Abstract

We investigate the radial and azimuthal polarization degradation in high-power lasers induced by thermal aberrations. Thermal and propagation simulations, supported by measurements, show that thermally induced wavefront aberrations can strongly affect the polarization. Depolarization induced by primary aberrations and high-order azimuthal aberrations that arise in high-power rod-based lasers was analyzed along the beam propagation axis. Implications for pump-chamber design and amplifier architecture, in order to eliminate the depolarization effect, are discussed.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. S. C. Tidwell, D. H. Ford, and W. D. Kimura, "Generating radially polarized beams interferometrically," Appl. Opt. 29, 2234-2239 (1990).
    [CrossRef] [PubMed]
  2. 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]
  3. R. Oron, S. Blit, N. Davidson, and A. A. Friesem, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
    [CrossRef]
  4. Z. Bomson, G. Biener, V. Kleiner, and E. Hasman, "Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings," Opt. Lett. 27, 285-287 (2002).
    [CrossRef]
  5. R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  6. N. Passilly, R. de S. Denis, K. Aït-Ameur, F. Treussart, R. Hierle, and R. J.-F. Roch, "Simple interferometric technique for generation of a radially polarized light beam," J. Opt. Soc. Am. A 22, 984-991 (2005).
    [CrossRef]
  7. M. S. Roth, E. W. Wyss, H. Glur, and H. P. Weber, "Generation of radially polarized beams in a Nd:YAG laser with self adaptive overcompensation of the thermal lens," Opt. Lett. 30, 1665-1667 (2005).
    [CrossRef] [PubMed]
  8. Y. Kozawa and S. Sato, "Generation of a radially polarized laser beam by use of a conical Brewster prism," Opt. Lett. 30, 3063-3065 (2005).
    [CrossRef] [PubMed]
  9. K. Yonezawa, Y. Kozawa, and S. Sato, "Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal," Opt. Lett. 31, 2151-2153 (2006).
    [CrossRef] [PubMed]
  10. A. V. Nesterov and V. G. Niziev, "Laser beams with axially symmetric polarization," J. Phys. D 33, 1817-1822 (2000).
    [CrossRef]
  11. V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser beam cutting efficiency," J. Phys. D 32, 1455-1461 (1999).
    [CrossRef]
  12. M. Meier, H. Glur, E. Wyss, T. Feurer, and V. Romano, "Laser microhole drilling using Q-switched radially and tangentially polarized beams," in Proc. SPIE 6053, 313-318 (2005).
  13. Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Methods Phys. Res. A 424, 296-303 (1999).
    [CrossRef]
  14. 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]
  15. I. Moshe, S. Jackel, A. Meir, Y. Lumer, and E. Leibush, "2kW, M2<10 radially polarized beams from aberration-compensated rod-based Nd:YAG lasers," Opt. Lett. 32, 47-49 (2007).
    [CrossRef]
  16. I. Moshe and S. Jackel, "Influence of birefringence-induced bifocusing on optical beams," J. Opt. Soc. Am. B 22, 1228-1235 (2005).
    [CrossRef]
  17. I. Moshe, S. Jackel, and A. Meir, "Correction of spherical and azimuthal aberrations in radially polarized beams from strongly pumped laser rods," Appl. Opt. 44, 7823-7827 (2005).
    [CrossRef] [PubMed]
  18. A. E. Siegman, "Analysis of laser beam quality degradation causedby quartic phase aberrations," Appl. Opt. 32, 5893-5901 (1993).
    [CrossRef] [PubMed]
  19. A. M. Bonnefois, M. Gilebrt, P.-Y. Thro, and J.-M. Weulersse, "Thermal lensing and spherical aberration in high-power transversally pumped laser rods", Opt. Commun. 259, 223-235 (2005).
    [CrossRef]
  20. J. D Foster and L. M. Osternik, "Thermal effects in Nd:YAG laser," J. Appl. Phys. 41, 3656-3663 (1970).
    [CrossRef]
  21. 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]
  22. A. V. Nesterov, V. G. Niziev, and A. L. Sokolov, "Transformation problem for radiation with radial polarization," Opt. Spectrosc. 90, 1018-1022 (2001).
    [CrossRef]
  23. D. P. Biss and T. G. Brown, "Primary aberrations in focused radially polarized vortex beams," Opt. Express 12, 384-393 (2004).
    [CrossRef] [PubMed]
  24. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).
  25. A. E. Siegman, Lasers (University Science, 1986).
  26. A. E. Siegman, "New developments in laser resonators," Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2-14 (1990).
  27. E. Leibush, S. Jackel, S. Goldring, I. Moshe, Y. Tsuk, and A. Meir, "Elimination of spherical aberration in multi-kW, Nd:YAG, rod pump-chambers by pump distribution control," in Advanced Solid-State Photonics Conference (Optical Society of America, 2005), paper MB45.
  28. S. Goldring, R. Lavi, A. Tal, E. Lebiush, Y. Tsuk, and S. Jackel, "Characterization of radiative and nonradiative processes in Nd:YAG lasers by comparing direct and band pumping," IEEE J. Quantum Electron. 40, 384-389 (2004).
    [CrossRef]
  29. M.Abramovitz and I.Stegun, eds., Handbook of Mathematical Functions (Dover, 1972).

2007 (1)

2006 (1)

2005 (7)

2004 (2)

S. Goldring, R. Lavi, A. Tal, E. Lebiush, Y. Tsuk, and S. Jackel, "Characterization of radiative and nonradiative processes in Nd:YAG lasers by comparing direct and band pumping," IEEE J. Quantum Electron. 40, 384-389 (2004).
[CrossRef]

D. P. Biss and T. G. Brown, "Primary aberrations in focused radially polarized vortex beams," Opt. Express 12, 384-393 (2004).
[CrossRef] [PubMed]

2003 (2)

2002 (1)

2001 (1)

A. V. Nesterov, V. G. Niziev, and A. L. Sokolov, "Transformation problem for radiation with radial polarization," Opt. Spectrosc. 90, 1018-1022 (2001).
[CrossRef]

2000 (2)

A. V. Nesterov and V. G. Niziev, "Laser beams with axially symmetric polarization," J. Phys. D 33, 1817-1822 (2000).
[CrossRef]

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

1999 (3)

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser beam cutting efficiency," J. Phys. D 32, 1455-1461 (1999).
[CrossRef]

Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Methods Phys. Res. A 424, 296-303 (1999).
[CrossRef]

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]

1993 (1)

1990 (2)

S. C. Tidwell, D. H. Ford, and W. D. Kimura, "Generating radially polarized beams interferometrically," Appl. Opt. 29, 2234-2239 (1990).
[CrossRef] [PubMed]

A. E. Siegman, "New developments in laser resonators," Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2-14 (1990).

1970 (2)

J. D Foster and L. M. Osternik, "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]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[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]

S. Goldring, R. Lavi, A. Tal, E. Lebiush, Y. Tsuk, and S. Jackel, "Characterization of radiative and nonradiative processes in Nd:YAG lasers by comparing direct and band pumping," IEEE J. Quantum Electron. 40, 384-389 (2004).
[CrossRef]

J. Appl. Phys. (1)

J. D Foster and L. M. Osternik, "Thermal effects in Nd:YAG laser," J. Appl. Phys. 41, 3656-3663 (1970).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Phys. D (3)

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]

A. V. Nesterov and V. G. Niziev, "Laser beams with axially symmetric polarization," J. Phys. D 33, 1817-1822 (2000).
[CrossRef]

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser beam cutting efficiency," J. Phys. D 32, 1455-1461 (1999).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (1)

Y. Liu, D. Cline, and P. He, "Vacuum laser acceleration using a radially polarized CO2 laser beam," Nucl. Instrum. Methods Phys. Res. A 424, 296-303 (1999).
[CrossRef]

Opt. Commun. (1)

A. M. Bonnefois, M. Gilebrt, P.-Y. Thro, and J.-M. Weulersse, "Thermal lensing and spherical aberration in high-power transversally pumped laser rods", Opt. Commun. 259, 223-235 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Opt. Spectrosc. (1)

A. V. Nesterov, V. G. Niziev, and A. L. Sokolov, "Transformation problem for radiation with radial polarization," Opt. Spectrosc. 90, 1018-1022 (2001).
[CrossRef]

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. Soc. Photo-Opt. Instrum. Eng. (1)

A. E. Siegman, "New developments in laser resonators," Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2-14 (1990).

Proc. SPIE (1)

M. Meier, H. Glur, E. Wyss, T. Feurer, and V. Romano, "Laser microhole drilling using Q-switched radially and tangentially polarized beams," in Proc. SPIE 6053, 313-318 (2005).

Other (4)

E. Leibush, S. Jackel, S. Goldring, I. Moshe, Y. Tsuk, and A. Meir, "Elimination of spherical aberration in multi-kW, Nd:YAG, rod pump-chambers by pump distribution control," in Advanced Solid-State Photonics Conference (Optical Society of America, 2005), paper MB45.

M.Abramovitz and I.Stegun, eds., Handbook of Mathematical Functions (Dover, 1972).

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

A. E. Siegman, Lasers (University Science, 1986).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Measured pump profile of the pump chamber used in the experiments. The fivefold symmetry is evident.

Fig. 2
Fig. 2

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

Fig. 3
Fig. 3

Experimental setup for characterizing beam propagation through the rod. The lens before the rod is adjusted so that the beam propagation through the rod is symmetric.

Fig. 4
Fig. 4

Radial polarization measurement setup. The measurement plane is relay imaged onto the CCD camera. Wave plates and a linear polarizer are used in order to measure the different Stokes parameters of the beam.

Fig. 5
Fig. 5

Wavefront measurement of the radially polarized beam after passage through the high-power pump chamber. The deviation is measured in wavelengths.

Fig. 6
Fig. 6

Measurement of the radially polarized beam, at the REF and measurements plus simulations at the TF of a high-power rod-based laser. The pictures give the total intensity at the (a) REF and (f) TF, and (k) for the TF simulation. The intensity after the linear polarizer is rotated by 0°, 90°, and 45°, respectively, is shown at the (b)–(d) REF and (g)–(i) TF, as well as for the (l)–(n) TF simulation. The local angle of deviation from radial polarization of the beam is shown at the (e) REF TF, (j) and (o) for the TF simulation). The total degree of radial polarization is 96% at the REF, 70% at the TF, and was calculated as 73% at TF from the simulation.

Fig. 7
Fig. 7

Beam diameter after the laser rod was obtained from the measurement and from the simulation. The diameter was calculated using the second moment of the intensity distribution. Beam-quality parameter M 2 is 24 and 22. (b) Polarization degree after the laser rod as obtained from the measurement and from the simulation. Minimum degrees of polarization are 70% and 73%. A small deviation ( 1 2 cm ) between the plane of minimum polarization and the thermal focus can be seen.

Fig. 8
Fig. 8

Propagation calculations for radially polarized beams with different optical aberrations: (a) spherical aberration, no polarization degradation; (b) astigmatism, polarization dropped to 84% with 0.8 λ of aberration; (c) coma, major polarization degradation caused by beam-center shift. When beam shift was compensated, polarization purity was significantly improved.

Fig. 9
Fig. 9

Comparison of the effect of different azimuthal aberrations at focus. It can be seen that the higher the order of the azimuthal aberration, the lower its effect on radial polarization.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

U r a d ( r , φ ) = A exp ( r 2 w 2 ) ( cos ( φ ) x ̂ + sin ( φ ) y ̂ ) = A exp ( r 2 w 2 ) r r ̂ ,
U a z i m ( r , φ ) = A exp ( r 2 w 2 ) ( sin ( φ ) x ̂ + cos ( φ ) y ̂ ) = A exp ( r 2 w 2 ) r φ ̂ ,
U r a d ( r , φ ) = A f ( r ) r ̂ , U a z i m ( r , φ ) = A f ( r ) φ ̂ ,
U ( r , φ ) = U r a d ( r , φ ) + U a z i m ( r , φ ) = f r ( r , φ ) r ̂ + f a z ( r , φ ) φ ̂ ,
χ r = f r 2 r d r d φ U 2 r d r d φ .
E ( x , y , L ) = i exp ( i k L ) λ L exp ( i k 2 L ( ( x x 0 ) 2 + ( y y 0 ) 2 ) ) E ( x 0 , y 0 , 0 ) d x 0 d y 0 .
J n ( z ) = 1 2 π i n 0 2 π exp ( i z cos φ ) exp ( i n φ ) d φ = 1 2 π i 0 2 π exp ( i z cos φ ) cos ( n φ ) d φ ,
0 2 π exp ( i z cos φ ) sin ( n φ ) d φ = 0 .
E ( r , φ , L ) = i exp ( i k L ) λ L 0 0 2 π exp ( i k 2 L ( r 2 + r 0 2 2 r r 0 cos ( φ φ 0 ) ) ) E ( r 0 , φ 0 , 0 ) r 0 d r 0 d φ 0 .
E ( r , φ , 0 ) = f ( r ) r ̂ = f ( r ) cos ( φ ) x ̂ + f ( r ) sin ( φ ) y ̂ .
E ( r , φ , L ) = i exp ( i k L ) λ L 0 exp ( i k 2 L ( r 2 + r 0 2 ) ) f ( r 0 ) r 0 d r 0 × 0 2 π exp ( i k r r 0 cos ( φ φ 0 ) L ) ( cos ( φ 0 ) x ̂ + sin ( φ 0 ) y ̂ ) d φ 0 ,
W x ( z , φ ) = 0 2 π exp [ i z cos ( φ φ 0 ) ] cos ( φ 0 ) d φ 0 , z = k r r 0 L .
W x ( z , φ ) = 0 2 π exp [ i z cos ( φ φ 0 ) ] cos ( φ 0 ) d φ 0 = 0 2 π exp [ i z cos ( φ 0 ) ] [ cos ( φ 0 ) cos ( φ ) sin ( φ 0 ) sin ( φ ) ] d φ 0 = 2 π i J 1 ( z ) cos ( φ ) .
0 2 π exp [ i z cos ( φ φ 0 ) ] [ cos ( φ 0 ) x ̂ + sin ( φ 0 ) y ̂ ] d φ 0 = 2 π i J 1 ( z ) [ cos ( φ ) x ̂ + sin ( φ ) y ̂ ] = 2 π i J 1 ( z ) r ̂ .
E ( r , φ , L ) = i exp ( i k L ) λ L 0 exp ( i k 2 L ( r 2 + r 0 2 ) ) f ( r 0 ) 2 π i J 1 ( k r r 0 L ) r 0 d r 0 r ̂ .
E ( r , φ , 0 ) = f ( r ) exp [ i a ( r ) cos ( n φ ) ] r ̂ .
E ( r , φ , L ) = i exp ( i k L ) λ L 0 exp ( i k 2 L ( r 2 + r 0 2 ) ) f ( r 0 ) r 0 d r 0 × 0 2 π exp ( i k r r 0 cos ( φ φ 0 ) L ) exp [ i a ( r 0 ) cos ( n φ 0 ) ] [ cos ( φ 0 ) x ̂ + sin ( φ 0 ) y ̂ ] d φ 0 .
W x ( z , φ ) 0 2 π exp [ i z cos ( φ φ 0 ) ] cos ( φ 0 ) [ 1 + i a ( r 0 ) cos ( n φ 0 ) ] d φ 0 = 2 π i J 1 ( z ) cos ( φ ) + i a ( r 0 ) 0 2 π exp [ i z cos ( φ φ 0 ) ] cos ( φ 0 ) cos ( n φ 0 ) d φ 0 .
0 2 π exp [ i z cos ( φ φ 0 ) ] cos ( m φ 0 ) d φ 0 = 0 2 π exp [ i z cos ( φ 0 ) ] [ cos ( m φ 0 ) cos ( m φ ) sin ( m φ 0 ) sin ( m φ ) ] d φ 0 = cos ( m φ ) 0 2 π exp [ i z cos ( φ 0 ) ] cos ( m φ 0 ) d φ 0 = 2 π i m J m ( z ) cos ( m φ ) .
0 2 π exp [ i z cos ( φ φ 0 ) ] cos ( φ 0 ) cos ( n φ 0 ) d φ 0 = 1 2 0 2 π exp [ i z cos ( φ φ 0 ) ] [ cos ( ( n + 1 ) φ 0 ) + cos ( ( n 1 ) φ 0 ) ] d φ 0 = π i n + 1 [ cos ( ( n + 1 ) φ ) J n + 1 ( z ) cos ( ( n 1 ) φ ) J n 1 ( z ) ] .
W x ( z , φ ) = 2 π i J 1 ( z ) cos ( φ ) a ( r 0 ) π i n [ cos ( ( n + 1 ) φ ) J n + 1 ( z ) cos ( ( n 1 ) φ ) J n 1 ( z ) ] ,
W y ( z , φ ) = 2 π i J 1 ( z ) sin ( φ ) a ( r 0 ) π i n [ sin ( ( n + 1 ) φ ) J n + 1 ( z ) + sin ( ( n 1 ) φ ) J n 1 ( z ) ] .
0 2 π exp [ i z cos ( φ φ 0 ) ] exp [ i a ( r 0 ) cos ( n φ 0 ) ] [ cos ( φ 0 ) x ̂ + sin ( φ 0 ) y ̂ ] d φ 0 = W x ( z , φ ) x ̂ + W y ( z , φ ) y ̂ = 2 π i J 1 ( z ) r ̂ π i n a ( r 0 ) cos ( n φ ) ( J n + 1 ( z ) J n 1 ( z ) ) r ̂ π i n a ( r 0 ) sin ( n φ ) ( J n + 1 ( z ) + J n 1 ( z ) ) φ ̂ .

Metrics