Abstract

A simulation and experiment were performed to demonstrate that a laser using volume Bragg grating as one of the cavity mirrors can achieve lasing even if the laser cavity length exceeds the traditional stable cavity condition. The laser transverse mode changes from a Gaussian beam into a ring-shaped mode as the laser cavity length increases from stable to unstable cavity conditions. At the same time, the effective modal reflectivity is reduced as the cavity length increases.

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References

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  1. L. B. Glebov, Volume Bragg Gratings in PTR Glass—New Optical Elements for Laser Design (Optical Society of America, 2008), p. MD1.
  2. B. L. Volodin, S. V. Dolgy, E. D. Melnik, E. Downs, J. Shaw, and V. S. Ban, Opt. Lett. 29, 1891 (2004).
    [CrossRef]
  3. T.-Y. Chung, V. Smirnov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, in Lasers and Electro-Optics, 2006 and 2006 Quantum Electronics and Laser Science Conference. CLEO/QELS 2006. Conference on (2006), pp. 1–2.
  4. H.-T. Hsieh, W. Liu, F. Havermeyer, C. Moser, and D. Psaltis, Appl. Opt. 45, 3774 (2006).
    [CrossRef]
  5. J. E. Hellstrom, B. Jacobsson, V. Pasiskevicius, and F. Laurell, IEEE J. Quantum Electron. 44, 81 (2008).
    [CrossRef]
  6. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).
  7. M. Born, E. Wolf, and A. B. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
  8. M. Nazarathy and J. Shamir, J. Opt. Soc. Am. 72, 356 (1982).
    [CrossRef]
  9. Å. Björck and S. Hammarling, Linear Algebra Appl. 52, 127 (1983).

2008 (1)

J. E. Hellstrom, B. Jacobsson, V. Pasiskevicius, and F. Laurell, IEEE J. Quantum Electron. 44, 81 (2008).
[CrossRef]

2006 (1)

2004 (1)

1983 (1)

Å. Björck and S. Hammarling, Linear Algebra Appl. 52, 127 (1983).

1982 (1)

Ban, V. S.

Bass, M.

T.-Y. Chung, V. Smirnov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, in Lasers and Electro-Optics, 2006 and 2006 Quantum Electronics and Laser Science Conference. CLEO/QELS 2006. Conference on (2006), pp. 1–2.

Bhatia, A. B.

M. Born, E. Wolf, and A. B. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

Björck, Å.

Å. Björck and S. Hammarling, Linear Algebra Appl. 52, 127 (1983).

Born, M.

M. Born, E. Wolf, and A. B. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

Chung, T.-Y.

T.-Y. Chung, V. Smirnov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, in Lasers and Electro-Optics, 2006 and 2006 Quantum Electronics and Laser Science Conference. CLEO/QELS 2006. Conference on (2006), pp. 1–2.

Dolgy, S. V.

Downs, E.

Glebov, L. B.

L. B. Glebov, Volume Bragg Gratings in PTR Glass—New Optical Elements for Laser Design (Optical Society of America, 2008), p. MD1.

T.-Y. Chung, V. Smirnov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, in Lasers and Electro-Optics, 2006 and 2006 Quantum Electronics and Laser Science Conference. CLEO/QELS 2006. Conference on (2006), pp. 1–2.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

Hammarling, S.

Å. Björck and S. Hammarling, Linear Algebra Appl. 52, 127 (1983).

Havermeyer, F.

Hellstrom, J. E.

J. E. Hellstrom, B. Jacobsson, V. Pasiskevicius, and F. Laurell, IEEE J. Quantum Electron. 44, 81 (2008).
[CrossRef]

Hemmer, M.

T.-Y. Chung, V. Smirnov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, in Lasers and Electro-Optics, 2006 and 2006 Quantum Electronics and Laser Science Conference. CLEO/QELS 2006. Conference on (2006), pp. 1–2.

Hsieh, H.-T.

Jacobsson, B.

J. E. Hellstrom, B. Jacobsson, V. Pasiskevicius, and F. Laurell, IEEE J. Quantum Electron. 44, 81 (2008).
[CrossRef]

Laurell, F.

J. E. Hellstrom, B. Jacobsson, V. Pasiskevicius, and F. Laurell, IEEE J. Quantum Electron. 44, 81 (2008).
[CrossRef]

Liu, W.

Melnik, E. D.

Moser, C.

Nazarathy, M.

Pasiskevicius, V.

J. E. Hellstrom, B. Jacobsson, V. Pasiskevicius, and F. Laurell, IEEE J. Quantum Electron. 44, 81 (2008).
[CrossRef]

Psaltis, D.

Richardson, M. C.

T.-Y. Chung, V. Smirnov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, in Lasers and Electro-Optics, 2006 and 2006 Quantum Electronics and Laser Science Conference. CLEO/QELS 2006. Conference on (2006), pp. 1–2.

Shamir, J.

Shaw, J.

Smirnov, V.

T.-Y. Chung, V. Smirnov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, in Lasers and Electro-Optics, 2006 and 2006 Quantum Electronics and Laser Science Conference. CLEO/QELS 2006. Conference on (2006), pp. 1–2.

Volodin, B. L.

Wolf, E.

M. Born, E. Wolf, and A. B. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

J. E. Hellstrom, B. Jacobsson, V. Pasiskevicius, and F. Laurell, IEEE J. Quantum Electron. 44, 81 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

Linear Algebra Appl. (1)

Å. Björck and S. Hammarling, Linear Algebra Appl. 52, 127 (1983).

Opt. Lett. (1)

Other (4)

T.-Y. Chung, V. Smirnov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, in Lasers and Electro-Optics, 2006 and 2006 Quantum Electronics and Laser Science Conference. CLEO/QELS 2006. Conference on (2006), pp. 1–2.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

M. Born, E. Wolf, and A. B. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

L. B. Glebov, Volume Bragg Gratings in PTR Glass—New Optical Elements for Laser Design (Optical Society of America, 2008), p. MD1.

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Figures (8)

Fig. 1.
Fig. 1.

Laser cavity configuration.

Fig. 2.
Fig. 2.

Solid, dotted, and dashed curves indicate the Gaussian mode spot size along the optical axis of Fig. 1 cavity obtained using a flat mirror instead of the VBG when the z1 distance is 5.60, 5.70, and 5.76 cm, respectively. M is located at position 0 and the dashed–dotted line indicates the position of L.

Fig. 3.
Fig. 3.

Numerical solutions of the cavity eigenequation: (a) the laser output mode in far field angular distribution and the corresponding (b) effective cavity reflectivity as a function of z1.

Fig. 4.
Fig. 4.

Cross sections of the simulated beam profile when z1 is (a) 5.70 cm, (b) 5.79 cm, (c) 5.85 cm, and (d) 6.20 cm.

Fig. 5.
Fig. 5.

VBG angular reflectivity and the corresponding laser far field intensity distribution when z1 is 6.2 cm.

Fig. 6.
Fig. 6.

Laser output beam profiles when z1 equals (a) 5.5 cm, (b) 5.7 cm, and (c) 6.2 cm.

Fig. 7.
Fig. 7.

Cross sections of the angular beam profile of the laser output when z1 equals 6.2 cm from the (a) experiment and (b) simulation.

Fig. 8.
Fig. 8.

Laser output power versus pump power. The solid and dashed curves indicate when z1 is 5.5 and 6.2 cm, respectively.

Equations (1)

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F1R[z1]FQ[1f]F1R[z2]FQ[2S]·F1R[z2]FQ[1f]F1R[z1]r˜VBGFU(x,y)=r·U(x,y),

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