Abstract

Improvement of the beam-quality parameter of partially polarized beams is investigated. We focus on the use of a Mach–Zehnder-type interferometric arrangement with crossed polarizers. The analysis has been carried out within the framework of the intensity moment formalism. Conditions are given under which the beam-quality parameter is optimized.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Lavi, R. Prochaska, E. Keren, “Generalized beam parameters and transformation law for partially coherent light,” Appl. Opt. 27, 3696–3703 (1988).
    [Crossref] [PubMed]
  2. M. J. Bastiaans, “Propagation laws for the second-order moments of the Wigner distribution function in first-order optical systems,” Optik 82, 173–181 (1989).
  3. A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
    [Crossref]
  4. J. Serna, R. Martínez-Herrero, P. M. Mejías, “Parametric characterization of general partially coherent beams propagating through ABCD optical systems,” J. Opt. Soc. Am. A 8, 1094–1098 (1991).
    [Crossref]
  5. H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, 1027–1049 (1992).
    [Crossref]
  6. ISO standard 11146, Lasers and Laser Related Equipment. Test methods for laser beam parameters: beam widths, divergence angle, and beam propagation factor (International Organization for Standardization, Geneva, Switzerland, 1999).
  7. R. Martínez-Herrero, P. M. Mejías, G. Piquero, “Quality improvement of partially coherent symmetric-intensity beams caused by quartic phase distortions,” Opt. Lett. 17, 1650–1651 (1992).
    [Crossref] [PubMed]
  8. A. E. Siegman, J. Ruff, “Effects of spherical aberration on laser beam quality,” in Laser Energy Distribution Profiles, J. M. Darchuk, ed., Proc. SPIE1834, 130–139 (1992).
    [Crossref]
  9. J. Serna, G. Piquero, P. M. Mejías, R. Martínez-Herrero, “Parametric characterization of Hermite–Gauss mode beams and Gauss–Schell model fields propagating through super-Gaussian apertures,” Opt. Quantum Electron. 28, 1039–1048 (1996).
    [Crossref]
  10. S. C. Tidwell, D. H. Ford, W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2334–2339 (1990).
    [Crossref]
  11. N. Kugler, S. Dong, Q. Lü, H. Weber, “Investigation of the misalignment sensitivity of a birefringence compensated two-rod Nd:YAG laser system,” Appl. Opt. 36, 9359–9366 (1997).
    [Crossref]
  12. T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, Al/Ga/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
    [Crossref]
  13. Q. Lü, S. Dong, H. Weber, “Analysis of TEM00 laser beam quality degradation caused by a birefringent Nd:YAG rod,” Opt. Quantum Electron. 27, 777–783 (1995).
    [Crossref]
  14. R. Martínez-Herrero, P. M. Mejías, J. M. Movilla, “Spatial characterization of general partially polarized beams,” Opt. Lett. 22, 206–208 (1997).
    [Crossref] [PubMed]
  15. J. M. Movilla, G. Piquero, P. M. Mejías, R. Martínez-Herrero, “Parametric characterization of nonuniformly polarized beams,” Opt. Commun. 149, 230–234 (1998).
    [Crossref]
  16. F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23, 241–243 (1998).
    [Crossref]
  17. G. Nemes, “Measuring and handling general astigmatic beams,” in Laser Beam Characterization, P. M. Mejías, H. Weber, R. Martínez-Herrero, A. González-Ureña, eds. (Sociedad Española de Óptica, Madrid, 1993), pp. 325–358.
  18. G. Piquero, J. M. Movilla, P. M. Mejías, R. Martínez-Herrero, “Beam quality of partially polarized beams propagating through lenslike birefringent elements,” J. Opt. Soc. Am. A 16, 2666–2668 (1999).
    [Crossref]

1999 (1)

1998 (2)

J. M. Movilla, G. Piquero, P. M. Mejías, R. Martínez-Herrero, “Parametric characterization of nonuniformly polarized beams,” Opt. Commun. 149, 230–234 (1998).
[Crossref]

F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23, 241–243 (1998).
[Crossref]

1997 (2)

1996 (1)

J. Serna, G. Piquero, P. M. Mejías, R. Martínez-Herrero, “Parametric characterization of Hermite–Gauss mode beams and Gauss–Schell model fields propagating through super-Gaussian apertures,” Opt. Quantum Electron. 28, 1039–1048 (1996).
[Crossref]

1995 (1)

Q. Lü, S. Dong, H. Weber, “Analysis of TEM00 laser beam quality degradation caused by a birefringent Nd:YAG rod,” Opt. Quantum Electron. 27, 777–783 (1995).
[Crossref]

1992 (3)

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, Al/Ga/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, 1027–1049 (1992).
[Crossref]

R. Martínez-Herrero, P. M. Mejías, G. Piquero, “Quality improvement of partially coherent symmetric-intensity beams caused by quartic phase distortions,” Opt. Lett. 17, 1650–1651 (1992).
[Crossref] [PubMed]

1991 (1)

1990 (1)

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2334–2339 (1990).
[Crossref]

1989 (1)

M. J. Bastiaans, “Propagation laws for the second-order moments of the Wigner distribution function in first-order optical systems,” Optik 82, 173–181 (1989).

1988 (1)

Anderson, E. H.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, Al/Ga/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]

Bastiaans, M. J.

M. J. Bastiaans, “Propagation laws for the second-order moments of the Wigner distribution function in first-order optical systems,” Optik 82, 173–181 (1989).

Dong, S.

N. Kugler, S. Dong, Q. Lü, H. Weber, “Investigation of the misalignment sensitivity of a birefringence compensated two-rod Nd:YAG laser system,” Appl. Opt. 36, 9359–9366 (1997).
[Crossref]

Q. Lü, S. Dong, H. Weber, “Analysis of TEM00 laser beam quality degradation caused by a birefringent Nd:YAG rod,” Opt. Quantum Electron. 27, 777–783 (1995).
[Crossref]

Erdogan, T.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, Al/Ga/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]

Ford, D. H.

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2334–2339 (1990).
[Crossref]

Gori, F.

Hall, D. G.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, Al/Ga/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]

Keren, E.

Kimura, W. D.

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2334–2339 (1990).
[Crossref]

King, O.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, Al/Ga/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]

Kugler, N.

Lavi, S.

Lü, Q.

N. Kugler, S. Dong, Q. Lü, H. Weber, “Investigation of the misalignment sensitivity of a birefringence compensated two-rod Nd:YAG laser system,” Appl. Opt. 36, 9359–9366 (1997).
[Crossref]

Q. Lü, S. Dong, H. Weber, “Analysis of TEM00 laser beam quality degradation caused by a birefringent Nd:YAG rod,” Opt. Quantum Electron. 27, 777–783 (1995).
[Crossref]

Martínez-Herrero, R.

Mejías, P. M.

Movilla, J. M.

Nemes, G.

G. Nemes, “Measuring and handling general astigmatic beams,” in Laser Beam Characterization, P. M. Mejías, H. Weber, R. Martínez-Herrero, A. González-Ureña, eds. (Sociedad Española de Óptica, Madrid, 1993), pp. 325–358.

Piquero, G.

G. Piquero, J. M. Movilla, P. M. Mejías, R. Martínez-Herrero, “Beam quality of partially polarized beams propagating through lenslike birefringent elements,” J. Opt. Soc. Am. A 16, 2666–2668 (1999).
[Crossref]

J. M. Movilla, G. Piquero, P. M. Mejías, R. Martínez-Herrero, “Parametric characterization of nonuniformly polarized beams,” Opt. Commun. 149, 230–234 (1998).
[Crossref]

J. Serna, G. Piquero, P. M. Mejías, R. Martínez-Herrero, “Parametric characterization of Hermite–Gauss mode beams and Gauss–Schell model fields propagating through super-Gaussian apertures,” Opt. Quantum Electron. 28, 1039–1048 (1996).
[Crossref]

R. Martínez-Herrero, P. M. Mejías, G. Piquero, “Quality improvement of partially coherent symmetric-intensity beams caused by quartic phase distortions,” Opt. Lett. 17, 1650–1651 (1992).
[Crossref] [PubMed]

Prochaska, R.

Rooks, M. J.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, Al/Ga/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]

Ruff, J.

A. E. Siegman, J. Ruff, “Effects of spherical aberration on laser beam quality,” in Laser Energy Distribution Profiles, J. M. Darchuk, ed., Proc. SPIE1834, 130–139 (1992).
[Crossref]

Serna, J.

J. Serna, G. Piquero, P. M. Mejías, R. Martínez-Herrero, “Parametric characterization of Hermite–Gauss mode beams and Gauss–Schell model fields propagating through super-Gaussian apertures,” Opt. Quantum Electron. 28, 1039–1048 (1996).
[Crossref]

J. Serna, R. Martínez-Herrero, P. M. Mejías, “Parametric characterization of general partially coherent beams propagating through ABCD optical systems,” J. Opt. Soc. Am. A 8, 1094–1098 (1991).
[Crossref]

Siegman, A. E.

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[Crossref]

A. E. Siegman, J. Ruff, “Effects of spherical aberration on laser beam quality,” in Laser Energy Distribution Profiles, J. M. Darchuk, ed., Proc. SPIE1834, 130–139 (1992).
[Crossref]

Tidwell, S. C.

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2334–2339 (1990).
[Crossref]

Weber, H.

N. Kugler, S. Dong, Q. Lü, H. Weber, “Investigation of the misalignment sensitivity of a birefringence compensated two-rod Nd:YAG laser system,” Appl. Opt. 36, 9359–9366 (1997).
[Crossref]

Q. Lü, S. Dong, H. Weber, “Analysis of TEM00 laser beam quality degradation caused by a birefringent Nd:YAG rod,” Opt. Quantum Electron. 27, 777–783 (1995).
[Crossref]

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, 1027–1049 (1992).
[Crossref]

Wicks, G. W.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, Al/Ga/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, Al/Ga/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992).
[Crossref]

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

Opt. Commun. (1)

J. M. Movilla, G. Piquero, P. M. Mejías, R. Martínez-Herrero, “Parametric characterization of nonuniformly polarized beams,” Opt. Commun. 149, 230–234 (1998).
[Crossref]

Opt. Lett. (3)

Opt. Quantum Electron. (3)

J. Serna, G. Piquero, P. M. Mejías, R. Martínez-Herrero, “Parametric characterization of Hermite–Gauss mode beams and Gauss–Schell model fields propagating through super-Gaussian apertures,” Opt. Quantum Electron. 28, 1039–1048 (1996).
[Crossref]

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, 1027–1049 (1992).
[Crossref]

Q. Lü, S. Dong, H. Weber, “Analysis of TEM00 laser beam quality degradation caused by a birefringent Nd:YAG rod,” Opt. Quantum Electron. 27, 777–783 (1995).
[Crossref]

Optik (1)

M. J. Bastiaans, “Propagation laws for the second-order moments of the Wigner distribution function in first-order optical systems,” Optik 82, 173–181 (1989).

Other (4)

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[Crossref]

ISO standard 11146, Lasers and Laser Related Equipment. Test methods for laser beam parameters: beam widths, divergence angle, and beam propagation factor (International Organization for Standardization, Geneva, Switzerland, 1999).

A. E. Siegman, J. Ruff, “Effects of spherical aberration on laser beam quality,” in Laser Energy Distribution Profiles, J. M. Darchuk, ed., Proc. SPIE1834, 130–139 (1992).
[Crossref]

G. Nemes, “Measuring and handling general astigmatic beams,” in Laser Beam Characterization, P. M. Mejías, H. Weber, R. Martínez-Herrero, A. González-Ureña, eds. (Sociedad Española de Óptica, Madrid, 1993), pp. 325–358.

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 (1)

Fig. 1
Fig. 1

Schematic of a MZT system. Planes Π i and Π o are, respectively, the input and the output planes of the system. P 1 and P 2 are orthogonally oriented linear polarizers.

Equations (35)

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

Er, z=Esr; z, Epr; z,
αβj=1Ijk24π2  αβEj*r+s/2, z×Ejr-s/2, zexpiksηdsdrdη,
Ij= |Ejr|2dr,  j=s, p
x2+y2=r2=IsIr2s+IpIr2p,
xu+yv=rη=IsIrηs+IpIrηp,
u2+v2=η2=IsIη2s+IpIη2p,
Rs,p=r2s, prηs,p,
zRs,p=r2s,pwη2s,p1/2,
zws,p=-rηs,pη2s,p,
Q3-D=IsI2Q3-Ds+IpI2Q3-Dp+IsIpI2Q3-Dsp,
Q3-D=r2η2-rη2,
Q3-Ds=r2sη2s-rηs2,
Q3-Dp=r2pη2p-rηp2,
Q3-Dsp=r2sη2p+r2pη2s-2rηsrηp.
r2jo=Aj2r2ji+2AjBjrηji+Bj2η2ji,
rηjo=AjCjr2ji+AjDj+BjCjrηji+BjDjη2ji,
η2jo=Cj2r2ji+2CjDjrηji+Dj2η2ji.
A1=1, B1=L1, C1=0, D1=1,
A2=1, B2=L2, C2=0, D2=1.
ΔQ3-DQ3-Do-Q3-Di=IsIpI2L2-L12η2sη2p+2L2-L1×rηpη2s-rηsη2p,
ΔQ3-D<0  |L2-L1|<2|Hs-Hp|,
signL2-L1=signHs-Hp,
Hs,prηs,pη2s,p.
L2-L1=Hs-Hp.
ΔQ3-Dopt=-IsIpI2η2sη2pHs-Hp2.
ΔQ3-D=IsIpI2η2sη2pL2-L12-2LL2-L1.
L2-L1=L
ΔQ3-Dopt=-IsIpI2η2sη2pL2.
A1=m1, B1=0, C1=0, D1=m1-1,
A2=m2, B2=0, C2=0, D2=m2-1.
ΔQ3-D=IsIpI2[m2-1r2sη2p+m-2-1r2pη2pη2s,
m=m1m2-1,
min1, b/a<m2<max1, b/a.
m2=zRp/zRs.
ΔQ3-Dopt=-IsIpI2η2sη2pzRs-zRp2.

Metrics