Resonant in-band pumping of cryo-cooled Er<sup>3+</sup>:YAG laser at 1532, 1534 and 1546 nm: a comparative study

doi:10.1364/OME.1.000223

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Resonant in-band pumping of cryo-cooled Er³⁺:YAG laser at 1532, 1534 and 1546 nm: a comparative study

Nikolay Ter-Gabrielyan, Viktor Fromzel, Larry D. Merkle, and Mark Dubinskii »View Author Affiliations

Optical Materials Express, Vol. 1, Issue 2, pp. 223-233 (2011)
http://dx.doi.org/10.1364/OME.1.000223

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Abstract

Spectroscopic features of Er:YAG at cryogenic temperatures are studied in detail. We report that the major absorption line at ~1532.3 nm is much narrower and much stronger than previously measured. Spectroscopic analysis suggests that its impact on the laser performance is limited because of the strong pump saturation effect. It is shown that the high efficiency of the laser is, in fact, achieved due to absorption in the wing of this line, which is comprised of a few other transitions. It is also shown that pumping into the relatively weak 1534 nm absorption line provides practically the same laser efficiency (~75%) as pumping into the major 1532 nm absorption line. This is explained by a numerical laser model which takes into account saturation effects of pump and laser intensities. The model is validated by experimental data.

1. Introduction

Recent developments in resonantly-pumped, cryo-cooled, eye-safe Er:YAG lasers have demonstrated great progress in reducing the thermal load and improving the laser efficiency [1

M. Dubinskii, N. Ter-Gabrielyan, G. A. Newburgh, and L. D. Merkle, “Cryogenically cooled Er:YAG laser.” in CLEO/Europe and IQEC 2007 conference Digest, (OSA 2007), paper CA6–5.

–3

S. D. Setzler, M. J. Shaw, M. J. Kukla, J. R. Unternahrer, K. M. Dinndorf, J. A. Beattie, and E. P. Chicklis, “A 400 W cryogenic Er:YAG slab laser at 1645 nm,” Proc. SPIE 7686, 76860C (2010).

]. In spite of the perceived complexity from the engineering point of view, cryogenic cooling offers numerous benefits. Along with improved thermal and thermo-optical properties of the host materials [4

R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y₃Al₅O₁₂, Lu₃Al₅O₁₂, YALO₃, LiLuF₄, BaY₂F₈, KGd(WO₄)₂, and KY(WO₄)₂ laser crystals in the 80-300 K temperature range,” J. Appl. Phys. 98, 103514 (2005). [CrossRef]

], most transitions in Er:YAG become narrower and stronger. The reduction of the thermal population of terminal laser energy levels enables the lowest quantum defect (QD) operating schemes that are either inefficient or impossible at room temperature.

The ⁴I_15/2 → ⁴I_13/2 absorption spectrum of the Er in YAG consists of two distinct groups of transitions in the wavelength ranges of 1450–1490 nm and 1520–1550 nm. This clear distinction arises from the large split in the energy levels of the ⁴I_13/2 manifold, see Fig. 1 .

Fig. 1 a. The energy level diagram with major pump and laser transitions. b. Absorption spectrum of Er(0.5%):YAG at 77K taken with Cary 6000i spectrophotometer (0.05 nm resolution).

Both groups originate from the four lowest Stark sublevels of the ⁴I_15/2 manifold. The transitions of the first group terminate at four upper Stark sublevels of the ⁴I_13/2 manifold and, they remain broad (around 1nm), even at cryogenic temperatures. Recently, a record ~400W laser output at 1645 nm from a cryogenically cooled Er:YAG laser was reported with pumping into the 1452.85 nm absorption line using spectrally-narrowed diode lasers with a bandwidth of approximately 1.2 nm full width at half maximum (FWHM) [3

S. D. Setzler, M. J. Shaw, M. J. Kukla, J. R. Unternahrer, K. M. Dinndorf, J. A. Beattie, and E. P. Chicklis, “A 400 W cryogenic Er:YAG slab laser at 1645 nm,” Proc. SPIE 7686, 76860C (2010).

]. However, pumping into any of the 14XX nm lines does not offer the lowest QD, defined as

Q D = λ_{l a s} / λ_{p} - 1

. Meanwhile, QD defines the theoretical limit of laser optical-to-optical efficiency – the smaller the QD, the higher the laser efficiency, and the lower the thermal load which can be potentially achieved. The second group of lines, which terminate at the four lowest Stark sublevels of the ⁴I_13/2 manifold, enables laser schemes with much lower QD. Unfortunately, at cryogenic temperatures these absorption lines become extremely narrow and require even more advanced pump sources targeting the 15XX nm wavelength range. With continuing technological advances, it has become possible to develop and implement diode pump lasers with the output bandwidth as narrow as 0.2 nm [5

V. Fromzel, N. Ter-Gabrielyan, M. Dubinskii, G. Venus, I. Divliansky, L. Glebov, O. Mokhun, and V. Smirnov, “Cryo-cooled Er:YAG laser resonantly pumped by a fiber coupled ultra-spectrally-narrowed diode source,” presented at Solid State and Diode Laser Technology Review, 15–18 June 2010, Broomfield, Colorado.

] around 1532 nm, but moving in this direction is very costly and may not be very practical.

Previous attempts to operate Er:YAG lasers in the lowest-QD mode relied heavily on pumping into the 1532 nm absorption band. It has generally been assumed that the strongest Z₂→Y₁ absorption line centered at ~1532.3 nm was the one mostly responsible for the efficient resonant excitation of Er³⁺ ions into ⁴I_13/2 manifold, while the impact of all other adjacent transitions was minimal. While this assumption is satisfactory for lasers operating at room temperature, experimental evidence suggests that cryogenic operation requires a more detailed analysis of Er:YAG fine spectral features. For example, we recently found that the widths and strengths of absorption lines in the 1520–1550 nm range measured by standard spectrophotometry were not adequately defined due to their extremely narrow bandwidths [6

N. E. Ter-Gabrielyan, L. D. Merkle, V.Fromzel, J.O.White, J. McElhenny and A. Michael, “Cryogenic Er:YAG lasers: aspects of diode pumping,” Solid State and Diode Laser Technology Review, Technical Digest, pp. 110–113, 15–18 June 2010, Broomfield, Colorado.

]. At 77 K, the absorption cross-sections of these transitions are very strong (~10⁻¹⁸–10⁻¹⁹ cm²) and have a bandwidth of only ~0.02–0.05 nm. For comparison, a typical line-narrowed pump diode spectrum has a bandwidth of 0.5–1 nm. Also, with such strong absorption, significant pump saturation should take place. Indeed, for the strongest transition at 1532 nm with an absorption coefficient of ~50 cm⁻¹ at 1% of Er concentration, the pump saturation fluence is only 86 W/cm².

In this paper, we present the investigative results of a cryogenic Er:YAG laser utilizing different pumping transitions which can be used for the optimization of the lowest QD operation. In the first step, we carried out a detailed spectroscopic study of an Er:YAG absorption spectrum in the 1520–1550 nm wavelength range, including an investigation of the fine structure of the strongest 1532 nm absorption band. In the second step, we numerically simulated the laser operation. In order to anchor the modeling results, we also carried out laser experiments with a cryogenically-cooled Er:YAG resonantly in-band pumped at 1532-, 1534- and 1546 nm and achieved a laser operation with very high efficiency (~75%).

2. Spectroscopy

The necessity of detailed spectroscopic studies of the Er³⁺ in YAG at cryogenic temperatures was caused by insufficient knowledge of its fine spectral features. We focused our attention on the 1520–1550 nm wavelength range which is the most suitable for pumping aimed at achieving the lowest QD operation.

High resolution absorption spectra were derived from spectral scanning through a thin Er:YAG sample with the collimated output of a tunable narrow-band (~800KHz) diode laser (Santec model TSL-210). The transmitted power was measured with a Germanium detector (New Focus model 2033). The AR-coated samples were mounted on a temperature controlled “cold finger” inside a standard liquid nitrogen cryostat. In order to properly address the dynamic range issue, we used Er:YAG samples with different Er³⁺ concentrations and with different thicknesses depending on the absorption strength of a particular absorption transition. For the strongest absorption line, around 1532 nm, we used 1-mm thick Er:YAG samples with the lowest Er-concentrations of 0.15 and 0.2%. Weaker absorption lines were studied with 2.5 mm thick Er(1%):YAG crystals. All samples were acquired from Scientific Materials, Inc.

The resulting absorption spectrum of Er:YAG at 77 K is shown in Fig. 2a . It can be seen that along with the 1532 nm absorption band, which is commonly used for pumping, there are also two absorption transitions centered at ~1534- and ~1546 nm. Their utilization for effective pumping at cryogenic temperatures has not been investigated previously, though pumping into the 1549 nm absorption line at room temperature (the same as 1546 nm line at 77 K) was successfully demonstrated in [7

K. Spariosu and M. Birnbaum, “Intracavity 1549-um pumped 1634-mm Er:YAG lasers at 300 K,” IEEE J. Quantum Electron. 30(4), 1044–1049 (1994). [CrossRef]

Fig. 2 a. Fragment of the ⁴I_15/2 → ⁴I_13/2 absorption cross section spectrum of Er³⁺:YAG crystal at 77K taken with the 1 pm spectral resolution; b. Close-up of the Lorentzian fit simulation of the 1532 nm absorption band at 77 K.

A detailed spectroscopic investigation of the 1532 nm absorption band revealed that, in fact, it has a complex structure. We found that this band consists of an extremely strong and narrow peak with at least five relatively weak satellites, three of which form a long-wavelength shoulder. Only one of these satellite transitions was identified with the primary energy level scheme. Lorentzian fitting of the observed absorption spectrum with the six transitions is shown in Fig. 2b. Cross sections, FWHM and their relative strengths of each transition with respect to the total integral under the envelope are summarized in the Table 1 .

Table 1 Components of the 1532 nm absorption band simulated with Lorentzian fit.

Center wavelength [pm]	Peak X-section [cm²]	FWHM [pm]	Relative strength [%]
1532.0	9.0 x10⁻²¹	19	0.9
1532.2	4.8 x 10⁻²¹	15	0.4
1532.3 (Z₂ →Y₁)	7.6 x 10⁻¹⁹	21	80.0
1532.4	1.8 x 10⁻²⁰	23	2.1
1532.4	9.8 x 10⁻²¹	21	1.1
1532.5 (Z₄ →Y₃)	1.6 x 10⁻²⁰	205	15.6

The two most intense and well-defined transitions, 1532.3 nm (Z₂→Y₁ major peak) and ~1532.5 nm (Z₄→Y₃ satellite), are displayed in the table in bold. The origin of the other transitions is not clear; they may be associated with minority sites, clusters or vibronics, but their precise identification is beyond the scope of this paper.

Figure 3 shows the temperature evolution of the 1532 nm absorption band. The most striking behavior was observed for the major 1532.3 nm ultra-narrow absorption peak. It remains quite narrow (~20–40 pm) in the entire 77–100 K temperature range and its maximum cross-section (~7.6∙10⁻¹⁹ cm²), measured with adequate resolution, is much higher than reported earlier [6

]. Its temperature dependence is consistent with thermal broadening due to phonon scattering, with a residual (temperature independent) contribution less than 0.02 nm. It is best fit by a Debye temperature of approximately 450 K, reasonably consistent with that reported for another transition in this material by Beghi et al [8

M. G. Beghi, C. E. Bottani, and V. Russo, “Debye temperature of erbium-doped yttrium aluminum garnet from luminescence and Brillouin scattering data,” J. Appl. Phys. 87(4), 1769–1774 (2000). [CrossRef]

Fig. 3 Temperature behavior of the 1532.3 and 1534 nm (inset) absorption bands.

The 1534- and the 1546 nm absorption transitions both originate at the Z₄ Stark sublevel (79 cm⁻¹) of the ⁴I_15/2 manifold and terminate at the Y₂ (6598 cm⁻¹) and the Y₁ (6548 cm⁻¹) Stark sublevels of the ⁴I_13/2 manifold, respectively (see Fig. 1a). Their intensities and bandwidths are very similar to those of the wide satellite transition at ~1532.5 nm (Z₄→Y₃ ). Therefore, one can expect that the performance of the cryogenically-cooled Er:YAG laser resonantly pumped into the 1532-, 1534- or 1546 nm lines will be very similar. Thetemperature behavior of the 1534 nm absorption line is shown in the inset of Fig. 3. Its cross-section remains nearly constant within the 77–150K temperature range (~2.1∙10⁻²⁰ cm²), while its bandwidth (~180 pm FWHM at 77 K) changes consistently with the theory of thermal broadening of a homogeneously broadened line. The 1546 nm absorption behaves similarly, but has a much lower cross-section (~7∙10⁻²¹ cm²) and a much wider bandwidth (~700 pm).

3. Modeling

In order to analyze the impact of the weak, long-wavelength shoulder of the 1532 nm absorption band on the performance of a cryogenically cooled Er:YAG laser, a theoretical model has been developed. This model also explains why the relatively weak 1534- and 1546 nm absorption transitions can be used for pumping with efficiency not lower than that of the major 1532 nm absorption band. The model is based on well-known, general quasi-four-level laser equations and takes into account saturation effects of the pump and laser intensities on the laser absorption coefficient, as was shown in [9

Y. Sato and T. Taira, “Saturation factors of pump absorption in solid-state lasers,” IEEE J. Quantum Electron. 40(3), 270–280 (2004). [CrossRef]

]. For cryogenic Er:YAG lasers, the pump saturation effect is important due to the strong absorption and long fluorescence lifetime. The model also takes into account the pump-absorption spectral overlap which noticeably varies with the pumping wavelength. The influence of up-conversion was treated as a reduction in the effective lifetime of the ⁴I_13/2 manifold. Below we will briefly describe the basic features of this model.

Let N₂(λ_p,z) be the local population density of the upper energy manifold ⁴I_13/2 and λ_p be the pumping wavelength corresponding to the Z_i →Y_j transition between Stark levels of ⁴I_13/2 and ⁴I_15/2 manifold, see Fig. 1a. When only ⁴I_13/2 and ⁴I_15/2 manifolds are involved and the laser transition occurs between the Y₂ and the Z₅ Stark levels (λ_las = 1618 nm), the local population density in the steady state can be derived as:

\begin{array}{l} \frac{I_{p} (λ, z) \cdot σ_{p} (λ) \cdot λ_{p}}{h \cdot c} \cdot [N_{0} \cdot f_{Z i} - N_{2} (λ, z) \cdot (f_{Z i} + f_{Y j})] = \\ \frac{N_{2} (λ, z)}{τ} + \frac{I_{l a s} \cdot σ_{l a s} \cdot λ_{l a s}}{h \cdot c} \cdot [N_{2} (λ, z) \cdot (f_{Y 2} + f_{Z 5})] - N_{0} \cdot f_{Z 5}] \end{array}

(1)

Herein: N₀ is the total Er³⁺ concentration; λ_p is the wavelength of the peak of the absorption line; σ_p(λ) is the absorption cross-section such that

σ_{p} (λ) = σ (λ_{p}) \cdot g (λ)

, where σ(λ_p) is the peak absorption cross-section and g(λ) is the spectral shape of the absorption line with the bandwidth of Δλ_abs normalized as

\int_{Δ λ_{a b s}} g (λ) \cdot d λ = 1

; λ_las is the laser wavelength; σ_las is the absorption cross-section, its wavelength dependence can be ignored since laser emission has a very narrow spectrum; τ is the fluorescence lifetime; f_Zi, f_Yj, f_Y2 and f_Z5 are the Bolzmann occupation factors of the corresponding Stark levels. The local pump intensity - I_p(λ, z) and the local laser intensity - I_las are defined as:

I_{p} (λ, z) = \frac{8 \cdot P_{p} (z) \cdot G_{p} (λ)}{π \cdot d_{p}^{2}}

(2)

and

I_{l a s} = \frac{8 \cdot P_{l a s}}{π \cdot d_{l a s}^{2}}

(3)

Here: P_p(z) is the pump power along laser axis z; G_p(λ) is the spectral distribution of the pump power and normalized as

\int_{Δ λ_{p u m p}} G (λ) \cdot d λ = 1

;

Δλ_pump is the bandwidth of the pump spectrum; d_p and d_las are diameters of the pump and laser beams in the crystal; P_las is the laser output power.

For simplicity, we assume that the laser operates at a single wavelength and the transverse distributions of the pump and the laser beams have top hat profiles. A small dependence of P_las on z inside the laser medium was neglected. Following [9

Y. Sato and T. Taira, “Saturation factors of pump absorption in solid-state lasers,” IEEE J. Quantum Electron. 40(3), 270–280 (2004). [CrossRef]

], the pump saturated absorption coefficient can be expressed as:

α (λ, z) = \frac{1 + (1 - \frac{f_{Y j} \cdot f_{Z 5}}{f_{Z i} \cdot f_{Y 2}}) \cdot \frac{I_{l a s}}{I_{S l a s}}}{1 + (1 + \frac{f_{Z 5}}{f_{Y 2}}) \cdot \frac{I_{l a s}}{I_{S l a s}} + (1 + \frac{f_{Y j}}{f_{Z i}}) \cdot \frac{I_{p} (λ, z)}{I_{S P} (λ)}} \cdot α_{0} (λ)

(4)

where

I_{S P} (λ) = \frac{h \cdot c}{σ_{p} (λ) \cdot λ_{p} \cdot τ \cdot f_{Z i}}

and

I_{S l a s} = \frac{h \cdot c}{σ_{l a s} \cdot λ_{l a s} \cdot τ \cdot f_{Y k}}

are the pump and the laser saturation intensities; α₀(λ) is the unsaturated pump absorption coefficient:

α_{0} (λ) = σ_{p} (λ) \cdot N_{0} \cdot f_{Z i}

(5)

Pump intensity I_p(λ, z) decreases with pump propagation along axis z in accordance with the saturated absorption coefficient (Eq. (4)), and in the absence of lasing (I_las = 0), i.e. before the laser threshold is reached, it can be defined at any point z from the numerical solution of the transcendental equation:

[1 + \frac{I_{p} (λ, z + d z) \cdot (1 + \frac{f_{Y j}}{f_{Z i}})}{I_{S P} (λ)}] \cdot \ln [\frac{I_{p} (λ, z + d z)}{I_{p} (λ, z)}] = - α_{0} (λ) \cdot d z

(6)

I_{p} (λ, 0) = I_{p 0} (λ)

is the incident pump intensity, then by using Eq. (6) one can calculate the pump intensity at every point z along the laser axis. According to Eq. (2), the difference between the calculated values of the pump intensities

Δ I_{p} (λ, z) = I_{p} (λ, z + d z) - I_{p} (λ, z)

defines the absorbed pump power in every elementary volume

d V = π \cdot d_{p}^{2} \cdot d z / 4

. By integrating ΔI_p(λ,z) over the length of the active medium and then over the wavelengths under the absorption contour and converting pump intensity into absorbed power, one can finally calculate the averaged population density N₂(P_p) and the total absorbed pump power P_abs(P_p):

N_{2} (P_{p}) = \iint_{λ, z} N_{2} (λ, z) \cdot d λ \cdot d z = \frac{τ}{2 \cdot l_{a} \cdot h ν_{p}} \cdot \iint_{Δ λ_{a b s}, z} [I_{p 0} (λ) - I_{p} (λ, z)] \cdot d λ \cdot d z

(7)

P_{a b s} (P_{p}) = \frac{π \cdot d_{p}^{2}}{8} \cdot \iint_{z, Δ λ_{a b s}} [I_{p 0} (λ) - I_{p} (λ, z)] \cdot d λ \cdot d z

(8)

where l_a is the length of the active medium.

It should be emphasized that, according to definition (2), both P_abs and N₂ in Eqs. (7) and (8) are implicit functions of the incident pump power P_p . Then, the laser gain coefficient, α_g(P_p), which also varies with P_p , can be expressed by:

α_{g} (P_{p}) = σ_{g} \cdot [N_{2} (P_{p}) \cdot f_{Y 2} - (N_{0} - N_{2} (P_{p})) \cdot f_{Z 5}]

(9)

The threshold pump power, P_th , is defined as the incident pump P_p , for which the laser gain determined by expression (9) equals the total laser cavity losses, α_loss :

α_{g} (P_{p}) = α_{l o s s} = \frac{\ln {(R_{o u t} \cdot R_{H R})}^{- 1} + L}{2 \cdot l_{a}}

(10)

where R_out and R_HR = 1 are the reflection coefficients of the laser resonator mirrors and L is the passive round-trip resonator loss.

Further calculations are carried out in two approximation steps. At first, we assumed that the absorption is independent of the intensity of the laser emission I_las even after the pump exceeds the laser threshold. In this approximation the absorption saturation is caused only by the pump interaction with the laser medium and the intracavity laser emission does not affect the absorption. Then, the laser output power P_out,1 can be expressed by:

P_{o u t, 1} = \frac{\ln {(R_{1})}^{- 1}}{\ln {(R_{1})}^{- 1} + L} \cdot \frac{λ_{p}}{λ_{g}} \cdot (P_{p} - P_{t h}) \cdot K_{a b s} (P_{t h})

(11)

Here

K_{a b s} (P_{t h}) = P_{a b s} (P_{t h}) / P_{t h}

is the absorption of the laser medium when pumping reaches the threshold and, in the first order of approximation, the absorption coefficient remains constant after the threshold.

In the second step, we take into account the influence of the laser emission on the absorption coefficient which, according to Eq. (4), causes partial or full “restoration” of the saturated absorption. With I_las > 0, the saturated absorption coefficient (4) can be expressed as:

α_{a b s . l a s} = \frac{1 + (1 - \frac{f_{2 j} \cdot f_{1 m}}{f_{1 i} \cdot f_{2 k}}) \cdot \frac{I_{l a s}}{I_{S l a s}}}{1 + (1 + \frac{f_{1 i}}{f_{2 k}}) \cdot \frac{I_{l a s}}{I_{S l a s}} + (\frac{k_{0}}{α_{a b s}} - 1)} \cdot k_{0}

(12)

where

I_{l a s} = \frac{P_{o u t, 1} \cdot 8}{π \cdot d_{l a s}^{2}} \cdot \frac{(1 + R_{1})}{(1 - R_{1})}

(13)

α_{a b s} = \frac{\ln {(1 - K_{a b s})}^{- 1}}{l_{a}}

(14)

and

k_{0} = \frac{\ln {(1 - K_{a b s} (P_{p, \min}))}^{- 1}}{l_{a}}

(15)

Here, K_abs(P_p,min) is the unsaturated absorption of the laser medium, when the incident pump power is very low and thus the saturation can be neglected. One can see that if I_las = 0, the Eq. (12) reduces to α_abs.las = α_abs . Using Eq. (12) with I_las ≠ 0, the laser output power can be finally determined by:

P_{o u t} = \frac{\ln {(R_{o u t})}^{- 1}}{\ln {(R_{o u t})}^{- 1} + L} \cdot \frac{λ_{p}}{λ_{g}} \cdot (P_{p} - P_{t h}) \cdot [1 - \exp (- α_{a b s . l a s} \cdot l_{a})]

(16)

For Er:YAG with Er³⁺ concentration less than 1%, up-conversion losses are low and can be neglected [10

J. W. Kim, J. I. Mackenzie, and W. A. Clarkson, “Influence of energy-transfer-upconversion on threshold pump power in quasi-three-level solid-state lasers,” Opt. Express 17(14), 11935–11943 (2009). [CrossRef] [PubMed]

]. For higher Er³⁺ concentrations, the influence of the up-conversion becomes more noticeable. These losses can be described by introducing an additional term in Eq. (1) - w_upN₂ ² , where w_up is the up-conversion coefficient. For a continuous wave (CW) Er:YAG laser, the population of the upper ⁴I_13/2 manifold - N₂ is relatively low (N₂ << N₀ ) and it remains constant after the laser threshold is reached. Thus, w_upN₂ can be interpreted as a modification of the decay time the same way as τ enters the term N₂/τ in Eq. (1). Let us introduce the effective lifetime of the upper laser level, τ_eff :

τ_{e f f}^{- 1} = τ^{- 1} + w_{u p} \cdot N_{2} (P_{t h})

(17)

Expression (17) shows that the up-conversion essentially shortens the upper level lifetime; hence, it mainly impacts the laser threshold. The up-conversion coefficient w_up for cryogenically-cooled Er:YAG is unknown. By using a smaller value of τ than its fluorescence value of τ ~10 ms [2

N. Ter-Gabrielyan, M. Dubinskii, G. A. Newburgh, A. Michael, and L. D. Merkle, “Temperature dependence of a diode-pumped cryogenic Er:YAG laser,” Opt. Express 17(9), 7159–7169 (2009). [CrossRef] [PubMed]

], it is possible to estimate the up-conversion parameter. A good fit between experimental and calculated data can serve as a criterion for the accuracy of this approach. In our case all spectroscopic and laser parameters employed in the laser modeling (except τ_eff ) were independently measured. Then, by varying the value of τ_eff only, one can find the best fit between the experimental and the calculated laser outputs described by Eq. (16). The results of the above approach and modeling were validated by the experimental data and will be presented below.

4. Laser experiments

Laser experiments were carried out with the 5-mm and 10-mm long Er(2%):YAG crystals cooled to ~80 K. Crystals were mounted on the copper cold finger inside a boil-off liquid nitrogen cryostat, see Fig. 4 . They were end-pumped by a narrowband (0.25–0.3 nm FWHM) Er-fiber laser, which could deliver up to 60 W of CW power tuned to a specific absorption peak. To reduce the thermal load of the gain medium for CW pump powers exceeding 20 W, we used the same pump laser in a quasi-CW regime (chopped) with a duty cycle of 25% (t_pulse = 25 ms, f = 10 Hz), which is, in all aspects, equivalent to the CW mode. During the experiments, only the pumping wavelength was allowed to change between 1532-, 1534- or 1546 nm absorption transitions, while the laser resonator and pumping geometry remained unchanged. The collimated pump beam was focused into the crystal by a spherical lens with a focal length of 100 mm. The pumped region inside the crystal had a cylindrical shape with the diameter of ~470 μm (at e ⁻²) along the entire crystal length. A plano-concave laser cavity (l_cav = 65 mm, R_out = 0.85) provided nearly perfect matching between the TEM₀₀-mode of the cavity and the pumped volume. The laser output wavelength was 1618 nm.

Fig. 4 Experimental setup. HRM - high-reflecting mirror, OC - output coupler. LN2 - liquid nitrogen.

5. Results and discussion

Figure 5 shows the CW performance of the cryo-cooled Er(2%):YAG laser pumped in the 1532-, 1534- and 1546 nm absorption bands with a 20W pump source. Figures (a) and (b) correspond to the 5-mm long laser crystal; (c) and (d) - for the 10 mm.

Fig. 5 CW laser output vs. incident (a, c) and absorbed (b, d) pump power for the cryo-cooled Er:YAG laser with the l_a = 5 mm (a,b) and l_a = 10mm (c,d) long crystals pumped into one of the absorption bands: 1534-, 1546- or 1532 nm. Dots - experimental data; Solid lines - simulation results.

As was expected, the laser outputs corresponding to pumping into each of these three absorption transitions were almost identical with respect to the absorbed pump power (see Figs. 5b and 5d). Pumping into the 1534- and 1532 nm absorption lines provided nearly identical laser outputs even with respect to the incident pump power (see Figs. 5a and 5c), whereas pumping into the 1546 nm absorption lines resulted in lower laser output and efficiency. Similar results were obtained with the quasi-CW (QCW) pumping up to ~53 W of incident power into the same three absorption lines, see Fig. 6 . As in the previous case, pumping into the 1532- and 1534 nm absorption bands yielded approximately the same laser output and pumping into the 1546 nm transition resulted in lower output with respect to the incident pump power. But with respect to the absorbed power, pumping in these three transitions yielded identical results. The obtained laser efficiency was ~75% with respect to the absorbed and ~53% with respect to the incident pump power.

Fig. 6 Performance of the cryo-cooled Er:YAG laser with 5-mm long crystal pumped by Er- fiber laser in QCW mode.

Employing the model described above, we simulated the performance of the cryogenically cooled Er(2%):YAG laser resonantly pumped in several absorption transitions. In the modeling, we used independently measured spectroscopic parameters of the crystal: σ_p , σ_g , Δλ_abs , g(λ), τ, N₀ , f_Zi, f_Yj, f_Z5, f_Y2 , parameters of the pump source - G_p(λ), Δλ_pump and parameters of the laser - l_a , R_out , R_HR , L, d_p , d_las .

For example, for the 1534 nm pumping, these parameters were taken as: σ_p = 2.2∙10⁻²⁰ cm², σ_g = 1.1∙10⁻²⁰ cm², Δλ_abs = 180 pm (FWHM), g(λ) – Lorentzian shape, τ = 10 ms, N₀ = 2.76∙10²⁰ cm⁻³, f_Zi = f_Z4 = 0.103, f_Z5 = 0.00018, f_Y2 = 0.222, f_Yj = f_Y2 = 0.222, Δλ_pump = 300 pm, G_p(λ) – Gaussian shape, l_a = 5- and 10 mm, R_out = 0.85, L = 0.05, d_p = d_las = 0.47 mm. By varying τ, we determined that the best fit between the experimental data and modeling occurs when τ_eff = 3.7 ms for 5 mm long and τ_eff = 5.5 ms for 10 mm long laser crystals, respectively. This effective lifetime is much shorter than the fluorescence time τ ~10 ms measured at 77K directly [2

]. Using Eq. (17) with the averaged population of the upper laser manifold N₂ ~8.5∙10¹⁹ cm⁻³ for the 5 mm long laser crystal and N₂ ~4.4∙10¹⁹ cm⁻³ for the 10 mm long one, we estimated w_up ~2∙10⁻¹⁸ cm³/s. This value is close to the indirect estimation of the w_up at 77K made in [11

J. O. White, M. Dubinskii, L. D. Merkle, I. Kudryashov, and D. Garbuzov, “Resonant pumping and upconversion in 1.6 um Er³⁺ lasers,” J. Opt. Soc. Am. B 24(9), 2454–2460 (2007). [CrossRef]

] and nearly twice lower than the up-conversion parameter estimated for room temperature (3.5∙10⁻¹⁸ cm³/s for 1% of Er in YAG [12

M. O. Iskandarov, A. A. Nikitichev, and A. I. Stepanov, “Quasi-two-level Er³⁺:Y₃Al₅O₁₂ laser for 1.6 µm range,” J. Opt. Technol. 68(12), 885–888 (2001). [CrossRef]

]).

The results of the numerical modeling are shown in Fig. 5 by solid lines. One can see a good fit between the experimental and the calculated data. All calculated curves correspond to the same up-conversion parameter. Thus, in the case of the 1532 nm resonant pumping, the modeling shows that the major contribution to the laser operation comes not from the strongest and extremely narrow peak corresponding to Z₁→Y₂ line (1532.3 nm), but from the much weaker and broader satellite transition Z₄→Y₃ centered at 1532.5 nm (see Fig. 2b, olive bell-curve) forming a long-wavelength shoulder of the 1532 nm absorption band. The predominance of the satellite contribution to the absorbed pump power remains even when bandwidth-narrowed diodes (0.2–0.4 nm) are used. In the case of pumping in the weaker 1534 nm and 1546 nm absorption lines, modeling explains why such pumping is as effective as pumping into the 1532 nm band and provides nearly the same laser efficiency: this is simply because spectroscopic features of 1534- and 1546 nm lines are very similar to those of the satellite transition Z₄ →Y₃ at 1532.5 nm

6. Conclusion

Presented here are the results of a thorough spectroscopic and laser characterization of the cryogenically cooled, resonantly-pumped Er³⁺-doped YAG. We found that the strongest absorption line at ~1532.3 nm, which is normally used for achieving the lowest QD laser operation, is much narrower and stronger than it was previously reported. The actual spectral width of this line, measured with a spectral resolution of about 1 pm, was found to be only ~20 pm with a peak absorption cross section of ~7.6∙10⁻¹⁹ cm². Our spectroscopic analysis suggests that, due to the extreme narrowness of this absorption line, its impact on the laser performance is limited because of the strong pump saturation effect. The nearby satellite absorption line, forming the tail of the 1532 nm absorption band, is mainly responsible for the high efficiency of the cryo-cooled Er:YAG laser. Experiments with a tunable spectrally-narrowed pump source and the results of the numeric simulation confirm this point. More than 25 W of the QCW output was achieved with the 75% slope efficiency (versus the absorbed pump). The results of our modeling and experiments demonstrated that because of the moderate pump saturation, the significantly weaker and broader 1534- or 1546 nm absorption lines can be used for efficient laser pumping and obtaining practically the same slope efficiency. The shapes of these transitions indicate that both of them are dominated by homogeneous broadening.

References and links

1.	M. Dubinskii, N. Ter-Gabrielyan, G. A. Newburgh, and L. D. Merkle, “Cryogenically cooled Er:YAG laser.” in CLEO/Europe and IQEC 2007 conference Digest, (OSA 2007), paper CA6–5.
2.	N. Ter-Gabrielyan, M. Dubinskii, G. A. Newburgh, A. Michael, and L. D. Merkle, “Temperature dependence of a diode-pumped cryogenic Er:YAG laser,” Opt. Express 17(9), 7159–7169 (2009). [CrossRef] [PubMed]
3.	S. D. Setzler, M. J. Shaw, M. J. Kukla, J. R. Unternahrer, K. M. Dinndorf, J. A. Beattie, and E. P. Chicklis, “A 400 W cryogenic Er:YAG slab laser at 1645 nm,” Proc. SPIE 7686, 76860C (2010).
4.	R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y₃Al₅O₁₂, Lu₃Al₅O₁₂, YALO₃, LiLuF₄, BaY₂F₈, KGd(WO₄)₂, and KY(WO₄)₂ laser crystals in the 80-300 K temperature range,” J. Appl. Phys. 98, 103514 (2005). [CrossRef]
5.	V. Fromzel, N. Ter-Gabrielyan, M. Dubinskii, G. Venus, I. Divliansky, L. Glebov, O. Mokhun, and V. Smirnov, “Cryo-cooled Er:YAG laser resonantly pumped by a fiber coupled ultra-spectrally-narrowed diode source,” presented at Solid State and Diode Laser Technology Review, 15–18 June 2010, Broomfield, Colorado.
6.	N. E. Ter-Gabrielyan, L. D. Merkle, V.Fromzel, J.O.White, J. McElhenny and A. Michael, “Cryogenic Er:YAG lasers: aspects of diode pumping,” Solid State and Diode Laser Technology Review, Technical Digest, pp. 110–113, 15–18 June 2010, Broomfield, Colorado.
7.	K. Spariosu and M. Birnbaum, “Intracavity 1549-um pumped 1634-mm Er:YAG lasers at 300 K,” IEEE J. Quantum Electron. 30(4), 1044–1049 (1994). [CrossRef]
8.	M. G. Beghi, C. E. Bottani, and V. Russo, “Debye temperature of erbium-doped yttrium aluminum garnet from luminescence and Brillouin scattering data,” J. Appl. Phys. 87(4), 1769–1774 (2000). [CrossRef]
9.	Y. Sato and T. Taira, “Saturation factors of pump absorption in solid-state lasers,” IEEE J. Quantum Electron. 40(3), 270–280 (2004). [CrossRef]
10.	J. W. Kim, J. I. Mackenzie, and W. A. Clarkson, “Influence of energy-transfer-upconversion on threshold pump power in quasi-three-level solid-state lasers,” Opt. Express 17(14), 11935–11943 (2009). [CrossRef] [PubMed]
11.	J. O. White, M. Dubinskii, L. D. Merkle, I. Kudryashov, and D. Garbuzov, “Resonant pumping and upconversion in 1.6 um Er³⁺ lasers,” J. Opt. Soc. Am. B 24(9), 2454–2460 (2007). [CrossRef]
12.	M. O. Iskandarov, A. A. Nikitichev, and A. I. Stepanov, “Quasi-two-level Er³⁺:Y₃Al₅O₁₂ laser for 1.6 µm range,” J. Opt. Technol. 68(12), 885–888 (2001). [CrossRef]

OCIS Codes
(140.3500) Lasers and laser optics : Lasers, erbium
(140.3580) Lasers and laser optics : Lasers, solid-state

ToC Category:
Laser Materials

History
Original Manuscript: April 1, 2011
Revised Manuscript: May 13, 2011
Manuscript Accepted: May 16, 2011
Published: May 18, 2011

Virtual Issues
Advances in Optical Materials (2011) Optical Materials Express

Citation
Nikolay Ter-Gabrielyan, Viktor Fromzel, Larry D. Merkle, and Mark Dubinskii, "Resonant in-band pumping of cryo-cooled Er³⁺:YAG laser at 1532, 1534 and 1546 nm: a comparative study," Opt. Mater. Express 1, 223-233 (2011)
http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-1-2-223

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References

M. Dubinskii, N. Ter-Gabrielyan, G. A. Newburgh, and L. D. Merkle, “Cryogenically cooled Er:YAG laser.” in CLEO/Europe and IQEC 2007 conference Digest, (OSA 2007), paper CA6–5.
N. Ter-Gabrielyan, M. Dubinskii, G. A. Newburgh, A. Michael, and L. D. Merkle, “Temperature dependence of a diode-pumped cryogenic Er:YAG laser,” Opt. Express 17(9), 7159–7169 (2009). [CrossRef] [PubMed]
S. D. Setzler, M. J. Shaw, M. J. Kukla, J. R. Unternahrer, K. M. Dinndorf, J. A. Beattie, and E. P. Chicklis, “A 400 W cryogenic Er:YAG slab laser at 1645 nm,” Proc. SPIE 7686, 76860C (2010).
R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YALO3, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80-300 K temperature range,” J. Appl. Phys. 98, 103514 (2005). [CrossRef]
V. Fromzel, N. Ter-Gabrielyan, M. Dubinskii, G. Venus, I. Divliansky, L. Glebov, O. Mokhun, and V. Smirnov, “Cryo-cooled Er:YAG laser resonantly pumped by a fiber coupled ultra-spectrally-narrowed diode source,” presented at Solid State and Diode Laser Technology Review, 15–18 June 2010, Broomfield, Colorado.
N. E. Ter-Gabrielyan, L. D. Merkle, V.Fromzel, J.O.White, J. McElhenny and A. Michael, “Cryogenic Er:YAG lasers: aspects of diode pumping,” Solid State and Diode Laser Technology Review, Technical Digest, pp. 110–113, 15–18 June 2010, Broomfield, Colorado.
K. Spariosu and M. Birnbaum, “Intracavity 1549-um pumped 1634-mm Er:YAG lasers at 300 K,” IEEE J. Quantum Electron. 30(4), 1044–1049 (1994). [CrossRef]
M. G. Beghi, C. E. Bottani, and V. Russo, “Debye temperature of erbium-doped yttrium aluminum garnet from luminescence and Brillouin scattering data,” J. Appl. Phys. 87(4), 1769–1774 (2000). [CrossRef]
Y. Sato and T. Taira, “Saturation factors of pump absorption in solid-state lasers,” IEEE J. Quantum Electron. 40(3), 270–280 (2004). [CrossRef]
J. W. Kim, J. I. Mackenzie, and W. A. Clarkson, “Influence of energy-transfer-upconversion on threshold pump power in quasi-three-level solid-state lasers,” Opt. Express 17(14), 11935–11943 (2009). [CrossRef] [PubMed]
J. O. White, M. Dubinskii, L. D. Merkle, I. Kudryashov, and D. Garbuzov, “Resonant pumping and upconversion in 1.6 um Er3+ lasers,” J. Opt. Soc. Am. B 24(9), 2454–2460 (2007). [CrossRef]
M. O. Iskandarov, A. A. Nikitichev, and A. I. Stepanov, “Quasi-two-level Er3+:Y3Al5O12 laser for 1.6 µm range,” J. Opt. Technol. 68(12), 885–888 (2001). [CrossRef]

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