Abstract

A novel non-planar ring cavity is presented. It is shown that by using a fractional image rotation, i.e. a rotation whose angle cannot be expressed as 2π/n, where n is a small integer, the number of modes that can oscillate in the cavity is greatly reduced. This Fractional Image Rotation Enhancement (FIRE) cavity can thus be used to increase the beam quality in cases of low transversal mode discrimination, such as lasers with large pump and beam size and high-pulse-energy optical parametric oscillators (OPOs), especially when compactness and efficiency are key parameters. The experimental results obtained with a FIRE OPO for mid-IR (3–5 μm) generation based on a ZnGeP2 crystal pumped by a Ho3+:LiLuF4 MOPA system at 2.05 μm are compared to those realized with the same crystal and pump arrangement using a standard Rotated Image Singly-Resonant Twisted RectAngle (RISTRA) cavity. An increase of the beam quality from M2 of 2.08–2.29 to M2 of 1.88–1.99 is reached at 20 mJ pulse energy when the FIRE cavity is used.

© 2014 Optical Society of America

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References

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  1. A. Dergachev, D. Armstrong, A. Smith, T. Drake, and M. Dubois, “3.4-μm ZGP RISTRA nanosecond optical parametric oscillator pumped by a 2.05-μm Ho:YLF MOPA system,” Opt. Express15, 14404–14413 (2007).
    [CrossRef] [PubMed]
  2. M. Eichhorn, G. Stoeppler, M. Schellhorn, K. T. Zawilski, and P. G. Schunemann, “Gaussian- versus flat-top-pumping of a mid-IR ZGP RISTRA OPO,” Appl. Phys. B108, 109–115 (2012).
    [CrossRef]
  3. G. Stöppler, M. Schellhorn, and M. Eichhorn, “Enhanced beam quality for medical applications at 6.45 μm by using a RISTRA ZGP OPO,” Laser Physics22, 1095–1098 (2012).
    [CrossRef]
  4. G. Marchev, A. Tyazhev, V. Petrov, P. G. Schunemann, K. T. Zawilski, G. Stöppler, and M. Eichhorn, “Optical parametric generation in CdSiP2at 6.125 μm pumped by 8 ns long pulses at 1064 nm,” Opt. Lett.37, 740–742 (2012).
    [CrossRef] [PubMed]
  5. C. Kieleck, M. Eichhorn, A. Hirth, D. Faye, and E. Lallier, “High-efficiency 20-50 kHz mid-infrared orientation-patterned GaAs optical parametric oscillator pumped by a 2 μm Holmium laser,” Opt. Lett.34, 262–264 (2009).
    [CrossRef] [PubMed]
  6. A. V. Smith and D. J. Armstrong, “Nanosecond optical parametric oscillator with 90° image rotation: design and performance,” J. Opt. Soc. Am. B19, 1801–1814 (2002).
    [CrossRef]
  7. A. C. Nilsson, E. K. Gustafson, and R. L. Byer, “Eigenpolarization theory of monolithic nonplanar ring oscillators,” IEEE J. Quantum Electron.25, 767–790 (1989).
    [CrossRef]
  8. C. Gao, L. Zhu, R. Wang, M. Gao, Y. Zheng, and L. Wang, “6.1 W single frequency laser output at 1645 nm from a resonantly pumped Er:YAG nonplanar ring oscillator,” Optics Lett.37, 1859–1861 (2012).
    [CrossRef]
  9. J. A. Arnaud, “Nonorthogonal optical waveguides and resonators,” Bell Syst. Tech. J.492311–2348 (1970).
    [CrossRef]
  10. A. E. Siegman, Lasers (University Science Books, 1986).
  11. R. Borghi and M. Santarsiero, “Modal structure analysis for a class of axially symmetric flat-topped laser beams,” IEEE J. Quantum Electron, 35, 745–750 (1999).
    [CrossRef]
  12. I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, 7th edition (Academic Press, 2007).
  13. I. Kimel and L. R. Elias, “Relations between Hermite and Laguerre Gaussian modes,” IEEE J. Quantum Electron, 29, 2562–2567 (1993).
    [CrossRef]
  14. M. Schellhorn, “High-energy, in-band pumped Q-switched Ho3+:LuLiF4 2 μm laser,” Opt. Lett.35, 2609–2611 (2010).
    [CrossRef] [PubMed]
  15. M. Schellhorn and Marc Eichhorn, “High-energy Ho:LLF MOPA laser system using a top-hat pump profile for the amplifier stage,” Appl. Phys. B109, 351–357 (2012).
    [CrossRef]
  16. Y. A. Anan’ev, Laser resonators and the beam divergence problem (Adam Hilger, 1992).
  17. SNLO program, http://as-photonics.com/RISTRA-Modeling.html , AS Photonics LLC.

2012 (5)

M. Eichhorn, G. Stoeppler, M. Schellhorn, K. T. Zawilski, and P. G. Schunemann, “Gaussian- versus flat-top-pumping of a mid-IR ZGP RISTRA OPO,” Appl. Phys. B108, 109–115 (2012).
[CrossRef]

G. Stöppler, M. Schellhorn, and M. Eichhorn, “Enhanced beam quality for medical applications at 6.45 μm by using a RISTRA ZGP OPO,” Laser Physics22, 1095–1098 (2012).
[CrossRef]

G. Marchev, A. Tyazhev, V. Petrov, P. G. Schunemann, K. T. Zawilski, G. Stöppler, and M. Eichhorn, “Optical parametric generation in CdSiP2at 6.125 μm pumped by 8 ns long pulses at 1064 nm,” Opt. Lett.37, 740–742 (2012).
[CrossRef] [PubMed]

C. Gao, L. Zhu, R. Wang, M. Gao, Y. Zheng, and L. Wang, “6.1 W single frequency laser output at 1645 nm from a resonantly pumped Er:YAG nonplanar ring oscillator,” Optics Lett.37, 1859–1861 (2012).
[CrossRef]

M. Schellhorn and Marc Eichhorn, “High-energy Ho:LLF MOPA laser system using a top-hat pump profile for the amplifier stage,” Appl. Phys. B109, 351–357 (2012).
[CrossRef]

2010 (1)

2009 (1)

2007 (1)

2002 (1)

1999 (1)

R. Borghi and M. Santarsiero, “Modal structure analysis for a class of axially symmetric flat-topped laser beams,” IEEE J. Quantum Electron, 35, 745–750 (1999).
[CrossRef]

1993 (1)

I. Kimel and L. R. Elias, “Relations between Hermite and Laguerre Gaussian modes,” IEEE J. Quantum Electron, 29, 2562–2567 (1993).
[CrossRef]

1989 (1)

A. C. Nilsson, E. K. Gustafson, and R. L. Byer, “Eigenpolarization theory of monolithic nonplanar ring oscillators,” IEEE J. Quantum Electron.25, 767–790 (1989).
[CrossRef]

1970 (1)

J. A. Arnaud, “Nonorthogonal optical waveguides and resonators,” Bell Syst. Tech. J.492311–2348 (1970).
[CrossRef]

Anan’ev, Y. A.

Y. A. Anan’ev, Laser resonators and the beam divergence problem (Adam Hilger, 1992).

Armstrong, D.

Armstrong, D. J.

Arnaud, J. A.

J. A. Arnaud, “Nonorthogonal optical waveguides and resonators,” Bell Syst. Tech. J.492311–2348 (1970).
[CrossRef]

Borghi, R.

R. Borghi and M. Santarsiero, “Modal structure analysis for a class of axially symmetric flat-topped laser beams,” IEEE J. Quantum Electron, 35, 745–750 (1999).
[CrossRef]

Byer, R. L.

A. C. Nilsson, E. K. Gustafson, and R. L. Byer, “Eigenpolarization theory of monolithic nonplanar ring oscillators,” IEEE J. Quantum Electron.25, 767–790 (1989).
[CrossRef]

Dergachev, A.

Drake, T.

Dubois, M.

Eichhorn, M.

M. Eichhorn, G. Stoeppler, M. Schellhorn, K. T. Zawilski, and P. G. Schunemann, “Gaussian- versus flat-top-pumping of a mid-IR ZGP RISTRA OPO,” Appl. Phys. B108, 109–115 (2012).
[CrossRef]

G. Stöppler, M. Schellhorn, and M. Eichhorn, “Enhanced beam quality for medical applications at 6.45 μm by using a RISTRA ZGP OPO,” Laser Physics22, 1095–1098 (2012).
[CrossRef]

G. Marchev, A. Tyazhev, V. Petrov, P. G. Schunemann, K. T. Zawilski, G. Stöppler, and M. Eichhorn, “Optical parametric generation in CdSiP2at 6.125 μm pumped by 8 ns long pulses at 1064 nm,” Opt. Lett.37, 740–742 (2012).
[CrossRef] [PubMed]

C. Kieleck, M. Eichhorn, A. Hirth, D. Faye, and E. Lallier, “High-efficiency 20-50 kHz mid-infrared orientation-patterned GaAs optical parametric oscillator pumped by a 2 μm Holmium laser,” Opt. Lett.34, 262–264 (2009).
[CrossRef] [PubMed]

Eichhorn, Marc

M. Schellhorn and Marc Eichhorn, “High-energy Ho:LLF MOPA laser system using a top-hat pump profile for the amplifier stage,” Appl. Phys. B109, 351–357 (2012).
[CrossRef]

Elias, L. R.

I. Kimel and L. R. Elias, “Relations between Hermite and Laguerre Gaussian modes,” IEEE J. Quantum Electron, 29, 2562–2567 (1993).
[CrossRef]

Faye, D.

Gao, C.

C. Gao, L. Zhu, R. Wang, M. Gao, Y. Zheng, and L. Wang, “6.1 W single frequency laser output at 1645 nm from a resonantly pumped Er:YAG nonplanar ring oscillator,” Optics Lett.37, 1859–1861 (2012).
[CrossRef]

Gao, M.

C. Gao, L. Zhu, R. Wang, M. Gao, Y. Zheng, and L. Wang, “6.1 W single frequency laser output at 1645 nm from a resonantly pumped Er:YAG nonplanar ring oscillator,” Optics Lett.37, 1859–1861 (2012).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, 7th edition (Academic Press, 2007).

Gustafson, E. K.

A. C. Nilsson, E. K. Gustafson, and R. L. Byer, “Eigenpolarization theory of monolithic nonplanar ring oscillators,” IEEE J. Quantum Electron.25, 767–790 (1989).
[CrossRef]

Hirth, A.

Kieleck, C.

Kimel, I.

I. Kimel and L. R. Elias, “Relations between Hermite and Laguerre Gaussian modes,” IEEE J. Quantum Electron, 29, 2562–2567 (1993).
[CrossRef]

Lallier, E.

Marchev, G.

Nilsson, A. C.

A. C. Nilsson, E. K. Gustafson, and R. L. Byer, “Eigenpolarization theory of monolithic nonplanar ring oscillators,” IEEE J. Quantum Electron.25, 767–790 (1989).
[CrossRef]

Petrov, V.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, 7th edition (Academic Press, 2007).

Santarsiero, M.

R. Borghi and M. Santarsiero, “Modal structure analysis for a class of axially symmetric flat-topped laser beams,” IEEE J. Quantum Electron, 35, 745–750 (1999).
[CrossRef]

Schellhorn, M.

M. Schellhorn and Marc Eichhorn, “High-energy Ho:LLF MOPA laser system using a top-hat pump profile for the amplifier stage,” Appl. Phys. B109, 351–357 (2012).
[CrossRef]

G. Stöppler, M. Schellhorn, and M. Eichhorn, “Enhanced beam quality for medical applications at 6.45 μm by using a RISTRA ZGP OPO,” Laser Physics22, 1095–1098 (2012).
[CrossRef]

M. Eichhorn, G. Stoeppler, M. Schellhorn, K. T. Zawilski, and P. G. Schunemann, “Gaussian- versus flat-top-pumping of a mid-IR ZGP RISTRA OPO,” Appl. Phys. B108, 109–115 (2012).
[CrossRef]

M. Schellhorn, “High-energy, in-band pumped Q-switched Ho3+:LuLiF4 2 μm laser,” Opt. Lett.35, 2609–2611 (2010).
[CrossRef] [PubMed]

Schunemann, P. G.

M. Eichhorn, G. Stoeppler, M. Schellhorn, K. T. Zawilski, and P. G. Schunemann, “Gaussian- versus flat-top-pumping of a mid-IR ZGP RISTRA OPO,” Appl. Phys. B108, 109–115 (2012).
[CrossRef]

G. Marchev, A. Tyazhev, V. Petrov, P. G. Schunemann, K. T. Zawilski, G. Stöppler, and M. Eichhorn, “Optical parametric generation in CdSiP2at 6.125 μm pumped by 8 ns long pulses at 1064 nm,” Opt. Lett.37, 740–742 (2012).
[CrossRef] [PubMed]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Smith, A.

Smith, A. V.

Stoeppler, G.

M. Eichhorn, G. Stoeppler, M. Schellhorn, K. T. Zawilski, and P. G. Schunemann, “Gaussian- versus flat-top-pumping of a mid-IR ZGP RISTRA OPO,” Appl. Phys. B108, 109–115 (2012).
[CrossRef]

Stöppler, G.

G. Stöppler, M. Schellhorn, and M. Eichhorn, “Enhanced beam quality for medical applications at 6.45 μm by using a RISTRA ZGP OPO,” Laser Physics22, 1095–1098 (2012).
[CrossRef]

G. Marchev, A. Tyazhev, V. Petrov, P. G. Schunemann, K. T. Zawilski, G. Stöppler, and M. Eichhorn, “Optical parametric generation in CdSiP2at 6.125 μm pumped by 8 ns long pulses at 1064 nm,” Opt. Lett.37, 740–742 (2012).
[CrossRef] [PubMed]

Tyazhev, A.

Wang, L.

C. Gao, L. Zhu, R. Wang, M. Gao, Y. Zheng, and L. Wang, “6.1 W single frequency laser output at 1645 nm from a resonantly pumped Er:YAG nonplanar ring oscillator,” Optics Lett.37, 1859–1861 (2012).
[CrossRef]

Wang, R.

C. Gao, L. Zhu, R. Wang, M. Gao, Y. Zheng, and L. Wang, “6.1 W single frequency laser output at 1645 nm from a resonantly pumped Er:YAG nonplanar ring oscillator,” Optics Lett.37, 1859–1861 (2012).
[CrossRef]

Zawilski, K. T.

G. Marchev, A. Tyazhev, V. Petrov, P. G. Schunemann, K. T. Zawilski, G. Stöppler, and M. Eichhorn, “Optical parametric generation in CdSiP2at 6.125 μm pumped by 8 ns long pulses at 1064 nm,” Opt. Lett.37, 740–742 (2012).
[CrossRef] [PubMed]

M. Eichhorn, G. Stoeppler, M. Schellhorn, K. T. Zawilski, and P. G. Schunemann, “Gaussian- versus flat-top-pumping of a mid-IR ZGP RISTRA OPO,” Appl. Phys. B108, 109–115 (2012).
[CrossRef]

Zheng, Y.

C. Gao, L. Zhu, R. Wang, M. Gao, Y. Zheng, and L. Wang, “6.1 W single frequency laser output at 1645 nm from a resonantly pumped Er:YAG nonplanar ring oscillator,” Optics Lett.37, 1859–1861 (2012).
[CrossRef]

Zhu, L.

C. Gao, L. Zhu, R. Wang, M. Gao, Y. Zheng, and L. Wang, “6.1 W single frequency laser output at 1645 nm from a resonantly pumped Er:YAG nonplanar ring oscillator,” Optics Lett.37, 1859–1861 (2012).
[CrossRef]

Appl. Phys. B (2)

M. Eichhorn, G. Stoeppler, M. Schellhorn, K. T. Zawilski, and P. G. Schunemann, “Gaussian- versus flat-top-pumping of a mid-IR ZGP RISTRA OPO,” Appl. Phys. B108, 109–115 (2012).
[CrossRef]

M. Schellhorn and Marc Eichhorn, “High-energy Ho:LLF MOPA laser system using a top-hat pump profile for the amplifier stage,” Appl. Phys. B109, 351–357 (2012).
[CrossRef]

Bell Syst. Tech. J. (1)

J. A. Arnaud, “Nonorthogonal optical waveguides and resonators,” Bell Syst. Tech. J.492311–2348 (1970).
[CrossRef]

IEEE J. Quantum Electron (2)

R. Borghi and M. Santarsiero, “Modal structure analysis for a class of axially symmetric flat-topped laser beams,” IEEE J. Quantum Electron, 35, 745–750 (1999).
[CrossRef]

I. Kimel and L. R. Elias, “Relations between Hermite and Laguerre Gaussian modes,” IEEE J. Quantum Electron, 29, 2562–2567 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. C. Nilsson, E. K. Gustafson, and R. L. Byer, “Eigenpolarization theory of monolithic nonplanar ring oscillators,” IEEE J. Quantum Electron.25, 767–790 (1989).
[CrossRef]

J. Opt. Soc. Am. B (1)

Laser Physics (1)

G. Stöppler, M. Schellhorn, and M. Eichhorn, “Enhanced beam quality for medical applications at 6.45 μm by using a RISTRA ZGP OPO,” Laser Physics22, 1095–1098 (2012).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Optics Lett. (1)

C. Gao, L. Zhu, R. Wang, M. Gao, Y. Zheng, and L. Wang, “6.1 W single frequency laser output at 1645 nm from a resonantly pumped Er:YAG nonplanar ring oscillator,” Optics Lett.37, 1859–1861 (2012).
[CrossRef]

Other (4)

Y. A. Anan’ev, Laser resonators and the beam divergence problem (Adam Hilger, 1992).

SNLO program, http://as-photonics.com/RISTRA-Modeling.html , AS Photonics LLC.

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, 7th edition (Academic Press, 2007).

A. E. Siegman, Lasers (University Science Books, 1986).

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Figures (7)

Fig. 1:
Fig. 1:

Calculated number of modes for the different types of resonators as a function of the beam size relative to the fundamental mode size.

Fig. 2:
Fig. 2:

Intensity of the beam obtained form Eq. (2b) (non image-rotating case, top left) and Eq. (2d) (FIRE case, bottom left). On the right, the calculated distribution of the LG(l, p) modal weights for the two cases under investigation are shown. Height of the bars are proportional to the corresponding modal weights. Note that since λl,p = λl,p, only the modal weights for modes having l > 0 are reported here.

Fig. 3:
Fig. 3:

Schematic of the experimental set-up used fir the current work. The same set-up can either accommodate a RISTRA or a FIRE cavity.

Fig. 4:
Fig. 4:

Spectral profile of the Ho3+:LLF MOPA pump system.

Fig. 5:
Fig. 5:

OPO output performance obtained from FIRE and RISTRA cavity under identical conditions (100 Hz, 30 ns pumped at 2.053 μm).

Fig. 6:
Fig. 6:

OPO output performance simulated using the SNLO software [17].

Fig. 7:
Fig. 7:

Beam propagation factor measurement for signal and idler in the case of RISTRA (top) and FIRE (bottom) cavities.

Equations (26)

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LG l , p ( ρ , φ ) e i l φ ( 2 ρ ) | l | L p | l | ( 4 ρ 2 ) e ρ 2 e i ( π R λ π 4 ( 2 p + l + 1 ) ) f ( ρ ) e i l φ
U ( θ ) = e θ φ = k = 0 1 k ! ( θ ) k k φ k
U ( θ ) LG l , p ( ρ , φ ) f ( ρ ) k = 0 1 k ! ( θ ) k k φ k e i l φ f ( ρ ) e i l φ k = 0 1 k ! ( θ ) k ( i l ) k f ( ρ ) e i l φ e i l θ ,
e i l θ = 1 l = 2 π n θ with n { , 2 , 1 , 0 , 1 , 2 , } .
w eff = w 0 2 p + | l | + 1 ,
2 p + | l | + 1 w max w 0 = x .
M 2 = ( w eff w 0 ) 2 = 2 p + | l | + 1 .
E ( r , φ ) = n = 0 p = 0 r n , p ψ l , p ( r , φ )
E ( r , φ ) = n = 0 p = 0 r n , p ψ 4 n , p ( r , φ )
E ( r , φ ) = p = 0 f p ψ 0 , p ( r , φ )
M 2 = l = 0 p = 0 | c l , p | 2 ( 2 p + | l | + 1 ) M R 2 = n = 0 p = 0 | r n , p | 2 ( 2 p + 4 n + 1 ) M F 2 = p = 0 | f p | 2 ( 2 p + 1 )
I ( x , y ) = n , m λ n , m | ψ n , m ( x , y ) | 2
λ n , m = 4 π 4 v 0 4 0 0 I ˜ ( p , q ) n ( π 2 v 0 2 p 2 ) m ( π 2 v 0 2 q 2 ) p q d p d q
n ( t ) = L n ( t ) exp ( t / 2 ) ,
I ( r , w 0 ) = exp [ ( N + 1 ) r 2 w 0 2 ] n = 0 N 1 n ! [ ( N + 1 ) r 2 w 0 2 ] n
I ˜ ( p , q ) = π α L N 1 [ π 2 α ( p 2 + q 2 ) ] exp [ π 2 α ( p 2 + q 2 ) ]
L N 1 ( x + y ) = k = 0 N L k ( x ) L N k ( y )
I ˜ ( p , q ) = π α k = 0 N L k ( π 2 p 2 α ) L N k ( π 2 q 2 α ) exp [ π 2 α ( p 2 + q 2 ) ]
λ n , m = 4 π 5 v 0 4 α k = 0 N 0 0 L k ( π 2 p 2 α ) L N k ( π 2 q 2 α ) × exp [ π 2 α ( p 2 + q 2 ) ] n ( π 2 v 0 2 p 2 ) m ( π 2 v 0 2 q 2 ) p q d p d q
λ n , m = π 5 v 0 4 α k = 0 N [ 0 e ( μ + λ / 2 ) x L k ( μ x ) L n ( λ x ) d x × 0 e ( μ + λ / 2 ) y L N k ( μ y ) L m ( λ y ) d y ]
0 e b x x α L n α ( λ x ) L m α ( μ x ) d x = Γ ( m + n + α + 1 ) m ! n ! ( b λ ) n ( b μ ) m b m + n + α + 1 d x × F [ m , n ; m n α , b ( b λ μ ) ( b μ ) ( b λ ) ]
0 e ( μ + λ / 2 ) b x L n ( λ x ) L m ( μ x ) d x = Γ ( m + n + 1 ) m ! n ! ( μ λ / 2 ) n ( λ / 2 ) m ( μ + λ / 2 ) m + n + 1 × F [ m , n ; m n , λ / 2 + μ λ / 2 μ ]
λ n , m = π 5 v 0 4 α k = 0 N { c k , n , m F [ k , n ; k n , λ / 2 + μ λ / 2 μ ] × F [ N k , m ; N + k m , λ / 2 + μ λ / 2 μ ] }
c k , n , m = ( k + n ) ! ( N k + m ) ! k ! n ! ( N k ) ! m ! ( μ λ / 2 ) n + m ( λ / 2 ) N ( μ + λ / 2 ) N + m + n + 2
c l , p = 0 2 π 0 E ( r , φ ) ψ l , p * ( r , φ ) r d r d φ
c l , p = 0 E ( r ) ψ l , p ( r ) r d r 0 2 π e i l φ d φ

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