	Value	Comment
TISA crystal length l, mm	20
SR resonator length $l^{'}$ , cm	150	stable ring resonator
UR resonator length $l^{'}$ , cm	98.5	unstable ring resonator
Pump beam radius $ω_{p}$ , mm	0.75	top hat beam profile
Pump wavelength $λ_{p}$ , nm	532
Pump pulse length τ, ns	25
Pump pulse energy $E_{pump}$ , mJ	200
Repetition rate, Hz	250	according to pump laser
Stored pump pulse energy, %	48.5	see [85]
Lasing wavelength $λ_{L}$ , nm	820
Virtual noise mode wavelength, nm	820
Number of noise photons— stable resonator, $M$	500
Number of noise photons— unstable resonator, $M$	328
Stim. em. cross section $σ_{seed}$ , $σ_{spon}$ at $820 nm$ , ${cm}^{2}$	$2.85 \cdot 10^{- 19}$	π polarization
Fluorescence lifetime $τ_{f}$ , $μs$	3.15	at $300 K$
SR: Output coupler reflectivity R, %	50.7	$R_{opt}$ at $820 nm$ for $200 mJ$
UR: VRM reflectivity $R_{0}$ , %	60
UR: Magnification M, dim.-less	1.6
Dissipative loss $L$ , %	2
Inversion reduction factor γ, dim.-less	1
Initial inversion density $N (0)$ , $1 / m^{3}$	$(\frac{E_{ST}}{E_{L}}) / V$	see Eq. (18)
Initial photon density $ϕ_{seed} (0)$ , $1 / m^{3}$	0
Initial photon density $ϕ_{spon} (0)$ , $1 / m^{3}$	0

Parameter	Stable resonator	Unstable resonator
Mode volume	−	+
Intracavity intensity	−	+
Beam propagation	+	+
Lasing threshold	+	−
Pulse energy	+	+
Laser efficiency	+	+
Injection seeding	+	+
Mode discrimination	−	+
Frequency stabilization	+	+
Spectral properties	+	$+ / 0$
Design complexity	+	$0 / -$
System maintenance	+	0

Abstract

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Applied Optics