850 nm EMISSION IN Er:YLiF 4 UPCONVERSION LASERS

Transcription

1 LASERS AND PLASMA PHYSICS 850 nm EMISSION IN Er:YLiF 4 UPCONVERSION LASERS OCTAVIAN TOMA 1, SERBAN GEORGESCU 1 1 National Institute for Laser, Plasma and Radiation Physics, 409 Atomistilor Street, Magurele, Ilfov, , Romania, octavian.toma@inflpr.ro Received January 29, 2009 Upconversion-pumped laser emission in Er:YLiF 4 on transition 4 S 3/2 4 I 13/2 (850 nm) is studied using a model based on rate equations. The emission regimes are investigated and threshold values of the pump photon flux are calculated for two different pump wavelengths 795 nm and 970 nm. 1. INTRODUCTION The upconversion-pumped lasers are promising sources of visible coherent radiation, with possible applications in spectroscopy, display technology, biology, imaging, and optical data storage. Among the active ions used in these lasers, Er 3+ is one of the most investigated, due to its multitude of resonances between various transitions. The most interesting laser transition of Er 3+ is 4 S 3/2 4 I 15/2, which yields radiation in green (around 550 nm). Laser emission on this transition was studied in a series of papers [1 4], and the influence of the pump wavelength and emission reabsorption on the emission regime were discussed. Transition 4 S 3/2 4 I 13/2, with emission around 850 nm, was also used to obtain visible radiation (in blue, 425 nm), by intracavity frequency doubling [5]. Parasitic emission on this transition was observed accompanying emission on transition 4 S 3/2 4 I 15/2 [6 8]. It is therefore important to know the conditions that would lead to laser oscillation on this transition, whether wanted or unwanted. In this work, we model the upconversion-pumped laser emission at 850 nm on transition 4 S 3/2 4 I 13/2 in Er(1%):YLiF 4 (Er:YLF), a crystal with low-energy phonons that yielded good performances in upconversion lasers. The transition is self-saturated, due to the lifetime of the final laser level being longer than the lifetime of the initial one. The best experimental results on this transition at room temperature were therefore obtained [5,9 12] for pump mechanisms using the final laser level 4 I 13/2 as the intermediate pump level, the pump being used to deplete it and avoid Rom. Journ. Phys., Vol. 55, Nos. 7 8, P , Bucharest, 2010

2 2 850 nm emission in Er:YLiF 4 upconversion lasers 791 self-saturation. We study one such pump mechanism, consisting of ground-state absorption (GSA) 4 I 15/2 4 I 9/2 at 795 nm, followed by non-radiative decay to 4 I 13/2 and excited-state absorption (ESA) [b] 4 I 13/2 2 H2 11/2 (see Fig. 1). For comparison, we also discuss another pump mechanism, that yielded good results for the transition 4 S 3/2 4 I 15/2 : GSA 4 I 15/2 4 I 11/2 at 970 nm, followed by ESA [d] (see Fig. 1) at the same wavelength on the transition 4 I 11/2 4 F 7/2 and non-radiative decay to thermalized levels ( 4 S 3/2, 2 H2 11/2 ). 2. MATHEMATICAL MODEL The mathematical model includes CW pumping by the two upconversion mechanisms mentioned above, based on successive absorption processes. At the chosen concentration of 1 at. %, the energy-transfer processes can be neglected. This concentration is the usual compromise in the experiments between high concentrations that would activate the cross-relaxation between levels 4 S 3/2 and 4 I 15/2, depleting the initial laser level, and low concentrations that would provide low absorption coefficient of the pump power. The absorption process 4 I 11/2 4 F 7/2 is considered here to feed directly the thermalized levels ( 4 S 3/2, 2 H2 11/2 ); this assumption is made possible by the fact that the level 4 F 7/2 is close to 2 H2 11/2 on the energy scale, therefore having short lifetime and decaying predominantly by multiphonon transitions to 2 H2 11/2 (see Table I in Ref. [4]). The laser emission takes place between Stark levels 2 of 4 S 3/2 and 7 of 4 I 13/2, according to Ref. [5,9] and the energy levels in Ref. [13]. The mathematical model is based on the following rate equation system: (6) (5) (4) [b] [d] 4 F7/2 2 H211/2 4 S3/2 4 F9/2 E(cm -1 ) (3) (2) (1) (0) 795 nm 970 nm 850 nm 4 I9/2 4 I11/2 4 I13/2 4 I15/2 Fig. 1 Energy level scheme of Er 3+ :YLF. The two pump mechanisms of 4 S 3/2 are represented: pumping at 795 nm and pumping at 970 nm. The laser transition at 850 nm is also represented. The notations were kept the same as in Ref. [4].

3 792 Octavian Toma, Serban Georgescu 3 dn 1 dt = N 1 N 2 N 3 N 4 N 5 + β 21 + β 31 + β 41 + β 51 σ b φ 2 N 1 T 1 T 2 T 3 T 4 +σ 51 (f 52 N 5 f 17 N 1 )ϕ dn 2 dt = N 2 N 3 N 4 N 5 + β 32 + β 42 + β 52 + σ 04 φ 4 N 0 σ d φ 4 N 2 T 2 T 3 T 4 dn 3 dt = N 3 N 4 N 5 + β 43 + β 53 + σ 02 φ 2 N 0 T 3 T 4 dn 4 = N 4 N 5 + β 54 dt T 4 (1) dn 5 dt = N 5 + σ b φ 2 N 1 + σ d φ 4 N 2 σ 51 (f 52 N 5 f 17 N 1 )ϕ dϕ = v [σ 51 (f 52 N 5 f 17 N 1 ) ]ϕ + k N 5 dt N t = N 0 + N 1 + N 2 + N 3 + N 4 + N 5 where N i represent the concentrations of the populations of the Er 3+ energy levels 4 I 15/2, 4 I 13/2, 4 I 11/2, 4 I 9/2, 4 F 9/2 and 4 S 3/2 thermalized with 2 H2 11/2 (numbered 0 to 5, see Fig. 1), while T i represent the lifetimes of the first five excited levels and β ij represent the branching ratios of transitions i j. The total concentration of erbium ions is N t = cm 3. The laser photon flux was denoted by ϕ. φ 2 and φ 4 represent, respectively, the pump photon flux corresponding to the pump wavelengths 795 nm and 970 nm. σ 02 and σ 04 represent the absorption cross-sections for pumping respectively at 795 and 970 nm, while σ b and σ d are the cross-sections of the corresponding ESA. f 52 σ 51 is the stimulated emission cross-section of the laser transition 4 S 3/2 (2) 4 I 13/2 (7), while f 17 σ 51 is the corresponding absorption cross-section, where f 52 = and f 17 = are the fractional populations of the initial, respectively final laser level, calculated using the data in Ref. [13]. represents the losses in the laser resonator, while k is a factor taking into account the contribution of the spontaneous emission to the onset of laser oscillation. In this work, k was used only as a starter of the laser oscillation and assumed to have a conveniently low value (10 10 cm µs 1 ). We model a continuously pumped Er:YLF laser with a monolithic resonator, assuming spatial uniformity of the pump radiation inside the active medium. The symbol v in (1) denotes the speed of light in the active medium (with refraction index n = 1.47 [14]). The notations were kept (as much as possible) the same as in Ref. [4] to facilitate the comparison and corroboration of the results of the two models. The values of the branching ratios of various transitions were taken from Ref. [15]; the lifetimes of the five energy levels included in this model were T 1 = µs, T 2 = 4000 µs, T 3 = 6.6 µs, T 4 = 100 µs, and = 400 µs [16]. The values used for the cross-sections of pump and stimulated emission transitions are:

4 4 850 nm emission in Er:YLiF 4 upconversion lasers 793 σ 51 = cm 2 [5], σ 02 = cm 2, σ b = cm 2, σ 04 = cm 2, and σ d = cm 2 [15]. 3. STEADY-STATE SOLUTIONS The steady-state solutions of the rate-equations system (1) are calculated. The term that takes into account spontaneous emission in the sixth of the equations (1) is important only for starting the laser oscillation, but it is negligible in the presence of laser emission. Neglecting this term, the steady-state system has two solutions. One of them corresponds to ϕ = 0; this solution corresponds to no laser emission. We will not discuss this solution here because, while obtained by neglecting spontaneous emission, it corresponds to a situation that demands spontaneous emission being taken into account. The second solution corresponds to σ 51 (f 52 N 5 f 17 N 1 ) = 0 and non-zero laser photon flux. Only this solution will be discussed in the following. The stability analysis of the steady-state solutions provides information about the asymptotic behavior of the laser; if a solution is stable, it qualifies for describing the behavior of the laser at steady state. However, the information offered by the stability analysis must be correlated with the integration of the differential equations and analytical calculations of the CW emission thresholds in order to obtain a complete description of the behavior of this laser system nm PUMPING The steady-state solution for 795 nm pumping was obtained setting φ 4 = 0 in equations (1) and setting all derivatives on the left to zero. The analytical expression of this solution is N 0 = N t + f 17 σ 51 T σ 02 T 23 φ 2 (1 + σ 02 T 23 φ 2 ) N 5 N 1 = f 52 f 17 N 5 f 17 σ 51 N 2 = β 32 σ 02 T 2 φ 2 N 0 + β 5432 T 2 N 5 N 3 = β 543 T 3 N 5 + σ 02 T 3 φ 2 N 0 T 4 N 4 = β 54 N 5 (2) ( N t + N 5 = ϕ = 1 f 17 σ 51 T 1 + β 321 T 25 f 52 f 17 T 1 + β 321 β T ( 5 f52 f 17 σ b φ 2 1 ) f 17 σ 51 ) N 5 σ b f 17 σ 51 φ 2

5 794 Octavian Toma, Serban Georgescu 5 where the following notations were used: β 543 = β 54 β 43 + β 53 β 5432 = β 543 β 32 + β 54 β 42 + β 52 β = β 5432 β 21 + β 543 β 31 + β 54 β 41 + β 51 β 321 = β 32 β 21 + β 31 β 321 = β 321σ 02 T 25 φ 2 (3) 1 + σ 02 T 23 φ 2 T 23 = β 32 T 2 + T 3 ( T 25 = β 5432 T 2 + β 543 T 3 + β 54 T f ) 52 f nm PUMPING For pumping at 970 nm, φ 2 = 0 and the rate equations (1) have the steady-state solution { 1 + σ d T 2 φ 4 N 0 = N t + [ f52 + T } 25 (φ 4 ) ]N (σ 04 + σ d )T 2 φ 4 σ 51 f 17 f 17 N 1 = f 52 N 5 f 17 σ 51 f 17 N 2 = β 5432T 2 N 5 + σ 04 T 2 φ 4 N 0 (1 + σ d T 2 φ 4 ) N 3 = β 543 T 3 N 5 (4) N 4 = β 54 T 4 N 5 N 5 = σ 51 f 17 [ 1 T 1 + β 21 (φ 4 )σ 04 φ 4 ] + β 21 (φ 4 )σ 04 φ 4 N t f 52 f 17 [ 1 T 1 + β 21 (φ 4 )σ 04 φ 4 ] + 1 [1 β (φ 4 ) + β 21 (φ 4 )σ 04 T 25 (φ 4 )φ 4 ] ϕ = N σ dφ 4 N 2 where the following additional notations were used: β 21 (φ 4 ) = β 21 + σ d T 2 φ (σ 04 + σ d )T 2 φ 4 β 21 + σ d T 2 φ 4 β (φ 4 ) = β β 543 β 31 + β 54 β 41 + β 51 (5) 1 + σ d T 2 φ 4 β 5432 T 2 T 25 (φ 4 ) = + β 543 T 3 + β 54 T σ d T 2 φ 4

6 6 850 nm emission in Er:YLiF 4 upconversion lasers RESULTS AND DISCUSSION nm PUMPING The CW threshold for 795 nm pumping was calculated solving the rate equation system (1) in steady-state conditions with ϕ = 0 and φ 4 = 0. The threshold pump flux was obtained as the real positive solution of a second degree equation with the following coefficients (in the increasing order of the degree): a 0 = σ 51 T 1 a 1 = [ ( (β )σ b β T ) ] 23 + β 321 f 17 N t σ 02 (6) σ 51 σ 51 T 1 { } a 2 = [(β )T 23 β 321 T 25 ] + β 321 f 52 N t σ 02 σ b σ 51 where T 25 = β 5432 T 2 + β 543 T 3 + β 54 T 4 + (7) and the other notations are specified above. The threshold pump photon flux presents a singularity at a value of resonator losses β 321 f 52 σ 51 N t 2 = (8) β 321 T 25 + (1 β )T 23 where a 2 becomes zero. For values of greater than 2, the second-degree equation with coefficients given by (6) yields negative values for the CW laser threshold, without physical meaning. That is, for values of resonator losses greater than 2, CW laser emission is impossible regardless of the pump photon flux. This interpretation was verified by the stability analysis of the steady-state solution (2): for > 2, the solution is unstable at all values of the pumping photon flux. The CW emission threshold is represented in Fig. 2 for values of usual in experiments nm PUMPING The threshold of CW laser emission for 970 nm pumping was calculated solving the rate equation system (1) at steady state, with ϕ = 0 and φ 2 = 0. The threshold pump power was obtained as the real positive solution of a second-degree equation

7 796 Octavian Toma, Serban Georgescu 7 φ 2 (10 16 cm 2 µs 1 ) CW (cm -1 ) p 2 (kw/cm 2 ) Fig. 2 Emission threshold for pump wavelength 795 nm. The vertical axis on the right represents the pump power density corresponding to the pump photon flux. with the following coefficients (in the increasing order of the degree): b 0 = σ 51 b 1 = f 17 β 21 σ 04 T 1 N t [(1 β 5432 )σ d T 2 + σ 04 (β 21 T 1 + T 2 )] (9) σ 51 ) b 2 = σ 04 σ d T 2 ( f 52 N t f 17 β 5431 T 1 N t σ 51 T 152 where the following additional notations were used: β 5431 = β 543 β 31 + β 54 β 41 + β 51 T 152 = β 5431 T 1 + β 543 T 3 + β 54 T 4 + (10) The threshold pump power has a singularity for 4 = f 52 f 17 β 5431 T 1 T 152 σ 51 N t (11) Similarly to 795 nm pumping, for > 4, CW laser emission cannot be obtained regardless of the pumping photon flux. The stability analysis of the solution corresponding to 970 nm pumping confirmed this result: the solution was found to be unstable for > 4, at all values of the pump photon flux. The results of the investigation of the laser emission regime are summarized in Fig. 3, for usual values of. At low values of the pump flux, the laser emission is self-saturated due to the lifetime of 4 I 13/2 level being longer than the lifetime of

8 8 850 nm emission in Er:YLiF 4 upconversion lasers 797 φ 4 (10 16 cm 2 µs 1 ) CW SELF-SATURATING (cm -1 ) 100 p 4 (kw/cm 2 ) Fig. 3 Emission thresholds for pump wavelength 970 nm. The vertical axis on the right represents the pump power density corresponding to the pump photon flux. 4 S 3/2 : emission starts, but soon stops because of the accumulation of population on the final laser level 4 I 13/2. The threshold of this emission regime was determined by repeated numerical integration (fourth order Runge-Kutta method) of Eqs. (1) with initial conditions N 0 = N t, N i = 0 for i > 0 and ϕ = 0 and various values of φ 4. The threshold value of φ 4 was chosen as the lowest value for which the laser gain is greater than the resonator losses for at least one moment. CW laser emission can be obtained for greater values of φ 4, higher than the CW threshold represented by the upper continuous line in Fig 3. A comparison of Figs. 2 and 3 shows easily that the CW threshold is much lower for 795 nm pumping than for 970 nm pumping. Besides, the ESA from 4 I 13/2 which represents the second step of the pump mechanism for 795 nm pumping depletes the 4 I 13/2 level, facilitating the obtaining of population inversion between the laser levels (one absorbed photon on this transition increases population inversion with two units) and hindering self-saturation of the laser emission. The maximum values of the resonator losses for which CW laser emission can still be obtained also reflect the contribution of the ESA from 4 I 13/2 : the maximum value 2 for 795 nm pumping is greater than the maximum value 4 for 970 nm pumping. However, the threshold of the self-saturated emission obtained for 970 nm pumping is lower than the CW threshold for 795 nm pumping, due to the greater efficiency of the mechanism [d] in populating the initial laser level. A complete picture of the emission thresholds of the upconversion-pumped Er:YLF laser emitting at 850 nm is represented in Fig. 4. The dotted lines represent vertical asymptotes of the two CW emission thresholds: upper dashed line (970 nm

9 798 Octavian Toma, Serban Georgescu 9 φ 2, φ 4 (10 16 cm 2 µs 1 ) nm pumping 970 nm pumping (cm -1 ) Fig. 4 The dependence of emission thresholds for laser transition 4 S 3/2 4 I 13/2 on the resonator losses, for pump wavelengths 795 nm (continuous line) and 970 nm (dashed line). The dotted lines represent vertical asymptotes of the two CW emission thresholds: upper dashed line (970 nm pumping) - = cm 1 ; continuous line (795 nm pumping) - = cm 1. The lower dashed line represents the threshold of the self-saturated laser emission observed for 970 nm pumping. pumping) - = cm 1 ; continuous line (795 nm pumping) - = cm 1. The lower dashed line represents the threshold of the self-saturated laser emission observed for 970 nm pumping. 5. CONCLUSIONS The laser emission at 850 nm in Er(1%):YLiF 4 on transition 4 S 3/2 4 I 13/2, CW-pumped by upconversion processes at two wavelengths (795 nm and 970 nm) was studied using a model based on rate equations. For 795 nm, the absorption of pump radiation from 4 I 13/2 depletes this level, thus facilitating CW laser emission, which is the only emission regime in this case. For 970 nm, there are two emission regimes possible: self-saturated emission at low pump powers and CW emission for greater pump powers, due to the final laser level being longer-lived than the initial one. CW emission thresholds were analytically calculated for each pump wavelength. REFERENCES 1. O. Toma, S. Georgescu, Dynamics of an upconversion Er:YAG laser with reabsorption losses, J. Opt. Soc. Am. B 21, (2004). 2. O. Toma, S. Georgescu, The influence of pump wavelength on Er:YAG green-emitting laser characteristics, IEEE J. Quantum Electron. 42, (2006). 3. O. Toma, S. Georgescu, Pump wavelengths for an upconversion-pumped Er:YAG green-emitting laser, Rom. J. Phys. 51, (2006).

10 nm emission in Er:YLiF 4 upconversion lasers O. Toma, Emission regimes of a green Er:YLiF 4 laser, IEEE J. Quantum Electron. 43, (2007). 5. P. E.-A. Möbert, E. Heumann, G. Huber, B. H. T. Chai, 540 mw of blue output power at 425 nm generated by intracavity frequency doubling an upconversion-pumped Er 3+ :YLiF 4 laser, Appl. Phys. Lett. 73, (1998). 6. T. J. Whitley, C. A. Millar, R. Wyatt, M. C. Brierley, D. Szebesta, Upconversion pumped green lasing in erbium doped fluorozirconate fibre, Electron. Lett. 27, (1991). 7. R. Brede, E. Heumann, J. Koetke, T. Danger, G. Huber, B. Chai, Green up-conversion laser emission in Er-doped crystals at room temperature, Appl. Phys. Lett. 63, (1993). 8. T. Danger, J. Koetke, R. Brede, E. Heumann, G. Huber, B. H. T. Chai, Spectroscopy and green upconversion laser emission of Er 3+ -doped crystals at room temperature, J. Appl. Phys. 76, (1994). 9. S. A. Pollack, D. B. Chang, M. Birnbaum, Threefold upconversion laser at 0.85, 1.23, and 1.73 µm in Er:YLF pumped with a 1.53 µm Er glass laser, Appl. Phys. Lett. 54, (1989). 10. P. Xie, S. C. Rand, Continuous-wave trio upconversion laser, Appl. Phys. Lett. 57, (1990). 11. P. Xie, S. C. Rand, Astigmatically compensated, high gain cooperative up-conversion laser, Appl. Phys. Lett. 60, (1992). 12. C. A. Millar, M. C. Brierley, M. H. Hunt, S. F. Carter, Efficient up-conversion pumping at 800 nm of an erbium-doped fluoride fibre laser operating at 850 nm, Electron. Lett. 26, (1990). 13. M. A. C. dos Santos, E. Antic-Fidancev, J. Y. Gesland, J. C. Kruppa, M. Lemaitre-Blaise, P. Porcher, Absorption and fluorescence of Er 3+ -doped LiYF 4 : measurements and simulation, J. Alloys Comp , (1998). 14. D. E. Castleberry, A. Linz, Measurement of the refractive indices of LiYF 4, Appl. Opt. 14, 2056 (1975). 15. M. Pollnau, T. Graf, J. E. Balmer, W. Lüthy, H. P. Weber, Explanation of the CW operation of the Er 3+ 3-µm crystal laser, Phys. Rev. A 49, (1994). 16. M. Pollnau, W. Lüthy, H. P. Weber, Population mechanisms of the green Er 3+ laser, J. Appl. Phys. 77, (1995).