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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 22 — Oct. 25, 2010
  • pp: 22880–22885
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Numerical study on terahertz random lasing in disordered ruby with three-level atomic system

Jinsong Liu, Yong Liu, Jiantao Lü, and Kejia Wang  »View Author Affiliations


Optics Express, Vol. 18, Issue 22, pp. 22880-22885 (2010)
http://dx.doi.org/10.1364/OE.18.022880


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Abstract

A scheme to generate terahertz (THz) emission using active disordered medium made of ruby grains with a three-level atomic system is proposed via a one-dimensional model. Our computed results reveal that THz random lasing phenomenon could occur under suitable conditions. The proposed scheme is based on the pumping of the 2 A ¯ level of ruby via a ruby laser operating on its R2 line (693.9 nm), and 0.87 THz random lasing is expected on the 2 A ¯ to E ¯ transition of the split E 2 level.

© 2010 OSA

1. Introduction

Lasing phenomenon in disordered media is one of the most significant and interesting topic in the field of laser physics and technique, and has been widely studied both experimentally and theoretically [1

1. N. M. Lawandy, R. M. Balachandra, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994). [CrossRef]

14

14. X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69(10), 104202 (2004). [CrossRef]

]. For more details, one can see a review article [15

15. D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008). [CrossRef]

] and the references therein. It is worth mentioning that, by combining Maxwell’s equations with four level rate equations of electronic population, a useful theoretical model was presented for one-dimensional (1D) case [5

5. X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85(1), 70–73 (2000). [CrossRef] [PubMed]

], and was further extended to two-dimensional (2D) case [6

6. P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66(14), 144202 (2002). [CrossRef]

]. Many properties of random lasing have been explored via this model [5

5. X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85(1), 70–73 (2000). [CrossRef] [PubMed]

14

14. X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69(10), 104202 (2004). [CrossRef]

].

The conventional ruby lasing takes place between the ground state of the Cr3+ ion (A42) and its first excited state (E2). Due to the trigonal crystal field and spin-orbit coupling, the upper level E2 is split to a pair of sublevels 2A¯ and E¯ (29.14 cm−1 or 0.87 THz apart), forming two primary lines often denoted by R1 (694.3 nm) and R2 (693.9 nm), respectively. We hence can suggest that 0.87 THz random lasing could be operated in ruby grains using the levels 2A¯ and E¯ by pumping the grains from the A42 level to the 2A¯ level via a ruby laser operating on its R2 line. In fact, the feasibility of 29 cm−1 far-infrared lasing based on the pumping of the 2A¯ level of ruby via the R2 line was discussed [17

17. N. M. Lawandy, “Far-infrared lasing in ruby,” IEEE J. Quantum Electron. 6(15), 401–403 (1979). [CrossRef]

]. The generation of coherent 0.87 THz pulses in bulk ruby based on a V-type energy scheme pumped by both R1 and R2 lines was also proposed [18

18. E. Kuznetsova, Y. Rostovtsev, N. G. Kalugin, R. Kolesov, O. Kocharovskaya, and M. O. Scully, “Generation of coherent terahertz pulses in ruby at room temperature,” Phys. Rev. A 74(2), 023819 (2006). [CrossRef]

]. It should be noted that, with the generation of 29 cm−1 photons, this scheme also supports the interaction of the electronics states 2A¯ (E2) and E¯ (E2) of the excited Cr3+ with the resonant 29 cm−1 phonons, such as the 29 cm−1 phonon “bottlenecked” effect at low temperatures [19

19. S. Geschwind, G. E. Devlin, R. L. Cohen, and S. R. Chinn, “Orbach relaxation and hyperfine structure in the excited, ” Phys. Rev. 137(4A), A1087–A1100 (1965). [CrossRef]

] and the reabsorption procession of 29 cm−1 phonons [20

20. K. F. Renk and J. Deisenhonefer, “Imprisonment of resonant phonons observed with a new technique for the detection of 10l2Hz phonons,” Phys. Rev. Lett. 26, 164–166 (1971).

]. Besides, the generation of THz radiation by difference-frequency mixing of the R1 and R2 lines in ZnTe was reported [21

21. T. Yajima and K. Inoue, “Submillimeter-wave generation by difference-frequency mixing of ruby lines in ZnTe,” IEEE J. Quantum Electron. 5(3), 140–146 (1969). [CrossRef]

]. Random laser is also called mirrorless laser. Recently, a kind of THz mirrorless laser was made by a quasi-crystal semiconductor [22

22. L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4(3), 165–169 (2010). [CrossRef]

].

2. Theoretical model

The binary layers of the system are consisted of two dielectric materials, as shown in Fig. 1(a)
Fig. 1 (a) Schematic illustration of 1D random medium made of ruby grains, and (b) the scheme of the energy levels for Cr3+.
. The white layer with a random variable thicknessanand a dielectric constant ε1 = ε0 simulates the air, while the black layer with a fixed thickness b=90 μm and a dielectric constant ε2 = 4ε0 simulates the scatters that are also the gain media with a three-level atomic system, and the scheme of the energy levels is shown in Fig. 1(b). The random variable an is described as an=a(1+wγ), where a =100 μm, wis the strength of randomness, and γ is a random value in the range [-0.5, 0.5].

For the 1D time-dependent Maxwell equations and for an active and non-magnetic medium, we have
Hyx=ε0εiEzt+Pzt,(i=1,2),
(1a)
Ezx=μ0Hyt,
(1b)
wherePzis the polarization density component in z direction, ε0 and μ0 are the electric permittivity and the magnetic permeability of vacuum, respectively.

For the three-level atomic system shown in Fig. 1(b), the rate equations read
dN1dt=N2τ21+N3τ31N1Wp,
(2a)
dN2dt=N3τ32N2τ21N2T+EzωldPzdt,
(2b)
dN3dt=N1WpN3τ31N3τ32+N2TEzωldPzdt,
(2c)
where Ni (i=1, 2, 3) is the population density in level i; The electrons in the level 1 are transferred to the upper level 3 by an external optical pump at 693.9 nm with a fixed rate Wp; Electrons in level 3 flow downward to level 2 quickly via nonradiation transition with decay rate 1/τ32; 1/τ31is the spontaneous transition rate from level 3 downward to level 1; 1/τ21is the spontaneous transition rate from level 2 downward to level 1; T is the time of flight between emission and re-absorption of a 29 cm−1 phonon and is on the order of 10−9—10−11s [17

17. N. M. Lawandy, “Far-infrared lasing in ruby,” IEEE J. Quantum Electron. 6(15), 401–403 (1979). [CrossRef]

], depending on how many 29 cm−1 phonons undergo reabsorption [20

20. K. F. Renk and J. Deisenhonefer, “Imprisonment of resonant phonons observed with a new technique for the detection of 10l2Hz phonons,” Phys. Rev. Lett. 26, 164–166 (1971).

]. It was reported that the 29 cm−1 phonons were absorbed and reemitted about 1000 times before they decay [20

20. K. F. Renk and J. Deisenhonefer, “Imprisonment of resonant phonons observed with a new technique for the detection of 10l2Hz phonons,” Phys. Rev. Lett. 26, 164–166 (1971).

]. Meanwhile the lifetime of the 29 cm−1 phonon is on the order of 10−6s. Accordingly, T is on the order of 10−9s. As a result, T is chosen as 1× 10−9 s in our system. The frequency between levels 3 and 2 is ωl=(E3-E2)/=2π×0.87THz. The stimulated transition rate is given by the termEzωldPzdt.

For such a system, the polarizationPzobeys the quantum population equation of motion

d2Pz/dt2+ΔωldPz/dt+ωl2Pz=κΔNEz.
(3)

The values of those parameters in the above equations that will be used in simulating the active part in the following numerical calculations are taken as: T2 = 2 × 10−14 s, τ32 = 1.1 × 10−9 s, τ21 = 3 × 10−3 s, τ31 = 3 × 10−6 s, and NT = i=13Ni = 1.6 × 1025 /m3.

When pumping is provided over the whole system, the electromagnetic fields can be calculated. In order to model such an open system, a Liao absorbing layer [23

23. A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986).

] is used to absorb the outward wave. The space and time increments have been chosen to beΔx=2×10−6 m and ΔtΔx/(2c), where Δt is taken to be 2×10−15 s, respectively. The pulse response is recorded during a time window of length Tw=5.2×10−10 s at all nodes in the system and Fourier transformed in order to obtain the intensity spectrum.

3. Numerical results

Firstly the wavelength dependence of the electromagnetic field intensity in the 1D system is calculated at different pump rates. As can be seen from Fig. 2(a)
Fig. 2 The spectral intensity in arbitrary units versus the wavelength for 1D disordered ruby medium shown in Fig. 1 at (a) Wp = 10s−1, (b) Wp = 30 s−1, (c) Wp = 100 s−1, and (d) Wp = 1000 s−1.
, when the pump rate is quite low (Wp=10 s−1), there are many discrete peaks near 344 μm (or 0.87 THz), each having quite weak peak intensity in the spectrum. Each peak corresponds to a lasing mode supported by the disordered medium, for which four peaks are indicated by their central wavelengths λ0, λ1, λ2 and λ3, respectively. As the pump rate increases, these peak intensities are nearly unchanged until the pump rate increases to a value (Wp=30 s−1) at which only those indicated modes are effectively amplified, as shown in Figs. 2(b) and 2(c). When the pump rate Wp further increases, the mode λ0 dominates the spectrum, as shown in Fig. 2(d). This means the mode λ0 perhaps has the minimum lasing threshold among the modes. Meanwhile, let us pay attention to the spectral width of the modes. The width becomes quite broader at Wp=30 s−1 than those at lower Wp. As the pump rate further increases, accompanied by the increase of the peak intensity, the spectral width becomes narrower and narrower until to a stable value.

In order to obtain the information about the threshold gain behavior for the modes in detail, numerical calculations are performed at different pump rates from which we can obtain the curves of the peak intensity and the spectral width vs the pump rate, as shown in Fig. 3
Fig. 3 The plot of the peak intensity and spectral width of the lasing modes vs the pump rate Wp. (a) The peak intensity for the four indicated modes, and the lasing threshold measured from the plots are WI0=30 s−1, WI1=60 s−1, WI2=50 s−1 and WI3=45 s−1; (b) the peak intensity and spectral width for the mode λ0; and (c) the spectral width for the four indicated modes, and the lasing threshold measured from the plots are WW0=43 s−1, WW1=82 s−1, WW2=78 s−1 and WW3=61 s−1.
. According to the traditional method, the pump thresholds for the four modes can be measured from the intensity curves in Fig. 3(a) as WI0=30 s−1, WI1=60 s−1, WI2=50 s−1 and WI3=45 s−1, which shows that different modes have different pump thresholds. Note that the mode λ0 has the minimum lasing threshold, which is easy to understand because the central wavelength of the mode λ0 is very near the transition wavelength of the active medium. The above numerical results clearly indicate that this 1D ruby disordered system could support random lasing phenomenon in THz domain.

As can be seen from Fig. 3(b), within a pump regime near the pump threshold, a jump occurs for the spectral width for the mode λ0. The peak value of the jump appears at the point that is very near the threshold of the mode. A method was proposed to determine the lasing threshold for a 2D random laser based on the spectral width [11

11. T. Ito and M. Tomita, “Polarization-dependent laser action in a two-dimensional random medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(2), 027601 (2002). [CrossRef] [PubMed]

]. That is, the lasing threshold is defined as such a pumping energy at which the spectral width becomes half of its maximal value. This method was used to analyze the threshold gain behavior for random lasing in a 2D disordered medium [8

8. J. S. Liu and Z. Xiong, “Theoretical investigation on the threshold property of localized modes based on spectral width in two-dimensional random media,” Opt. Commun. 268(2), 294–299 (2006). [CrossRef]

]. Based on this method and the width curves in Fig. 3(c), the thresholds are measured as WW0=43 s−1, WW1 = 82 s−1, WW2 = 78 s−1 and WW3 = 61 s−1. Obviously, the results from the two methods are consistent. Note that for a given mode, the specific value for its pump threshold depends on the defining fashion.

In order to check whether the results above are universal or not, we take huge amount calculation for different combinations of system parameters. All the results demonstrate that the conclusion we have obtained is universal.

Conclusions

In this work, we build a novel model for 1D active disordered medium made of ruby grains with a three-level atomic system to discuss random lasing phenomenon in THz domain. Our results suggest that THz random lasing could occur under suitable conditions. Our findings are significant for expanding random laser concept into THz domain and have potential application to construct new type of THz source.

Acknowledgments

Project supported by the National Science Foundation of China (Grant No. 60778003) and the Science Foundation of China Academy of Engineering Physics NSAF (Grant No. 10876010), and the Research Foundation of Wuhan National Laboratory (Grant No. P080008). The authors thank the reviewers for their valuable comments and helpful suggestions on the quality improvement of our present work.

References and links

1.

N. M. Lawandy, R. M. Balachandra, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994). [CrossRef]

2.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999). [CrossRef]

3.

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98(14), 143902 (2007). [CrossRef] [PubMed]

4.

S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93(5), 053903 (2004). [CrossRef] [PubMed]

5.

X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85(1), 70–73 (2000). [CrossRef] [PubMed]

6.

P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66(14), 144202 (2002). [CrossRef]

7.

C. M. Soukoulis, X. Jiang, J. Y. Xu, and H. Cao, “Dynamic response and relaxation oscillations in random lasers,” Phys. Rev. B 65(4), 041103 (2002). [CrossRef]

8.

J. S. Liu and Z. Xiong, “Theoretical investigation on the threshold property of localized modes based on spectral width in two-dimensional random media,” Opt. Commun. 268(2), 294–299 (2006). [CrossRef]

9.

J. S. Liu, H. Wang, and Z. Xiong, “Origin of light localization from orientational disorder in one and two-dimensional random media with uniaxial scatterers,” Phys. Rev. B 73(19), 195110 (2006). [CrossRef]

10.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008). [CrossRef] [PubMed]

11.

T. Ito and M. Tomita, “Polarization-dependent laser action in a two-dimensional random medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(2), 027601 (2002). [CrossRef] [PubMed]

12.

C. Wang and J. S. Liu, “Polarization dependence of lasing modes in two-dimensional random lasers,” Phys. Lett. A 353(2-3), 269–272 (2006). [CrossRef]

13.

J. S. Liu, H. Lu, and C. Wang, “Spectral time evolution of quasistate modes in two-dimensional random media,” Acta Phys. Sin. 54, 3116–3122 (2005) (in Chinese).

14.

X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69(10), 104202 (2004). [CrossRef]

15.

D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008). [CrossRef]

16.

X.-C. Zhang and J. Z. Xu, Introduction to THz Wave Photonics (Springer, Berlin, 2010).

17.

N. M. Lawandy, “Far-infrared lasing in ruby,” IEEE J. Quantum Electron. 6(15), 401–403 (1979). [CrossRef]

18.

E. Kuznetsova, Y. Rostovtsev, N. G. Kalugin, R. Kolesov, O. Kocharovskaya, and M. O. Scully, “Generation of coherent terahertz pulses in ruby at room temperature,” Phys. Rev. A 74(2), 023819 (2006). [CrossRef]

19.

S. Geschwind, G. E. Devlin, R. L. Cohen, and S. R. Chinn, “Orbach relaxation and hyperfine structure in the excited, ” Phys. Rev. 137(4A), A1087–A1100 (1965). [CrossRef]

20.

K. F. Renk and J. Deisenhonefer, “Imprisonment of resonant phonons observed with a new technique for the detection of 10l2Hz phonons,” Phys. Rev. Lett. 26, 164–166 (1971).

21.

T. Yajima and K. Inoue, “Submillimeter-wave generation by difference-frequency mixing of ruby lines in ZnTe,” IEEE J. Quantum Electron. 5(3), 140–146 (1969). [CrossRef]

22.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4(3), 165–169 (2010). [CrossRef]

23.

A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986).

24.

J. C. Walling, O. G. Peterson, H. P. Jenssen, R. C. Morris, and E. W. O’Dell, “Tunable alexandrite lasers,” IEEE J. Quantum Electron. 16(12), 1302–1315 (1980). [CrossRef]

OCIS Codes
(140.3070) Lasers and laser optics : Infrared and far-infrared lasers
(140.3430) Lasers and laser optics : Laser theory
(190.5890) Nonlinear optics : Scattering, stimulated
(260.5740) Physical optics : Resonance
(300.6495) Spectroscopy : Spectroscopy, teraherz

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: June 1, 2010
Revised Manuscript: August 12, 2010
Manuscript Accepted: October 4, 2010
Published: October 14, 2010

Citation
Jinsong Liu, Yong Liu, Jiantao Lü, and Kejia Wang, "Numerical study on terahertz random lasing in disordered ruby with three-level atomic system," Opt. Express 18, 22880-22885 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-22-22880


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References

  1. N. M. Lawandy, R. M. Balachandra, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994). [CrossRef]
  2. H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999). [CrossRef]
  3. C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98(14), 143902 (2007). [CrossRef] [PubMed]
  4. S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93(5), 053903 (2004). [CrossRef] [PubMed]
  5. X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85(1), 70–73 (2000). [CrossRef] [PubMed]
  6. P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66(14), 144202 (2002). [CrossRef]
  7. C. M. Soukoulis, X. Jiang, J. Y. Xu, and H. Cao, “Dynamic response and relaxation oscillations in random lasers,” Phys. Rev. B 65(4), 041103 (2002). [CrossRef]
  8. J. S. Liu and Z. Xiong, “Theoretical investigation on the threshold property of localized modes based on spectral width in two-dimensional random media,” Opt. Commun. 268(2), 294–299 (2006). [CrossRef]
  9. J. S. Liu, H. Wang, and Z. Xiong, “Origin of light localization from orientational disorder in one and two-dimensional random media with uniaxial scatterers,” Phys. Rev. B 73(19), 195110 (2006). [CrossRef]
  10. H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008). [CrossRef] [PubMed]
  11. T. Ito and M. Tomita, “Polarization-dependent laser action in a two-dimensional random medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(2), 027601 (2002). [CrossRef] [PubMed]
  12. C. Wang and J. S. Liu, “Polarization dependence of lasing modes in two-dimensional random lasers,” Phys. Lett. A 353(2-3), 269–272 (2006). [CrossRef]
  13. J. S. Liu, H. Lu, and C. Wang, “Spectral time evolution of quasistate modes in two-dimensional random media,” Acta Phys. Sin. 54, 3116–3122 (2005) (in Chinese).
  14. X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69(10), 104202 (2004). [CrossRef]
  15. D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008). [CrossRef]
  16. X.-C. Zhang and J. Z. Xu, Introduction to THz Wave Photonics (Springer, Berlin, 2010).
  17. N. M. Lawandy, “Far-infrared lasing in ruby,” IEEE J. Quantum Electron. 6(15), 401–403 (1979). [CrossRef]
  18. E. Kuznetsova, Y. Rostovtsev, N. G. Kalugin, R. Kolesov, O. Kocharovskaya, and M. O. Scully, “Generation of coherent terahertz pulses in ruby at room temperature,” Phys. Rev. A 74(2), 023819 (2006). [CrossRef]
  19. S. Geschwind, G. E. Devlin, R. L. Cohen, and S. R. Chinn, “Orbach relaxation and hyperfine structure in the excited, ” Phys. Rev. 137(4A), A1087–A1100 (1965). [CrossRef]
  20. K. F. Renk and J. Deisenhonefer, “Imprisonment of resonant phonons observed with a new technique for the detection of 10l2Hz phonons,” Phys. Rev. Lett. 26, 164–166 (1971).
  21. T. Yajima and K. Inoue, “Submillimeter-wave generation by difference-frequency mixing of ruby lines in ZnTe,” IEEE J. Quantum Electron. 5(3), 140–146 (1969). [CrossRef]
  22. L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4(3), 165–169 (2010). [CrossRef]
  23. A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986).
  24. J. C. Walling, O. G. Peterson, H. P. Jenssen, R. C. Morris, and E. W. O’Dell, “Tunable alexandrite lasers,” IEEE J. Quantum Electron. 16(12), 1302–1315 (1980). [CrossRef]

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