Abstract

We found an abrupt transverse-mode transition from an irregular to a Gaussian lasing pattern or billiard-like lasing patterns with increasing the pump power in a laser-diode-pumped thin-slice Nd:GdVO4 laser with coated dielectric mirrors on both ends. A variety of irregular stationary lasing patterns were observed with a slight change in the pump position due to polished crystal surface roughness and ineffective lasing field confinement in transverse directions. A physical interpretation for observed irregular patterns was given in terms of wave formations in gradient refractive index lens with undulated reflective end surfaces. Intensity modulation of the laser, resulting from the interference of non-orthogonal transverse mode pairs embedded in the irregular lasing patterns, and associated rich chaotic pulsations were demonstrated. Observed nonlinear dynamics were well reproduced by numerical simulation.

© 2005 Optical Society of America

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References

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  1. Y. Asakawa, R. Kawai, K. Ohki, and K. Otsuka, �??Laser-diode-pumped microchip LiNdP4O12 lasers under different pump-beam focusing condition,�?? Jpn. J. Appl. Phys. 38, L515-L517 (1999).
    [CrossRef]
  2. K. F. Huang, Y. F. Chen, H. C. Lai, and Y. P. Lan, �??Observation of the wave function of a quantum billiard from the transverse patterns of vertical cavity surface emitting lasers,�?? Phys. Rev. Lett. 89, 224102 (2002).
    [CrossRef] [PubMed]
  3. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, �??Whispering-gallery mode microdisk lasers,�?? Appl. Phys. Lett. 60, 289 (1992).
    [CrossRef]
  4. S.-B. Lee, J.-H. Lee, J.-S. Chang, H.-J. Moon, S. W. Kim, and K. An, �??Observation of scarred modes in ssymmetrically deformed microcylinder lasers,�?? Phys. Rev. Lett. 88, 033903 (2002).
    [CrossRef] [PubMed]
  5. K. Otsuka, J.-Y. Ko, T.-S. Lim, and H. Makino, �??Modal interference and dynamical instability in a solid-state slice laser with asymmetric end-pumping,�?? Phys. Rev. Lett. 87, 083903 (2002)..
    [CrossRef]
  6. K. Otsuka, J.-Y. Ko, H. Makino, T. Ohtomo, and A. Okamoto, �??Transverse effects in a microchip laser with aymmetric end-pumping: modal interference and dynamic instability,�?? Quantum and Semiclass. Opt. 5, R137-R415 (2003).
    [CrossRef]
  7. P. B. Wilkinson, T. M. Fromhold, R. P. Taylor, and A. P. Micolich, �??Electromagnetic wave chaos in gradient refractive index optical cavities,�?? Phys. Rev. Lett. 86, 5466 (2001).
    [CrossRef] [PubMed]
  8. Catalogue, CRYSTECH Inc.
  9. J. Nakano, �??Thermal properties of a solid-state laser crystal LiNdP4O12,�?? J. Appl. Phys. 52, 1239 (1981).
    [CrossRef]

Appl. Phys. Lett. (1)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, �??Whispering-gallery mode microdisk lasers,�?? Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

J. Appl. Phys. (1)

J. Nakano, �??Thermal properties of a solid-state laser crystal LiNdP4O12,�?? J. Appl. Phys. 52, 1239 (1981).
[CrossRef]

Jpn. J. Appl. Phys. (1)

Y. Asakawa, R. Kawai, K. Ohki, and K. Otsuka, �??Laser-diode-pumped microchip LiNdP4O12 lasers under different pump-beam focusing condition,�?? Jpn. J. Appl. Phys. 38, L515-L517 (1999).
[CrossRef]

Phys. Rev. Lett. (4)

K. F. Huang, Y. F. Chen, H. C. Lai, and Y. P. Lan, �??Observation of the wave function of a quantum billiard from the transverse patterns of vertical cavity surface emitting lasers,�?? Phys. Rev. Lett. 89, 224102 (2002).
[CrossRef] [PubMed]

P. B. Wilkinson, T. M. Fromhold, R. P. Taylor, and A. P. Micolich, �??Electromagnetic wave chaos in gradient refractive index optical cavities,�?? Phys. Rev. Lett. 86, 5466 (2001).
[CrossRef] [PubMed]

S.-B. Lee, J.-H. Lee, J.-S. Chang, H.-J. Moon, S. W. Kim, and K. An, �??Observation of scarred modes in ssymmetrically deformed microcylinder lasers,�?? Phys. Rev. Lett. 88, 033903 (2002).
[CrossRef] [PubMed]

K. Otsuka, J.-Y. Ko, T.-S. Lim, and H. Makino, �??Modal interference and dynamical instability in a solid-state slice laser with asymmetric end-pumping,�?? Phys. Rev. Lett. 87, 083903 (2002)..
[CrossRef]

Quantum and Semiclass. Opt. (1)

K. Otsuka, J.-Y. Ko, H. Makino, T. Ohtomo, and A. Okamoto, �??Transverse effects in a microchip laser with aymmetric end-pumping: modal interference and dynamic instability,�?? Quantum and Semiclass. Opt. 5, R137-R415 (2003).
[CrossRef]

Other (1)

Catalogue, CRYSTECH Inc.

Supplementary Material (2)

» Media 1: MOV (2259 KB)     
» Media 2: MOV (2375 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

(a) Experimental setup of symmetrically pumped LDM. (b) Example input-output characteristic of Nd:GdVO4 LDM. PD: photodiode, DO: digital oscilloscope, WFA; wave-front analyzer, SFP: scanning Fabry-Perot interferometer, IRV: PbS infrared viewer. The asymmetric pumping scheme is depicted in the inset.

Fig. 2.
Fig. 2.

Far-field lasing patterns for different pump powers corresponding to Fig. 1(b). Pump power; a: 27 mW, b: 36 mW, c: 87 mW, d: 139 mW, e: 164 mW, f: 241 mW. [Media 1]

Fig. 3.
Fig. 3.

Far-field patterns observed at different pump positions at a fixed pump power of 121 mW. The crystal was shifted horizontally. Relative positions are indicated.

Fig. 4.
Fig. 4.

Poincare sections indicating ray orbits on [x, sin θ] for different effective focal lengths of GRIN thermal lens. A sinusoidal surface roughness is assumed as shown in the figure. A 7/4 modulation period is assigned for each side (150 μm). (a),(b),(c): R = 2x10-4, (d): R = 2x10-3 Effective focal length: (a) 7.5 mm, (b) 4.75 mm, (c) 1.5 mm, (d) 7.5 mm.

Fig. 5.
Fig. 5.

Intensity profiles and wave-front distributions. (a) Symmetric pumping (pump power = 61 mW). (b) Asymmetric pumping (pump power = 481 mW)

Fig. 6.
Fig. 6.

Oscillation waveforms and corresponding power spectra indicating resonant excitation of chaotic pulsations in Nd:GdVO4 LDM. Global views of power spectra indicating high-speed modulations are indicated in insets. Pump power: (a) 240 mW, (b) 260 mW, (c) 271 mW

Fig. 7.
Fig. 7.

(a) Example scanning Fabry-Perot traces of Nd:GdVO4 LDM at different pump powers. (b) Chaotic pulsations featuring high-speed modulation at d in (a) where pump power = 155 mW. (c) Power spectrum.

Fig. 8.
Fig. 8.

Lasing pattern changes with increasing the pump power of asymmetrically LD-pumped Nd:GdVO4 LDM. Pump power; a: 165 mW, b: 241 mW, c: 291 mW, d: 366 mW, e: 394 mW, f: 434 mW. [Media 2]

Fig. 9.
Fig. 9.

Numerical result. Adopted parameters are w=1.05, K=2000, ΔΩ1,2=0.008, ΔΩ2,3=1.670, β=0.667, g 1=0.02, g 2=0.250, D 1=D 2=10-5. In notations in ref. [5], the definition of K should read K = τκ, where τ is the fluorescence lifetime and κ = 1/2τ p is the cavity damping rate.

Equations (3)

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d N i / d t = [ w 1 N i ( 1 + 2 N i ) ( E i 2 + i j β E j 2 ) ] / K
d E i / d t = N i E i + g E i E i + 1 cos ϕ i , j + 1 + g E i E i 1 cos ϕ i , j 1
d ϕ i , i ± 1 / d t = Δ Ω i , i ± 1 + D i ξ i ( t ) , i , j = 1,2,3

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