Abstract

A novel cavity design based on a confocal negative branch unstable resonator configuration is presented. A proper choice for the size of the field limiting aperture, set at the common focal plane of the mirrors, results in removal of the hot spot inside the cavity and in the smoothing of the spatial profile of the oscillating mode. Application of this scheme to a pulsed Nd:YAG oscillator is thoroughly characterized in a variety of operational modes (fixed-Q, Q-switching, mode-locking). The main results are a high efficiency of energy extraction and excellent phase and amplitude profiles of the output beam, which shows real transform-limited performances.

© 1985 Optical Society of America

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References

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  1. We indicate here for simplicity only the more recent and comprehensive reviews on the subjects: for unstable resonators, W. H. Steier, in Laser Handbook, Vol. 3, M. L. Stitch, Ed. (North-Holland, Amsterdam, 1979), pp. 3–39;and for telescopic resonators, D. C. Hanna, C. G. Sawyers, M. A. Yuratich, “Large Volume TEM00 Mode Operation of Nd:YAG Lasers,” Opt. Quantum Electron. 13, 493 (1981).
    [CrossRef]
  2. P. G. Gobbi, G. C. Reali, “A Novel Unstable Resonator Configuration with a Self Filtering Aperture,” to be published in Opt. Commun.
  3. A. E. Siegman, “Unstable Optical Resonator for Laser Applications,” Proc.IEEE 53, 277 (1965).
    [CrossRef]
  4. T. F. Ewanizky, “A High Radiance Flashlamp Pumped Dye Laser,” Appl. Phys. Lett. 25, 295 (1974).
    [CrossRef]
  5. T. F. Ewanizky, J. M. Craig, “Negative-Branch Unstable Resonator Nd:YAG Laser,” Appl. Opt. 15, 1465 (1976).
    [CrossRef] [PubMed]
  6. A. D. E. Brown, “Unstable, Q-Switched, Ruby Resonator in the Negative Branch Confocal Configuration,” Opt. Commun. 27, 253 (1978).
    [CrossRef]
  7. W. F. Krupke, W. R. Sooy, “Properties of an Unstable Confocal Resonator CO2 Laser System,” IEEE J. Quantum Electron. QE-5, 575 (1969).
    [CrossRef]
  8. A. H. Paxton, T. C. Salvi, “Unstable Resonator with Self-imaging Aperture,” Opt. Commun. 26, 305 (1978).
    [CrossRef]
  9. A. E. Siegman, R. Arrathoon, “Modes in Unstable Optical Resonators and Lens Waveguides,” IEEE J. Quantum Electron. QE-3, 156 (1967).
    [CrossRef]
  10. P. G. Gobbi, G. C. Reali, in preparation.
  11. J. G. Skinner, J. E. Geusic, “Diffraction-Limited Ruby Oscillator,” J. Opt. Soc. Am. 52, A1319 (1962).
  12. K. I. Zemskov, A. A. Isaev, M. A. Kazaryan, G. G. Petrash, S. G. Rautian, “Use of Unstable Resonators in Achieving the Diffraction Divergence of the Radiation Emitted from the High-Gain Pulsed Gas Lasers,” Sov. J. Quantum Electron. 4, 474 (1974).
    [CrossRef]
  13. Y. K. Park, R. L. Byer, “Electronic Linewidth Narrowing Method for Single Axial Mode Operation of Q-Switched Nd:YAG Lasers,” Opt. Commun. 37, 411 (1981).
    [CrossRef]
  14. A. J. Berry, D. C. Hanna, C. G. Sawyers, “High Power Single Frequency Operation of a Q-Switched TEM00 Mode Nd:YAG Laser,” Opt. Commun. 40, 54 (1981).
    [CrossRef]
  15. W. D. Fountain, M. Bass, “Single-Axial-Mode Operation of a Polarization-Coupled Stable/Unstable-Resonator Nd:YAG Laser Oscillator,” IEEE J. Quantum Electron. QE-18, 432 (1982).
    [CrossRef]
  16. W. H. Glenn, “The Fluctuation Model of a Passively Mode-Locked Laser,” IEEE J. Quantum Electron. QE-11, 8 (1975).
    [CrossRef]

1982 (1)

W. D. Fountain, M. Bass, “Single-Axial-Mode Operation of a Polarization-Coupled Stable/Unstable-Resonator Nd:YAG Laser Oscillator,” IEEE J. Quantum Electron. QE-18, 432 (1982).
[CrossRef]

1981 (2)

Y. K. Park, R. L. Byer, “Electronic Linewidth Narrowing Method for Single Axial Mode Operation of Q-Switched Nd:YAG Lasers,” Opt. Commun. 37, 411 (1981).
[CrossRef]

A. J. Berry, D. C. Hanna, C. G. Sawyers, “High Power Single Frequency Operation of a Q-Switched TEM00 Mode Nd:YAG Laser,” Opt. Commun. 40, 54 (1981).
[CrossRef]

1978 (2)

A. D. E. Brown, “Unstable, Q-Switched, Ruby Resonator in the Negative Branch Confocal Configuration,” Opt. Commun. 27, 253 (1978).
[CrossRef]

A. H. Paxton, T. C. Salvi, “Unstable Resonator with Self-imaging Aperture,” Opt. Commun. 26, 305 (1978).
[CrossRef]

1976 (1)

1975 (1)

W. H. Glenn, “The Fluctuation Model of a Passively Mode-Locked Laser,” IEEE J. Quantum Electron. QE-11, 8 (1975).
[CrossRef]

1974 (2)

K. I. Zemskov, A. A. Isaev, M. A. Kazaryan, G. G. Petrash, S. G. Rautian, “Use of Unstable Resonators in Achieving the Diffraction Divergence of the Radiation Emitted from the High-Gain Pulsed Gas Lasers,” Sov. J. Quantum Electron. 4, 474 (1974).
[CrossRef]

T. F. Ewanizky, “A High Radiance Flashlamp Pumped Dye Laser,” Appl. Phys. Lett. 25, 295 (1974).
[CrossRef]

1969 (1)

W. F. Krupke, W. R. Sooy, “Properties of an Unstable Confocal Resonator CO2 Laser System,” IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

1967 (1)

A. E. Siegman, R. Arrathoon, “Modes in Unstable Optical Resonators and Lens Waveguides,” IEEE J. Quantum Electron. QE-3, 156 (1967).
[CrossRef]

1965 (1)

A. E. Siegman, “Unstable Optical Resonator for Laser Applications,” Proc.IEEE 53, 277 (1965).
[CrossRef]

1962 (1)

J. G. Skinner, J. E. Geusic, “Diffraction-Limited Ruby Oscillator,” J. Opt. Soc. Am. 52, A1319 (1962).

Arrathoon, R.

A. E. Siegman, R. Arrathoon, “Modes in Unstable Optical Resonators and Lens Waveguides,” IEEE J. Quantum Electron. QE-3, 156 (1967).
[CrossRef]

Bass, M.

W. D. Fountain, M. Bass, “Single-Axial-Mode Operation of a Polarization-Coupled Stable/Unstable-Resonator Nd:YAG Laser Oscillator,” IEEE J. Quantum Electron. QE-18, 432 (1982).
[CrossRef]

Berry, A. J.

A. J. Berry, D. C. Hanna, C. G. Sawyers, “High Power Single Frequency Operation of a Q-Switched TEM00 Mode Nd:YAG Laser,” Opt. Commun. 40, 54 (1981).
[CrossRef]

Brown, A. D. E.

A. D. E. Brown, “Unstable, Q-Switched, Ruby Resonator in the Negative Branch Confocal Configuration,” Opt. Commun. 27, 253 (1978).
[CrossRef]

Byer, R. L.

Y. K. Park, R. L. Byer, “Electronic Linewidth Narrowing Method for Single Axial Mode Operation of Q-Switched Nd:YAG Lasers,” Opt. Commun. 37, 411 (1981).
[CrossRef]

Craig, J. M.

Ewanizky, T. F.

T. F. Ewanizky, J. M. Craig, “Negative-Branch Unstable Resonator Nd:YAG Laser,” Appl. Opt. 15, 1465 (1976).
[CrossRef] [PubMed]

T. F. Ewanizky, “A High Radiance Flashlamp Pumped Dye Laser,” Appl. Phys. Lett. 25, 295 (1974).
[CrossRef]

Fountain, W. D.

W. D. Fountain, M. Bass, “Single-Axial-Mode Operation of a Polarization-Coupled Stable/Unstable-Resonator Nd:YAG Laser Oscillator,” IEEE J. Quantum Electron. QE-18, 432 (1982).
[CrossRef]

Geusic, J. E.

J. G. Skinner, J. E. Geusic, “Diffraction-Limited Ruby Oscillator,” J. Opt. Soc. Am. 52, A1319 (1962).

Glenn, W. H.

W. H. Glenn, “The Fluctuation Model of a Passively Mode-Locked Laser,” IEEE J. Quantum Electron. QE-11, 8 (1975).
[CrossRef]

Gobbi, P. G.

P. G. Gobbi, G. C. Reali, in preparation.

P. G. Gobbi, G. C. Reali, “A Novel Unstable Resonator Configuration with a Self Filtering Aperture,” to be published in Opt. Commun.

Hanna, D. C.

A. J. Berry, D. C. Hanna, C. G. Sawyers, “High Power Single Frequency Operation of a Q-Switched TEM00 Mode Nd:YAG Laser,” Opt. Commun. 40, 54 (1981).
[CrossRef]

Isaev, A. A.

K. I. Zemskov, A. A. Isaev, M. A. Kazaryan, G. G. Petrash, S. G. Rautian, “Use of Unstable Resonators in Achieving the Diffraction Divergence of the Radiation Emitted from the High-Gain Pulsed Gas Lasers,” Sov. J. Quantum Electron. 4, 474 (1974).
[CrossRef]

Kazaryan, M. A.

K. I. Zemskov, A. A. Isaev, M. A. Kazaryan, G. G. Petrash, S. G. Rautian, “Use of Unstable Resonators in Achieving the Diffraction Divergence of the Radiation Emitted from the High-Gain Pulsed Gas Lasers,” Sov. J. Quantum Electron. 4, 474 (1974).
[CrossRef]

Krupke, W. F.

W. F. Krupke, W. R. Sooy, “Properties of an Unstable Confocal Resonator CO2 Laser System,” IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

Park, Y. K.

Y. K. Park, R. L. Byer, “Electronic Linewidth Narrowing Method for Single Axial Mode Operation of Q-Switched Nd:YAG Lasers,” Opt. Commun. 37, 411 (1981).
[CrossRef]

Paxton, A. H.

A. H. Paxton, T. C. Salvi, “Unstable Resonator with Self-imaging Aperture,” Opt. Commun. 26, 305 (1978).
[CrossRef]

Petrash, G. G.

K. I. Zemskov, A. A. Isaev, M. A. Kazaryan, G. G. Petrash, S. G. Rautian, “Use of Unstable Resonators in Achieving the Diffraction Divergence of the Radiation Emitted from the High-Gain Pulsed Gas Lasers,” Sov. J. Quantum Electron. 4, 474 (1974).
[CrossRef]

Rautian, S. G.

K. I. Zemskov, A. A. Isaev, M. A. Kazaryan, G. G. Petrash, S. G. Rautian, “Use of Unstable Resonators in Achieving the Diffraction Divergence of the Radiation Emitted from the High-Gain Pulsed Gas Lasers,” Sov. J. Quantum Electron. 4, 474 (1974).
[CrossRef]

Reali, G. C.

P. G. Gobbi, G. C. Reali, in preparation.

P. G. Gobbi, G. C. Reali, “A Novel Unstable Resonator Configuration with a Self Filtering Aperture,” to be published in Opt. Commun.

Salvi, T. C.

A. H. Paxton, T. C. Salvi, “Unstable Resonator with Self-imaging Aperture,” Opt. Commun. 26, 305 (1978).
[CrossRef]

Sawyers, C. G.

A. J. Berry, D. C. Hanna, C. G. Sawyers, “High Power Single Frequency Operation of a Q-Switched TEM00 Mode Nd:YAG Laser,” Opt. Commun. 40, 54 (1981).
[CrossRef]

Siegman, A. E.

A. E. Siegman, R. Arrathoon, “Modes in Unstable Optical Resonators and Lens Waveguides,” IEEE J. Quantum Electron. QE-3, 156 (1967).
[CrossRef]

A. E. Siegman, “Unstable Optical Resonator for Laser Applications,” Proc.IEEE 53, 277 (1965).
[CrossRef]

Skinner, J. G.

J. G. Skinner, J. E. Geusic, “Diffraction-Limited Ruby Oscillator,” J. Opt. Soc. Am. 52, A1319 (1962).

Sooy, W. R.

W. F. Krupke, W. R. Sooy, “Properties of an Unstable Confocal Resonator CO2 Laser System,” IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

Steier, W. H.

We indicate here for simplicity only the more recent and comprehensive reviews on the subjects: for unstable resonators, W. H. Steier, in Laser Handbook, Vol. 3, M. L. Stitch, Ed. (North-Holland, Amsterdam, 1979), pp. 3–39;and for telescopic resonators, D. C. Hanna, C. G. Sawyers, M. A. Yuratich, “Large Volume TEM00 Mode Operation of Nd:YAG Lasers,” Opt. Quantum Electron. 13, 493 (1981).
[CrossRef]

Zemskov, K. I.

K. I. Zemskov, A. A. Isaev, M. A. Kazaryan, G. G. Petrash, S. G. Rautian, “Use of Unstable Resonators in Achieving the Diffraction Divergence of the Radiation Emitted from the High-Gain Pulsed Gas Lasers,” Sov. J. Quantum Electron. 4, 474 (1974).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

T. F. Ewanizky, “A High Radiance Flashlamp Pumped Dye Laser,” Appl. Phys. Lett. 25, 295 (1974).
[CrossRef]

IEEE J. Quantum Electron. (4)

W. F. Krupke, W. R. Sooy, “Properties of an Unstable Confocal Resonator CO2 Laser System,” IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

A. E. Siegman, R. Arrathoon, “Modes in Unstable Optical Resonators and Lens Waveguides,” IEEE J. Quantum Electron. QE-3, 156 (1967).
[CrossRef]

W. D. Fountain, M. Bass, “Single-Axial-Mode Operation of a Polarization-Coupled Stable/Unstable-Resonator Nd:YAG Laser Oscillator,” IEEE J. Quantum Electron. QE-18, 432 (1982).
[CrossRef]

W. H. Glenn, “The Fluctuation Model of a Passively Mode-Locked Laser,” IEEE J. Quantum Electron. QE-11, 8 (1975).
[CrossRef]

J. Opt. Soc. Am. (1)

J. G. Skinner, J. E. Geusic, “Diffraction-Limited Ruby Oscillator,” J. Opt. Soc. Am. 52, A1319 (1962).

Opt. Commun. (4)

Y. K. Park, R. L. Byer, “Electronic Linewidth Narrowing Method for Single Axial Mode Operation of Q-Switched Nd:YAG Lasers,” Opt. Commun. 37, 411 (1981).
[CrossRef]

A. J. Berry, D. C. Hanna, C. G. Sawyers, “High Power Single Frequency Operation of a Q-Switched TEM00 Mode Nd:YAG Laser,” Opt. Commun. 40, 54 (1981).
[CrossRef]

A. H. Paxton, T. C. Salvi, “Unstable Resonator with Self-imaging Aperture,” Opt. Commun. 26, 305 (1978).
[CrossRef]

A. D. E. Brown, “Unstable, Q-Switched, Ruby Resonator in the Negative Branch Confocal Configuration,” Opt. Commun. 27, 253 (1978).
[CrossRef]

Proc.IEEE (1)

A. E. Siegman, “Unstable Optical Resonator for Laser Applications,” Proc.IEEE 53, 277 (1965).
[CrossRef]

Sov. J. Quantum Electron. (1)

K. I. Zemskov, A. A. Isaev, M. A. Kazaryan, G. G. Petrash, S. G. Rautian, “Use of Unstable Resonators in Achieving the Diffraction Divergence of the Radiation Emitted from the High-Gain Pulsed Gas Lasers,” Sov. J. Quantum Electron. 4, 474 (1974).
[CrossRef]

Other (3)

P. G. Gobbi, G. C. Reali, in preparation.

We indicate here for simplicity only the more recent and comprehensive reviews on the subjects: for unstable resonators, W. H. Steier, in Laser Handbook, Vol. 3, M. L. Stitch, Ed. (North-Holland, Amsterdam, 1979), pp. 3–39;and for telescopic resonators, D. C. Hanna, C. G. Sawyers, M. A. Yuratich, “Large Volume TEM00 Mode Operation of Nd:YAG Lasers,” Opt. Quantum Electron. 13, 493 (1981).
[CrossRef]

P. G. Gobbi, G. C. Reali, “A Novel Unstable Resonator Configuration with a Self Filtering Aperture,” to be published in Opt. Commun.

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Figures (9)

Fig. 1
Fig. 1

Schematic of the self-imaging (a) and self-filtering (b) unstable resonators: M1,M2, fully reflecting concave mirrors of focal lengths f1f2; PH, pinhole of diameter 2a placed in the common focal plane of the two mirrors.

Fig. 2
Fig. 2

Plot of the SFUR mode intensity vs the normalized radius r/ρA; solid line, linear scale; broken line, logarithmic scale. The phase, not shown, is constant across the beam cross section at the cavity focal plane where the mode has been calculated. The vertical broken lines evidentiate the dimensions of the filtering aperture and of its magnified image; in this case |M| = 4.

Fig. 3
Fig. 3

Schematic of the YAG SFUR experimental arrangement: M1,M2, high reflectivity mirrors, f1 = +250 mm and f2 = +1000 mm (M = −4); PC, Pockels cell; PH, stainless steel pinhole, 0.8-mm diameter; POL, dielectric polarizer; QWP, muiltiple-order quarterwave plate; YAG, 6.35- × 101.6-mm rod; D, variable aperture diaphragm.

Fig. 4
Fig. 4

Q-switched energy output as a function of the pump level above threshold; crosses, experimental points (at 1-Hz repetition rate); broken line, best fit of data derived from the numerical solution of the rate equations in case of Q-switch and large concentrated losses.

Fig. 5
Fig. 5

Intensity spatial profiles of the SFUR mode as recorded with a photodiode array in the near field (50 cm from the output coupler) and for different energy levels, 50 mJ (a) and 150 mJ (b).

Fig. 6
Fig. 6

Burn paper records of the SFUR mode. The first five rows from the top were taken close to the outcoupling polarizer with increasing optical attenuations of the beam (attenuation factors: ×1, ×2, ×4, ×10, ×25). The last three rows are relative to the unattenuated beam in free propagation at distances of 10; 20; 30 m, respectively.

Fig. 7
Fig. 7

Plots of the percentage energy content as a function of the half-angle beam divergence as measured with calibrated apertures in the focus of a 1-m positive lens; (a) 40-mJ and (b) 150-mJ pulse energy. The experimental points are reported with circles and S.D. bars; note that at higher energies saturation effects give rise to a spread of the focused spot (narrower central peak and higher tails). The dotted line (the same in both plots) represents the focalizability prediction of the mode profile shown in Fig. 2 and truncated at its first zero; the solid curves are derived from an approximate numerical analysis of the loaded cavity, where the only input parameter was the population inversion above threshold, as deduced from the data of Fig. 4.

Fig. 8
Fig. 8

Temporal profiles of the mode-locking trains obtained from SFUR in very different conditions: (a) high-dye transmittance, integrated energy = 20 mJ; (b) low-dye transmittance, integrated energy = 17 mJ.

Fig. 9
Fig. 9

SFUR energy yield in fixed-Q operation as a function of the electrical pump energy for two values of the discharge capacitor.

Equations (6)

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a = ( 0 , 61 λ f 1 ) 1 / 2 .
SFUR condition a = ρ A = ( 0.61 λ f 1 ) 1 / 2 ;
confocality L = f 1 + f 2 ;
effective magnification M eff = 1.5 M = 1.5 f 2 / f 1 ,
collimated dimension : D = | M eff | 2 ρ A .
k = 1 + 2 ln ( c ) / ln ( | M | ) .

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