Up conversion measurements in Er:YAG - OSA Publishing

Up conversion measurements in Er:YAG; comparison with 1.6 μm laser performance Norman P. Barnes,1,* Brian M. Walsh,1 Farzin Amzajerdian,1 Donald J. Reichle,1 George E. Busch,2 and William A. Carrion2 1

NASA Langley Research Center, Hampton, VA, 23681, USA 2 Coherent Applications, Inc., Hampton, VA 23681, USA *[email protected]

Abstract: Up conversion significantly affects Er:YAG lasers. Measurements performed here for low Er concentration are markedly different than reported high Er concentration. The results obtained here are used to predict laser performance and are compared with experimental results. ©2011 Optical Society of America OCIS codes: (140.3500) Lasers, erbium; (140.5560) Pumping; (190.7220) Up conversion.

References and links L. F. Johnson, J. E. Geusic, and L. G. Van Uitert, “Coherent oscillations From Tm3+, Ho3+, Yb3+ and Er3+ ions in yttrium aluminum garnet,” Appl. Phys. Lett. 7(5), 127–129 (1965). 2. J. Simkin, J. A. Koningstein, P. Myslinski, S. A. Boothroyd, and J. Chrostowski, “Upconversion dynamics of Er3+:YAlO3,” J. Appl. Phys. 73(12), 8046–8049 (1993). 3. V. Lopez, G. Paez, and M. Strojnik, “Characterization of upconversion coefficient in erbium-doped materials,” Opt. Lett. 31(11), 1660–1662 (2006). 4. M. O. Iskandarov, A. A. Nikitichev, and A. I. Stepanov, “Quasi two level Er3+;Y3Al5O12 laser for the 1.6 μm range,” J. Opt. Technol. 68(12), 885–888 (2001). 5. E. Georgiou, F. Kiriakidi, O. Musset, and J.-P. Boquillon, “1.65 μm Er:Yb:YAG Diode Pumped Laser Delivering 80 mJ,” Opt. Eng. 44(6), 064202 (2005). 6. D. Garbuzov, I. Kudryashov, and M. Dubinskii, “Resonantly diode laser pumped 1.6 μm erbium doped yttrium aluminum garnet solid state laser,” Appl. Phys. Lett. 86(13), 131115 (2005). 7. S. Bigotta and M. Eichhorn, “Q-switched resonantly diode upper Er3+:YAG laser with fiber like geometry,” Opt. Lett. 35(17), 2970–2972 (2010). 8. M. Eichhorn, “Multi kW class 1.64 μm Er3+:YAG lasers based on heat capacity operation,” Opt. Mater. Express 1(3), 321–331 (2011). 9. J. Koetke and G. Huber, “Infrared Excited State Absorption And Stimulated Emission Cross Section Of Er 3+ Doper Crystals,” Appl. Phys. B 61(2), 151–158 (1995). 10. M. Eichhorn, “Numerical modeling of diode end pumped high power Er3+:YAG lasers,” IEEE J. Quantum Electron. 44(9), 803–810 (2008). 11. W. Q. Shi, M. Bass, and M. Birnbaum, “Effects Of Energy Transfer Among Er3+ Ions On The Fluorescence Decay And Lasing Properties Of Heavily Doped Er:Y3Al5O12,” J. Opt. Soc. Am. B 7(8), 1456–1462 (1990). 12. M. J. Shaw, S. D. Setzler, K. M. Dinndorf, J. A. Beattie, M. J. Kukla, and E. P. Chicklis, “400W Resonantly Pumped Cryogenic Er:YAG Slab Laser at 1645nm,” in Proceedings of Advanced Solid State Photonics (Optical Society of America, 2010), paper APDP2. 1.

1.0 Introduction Er lasers operating on the 4I13/2 to 4I15/2 transition have the advantage of being nominally eye safe, operating in an atmospheric transmission window, and operating near the transmission peak of silica. The wavelength of this transition is around 1.6 μm., qualifying it as a nominally eye safe laser. In addition, this wavelength is near the peak of high performance InGaAs photo diodes. Although this transition has been known for many years [1], the development of diode pumping makes this laser practical. Although efficient normal mode performance has been demonstrated, Q-switched performance is significantly lower. Q-switching requires energy storage to the end of the pump pulse. During long pump pulses, the stored energy suffers losses from fluorescence and up conversion. To characterize these losses, the up conversion parameter, P22, must be known. The up conversion parameter is measured here using direct pumping of the upper laser level with laser diodes. In what is believed to be a novel analysis approach, the nonlinear #145255 - $15.00 USD

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Received 1 Apr 2011; revised 1 Jul 2011; accepted 17 Jul 2011; published 22 Jul 2011

1 August 2011 / Vol. 1, No. 4 / OPTICAL MATERIALS EXPRESS 678

differential equations describing Er dynamics were solved in closed form and the results were used to curve fit the fluorescence data. For a given Er concentration and pump intensity, a value for the up conversion parameter was obtained from both the rise and decay of the 4I13/2 manifold. Once obtained, the up conversion parameter is used in a model developed here to predict the performance of the diode pumped Er:YAG laser. Other authors [2] have obtained values for the up conversion parameter by numerically solving the differential equations and using fluorescent data to adjust the parameters. Another method of measuring the up conversion parameter, solved the steady state condition for the lowest 4 Er manifolds and the decay of the Er 4I13/2 manifold to characterize the process. This method requires 2 fluorescent decay curves and characterization of the pump pulse [3], The objective is the optimization of the Er:YAG laser operating on the 4I13/2 to 4I15/2 transition around 1.6 μm. End pumping configurations can be very efficient if a low beam divergence, high spectral brightness pump is available. To achieve this, an Er:Yb:glass laser was used as a pump and a slope efficiency of 0.52 resulted [4]. Although good performance can be attained, overall efficiency must factor in the efficiency of the pump laser. Diode pumping of the Er laser eliminates the efficiency penalty of a laser pumped device. Indirect diode pumping, that is, pumping the Yb in Er:Yb:YAG with subsequent energy transfer to Er [5], was demonstrated. Direct diode pumping of Er eliminates any efficiency penalty of the the Yb to Er energy transfer. With diode pumping at 1.470 μm, a slope efficiency of 0.26 was achieved [6]. Direct pumping of the Er 4I13/2 manifold and using, laser rods with a high aspect ratio to confine the pump radiation produced slope efficiencies greater than 0.50 in several configurations [7,8, and references within]. Here, the 4I13/2 manifold will be directly pumped by laser diodes but the pump is not confined. By using larger diameter laser rods and matching the pumped volume to the laser mode volume, good beam quality can be attained. Modeling and optimization is possible only if the pertinent laser parameters are accurate. To model the Er:YAG laser operating on the 4I13/2 to 4I15/2 transition, an accurate up conversion parameter is needed. Direct pumping of the upper laser manifold provides an efficient method of pumping the Er:YAG laser and generates the minimum amount of heat. Minimum heat generation is particularly important because Er:YAG operating on the 4I13/2 to 4I15/2 transition is a quasi 4 level laser. That is, there is a nonnegligible population density in the lower laser level which heating exacerbates. Until recently, high power laser diodes operating at the correct wavelengths were not available. Not only do the pump diodes need to be powerful, they must have high brightness. High brightness is necessary to effectively optimize the overlap between the pumped volume and the mode volume of the laser beam. This is characterized by an overlap efficiency of the pumped volume and the laser mode volume. Because the pump beam has a high divergence compared with the laser beam, the overlap efficiency may be improved by utilizing higher Er concentrations. However, higher Er concentrations tend to increase the threshold and decrease the laser efficiency because of up conversion. Rather than using high Er concentrations, pump absorption can be improved by tuning narrow spectral bandwidth diodes to an Er absorption feature. In the up conversion process 2, see Fig. 1, two nearby Er atoms in the 4I13/2 manifold interact to promote one Er atom to the 4I9/2 manifold and demote the other Er atom to the 4I15/2 manifold, This is illustrated in Fig. 1. Because of fast nonradiative processes of the 4I9/2 manifold, a quantum of energy is lost in this process. Once in the 4I11/2 manifold, the quantum of energy may disappear by radiative or nonradiative processes or undergo another up conversion, processes 1 in Fig. 1. An accurate value for the up conversion parameter, P22, is needed to accurately model this process, shown as process 2 in Fig. 1. An accurate value for the up conversion parameter, P22, is needed to accurately model the Er dynamics.

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Fig. 1. Er:YAG energy level diagram and dynamical processes.

2. Spectroscopic Measurements Measurements of the up conversion parameter were performed for different Er concentrations and for different levels of excitation. Typically, 10 mm cubes of Er:YAG were window polished on 3 sides, 2 of which were opposing surfaces. The other 3 sides have a fine ground finish. A 1.0 m fiber tended to homogenize the pump beam profile. The pump was imaged into the Er:YAG laser sample, beam radius 0.9 mm. Er concentrations were 0.001, 0.005, 0.010, and 0.020. The pumped volume was located near the third polished surface to minimize reabsorption. An InGaAs photo diode observed the fluorescence through the third polished surface. The fluorescence from the 4I13/2 to 4I15/2 transition was observed during the pump pulse and during the subsequent decay. A beam block allowed only the fluorescence from the first millimeter or so of the cube to reach the photo diode. This pumping arrangement minimizes the possibility of parasitic lasing and radiation trapping. The Er:YAG samples were pumped with pulses which simulated the pulses to be used in the laser experiment. The pump pulse lengths are nominally 6.0 ms. A 2 Hz pulse repetition frequency is used to minimize thermal effects. The rise and the decay of the fluorescence is averaged over 64 pulses with a digital oscilloscope. Data was collected for 4 Er:YAG samples each with a different Er concentrations, 0.001, 0.005, 0.010, and 0.020. Fluorescence from each sample was measured for 4 different pump energies. 3. Model The population density of the Er:YAG 4I13/2 manifold can be modeled using a single differential equation. The lowest four manifolds of Er are involved in the pumping dynamics. If any of the Er atoms are promoted to the 4I9/2 manifold, they will quickly decay to the Er 4 I11/2 manifold by nonradiative transitions. Therefore the population density of the 4I9/2 manifold can be effectively set to zero. In a similar fashion, any Er atoms reaching the Er 4I11/2 manifold tend to decay rapidly allowing this manifold population density to be approximated by zero as well. The approximation for the 4I9/2 manifold is very good. The approximation for the 4I11/2 manifold appears to be valid as well. The lifetime of the 4I11/2 manifold is short, ~0.1 ms, compared to the long pump length, 6.0 ms, and decays time constants associated with Er:YAG. With low populations of the manifolds above the 4I9/2 manifold, the differential equation of the 4I15/2 manifold is approximated as the negative of the differential equation for the 4I13/2 manifold. During pumping, the pertinent equations, with N1 and N2 denoting the populations of the Er 4I15/2 and 4I13/2 manifolds, respectively, are

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N1  N2

 CE NS ,

(1)

dN1 dN  2, dt dt

(2)

S C N   a N2  dN 2 N (3)   2   2  Q  P22 N 22  P E S . dt 2 FSAT In Eq. (1), the total population is assumed to reside in the two lowest manifolds, and the sum of N1 and N2 is set equal to the erbium concentration, CENS. Equation (2) represents the derivative with time of Eq. (1). In Eq. (3), up conversion causes the term (2 – ηQ)P22N22 and ground manifold depletion causes the term γaSPN2/FSAT, were SP is the pump intensity and FSAT is the pump saturation parameter [9]. ηQ is the fraction of the Er atoms reaching the 4F9/2 manifold that end up in the 4I13/2 manifold. This will depend on the nonradiative processes. The parameter γa is (1 + Z2/Z1) where Z1 and Z2 are the Boltzmann factors for the lower and upper pump absorption levels. When the upper laser manifold, Er 4I13/2, becomes populated, the pump absorption decreases. Solving the differential, Eq. (3), and applying the boundary conditions, the solution is N 2  2CE N S

 1  exp   Dt /   SP   , FSAT   D  1   D  1 exp   Dt /   

1





1

2



SP a , FSAT

(4)

(5)

and, 1/ 2

  S D  1  4  2  Q  P22C E N S P  2  . (6) FSAT   After the pumping ceases, SP vanishes leaving the first 2 terms in Eq. (3). Solving the differential equation, with N20 as the population density at a time of 0,

N2 

N 20 exp  t /  2  , 1   1  exp  t /  2 

(7)

where N20 is the population density at time t = 0, and

   2  Q  P22 2 N 20 .

(8)

Having such closed form expressions for the temporal behavior of the dynamics facilitates the curve fitting process. 4. Data Analysis and Discussion The up conversion parameter, (2 – ηQ)P22, can be deduced by curve fitting the derived equations to the data. Figures 2 and 3 are representative samples of the quality of the curve fit. Curve fitting was done for both the rise and the fall of the Er 4I13/2 to 4I15/2 fluorescence. A value for the up conversion parameter was calculated for the 4 different Er concentrations and different levels of excitation. Results appear in Table 1. The curve fitting correlation coefficient, R2, exceeded 0.9995 and was usually greater than 0.9999. The values appear to be consistent with the exception of a few outliers existing at higher Er concentrations.

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Fig. 2. Rise and decay of Er:YAG, 0.005 Er and 50.9 mJ incident pump.

Fig. 3. Rise and decay of Er:YAG. 0.010 Er and 111.5 mJ incident pump.

There appears to be a trend for the up conversion parameter to increase as the Er concentration increases. This nearly linear dependence on the Er concentration has been reported elsewhere [4]. Nevertheless, an average of the up conversion parameters was computed. During pumping and during decay the computed up conversion parameters are 3.82 ± 0.93 and 3.76 ± 1.44, respectively. If the 2 outliers are omitted, the uncertainty reduces to ± 0.51 and ± 0.82. The average value is 3.8x10 24 m3/s. This is in general agreement with an up conversion parameter for an 0.01 Er concentration reported elsewhere [10]. The model assumes that the up conversion parameter is independent of the pump energy. Comparing the up conversion parameters for a particular Er concentration but various pump energies, it appears that this is true. Comparing the up conversion parameter for a given pump energy but various Er concentrations,, a relatively small positive dependence may be noted. If this trend continues, the extrapolated values for the up conversion parameter at high Er concentrations would be in general agreement with other published values obtained at high Er concentrations [11]. If the concentration dependence is taken into account, the uncertainty reduces further. If the trend does not continue, there are several possible reasons why the results may differ. The published results [11] used a frequency doubled Nd:YAG to excite the Er 4S3/2 manifold. Thus, many other manifolds may contribute to the dynamics of the 4I13/2 manifold. In this work, the Er 4I13/2 manifold was directly excited. This minimizes the participation of other manifolds. The published work also utilized experimental data to compare with a numerical solution to the differential equation. In this analysis, closed form solutions to the differential equations were fitted to the experimental data. Values for the up conversion parameter determined here were obtained by minimizing the root mean squared difference between the data and the model. #145255 - $15.00 USD

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Table 1. Up Conversion Parameter, (2 – ηQ)P22, During Pumping and During Decay*

Pump Energy 19.5 mJ 50.3 mJ

CE = 0.001 during during pumping decay 3.06 3.78 3.55 3.11

CE = 0.005 during during pumping decay 3.32 4.84 3.22 3.52

82.7 mJ 4.19 2.23 111.5 mJ 3.50 2.09 3.55 *Values of P22 are in units of 1024 m3/s.

3.68

CE = 0.010 during during pumping decay 3.07 4.23 4.31 2.86 3.38 6.79

3.14 2.26

CE = 0.020 during during pumping decay 3.44 8.14 3.43 4.89 4.91 3.61

4.20 3.34

5. Experimental Arrangement High power laser diodes are now available for the direct pumping of the Er:YAG 4I13/2 manifold. Diodes for these demonstrations operated at 1.532 μm which corresponds to a strong Er:YAG absorption feature. Diodes were mounted on a heat sink to reduce heating and thus temperature tuning the diode away from the absorption feature. The output of the diodes was imaged on a single optical fiber with a core diameter of 0.40 mm and a numerical aperture of 0.22. Output of the optical fiber was collimated with a 35 mm focal length lens. A 80 mm focal length lens imaged the beam from the fiber through a dichroic mirror and into an Er:YAG laser rod, see Fig. 4. The laser resonator consisted of a flat HR mirror, the laser rod, a dichroic highly reflecting at the laser wavelength, 1.645 μm, but transparent at the pump wavelength, and a partially reflecting, 0.5 m radius of curvature output mirror. With this resonator, the laser beam radius can be easily adjusted to achieve the best performance. Laser performance was initially evaluated by measuring the laser output energy versus the incident pump energy.

Fig. 4. Experimental arrangement provides wide range of pump waist and beam radii.

Performance of the Er:YAG laser was nearly optimum by using Er concentrations of 0.005 and 0.010. The laser was operated normal mode, NM, with 6.0 ms current pulse lengths. Results of the laser output energy versus the incident pump energy appear in Fig. 5. As expected, there is a slight curvature upward in the data. Nevertheless the data were fit to a linear equation. Performance with a 0.005 Er:YAG cube yielded a threshold of 32.6 mJ and a slope efficiency of 0.359. Performance with a 0.010 Er:YAG cube yielded a threshold of 29.6 mJ and an optical to optical slope efficiency of 0.406. This room temperature performance can be compared to the pulsed performance of a cryogenically cooled Er:YAG laser which achieved 420 W quasi continuously with an optical to optical slope efficiency of 0.45 [12]. Cryogenic cooling has several benefits not the least of which is a decreased lower laser level population density.

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90 0.005 Er 0.010 Er

Laser Output Energy (mJ)

80 70 60 50 40 30 20 10 0 0

50

100 150 Pump Energy (mJ)

200

250

Fig. 5. Normal Mode performance achieves 0.406 optical to optical efficiency.

Q-switched, QS, operation was achieved using an acousto-optic modulator. The rise time interval of the fused silica acousto-optic modulator was approximately 0.15 μs. Although this rise time interval is relatively long, the relatively small Er emission cross section results in a long pulse evolution time interval. Double Q-switch pulses were sought, but not found. This supports the contention that double pulse threshold was not reached and the rise time interval is sufficiently fast. Insertion of the acousto-optic modulator increased the optical losses and significantly decreased the laser performance. Q-switching reduced the pulse energy significantly when long pump pulses were employed. Storing energy for long time intervals results in increased losses caused by fluorescence and up conversion. To mitigate these deleterious effects, shorter pump pulse lengths can be used. To this end, normal mode and Q-switched operation were assessed at different pump pulse lengths. Results for 3, 4, 5, and 6 ms long pump pulses were assessed. The results of 3 and 6 ms long pump pulses for a 0.010 Er:YAG cube are presented in Fig. 6. 16 3.0 ms NM 3.0 ms QS 6.0 ms NM 6.0 ms QS

Laser Output Energy (mJ)

14 12 10 8 6 4 2 0 0

50 100 Pump Energy (mJ)

150

Fig. 6. Short pump pulses improve Q-switch performance.

As the pump pulse becomes shorter, the normal mode threshold decreases but the slope efficiency remains about constant, as modeling predicted. The threshold for Q-switched operation is essentially the same as the normal mode threshold. However, slope efficiencies for Q-switched operation are larger for shorter pulses. Employing 3.0 ms long pump pulses, the Q-switched pulse energy reached 6.0 mJ. Laser models indicate the thresholds for normal mode and Q-switched operation are essentially equal, but the slope efficiencies are related by the storage efficiency. Figure 4 supports the equal threshold contention. The normal mode slope efficiency and Q-switched

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slope efficiency just above threshold can be compared. Without up conversion, the slope efficiencies would be in the ratio of the storage efficiency, ηS, where 2   exp   2 /  I  .  I 

S  

(9)

In the above expression, τ2 and τI are the upper laser manifold lifetime and pump current pulse length, respectively. For this experimental arrangement and the equation above, the storage efficiency is 0.70. However, the ratio of the normal mode and Q-switched slope efficiencies for Er:YAG does not display this behavior because of up conversion. To illustrate the size of the up conversion effect, the power lost by fluorescence and up conversion can be compared. hc  w p l 2

PF  N 2TH

L  I

PUP   2  Q  P22 N 22TH

,

hc

L

 w2p l.

(10)

(11)

where λL is the laser wavelength, wp is the pump beam radius in the laser rod and l is the laser rod length. N2TH is the laser manifold population density at threshold. Pump beam size is 0.3 mm. The energy going to spontaneous emission and up conversion are estimated by multiplying the power by the current pulse length. Evaluating these expressions yields ~8 and ~10 mJ, respectively. This can be compared with the laser output power averaged over the pump current pulse length of roughly 50 mJ. The power lost by the up conversion explains much of the limited Q-switched energy. The power lost through the up conversion process will be limited by ground state depletion. 6. Summary The up conversion parameter, P22, was measured for four different spectroscopic samples of Er:YAG, each with a different Er concentration. Each sample was also measured at several levels of excitation. Fluorescence versus time data was recorded during the pump pulse and for the subsequent decay. The differential equation for each of these situations was solved in closed form and the results were fit to the experimental data. An average value for the up conversion parameter is determined to be 3.8x10 24 m3/s. There appears to be a tendency for this parameter to increase with increasing Er concentration. An Er:YAG laser was constructed and evaluated with four different Er concentrations. End pumping was used to take advantage of the fiber coupled, 1.532 μm pump diodes. The diodes are directly pumping the upper laser manifold, Er 4I13/2. The best performance was obtained with a 10 mm cube of Er:YAG having 0.010 Er. With this material, an optical to optical slope efficiency of 0.406 was achieved in normal mode, room temperature operation. This laser was Q-switched using an acousto-optic modulator and 6.0 mJ pulses were obtained, which is shown to be limited by up conversion.

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