Abstract

We apply a new method of modeling Porro prism resonators, using the concept of rotating loss screens, to study stable and unstable Porro prism resonator. We show that the previously observed petal–like modal output is in fact only the lowest order mode, and reveal that a variety of kaleidoscope beam modes will be produced by these resonators when the intra–cavity apertures are sufficiently large to allow higher order modes to oscillate. We also show that only stable resonators will produce these modes.

© 2008 Optical Society of America

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References

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  1. B. A. See, K. Fuelop, and R. Seymour, "An Assessment of the Crossed Porro Prism Resonator," Technical Memorandum ERL-0162-TM, Electronics Research Lab Adelaide (Australia) (1980).
  2. M. Henriksson, L. Sjöqvista, and T. Uhrwing, "Numerical simulation of a battlefield Nd:YAG laser," Proc. SPIE 5989, 59890I (2005).
    [CrossRef]
  3. M. Henriksson and L. Sjöqvist, "Numerical simulation of a flashlamp pumped Nd:YAG laser," Report # ISRN FOI-R-1710-SE, Swedish Defence Research Agency, Linkoeping, Sensor Technology (2007).
  4. M. Ishizu, "Laser Oscillator," US Patent 6816533 (2004).
  5. A. Rapaport and L. Weichman, "Laser Resonator Design Using Optical Ray Tracing Software: Comparisons with Simple Analytical Models and Experimental Results," IEEE J. Quantum Electron. 37, 1401-1408 (2001).
    [CrossRef]
  6. I. A. Litvin, L. Burger, and A. Forbes, "Petal-like modes in Porro prism resonators," Opt. Express 15, 14065-14077 (2007).
    [CrossRef] [PubMed]
  7. N. Hodgson and H. Weber, Laser Resonators and Beam Propagation: Fundamentals, Advanced Concepts and Applications (Springer, 2005), Chap. 20.
  8. W. Liu, Y. Huo, X. Yin, and D. Zhao, "Modes of Multi-End-Pumped Nonplanar Ring Laser," IEEE Photon. Technol. Lett. 17, 1776-1778 (2005).
    [CrossRef]
  9. C. Bollig, W. A. Clarkson, D. C. Hanna, D. S. Lovering, and G. C. W. Jones, "Single-frequency operation of a monolithic Nd:glass ring laser via the acousto-optics effect," Opt. Commun. 133, 221-224 (1997).
    [CrossRef]
  10. Z. Bouchal, "Nondiffracting optical beams: physical properties, experiments, and applications," Czech. J. Phys. 53, 537-624 (2003).
    [CrossRef]
  11. M. Anguiano-Morales, A. Martinez, M. D. Iturbe-Castillo, and S. Chavez-Cerda, "Different field distributions obtained with an axicon and an amplitude mask," Opt. Commun. 281, 401-407 (2008).
    [CrossRef]

2008 (1)

M. Anguiano-Morales, A. Martinez, M. D. Iturbe-Castillo, and S. Chavez-Cerda, "Different field distributions obtained with an axicon and an amplitude mask," Opt. Commun. 281, 401-407 (2008).
[CrossRef]

2007 (1)

2005 (2)

W. Liu, Y. Huo, X. Yin, and D. Zhao, "Modes of Multi-End-Pumped Nonplanar Ring Laser," IEEE Photon. Technol. Lett. 17, 1776-1778 (2005).
[CrossRef]

M. Henriksson, L. Sjöqvista, and T. Uhrwing, "Numerical simulation of a battlefield Nd:YAG laser," Proc. SPIE 5989, 59890I (2005).
[CrossRef]

2003 (1)

Z. Bouchal, "Nondiffracting optical beams: physical properties, experiments, and applications," Czech. J. Phys. 53, 537-624 (2003).
[CrossRef]

2001 (1)

A. Rapaport and L. Weichman, "Laser Resonator Design Using Optical Ray Tracing Software: Comparisons with Simple Analytical Models and Experimental Results," IEEE J. Quantum Electron. 37, 1401-1408 (2001).
[CrossRef]

1997 (1)

C. Bollig, W. A. Clarkson, D. C. Hanna, D. S. Lovering, and G. C. W. Jones, "Single-frequency operation of a monolithic Nd:glass ring laser via the acousto-optics effect," Opt. Commun. 133, 221-224 (1997).
[CrossRef]

Anguiano-Morales, M.

M. Anguiano-Morales, A. Martinez, M. D. Iturbe-Castillo, and S. Chavez-Cerda, "Different field distributions obtained with an axicon and an amplitude mask," Opt. Commun. 281, 401-407 (2008).
[CrossRef]

Bollig, C.

C. Bollig, W. A. Clarkson, D. C. Hanna, D. S. Lovering, and G. C. W. Jones, "Single-frequency operation of a monolithic Nd:glass ring laser via the acousto-optics effect," Opt. Commun. 133, 221-224 (1997).
[CrossRef]

Bouchal, Z.

Z. Bouchal, "Nondiffracting optical beams: physical properties, experiments, and applications," Czech. J. Phys. 53, 537-624 (2003).
[CrossRef]

Burger, L.

Chavez-Cerda, S.

M. Anguiano-Morales, A. Martinez, M. D. Iturbe-Castillo, and S. Chavez-Cerda, "Different field distributions obtained with an axicon and an amplitude mask," Opt. Commun. 281, 401-407 (2008).
[CrossRef]

Clarkson, W. A.

C. Bollig, W. A. Clarkson, D. C. Hanna, D. S. Lovering, and G. C. W. Jones, "Single-frequency operation of a monolithic Nd:glass ring laser via the acousto-optics effect," Opt. Commun. 133, 221-224 (1997).
[CrossRef]

Forbes, A.

Hanna, D. C.

C. Bollig, W. A. Clarkson, D. C. Hanna, D. S. Lovering, and G. C. W. Jones, "Single-frequency operation of a monolithic Nd:glass ring laser via the acousto-optics effect," Opt. Commun. 133, 221-224 (1997).
[CrossRef]

Henriksson, M.

M. Henriksson, L. Sjöqvista, and T. Uhrwing, "Numerical simulation of a battlefield Nd:YAG laser," Proc. SPIE 5989, 59890I (2005).
[CrossRef]

Huo, Y.

W. Liu, Y. Huo, X. Yin, and D. Zhao, "Modes of Multi-End-Pumped Nonplanar Ring Laser," IEEE Photon. Technol. Lett. 17, 1776-1778 (2005).
[CrossRef]

Iturbe-Castillo, M. D.

M. Anguiano-Morales, A. Martinez, M. D. Iturbe-Castillo, and S. Chavez-Cerda, "Different field distributions obtained with an axicon and an amplitude mask," Opt. Commun. 281, 401-407 (2008).
[CrossRef]

Jones, G. C. W.

C. Bollig, W. A. Clarkson, D. C. Hanna, D. S. Lovering, and G. C. W. Jones, "Single-frequency operation of a monolithic Nd:glass ring laser via the acousto-optics effect," Opt. Commun. 133, 221-224 (1997).
[CrossRef]

Litvin, I. A.

Liu, W.

W. Liu, Y. Huo, X. Yin, and D. Zhao, "Modes of Multi-End-Pumped Nonplanar Ring Laser," IEEE Photon. Technol. Lett. 17, 1776-1778 (2005).
[CrossRef]

Lovering, D. S.

C. Bollig, W. A. Clarkson, D. C. Hanna, D. S. Lovering, and G. C. W. Jones, "Single-frequency operation of a monolithic Nd:glass ring laser via the acousto-optics effect," Opt. Commun. 133, 221-224 (1997).
[CrossRef]

Martinez, A.

M. Anguiano-Morales, A. Martinez, M. D. Iturbe-Castillo, and S. Chavez-Cerda, "Different field distributions obtained with an axicon and an amplitude mask," Opt. Commun. 281, 401-407 (2008).
[CrossRef]

Rapaport, A.

A. Rapaport and L. Weichman, "Laser Resonator Design Using Optical Ray Tracing Software: Comparisons with Simple Analytical Models and Experimental Results," IEEE J. Quantum Electron. 37, 1401-1408 (2001).
[CrossRef]

Sjöqvista, L.

M. Henriksson, L. Sjöqvista, and T. Uhrwing, "Numerical simulation of a battlefield Nd:YAG laser," Proc. SPIE 5989, 59890I (2005).
[CrossRef]

Uhrwing, T.

M. Henriksson, L. Sjöqvista, and T. Uhrwing, "Numerical simulation of a battlefield Nd:YAG laser," Proc. SPIE 5989, 59890I (2005).
[CrossRef]

Weichman, L.

A. Rapaport and L. Weichman, "Laser Resonator Design Using Optical Ray Tracing Software: Comparisons with Simple Analytical Models and Experimental Results," IEEE J. Quantum Electron. 37, 1401-1408 (2001).
[CrossRef]

Yin, X.

W. Liu, Y. Huo, X. Yin, and D. Zhao, "Modes of Multi-End-Pumped Nonplanar Ring Laser," IEEE Photon. Technol. Lett. 17, 1776-1778 (2005).
[CrossRef]

Zhao, D.

W. Liu, Y. Huo, X. Yin, and D. Zhao, "Modes of Multi-End-Pumped Nonplanar Ring Laser," IEEE Photon. Technol. Lett. 17, 1776-1778 (2005).
[CrossRef]

Czech. J. Phys. (1)

Z. Bouchal, "Nondiffracting optical beams: physical properties, experiments, and applications," Czech. J. Phys. 53, 537-624 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Rapaport and L. Weichman, "Laser Resonator Design Using Optical Ray Tracing Software: Comparisons with Simple Analytical Models and Experimental Results," IEEE J. Quantum Electron. 37, 1401-1408 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

W. Liu, Y. Huo, X. Yin, and D. Zhao, "Modes of Multi-End-Pumped Nonplanar Ring Laser," IEEE Photon. Technol. Lett. 17, 1776-1778 (2005).
[CrossRef]

Opt. Commun. (2)

C. Bollig, W. A. Clarkson, D. C. Hanna, D. S. Lovering, and G. C. W. Jones, "Single-frequency operation of a monolithic Nd:glass ring laser via the acousto-optics effect," Opt. Commun. 133, 221-224 (1997).
[CrossRef]

M. Anguiano-Morales, A. Martinez, M. D. Iturbe-Castillo, and S. Chavez-Cerda, "Different field distributions obtained with an axicon and an amplitude mask," Opt. Commun. 281, 401-407 (2008).
[CrossRef]

Opt. Express (1)

Proc. SPIE (1)

M. Henriksson, L. Sjöqvista, and T. Uhrwing, "Numerical simulation of a battlefield Nd:YAG laser," Proc. SPIE 5989, 59890I (2005).
[CrossRef]

Other (4)

M. Henriksson and L. Sjöqvist, "Numerical simulation of a flashlamp pumped Nd:YAG laser," Report # ISRN FOI-R-1710-SE, Swedish Defence Research Agency, Linkoeping, Sensor Technology (2007).

M. Ishizu, "Laser Oscillator," US Patent 6816533 (2004).

N. Hodgson and H. Weber, Laser Resonators and Beam Propagation: Fundamentals, Advanced Concepts and Applications (Springer, 2005), Chap. 20.

B. A. See, K. Fuelop, and R. Seymour, "An Assessment of the Crossed Porro Prism Resonator," Technical Memorandum ERL-0162-TM, Electronics Research Lab Adelaide (Australia) (1980).

Supplementary Material (4)

» Media 1: AVI (3288 KB)     
» Media 2: AVI (2458 KB)     
» Media 3: AVI (3415 KB)     
» Media 4: AVI (469 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

A typical Porro prism based Nd:YAG laser with passive Q–switch, showing the following optical elements: Porro prisms (elements a and h); intra–cavity lenses (elements b and g); a beamsplitter cube (element c); a quarter wave plate (element d), and a passive Q–switch (element e). The prism apexes are shown in red.

Fig. 2.
Fig. 2.

(a) Plot of the discrete set of angles α that give rise to a petal pattern, with the corresponding number of petals to be observed; (b) example of petal–like modes for α=60° (top) and α=45° (bottom).

Fig. 3.
Fig. 3.

Modal patterns for the three Porro angles with increasing effective Fresnel number to the right in each row. As NF is increased (through an increase in aperture size), the modes become more complex, departing from the petal–like standard. (Media 1), (Media 2), (Media 3).

Fig. 4.
Fig. 4.

The output modes of a number of Porro prism resonators arranged as a function of G (rows) and NF (columns). Note that in the petal–like cases the single repeating mode is shown, while in the higher order mode cases, only one of the oscillating modes is shown (Media 4).

Fig. 5.
Fig. 5.

A multi-pass beam pass is possible for a given resonator configuration. If the gain region is small and central then a Gaussian mode is expected. The resonator can be forced into a higher multi-pass mode by off-centre pumping.

Fig. 6.
Fig. 6.

Plot of spot size for 12 000 round trips (double passes) through a resonator with Porro angle 30° for G=0.9, NF =9.4, illustrating the periodic nature of the spot size and showing eventual convergence. The sequence of modes through one period is also show.

Fig. 7.
Fig. 7.

(a) Petal mode, (b) Experimental beam pattern, (c) Average of 5 cycles of higher-order modes at 1000 round trips.

Tables (1)

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Table 1. Periodicity comparison

Equations (6)

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N = j 2 π α
α = i π m ,
G = g 1 = g 2
N F = a 2 λ L .
M = ( 1 1 2 L 0 1 ) ( 1 0 f 1 1 ) ( 1 0 f 1 1 ) ( 1 L 0 1 ) ( 1 0 f 1 1 ) ( 1 0 f 1 1 ) ( 1 1 2 L 0 1 ) ,
v p = M p v 0 = i λ i p α i v i ,

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