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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 25 — Dec. 10, 2007
  • pp: 16342–16347
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Polarisation-mode coupling in (100)-cut Nd:YAG

Aaron McKay, Judith M. Dawes, and Jong-Dae Park  »View Author Affiliations


Optics Express, Vol. 15, Issue 25, pp. 16342-16347 (2007)
http://dx.doi.org/10.1364/OE.15.016342


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Abstract

We investigate the polarisation-mode dynamics and Lamb’s mode coupling constant for orthogonally polarised laser states in a dual-mode (100)-cut Nd:YAG laser with feedback, and compare with an anisotropic rate equation model. The anisotropic (100)-cut Nd:YAG exhibits thermally-induced depolarisation and polarisation-mode coupling dependent on the pump polarisation, crystal angle and laser polarisation directions. Here, the links between the depolarisation and polarisation-mode coupling are discussed with reference to a rate equation model which includes gain anisotropy in a quasi-isotropic laser cavity.

© 2007 Optical Society of America

1. Introduction

Multimode laser dynamics has been an intriguing subject from the early days of experimental observation. Tang et al. [1

1. C. L. Tang, H. Statz, and G. deMars, “Spectral output and spiking behavor of solid-state lasers,” J. Appl. Phys. 34, 2289–2295 (1963). [CrossRef]

] studied two-mode lasers considering the cross-saturation effects due to spatial hole burning, and predicted self-organised collective behaviour in transient oscillations of two-mode lasers where the total output behaves, in essence, like a single-mode laser. Otsuka et al. [2

2. K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A46, 1692–1696 (1992). [CrossRef] [PubMed]

] extended their study to include cross-saturation in the multimode rate equations, yielding additional dynamical oscillation frequencies associated with anti-phase motions. Recently dual-mode lasers have been applied to microwave photonics [3

3. M. Brunel, A. Amon, and M. Vallet, “Dual-polarization microchip laser at 1.53 µm,” Opt. Lett. 30, 2418–2420 (2005). [CrossRef] [PubMed]

, 4

4. L. Morvan, N. D. Lai, D. Dolfi, J.-P. Huignard, M. Brunel, F. Bretenaker, and A. Le Floch, “Building blocks for a two-frequency laser lidar-radar: a preliminary study,” Appl. Opt. 41, 5702–5712 (2002). [CrossRef] [PubMed]

], high precision metrology [5

5. W. Du, S. Zhang, and Y. Li, “Principles and realization of a novel instrument for high performance displacement measurement—nanometer laser ruler,” Opt. Laser Eng. 43, 1214–1225 (2005). [CrossRef]

] and spectroscopy [6

6. M. Brunel, O. Emile, F. Bretenaker, A. Le Floch, B. Ferrand, and E. Molva, “Tunable two-frequency lasers for lifetime measurements,” Opt. Rev. 4, 550–552 (1997). [CrossRef]

]. Alouini et al. [7

7. M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, “Existence of two coupling constants in microchip lasers,” Opt. Lett. 25, 896–898 (2000). [CrossRef]

] observed two types of coupling in microchip lasers—between longitudinal modes and between orthogonally-linearly-polarised eigenstates. They interpreted their results using Lamb’s mode-coupling constant, which was derived to analyse the coupling between longitudinal modes in gas lasers [8

8. W. E. Lamb, “Theory of an optical maser,” Phys. Rev. A 134, A1429–A1450 (1964).

]. In this model the atom-light interaction was assumed to be isotropic, so that gain anisotropy was neglected.

However, in solid-state lasers this assumption is no longer valid; in crystalline lasers, the active atoms are oriented according to the crystal symmetry. A yttrium aluminum garnet (YAG) crystal, in particular, has a cubic unit cell that contains 8 formula units with the dopant (here Nd3+-ions) substituting for the yttrium on the dodecahedral D2 sites [9

9. R. Bayerer, J. Heber, and D. Mateika, “Crystal-field analysis of Tb3+ doped Yttrium aluminium garnet using site-selective polarized spectroscopy,” Z. Phys. B Con. Mat. 64, 201–210 (1986). [CrossRef]

]. Relative to the cubic unit cell (or sub-unit cell [10

10. R. Dalgliesh, A. D. May, and G. Stephan, “Polarization states of a single-mode (microchip) Nd3+:YAG laser—Part II: Comparison of Theory and Experiment,” IEEE J. Quantum Electron. 34, 1493–1502 (1998). [CrossRef]

]), the neodymium ions are oriented along the face diagonals in 6 possible directions. The (100)-cut Nd:YAG therefore, with the optical axis along the z-axis, has a set of orthogonally-oriented dipoles at ±45° with respect to the x-y axes of the cubic unit cell and 2 more sets oriented at 0° and 90°. Dalgliesh et al. [11

11. R. Dalgliesh, A. D. May, and G. Stephan, “Polarization states of a single-mode (microchip) Nd3+:YAG laser—Part I: Theory,” IEEE J. Quantum Electron. 34, 1485–1492 (1998). [CrossRef]

] developed a microscopic theory of the polarisation states of a single-mode laser showing the phase relationship between the components of the dipole transition moments, considering the populations at six non-equivalent sites. They also estimated the relative strength of the dipole moment components at the lasing and pump wavelengths.

In our work, the coupling between polarisation modes arises from the mode competition for the same excited ions in Nd:YAG, and is heavily dependent on saturation and spatial hole burning effects within the laser medium. We extend the work of Alouini et al. [7

7. M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, “Existence of two coupling constants in microchip lasers,” Opt. Lett. 25, 896–898 (2000). [CrossRef]

] and Dalgliesh et al. [10

10. R. Dalgliesh, A. D. May, and G. Stephan, “Polarization states of a single-mode (microchip) Nd3+:YAG laser—Part II: Comparison of Theory and Experiment,” IEEE J. Quantum Electron. 34, 1493–1502 (1998). [CrossRef]

, 11

11. R. Dalgliesh, A. D. May, and G. Stephan, “Polarization states of a single-mode (microchip) Nd3+:YAG laser—Part I: Theory,” IEEE J. Quantum Electron. 34, 1485–1492 (1998). [CrossRef]

] to establish an anisotropic rate equation model that incorporates the orientations of the Nd3+-ions to study the behaviour of dual-mode Nd:YAG lasers. These lasers naturally oscillate on two orthogonal polarisations, with dual optical frequencies determined by the (tunable) birefringence in the cavity, with frequency separations of up to half the axial mode spacing. The lasers can generate a beat frequency in the RF or microwave wavelength region [3

3. M. Brunel, A. Amon, and M. Vallet, “Dual-polarization microchip laser at 1.53 µm,” Opt. Lett. 30, 2418–2420 (2005). [CrossRef] [PubMed]

,12

12. A. McKay, P. Dekker, D. W. Coutts, and J. M. Dawes, “Enhanced self-heterodyne performance using a Nd-doped ceramic YAG laser,” Opt. Commun. 272, 425–430 (2007). [CrossRef]

], and may be modulated to give frequency-modulated output [13

13. G. W. Baxter, J. M. Dawes, P. Dekker, and D. S. Knowles, “Dual-polarization frequency-modulated laser source,” IEEE Photon Technol. Lett. 8, 1015–1017 (1996). [CrossRef]

].

2. Anisotropic rate equation model

The anisotropic characteristics of solid-state lasers can be modelled using the Maxwell-Bloch equations from the coherent density matrix equations [11

11. R. Dalgliesh, A. D. May, and G. Stephan, “Polarization states of a single-mode (microchip) Nd3+:YAG laser—Part I: Theory,” IEEE J. Quantum Electron. 34, 1485–1492 (1998). [CrossRef]

] but quickly become complicated when considering multiple modes. Fortunately these equations can be reduced to relatively straightforward rate equations using some appropriate assumptions. The atomic polarisations are obtained as a function of the population difference between the upper and lower energy levels. For dual orthogonally-polarised lasers, further simplifications can be made if one assumes that the mode-beating frequency is large compared to the inverse of the population inversion lifetime, and the side bands generated by mode beating are not resonant with the laser cavity.

Accounting for the laser-atom interaction anisotropy in a (100)-cut Nd:YAG crystal, the rate equations for the photon density ϕj for the j-polarised beam for j=x or y, and the population inversion ni for each of the i atomic sites are:

dϕjdt=ϕjtr(2i=16(cjqiσq+cjriσr+cjsiσs)nilln(1R)Lj)
(1)
dnidt=Λiγc((cxqiσq+cxriσr+cxsiσs)ϕx+(cyqiσq+cyriσr+cysiσs)ϕy)niniτs
(2)

where the cavity round trip time tr is 0.88 ns, the output coupler reflectivity R is 0.97, and the cavity losses for x- and y-polarised beams Lj are 0.03 to 0.1. γ is the population inversion parameter, and τs=230 µs is the lifetime of population inversion. The effective stimulated emission cross-section can be calculated if the stimulated emission cross-sections σq, σr, σs along the atomic axes (q̂, r̂,ŝ) are known, by using a coordinate transformation (for example cixq, cixr,…) from the atomic axis frame to the laboratory frame [9

9. R. Bayerer, J. Heber, and D. Mateika, “Crystal-field analysis of Tb3+ doped Yttrium aluminium garnet using site-selective polarized spectroscopy,” Z. Phys. B Con. Mat. 64, 201–210 (1986). [CrossRef]

]. Λi is the pumping rate to the i-th group of ions, which depends on the atomic orientation, absorption cross-section along atomic axes, and the pump laser polarisation. The pumping rate is given by:

Λi=2γabsγabs2+Δω2[ppq2(Epxq2+Epyq2)+ppr2(Epxr2+Epyr2)+pps2(Epxs2+Epys2)+
2(ppq2EpxqEpyq+ppr2EpxrEpyr+pps2EpxsEpys)]
(3)

where the absorption half bandwidth γabs is 2×109 s-1, the pump laser frequency detuning Δω is 0 Hz from the absorption peak. Epxq, Epxr, Epxs are the electric field components of the x-directed electric field Ex along the atomic axes for the pump laser and similarly for the y-directed electric field component. The dipole moments at the pumpwavelength along the atomic axes are denoted ppq, ppr, pps and were adopted from Ref. [10

10. R. Dalgliesh, A. D. May, and G. Stephan, “Polarization states of a single-mode (microchip) Nd3+:YAG laser—Part II: Comparison of Theory and Experiment,” IEEE J. Quantum Electron. 34, 1493–1502 (1998). [CrossRef]

], as were values for σq, σr, σs. To simulate modulated feedback we used an additional loss term Lx(1+εcos(2πfmodt)) in place of the cavity loss term (Lx) in Eq. (1), where the feedback amplitude ε is ~10-5 and the modulation frequency fmod is 1 kHz.

3. Experimental laser arrangement and mode-coupling experiments

To investigate the polarisation-mode coupling dynamics and the validity of our anisotropic rate equation model, a laser with a 5-cm long linear cavity was set up incorporating a dielectric input mirror with high transmission at 808 nm and high reflectivity (HR) at 1064 nm; a 5-mm long 1-at.% doped (100)-cut Nd:YAG crystal in a rotatable mount; a 21-mm long z-cut LiNbO3 electro-optic crystal (LN); a 0.5-mm thick 30% reflecting étalon to maintain a single axial mode; and a 97% HR output mirror with radius of curvature of 15 cm. The pump source was a multi-mode fiber-coupled laser diode, whose polarisation was scrambled with a depolarising prism and then re-polarised by a Glan-Laser polarising cube and rotated using a half wave-plate (HWP). The polarisation axes of the dual-mode laser were fixed by applying a transverse electric field (~500 kV/m) across the LN. To measure the mode coupling [12

12. A. McKay, P. Dekker, D. W. Coutts, and J. M. Dawes, “Enhanced self-heterodyne performance using a Nd-doped ceramic YAG laser,” Opt. Commun. 272, 425–430 (2007). [CrossRef]

] we used a polarised feedback path consisting of a HWP and polarising beam splitter to select a polarisation, optical density filters to adjust the feedback, and a piezo-driven mirror. The path length of the feedback arm was modulated at 1 kHz to modulate the gain of one laser eigen-polarisation.

In dual-mode lasers a second relaxation oscillation appears in the low frequency noise spectrum [2

2. K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A46, 1692–1696 (1992). [CrossRef] [PubMed]

, 3

3. M. Brunel, A. Amon, and M. Vallet, “Dual-polarization microchip laser at 1.53 µm,” Opt. Lett. 30, 2418–2420 (2005). [CrossRef] [PubMed]

]. In general, this second or “anti-phase” relaxation oscillation is the result of the interaction between multiple oscillating modes. In dual polarisation lasers these oscillations are found in both orthogonal modes, oscillating out of phase with each other. They are typically much weaker (~30 dB) than the “in-phase” relaxation oscillations which are dominated by the equivalent single-mode laser characteristics. When mixed on a photodiode, the anti-phase components of the polarised relaxation oscillations cancel, and they are typically not detectable when monitored individually. There have been several techniques used to investigate these anti-phase dynamics [e.g., 3]. We investigate the anti-phase dynamics by introducing a slight perturbation caused by applying ~10 ppm polarisation-sensitive feedback. This perturbation caused additional frequency-modulated noise destroying the negative correlation between the anti-phase motions of the two polarisation eigenstates. This allowed the two relaxation oscillation frequencies to be viewed simultaneously on a single unpolarised photodetector and radio-frequency spectrum analyser. Weaker feedback caused a weak out-of-phase modulation to the laser modes, produced primarily by the cross-saturation and mode coupling effects [12

12. A. McKay, P. Dekker, D. W. Coutts, and J. M. Dawes, “Enhanced self-heterodyne performance using a Nd-doped ceramic YAG laser,” Opt. Commun. 272, 425–430 (2007). [CrossRef]

, 14

14. M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, “Differential measurement of the coupling constant between laser eigenstates,” Appl. Phys. Lett. 70, 2070–2072 (1997). [CrossRef]

]. Stronger feedback caused polarisation switching [15

15. M. A. van Eijkelenborg, C. A. Scharama, and J. P. Woerdman, “Quantum mechanical diffusion of the polarization of a laser,” Opt. Commun. 119, 97–103 (1995). [CrossRef]

, 17

17. G. Verschaffelt, G. van der Sande, J. Danckaert, T. Erneux, B. Ségard, and P. Glorieux, “Polarization switching in Nd:YAG lasers by means of modulating the pump polarization,” Proc. SPIE 6184, 61841V-1–61841V-9 (2006).

].

4. Results

We compared the experimental results of the anti- (triangles) and in-phase (squares) relaxation oscillations with the linearised solutions of Eqs. (1–3) (solid lines) in Fig. 1(a) using the parameters in Sec. 2. The experimental data (10 ppm feedback) show good agreement with our theory. We also applied the relationship between the relaxation oscillations and Lamb’s coupling constant from Brunel et al. [Eq. (2) in 3] to our experimental and theoretical data of Fig. 1(a) to determine the polarisation-mode coupling as a function of incident pump power as shown in Fig. 1(b). There is close agreement to the measured results within experimental error. Eqs. (1–3) were also solved numerically with the modulated loss term. Comparing the modelled intensity of both polarisations, we calculated a coupling constant which was consistent with our experimental results.

By varying the relative (100)-cut YAG angle to the laser polarisation axes the amount of coupling between orthogonal polarisation modes can be controlled. Thus, in Fig. 2(a) we modelled the effect of the polarisation-mode coupling as a function of the crystal angle for a set of fixed polarisation axes. Experimentally, the laser polarisation axes were fixed by applying 500 V across the LN crystal and aligning the pump polarisation to 45°±2° with respect to the induced laser axes. The gain crystal was rotated about the optical axis to measure the polarisation-mode coupling, shown as red squares in Fig. 2(a). After each rotation increment the laser mirrors and étalon were realigned to give equal power in each of the two orthogonal modes. As the crystal axes approached either 0° or 90° the étalon was adjusted to counteract the extra gain along the x or y axes of the cubic unit cell by introducing additional losses to one mode. When the axes of the cubic unit cell were aligned to the laser polarisation directions, the laser action was restricted to a single polarisation, so the coupling constant was not measurable.

Fig. 1. (a) In- and anti-phase relaxation oscillations due to the polarisation-mode coupling dynamics as a function of the incident pump power. (b) Experimental and modelled coupling constant as a function of incident pump power. Crystal and pump polarisation angles were set to 56° and 45° relative to the laser axes respectively.

Fig. 2. (a) Comparison of polarisation-mode coupling (modelled—red line and experimental data—squares) and pump-induced birefringence (modelled—blue line and experimental data—triangles) as a function of crystal angle in a (100)-cut Nd:YAG laser. Pump polarisation direction at 45° to the laser polarisation axes. (b) Influence of the pump polarisation on the normalised orthogonal polarisation modes at a crystal angle of 45° with the incident pump power set to 240 mW (circles), 310 mW (squares) and 380 mW (triangles). Red and blue data points refer to the orthogonal polarisation directions.

5. Conclusions

We have shown excellent experimental agreement with our model. The properties of polarisation-mode coupling and cross-saturation in the (100)-cut Nd:YAG have been explored using the anti-phase dynamics of an anisotropic gain material. Although our models suggest a broad parameter space of coupling variables, experimentally the dominating sets of orthogonally-oriented gain ions in (100)-cut Nd:YAG limited the dual-polarisation regime within the laser to crystal angles with weak mode coupling.

References and links

1.

C. L. Tang, H. Statz, and G. deMars, “Spectral output and spiking behavor of solid-state lasers,” J. Appl. Phys. 34, 2289–2295 (1963). [CrossRef]

2.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A46, 1692–1696 (1992). [CrossRef] [PubMed]

3.

M. Brunel, A. Amon, and M. Vallet, “Dual-polarization microchip laser at 1.53 µm,” Opt. Lett. 30, 2418–2420 (2005). [CrossRef] [PubMed]

4.

L. Morvan, N. D. Lai, D. Dolfi, J.-P. Huignard, M. Brunel, F. Bretenaker, and A. Le Floch, “Building blocks for a two-frequency laser lidar-radar: a preliminary study,” Appl. Opt. 41, 5702–5712 (2002). [CrossRef] [PubMed]

5.

W. Du, S. Zhang, and Y. Li, “Principles and realization of a novel instrument for high performance displacement measurement—nanometer laser ruler,” Opt. Laser Eng. 43, 1214–1225 (2005). [CrossRef]

6.

M. Brunel, O. Emile, F. Bretenaker, A. Le Floch, B. Ferrand, and E. Molva, “Tunable two-frequency lasers for lifetime measurements,” Opt. Rev. 4, 550–552 (1997). [CrossRef]

7.

M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, “Existence of two coupling constants in microchip lasers,” Opt. Lett. 25, 896–898 (2000). [CrossRef]

8.

W. E. Lamb, “Theory of an optical maser,” Phys. Rev. A 134, A1429–A1450 (1964).

9.

R. Bayerer, J. Heber, and D. Mateika, “Crystal-field analysis of Tb3+ doped Yttrium aluminium garnet using site-selective polarized spectroscopy,” Z. Phys. B Con. Mat. 64, 201–210 (1986). [CrossRef]

10.

R. Dalgliesh, A. D. May, and G. Stephan, “Polarization states of a single-mode (microchip) Nd3+:YAG laser—Part II: Comparison of Theory and Experiment,” IEEE J. Quantum Electron. 34, 1493–1502 (1998). [CrossRef]

11.

R. Dalgliesh, A. D. May, and G. Stephan, “Polarization states of a single-mode (microchip) Nd3+:YAG laser—Part I: Theory,” IEEE J. Quantum Electron. 34, 1485–1492 (1998). [CrossRef]

12.

A. McKay, P. Dekker, D. W. Coutts, and J. M. Dawes, “Enhanced self-heterodyne performance using a Nd-doped ceramic YAG laser,” Opt. Commun. 272, 425–430 (2007). [CrossRef]

13.

G. W. Baxter, J. M. Dawes, P. Dekker, and D. S. Knowles, “Dual-polarization frequency-modulated laser source,” IEEE Photon Technol. Lett. 8, 1015–1017 (1996). [CrossRef]

14.

M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, “Differential measurement of the coupling constant between laser eigenstates,” Appl. Phys. Lett. 70, 2070–2072 (1997). [CrossRef]

15.

M. A. van Eijkelenborg, C. A. Scharama, and J. P. Woerdman, “Quantum mechanical diffusion of the polarization of a laser,” Opt. Commun. 119, 97–103 (1995). [CrossRef]

16.

W. KoechnerSolid-state laser engineering (Springer, 1999).

17.

G. Verschaffelt, G. van der Sande, J. Danckaert, T. Erneux, B. Ségard, and P. Glorieux, “Polarization switching in Nd:YAG lasers by means of modulating the pump polarization,” Proc. SPIE 6184, 61841V-1–61841V-9 (2006).

18.

I. Shoji and T. Taira, “Intrinsic reduction of the depolarization loss in solid-state lasers by use of a (110)-cut Y3Al5O12 crystal,” Appl. Phys. Lett. 80, 3048–3050 (2002). [CrossRef]

19.

I. B. Mukhin, O. V. Palashov, E. A. Khazanov, and I. A. Ivanov, “Influence of the orientation of a crystal on thermal polarization effects in high-power solid-state lasers,” JETP Lett. V81, 90–94 (2005). [CrossRef]

OCIS Codes
(140.3530) Lasers and laser optics : Lasers, neodymium
(140.3580) Lasers and laser optics : Lasers, solid-state

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: September 24, 2007
Revised Manuscript: November 12, 2007
Manuscript Accepted: November 14, 2007
Published: November 26, 2007

Citation
Aaron McKay, Judith M. Dawes, and Jong-Dae Park, "Polarisation-mode coupling in (100)-cut Nd:YAG," Opt. Express 15, 16342-16347 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-25-16342


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References

  1. C. L. Tang, H. Statz, and G. deMars, "Spectral output and spiking behavor of solid-state lasers," J. Appl. Phys. 34, 2289-2295 (1963). [CrossRef]
  2. K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, "Alternate time scale in multimode lasers," Phys. Rev. A 46, 1692-1696 (1992). [CrossRef] [PubMed]
  3. M. Brunel, A. Amon, and M. Vallet, "Dual-polarization microchip laser at 1.53 m," Opt. Lett. 30, 2418-2420 (2005). [CrossRef] [PubMed]
  4. L. Morvan, N. D. Lai, D. Dolfi, J.-P. Huignard, M. Brunel, F. Bretenaker, and A. Le Floch, "Building blocks for a two-frequency laser lidar-radar: a preliminary study," Appl. Opt. 41, 5702-5712 (2002). [CrossRef] [PubMed]
  5. W. Du, S. Zhang, and Y. Li, "Principles and realization of a novel instrument for high performance displacement measurement—nanometer laser ruler," Opt. Laser Eng. 43, 1214-1225 (2005). [CrossRef]
  6. M. Brunel, O. Emile, F. Bretenaker, A. Le Floch, B. Ferrand, and E. Molva, "Tunable two-frequency lasers for lifetime measurements," Opt. Rev. 4, 550-552 (1997). [CrossRef]
  7. M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, "Existence of two coupling constants in microchip lasers," Opt. Lett. 25, 896-898 (2000). [CrossRef]
  8. W. E. Lamb, "Theory of an optical maser," Phys. Rev. A 134, A1429-A1450 (1964).
  9. R. Bayerer, J. Heber, and D. Mateika, "Crystal-field analysis of Tb3+ doped Yttrium aluminium garnet using site-selective polarized spectroscopy," Z. Phys. B Con. Mat. 64, 201-210 (1986). [CrossRef]
  10. R. Dalgliesh, A. D. May, and G. Stephan, "Polarization states of a single-mode (microchip) Nd3+:YAG laser— Part II: Comparison of Theory and Experiment," IEEE J. Quantum Electron. 34, 1493-1502 (1998). [CrossRef]
  11. R. Dalgliesh, A. D. May, and G. Stephan, "Polarization states of a single-mode (microchip) Nd3+:YAG laser— Part I: Theory," IEEE J. Quantum Electron. 34, 1485-1492 (1998). [CrossRef]
  12. A. McKay, P. Dekker, D.W. Coutts, and J. M. Dawes, "Enhanced self-heterodyne performance using a Nd-doped ceramic YAG laser," Opt. Commun. 272, 425-430 (2007). [CrossRef]
  13. G.W. Baxter, J.M. Dawes, P. Dekker, and D. S. Knowles, "Dual-polarization frequency-modulated laser source," IEEE Photon Technol. Lett. 8, 1015-1017 (1996). [CrossRef]
  14. M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, "Differential measurement of the coupling constant between laser eigenstates," Appl. Phys. Lett. 70, 2070-2072 (1997). [CrossRef]
  15. M. A. van Eijkelenborg, C. A. Scharama, and J. P. Woerdman, "Quantum mechanical diffusion of the polarization of a laser," Opt. Commun. 119, 97-103 (1995). [CrossRef]
  16. W. KoechnerSolid-state laser engineering (Springer, 1999).
  17. G. Verschaffelt, G. van der Sande, J. Danckaert, T. Erneux, B. Ségard, and P. Glorieux, "Polarization switching in Nd:YAG lasers by means of modulating the pump polarization," Proc. SPIE 6184, 61841V-1-61841V-9 (2006).
  18. I. Shoji and T. Taira, "Intrinsic reduction of the depolarization loss in solid-state lasers by use of a (110)-cut Y3Al5O12 crystal," Appl. Phys. Lett. 80, 3048-3050 (2002). [CrossRef]
  19. I. B. Mukhin, O. V. Palashov, E. A. Khazanov, and I. A. Ivanov, "Influence of the orientation of a crystal on thermal polarization effects in high-power solid-state lasers," JETP Lett. V81, 90-94 (2005). [CrossRef]

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