Abstract

The ability to generate and then amplify radially polarized light opens up the possibility of achieving very high-power, near diffraction-limited beams from rod-based solid-state lasers. Residual bifocusing rapidly degrades beam quality. Residual bifocusing results from nonradially symmetric pump distributions. We analyze how a nonradially symmetric pump distribution induces a nonradially symmetric stress map. This manifests itself as nonradially symmetric birefringence, and as depolarization to radially/azimuthally polarized beams (or as deterioration in birefringence compensated linearly polarized lasers). Here we analytically describe the birefringence terms of a nonradially symmetric strain map. The model results are supported by radial-depolarization measurements in our 2kW Nd:YAG pump chambers. For the current level of depolarization, beam quality degradation per rod is ΔM2=4 because of bifocusing alone. The degradation per rod can be reduced substantially by improving pump uniformity.

© 2008 Optical Society of America

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References

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  1. J. D. Foster and L. M. Osterink, “Thermal effects in Nd:YAG laser,” J. Appl. Phys. 41, 3656-3663 (1970).
    [Crossref]
  2. W. Koechner and D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6, 557-566 (1970).
    [Crossref]
  3. I. Moshe and S. Jackel, “Influence of birefringence-induced bifocusing on optical beams,” J. Opt. Soc. Am. B 22, 1228-1235(2005).
    [Crossref]
  4. Q. Lü, U. Wittrock, and S. Dong, “Photoelastic effect in Nd:YAG rod and slab lasers,” Opt. Laser Technol. 27, 95-101 (1995).
    [Crossref]
  5. M. Ostermeyer, D. Mudge, P. J. Veitch, and J. Munch, “Thermally induced birefringence in Nd:YAG slab lasers,” Appl. Opt. 45, 5368-5376 (2006).
    [Crossref] [PubMed]
  6. I. Moshe, S. Jackel and A. Meir, “Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects,” Opt. Lett. 28, 807-809 (2003).
    [Crossref] [PubMed]
  7. I. Moshe, S. Jackel, A. Meir, Y. Lumer, and E. Leibush “2 kW, M2<10 radially polarized beams from aberration-compensated rod-based Nd:YAG lasers,” Opt. Lett. 3247-49 (2007).
    [Crossref]
  8. A. M. Bonnefois, M. Gilbert, P.-Y. Thro and J.-M. Weulersse, “Thermal lensing and spherical aberration in high-power transversally pumped laser rods,” Opt. Commun. 259, 223-235 (2006).
    [Crossref]
  9. A. V. Nesterov, V. G. Niziev and V. P. Yakunin, “Generation of high power radially polarized beam,” J. Phys. D 32, 2871-2875 (1999).
    [Crossref]
  10. M. Meier, V. Romano, T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329-334 (2007).
    [Crossref]
  11. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901(2003).
    [Crossref] [PubMed]
  12. Y. Lumer, I. Moshe, A. Meir, Y. Paiken, G. Machavariani, and S. Jackel, “Effects of thermally induced aberrations on radially and azimuthally polarized beams,” J. Opt. Soc. Am. B 24, 2279-2286 (2007).
    [Crossref]
  13. S. Timoshenko and J. N. Goodier, Theory of Elasticity, (McGraw-Hill, 1951).
  14. M. Born and E. Wolf, Principles of Optics, 6th ed. (London Pergamon, 1980) ch. 14.
  15. A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2-14 (1990).
    [Crossref]
  16. D.C. Brown, “Ultrahigh-average-power diode-pumped Nd:YAG and Yb:YAG lasers,” IEEE J. Quantum Electron. 33, 861-873 (1997).
    [Crossref]

2007 (3)

2006 (2)

A. M. Bonnefois, M. Gilbert, P.-Y. Thro and J.-M. Weulersse, “Thermal lensing and spherical aberration in high-power transversally pumped laser rods,” Opt. Commun. 259, 223-235 (2006).
[Crossref]

M. Ostermeyer, D. Mudge, P. J. Veitch, and J. Munch, “Thermally induced birefringence in Nd:YAG slab lasers,” Appl. Opt. 45, 5368-5376 (2006).
[Crossref] [PubMed]

2005 (1)

2003 (2)

1999 (1)

A. V. Nesterov, V. G. Niziev and V. P. Yakunin, “Generation of high power radially polarized beam,” J. Phys. D 32, 2871-2875 (1999).
[Crossref]

1997 (1)

D.C. Brown, “Ultrahigh-average-power diode-pumped Nd:YAG and Yb:YAG lasers,” IEEE J. Quantum Electron. 33, 861-873 (1997).
[Crossref]

1995 (1)

Q. Lü, U. Wittrock, and S. Dong, “Photoelastic effect in Nd:YAG rod and slab lasers,” Opt. Laser Technol. 27, 95-101 (1995).
[Crossref]

1990 (1)

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2-14 (1990).
[Crossref]

1970 (2)

J. D. Foster and L. M. Osterink, “Thermal effects in Nd:YAG laser,” J. Appl. Phys. 41, 3656-3663 (1970).
[Crossref]

W. Koechner and D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6, 557-566 (1970).
[Crossref]

Bonnefois, A. M.

A. M. Bonnefois, M. Gilbert, P.-Y. Thro and J.-M. Weulersse, “Thermal lensing and spherical aberration in high-power transversally pumped laser rods,” Opt. Commun. 259, 223-235 (2006).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (London Pergamon, 1980) ch. 14.

Brown, C.

D.C. Brown, “Ultrahigh-average-power diode-pumped Nd:YAG and Yb:YAG lasers,” IEEE J. Quantum Electron. 33, 861-873 (1997).
[Crossref]

Dong, S.

Q. Lü, U. Wittrock, and S. Dong, “Photoelastic effect in Nd:YAG rod and slab lasers,” Opt. Laser Technol. 27, 95-101 (1995).
[Crossref]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901(2003).
[Crossref] [PubMed]

Feurer, T.

M. Meier, V. Romano, T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329-334 (2007).
[Crossref]

Foster, J. D.

J. D. Foster and L. M. Osterink, “Thermal effects in Nd:YAG laser,” J. Appl. Phys. 41, 3656-3663 (1970).
[Crossref]

Gilbert, M.

A. M. Bonnefois, M. Gilbert, P.-Y. Thro and J.-M. Weulersse, “Thermal lensing and spherical aberration in high-power transversally pumped laser rods,” Opt. Commun. 259, 223-235 (2006).
[Crossref]

Goodier, J. N.

S. Timoshenko and J. N. Goodier, Theory of Elasticity, (McGraw-Hill, 1951).

Jackel, S.

Koechner, W.

W. Koechner and D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6, 557-566 (1970).
[Crossref]

Leibush, E.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901(2003).
[Crossref] [PubMed]

Lü, Q.

Q. Lü, U. Wittrock, and S. Dong, “Photoelastic effect in Nd:YAG rod and slab lasers,” Opt. Laser Technol. 27, 95-101 (1995).
[Crossref]

Lumer, Y.

Machavariani, G.

Meier, M.

M. Meier, V. Romano, T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329-334 (2007).
[Crossref]

Meir, A.

Moshe, I.

Mudge, D.

Munch, J.

Nesterov, A. V.

A. V. Nesterov, V. G. Niziev and V. P. Yakunin, “Generation of high power radially polarized beam,” J. Phys. D 32, 2871-2875 (1999).
[Crossref]

Niziev, V. G.

A. V. Nesterov, V. G. Niziev and V. P. Yakunin, “Generation of high power radially polarized beam,” J. Phys. D 32, 2871-2875 (1999).
[Crossref]

Osterink, L. M.

J. D. Foster and L. M. Osterink, “Thermal effects in Nd:YAG laser,” J. Appl. Phys. 41, 3656-3663 (1970).
[Crossref]

Ostermeyer, M.

Paiken, Y.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901(2003).
[Crossref] [PubMed]

Rice, D. K.

W. Koechner and D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6, 557-566 (1970).
[Crossref]

Romano, V.

M. Meier, V. Romano, T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329-334 (2007).
[Crossref]

Siegman, A. E.

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2-14 (1990).
[Crossref]

Thro, P.-Y.

A. M. Bonnefois, M. Gilbert, P.-Y. Thro and J.-M. Weulersse, “Thermal lensing and spherical aberration in high-power transversally pumped laser rods,” Opt. Commun. 259, 223-235 (2006).
[Crossref]

Timoshenko, S.

S. Timoshenko and J. N. Goodier, Theory of Elasticity, (McGraw-Hill, 1951).

Veitch, P. J.

Weulersse, J.-M.

A. M. Bonnefois, M. Gilbert, P.-Y. Thro and J.-M. Weulersse, “Thermal lensing and spherical aberration in high-power transversally pumped laser rods,” Opt. Commun. 259, 223-235 (2006).
[Crossref]

Wittrock, U.

Q. Lü, U. Wittrock, and S. Dong, “Photoelastic effect in Nd:YAG rod and slab lasers,” Opt. Laser Technol. 27, 95-101 (1995).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (London Pergamon, 1980) ch. 14.

Yakunin, V. P.

A. V. Nesterov, V. G. Niziev and V. P. Yakunin, “Generation of high power radially polarized beam,” J. Phys. D 32, 2871-2875 (1999).
[Crossref]

Appl. Opt. (1)

Appl. Phys. A (1)

M. Meier, V. Romano, T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329-334 (2007).
[Crossref]

IEEE J. Quantum Electron. (2)

W. Koechner and D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6, 557-566 (1970).
[Crossref]

D.C. Brown, “Ultrahigh-average-power diode-pumped Nd:YAG and Yb:YAG lasers,” IEEE J. Quantum Electron. 33, 861-873 (1997).
[Crossref]

J. Appl. Phys. (1)

J. D. Foster and L. M. Osterink, “Thermal effects in Nd:YAG laser,” J. Appl. Phys. 41, 3656-3663 (1970).
[Crossref]

J. Opt. Soc. Am. B (2)

J. Phys. D (1)

A. V. Nesterov, V. G. Niziev and V. P. Yakunin, “Generation of high power radially polarized beam,” J. Phys. D 32, 2871-2875 (1999).
[Crossref]

Opt. Commun. (1)

A. M. Bonnefois, M. Gilbert, P.-Y. Thro and J.-M. Weulersse, “Thermal lensing and spherical aberration in high-power transversally pumped laser rods,” Opt. Commun. 259, 223-235 (2006).
[Crossref]

Opt. Laser Technol. (1)

Q. Lü, U. Wittrock, and S. Dong, “Photoelastic effect in Nd:YAG rod and slab lasers,” Opt. Laser Technol. 27, 95-101 (1995).
[Crossref]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901(2003).
[Crossref] [PubMed]

Proc. SPIE (1)

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2-14 (1990).
[Crossref]

Other (2)

S. Timoshenko and J. N. Goodier, Theory of Elasticity, (McGraw-Hill, 1951).

M. Born and E. Wolf, Principles of Optics, 6th ed. (London Pergamon, 1980) ch. 14.

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Figures (6)

Fig. 1
Fig. 1

(a) Measured pump profile of the pump chamber used in the experiments. (b) Calculated and simulated diagonal stress terms.

Fig. 2
Fig. 2

(a) Radial, (b) azimuthal, and (c) off-diagonal OPD terms resulting from the thermal stresses in units of wavelength.

Fig. 3
Fig. 3

Degree of radial polarization after a heated rod versus input degree of radial polarization. Below input polarization of 98%, the degradation is linear with a slope of approximately 1.

Fig. 4
Fig. 4

Beam quality and polarization degradation in a chain of heads.

Fig. 5
Fig. 5

Radially polarized beam used in the experiments, with M 2 = 2.3 and a degree of radial polarization of 98%. Total intensity and transmission through a linear polarizer with orientations indicated by the arrows.

Fig. 6
Fig. 6

(a) Measured and (d) simulated beam profiles after passage through a heated laser rod, using a radially polarized input beam. (b) Measured and (e) simulated azimuthal portion of the beam. (c) Measured and (f) simulated deviation angle from radial polarization.

Tables (1)

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Table 1 Numerical Values Used in the Calculations

Equations (14)

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ε r = 1 E [ σ r ν ( σ φ + σ z ) ] , ε φ = 1 E [ σ φ ν ( σ r + σ z ) ] , ε z = 1 E [ σ z ν ( σ r + σ φ ) ] , ε r φ = 2 ( 1 + ν ) E σ r φ ,
( B 0 + Δ B r r ) r 2 + ( B 0 + Δ B φ φ ) φ 2 + 2 Δ B r φ r φ = 1 ,
Δ B r r = 1 6 [ ε r ( 3 P 11 + 3 P 12 + 6 P 44 ) + ε φ ( P 11 + 5 P 12 2 P 44 ) + ε z ( 2 P 11 + 4 P 12 4 P 44 ) ]
Δ B φ φ = 1 6 [ ε r ( P 11 + 5 P 12 2 P 44 ) + ε φ ( 3 P 11 + 3 P 12 + 6 P 44 ) + ε z ( 2 P 11 + 4 P 12 4 P 44 ) ] ,
Δ B r φ = 1 3 ε r φ ( P 11 P 12 + 4 P 44 ) ,
Δ n i j = 1 2 n 0 3 Δ B i j ,
W T ( Δ n r r Δ n r φ Δ n r φ Δ n φ φ ) W = ( Δ n 1 0 0 Δ n 2 ) .
Δ n 1 = 1 2 ( Δ n r r + Δ n φ φ ) 1 2 [ ( Δ n φ φ Δ n r r ) 2 + 4 Δ n r φ 2 ] ,
Δ n 2 = 1 2 ( Δ n r r + Δ n φ φ ) + 1 2 [ ( Δ n φ φ Δ n r r ) 2 + 4 Δ n r φ 2 ] ,
W 11 = 2 ( Δ n φ φ Δ n r r ) 2 + 4 Δ n r φ 2 + ( Δ n φ φ Δ n r r ) 2 [ ( Δ n φ φ Δ n r r ) 2 + 4 Δ n r φ 2 ] 1 / 4 , W 22 = W 11 ,
W 21 = 2 | Δ n r φ | ( Δ n φ φ Δ n r r ) ( Δ n φ φ Δ n r r ) 2 + 4 Δ n r φ 2 + ( Δ n φ φ Δ n r r ) 2 + 4 Δ n r φ 2 , W 12 = W 21 .
J = ( J 1 0 0 J 2 ) , J 1 , 2 = exp ( i 2 π L λ Δ n 1 , 2 ) .
E in = ( E r E φ ) E biref = W J W T E in = [ ( J 1 W 11 2 + J 2 W 21 2 ) E r + W 11 W 21 ( J 1 - J 2 ) E φ ( J 2 W 11 2 + J 1 W 21 2 ) E φ + W 11 W 21 ( J 1 - J 2 ) E r ] .
E biref = E r · [ ( J 1 W 11 2 + J 2 W 21 2 ) r ^ + W 11 W 21 ( J 1 J 2 ) φ ^ ] .

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