Abstract

Group velocity mismatch (GVM) is a major concern in the design of optical parametric amplifiers (OPAs) and generators (OPGs) for pulses shorter than a few picoseconds. By simplifying the coupled propagation equations and exploiting their scaling properties, the number of free parameters for a collinear OPA is reduced to a level where the parameter space can be studied systematically by simulations. The resulting set of figures show the combinations of material parameters and pulse lengths for which high performance can be achieved, and they can serve as a basis for a design.

© 2007 Optical Society of America

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References

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  1. A. P. Sukhorukov and A. K. Shchednova, "Parametric amplification of light in the field of a modulated laser wave," Sov. Phys. JETP 33, 677-682 (1971).
  2. G. A. Bukauskas, V. I. Kabelka, A. Piskarskas, and A. Y. Stabinis, "Features of three-photon parametric interaction of ultrashort light packets in the nonlinear amplification regime," Sov. J. Quantum Electron. 4, 290-292 (1974).
    [CrossRef]
  3. W. H. Glenn, "Parametric amplification of ultrashort laser pulses," Appl. Phys. Lett. 11, 333-335 (1967).
    [CrossRef]
  4. S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "H-5 - Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. 4, 598-605 (1968).
    [CrossRef]
  5. M. F. Becker, C. K. Young, S. R. Gautam, and E. J. Powers, "Three-wave nonlinear optical interactions in dispersive media," IEEE Journal of Quantum Electronics 18, 113-123 (1982).
    [CrossRef]
  6. R. Danielius, A. Piskarskas, A. Stabinis, G. P. Banfi, P. Di Trapani, and R. Righini, "Traveling-wave parametric generation of widely tunable highly coherent femtosecond light pulses," J. Opt. Soc. Am. B 10, 2222-2232 (1993).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. T. Nishikawa and N. Uesugi, "Transverse beam profiles on traveling-wave optical parametric generation in KTiOPO4 crystals," J. Appl. Phys. 78, 6361-6366 (1995).
    [CrossRef]
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    [CrossRef]
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  19. D. E. Zelmon, E. A. Hanning, and P. G. Schunemann, "Refractive-index measurements and Sellmeier coefficients for zinc-germanium phosphide from 2 to 9 m with implications for phase matching in optical frequencyconversion devices," J. Opt. Soc. Am. B 18, 1307-1310 (2001).
    [CrossRef]
  20. G. Arisholm, R. Paschotta, and T. S¨udmeyer, "Limits to the power scalability of high-gain optical parametric amplifiers," J. Opt. Soc. Am. B 21, 578-590 (2004).
    [CrossRef]

2004

2003

G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum. 71, 1-18 (2003).
[CrossRef]

2002

2001

1999

1997

1995

G. M. Gale, M. Cavallari, T. J. Driscoll, and F. Hache, "Sub-20-fs tunable pulses in the visible from an 82-MHz optical parametric oscillator," Opt. Lett. 20, 1562-1564 (1995).
[CrossRef] [PubMed]

T. Nishikawa and N. Uesugi, "Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals," J. Appl. Phys. 77, 4941-4947 (1995).
[CrossRef]

T. Nishikawa and N. Uesugi, "Transverse beam profiles on traveling-wave optical parametric generation in KTiOPO4 crystals," J. Appl. Phys. 78, 6361-6366 (1995).
[CrossRef]

1993

1988

1982

M. F. Becker, C. K. Young, S. R. Gautam, and E. J. Powers, "Three-wave nonlinear optical interactions in dispersive media," IEEE Journal of Quantum Electronics 18, 113-123 (1982).
[CrossRef]

1975

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strizhevskii, "Method for compensating the phasematching dispersion in nonlinear optics," Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

1974

G. A. Bukauskas, V. I. Kabelka, A. Piskarskas, and A. Y. Stabinis, "Features of three-photon parametric interaction of ultrashort light packets in the nonlinear amplification regime," Sov. J. Quantum Electron. 4, 290-292 (1974).
[CrossRef]

1971

A. P. Sukhorukov and A. K. Shchednova, "Parametric amplification of light in the field of a modulated laser wave," Sov. Phys. JETP 33, 677-682 (1971).

1968

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "H-5 - Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. 4, 598-605 (1968).
[CrossRef]

1967

W. H. Glenn, "Parametric amplification of ultrashort laser pulses," Appl. Phys. Lett. 11, 333-335 (1967).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "H-5 - Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. 4, 598-605 (1968).
[CrossRef]

Arisholm, G.

Banfi, G. P.

Becker, M. F.

M. F. Becker, C. K. Young, S. R. Gautam, and E. J. Powers, "Three-wave nonlinear optical interactions in dispersive media," IEEE Journal of Quantum Electronics 18, 113-123 (1982).
[CrossRef]

Biegert, J.

Bierlein, J. D.

Bukauskas, G. A.

G. A. Bukauskas, V. I. Kabelka, A. Piskarskas, and A. Y. Stabinis, "Features of three-photon parametric interaction of ultrashort light packets in the nonlinear amplification regime," Sov. J. Quantum Electron. 4, 290-292 (1974).
[CrossRef]

Cavallari, M.

Cerullo, G.

G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum. 71, 1-18 (2003).
[CrossRef]

Chirkin, A. S.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "H-5 - Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. 4, 598-605 (1968).
[CrossRef]

Danielius, R.

De Silvestri, S.

G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum. 71, 1-18 (2003).
[CrossRef]

Di Trapani, P.

Drabovich, K. N.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "H-5 - Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. 4, 598-605 (1968).
[CrossRef]

Driscoll, T. J.

Dubietis, A.

Gale, G. M.

Gautam, S. R.

M. F. Becker, C. K. Young, S. R. Gautam, and E. J. Powers, "Three-wave nonlinear optical interactions in dispersive media," IEEE Journal of Quantum Electronics 18, 113-123 (1982).
[CrossRef]

Glenn, W. H.

W. H. Glenn, "Parametric amplification of ultrashort laser pulses," Appl. Phys. Lett. 11, 333-335 (1967).
[CrossRef]

Hache, F.

Hanning, E. A.

Hauri, C. P.

Jundt, D. H.

Kabelka, V. I.

G. A. Bukauskas, V. I. Kabelka, A. Piskarskas, and A. Y. Stabinis, "Features of three-photon parametric interaction of ultrashort light packets in the nonlinear amplification regime," Sov. J. Quantum Electron. 4, 290-292 (1974).
[CrossRef]

Karpenko, S. G.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strizhevskii, "Method for compensating the phasematching dispersion in nonlinear optics," Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

Keller, U.

Khokhlov, R. V.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "H-5 - Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. 4, 598-605 (1968).
[CrossRef]

Kornienko, N. E.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strizhevskii, "Method for compensating the phasematching dispersion in nonlinear optics," Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

Kovrigin, A. I.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "H-5 - Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. 4, 598-605 (1968).
[CrossRef]

McCarthy, N.

Nishikawa, T.

T. Nishikawa and N. Uesugi, "Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals," J. Appl. Phys. 77, 4941-4947 (1995).
[CrossRef]

T. Nishikawa and N. Uesugi, "Transverse beam profiles on traveling-wave optical parametric generation in KTiOPO4 crystals," J. Appl. Phys. 78, 6361-6366 (1995).
[CrossRef]

Paschotta, R.

Piche, M.

Piskarskas, A.

Powers, E. J.

M. F. Becker, C. K. Young, S. R. Gautam, and E. J. Powers, "Three-wave nonlinear optical interactions in dispersive media," IEEE Journal of Quantum Electronics 18, 113-123 (1982).
[CrossRef]

Righini, R.

Rousseau, G.

Schlup, P.

Schunemann, P. G.

Shchednova, A. K.

A. P. Sukhorukov and A. K. Shchednova, "Parametric amplification of light in the field of a modulated laser wave," Sov. Phys. JETP 33, 677-682 (1971).

Smith, A. V.

Stabinis, A.

Stabinis, A. Y.

G. A. Bukauskas, V. I. Kabelka, A. Piskarskas, and A. Y. Stabinis, "Features of three-photon parametric interaction of ultrashort light packets in the nonlinear amplification regime," Sov. J. Quantum Electron. 4, 290-292 (1974).
[CrossRef]

Strizhevskii, V. L.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strizhevskii, "Method for compensating the phasematching dispersion in nonlinear optics," Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

Sukhorukov, A. P.

A. P. Sukhorukov and A. K. Shchednova, "Parametric amplification of light in the field of a modulated laser wave," Sov. Phys. JETP 33, 677-682 (1971).

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "H-5 - Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. 4, 598-605 (1968).
[CrossRef]

Tamosauskas, G.

Uesugi, N.

T. Nishikawa and N. Uesugi, "Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals," J. Appl. Phys. 77, 4941-4947 (1995).
[CrossRef]

T. Nishikawa and N. Uesugi, "Transverse beam profiles on traveling-wave optical parametric generation in KTiOPO4 crystals," J. Appl. Phys. 78, 6361-6366 (1995).
[CrossRef]

Valiulis, G.

Vanherzeele, H.

Volosov, V. D.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strizhevskii, "Method for compensating the phasematching dispersion in nonlinear optics," Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

Young, C. K.

M. F. Becker, C. K. Young, S. R. Gautam, and E. J. Powers, "Three-wave nonlinear optical interactions in dispersive media," IEEE Journal of Quantum Electronics 18, 113-123 (1982).
[CrossRef]

Zelmon, D. E.

Zumsteg, F. C.

Appl. Opt.

Appl. Phys. Lett.

W. H. Glenn, "Parametric amplification of ultrashort laser pulses," Appl. Phys. Lett. 11, 333-335 (1967).
[CrossRef]

IEEE J. Quantum Electron.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "H-5 - Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. 4, 598-605 (1968).
[CrossRef]

IEEE Journal of Quantum Electronics

M. F. Becker, C. K. Young, S. R. Gautam, and E. J. Powers, "Three-wave nonlinear optical interactions in dispersive media," IEEE Journal of Quantum Electronics 18, 113-123 (1982).
[CrossRef]

J. Appl. Phys.

T. Nishikawa and N. Uesugi, "Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals," J. Appl. Phys. 77, 4941-4947 (1995).
[CrossRef]

T. Nishikawa and N. Uesugi, "Transverse beam profiles on traveling-wave optical parametric generation in KTiOPO4 crystals," J. Appl. Phys. 78, 6361-6366 (1995).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Rev. Sci. Instrum.

G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum. 71, 1-18 (2003).
[CrossRef]

Sov. J. Quantum Electron.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strizhevskii, "Method for compensating the phasematching dispersion in nonlinear optics," Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

G. A. Bukauskas, V. I. Kabelka, A. Piskarskas, and A. Y. Stabinis, "Features of three-photon parametric interaction of ultrashort light packets in the nonlinear amplification regime," Sov. J. Quantum Electron. 4, 290-292 (1974).
[CrossRef]

Sov. Phys. JETP

A. P. Sukhorukov and A. K. Shchednova, "Parametric amplification of light in the field of a modulated laser wave," Sov. Phys. JETP 33, 677-682 (1971).

Supplementary Material (2)

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Figures (9)

Fig. 1.
Fig. 1.

Power of idler (red), signal (blue) and pump (black) at different positions in the crystal (shown in each graph). The pulses are plotted in the frame moving with beam 1. The input pump pulse is shown by the dashed curve in the top row, and the vertical scale is the same for all the graphs. T and n g,3 are shown above each column. The movie shows the evolution of the pulses in (a) in smaller steps (1.8 MB). [Media 1]

Fig. 2.
Fig. 2.

Logarithm of signal amplitude gain vs. crystal length for various pulse lengths (shown in legend, in ps) and (a) n g,3 = 1.63, (b) n g,3 = 1.66, (c) n g,3 = 1.69, and (d) n g,3 = 2.0. The plateau at gain ≈ 13 corresponds to saturation of the gain by pump depletion.

Fig. 3.
Fig. 3.

Simulation results for n g,3 = 1.63. (a) Conversion efficiency as a function of L and T. The T-axis is nonlinear to show every sample point with the same size. (b) Idler pulse quality. The product has been normalised to the value for a transform-limited Gaussian pulse, so unity corresponds to the minimum time bandwidth product. The colour scale stops at 10. (c) Conversion efficiency as a function of crystal length for a few different pulse lengths (same data as in part (a)). The legend shows the pulse length in ps. The oscillations with z (for the long pulses) are due to repeated conversion and back conversion. (d) Time bandwidth products corresponding to part (c) (same data as in part (b)).

Fig. 4.
Fig. 4.

Like Fig. 3, but with (a,b) n g,3 = 1.645, (c,d) n g,3 = 1.66, (e,f) n g,3 = 1.72, (g,h) n g,3 = 1.8, and (i,j) n g,3 = 2.0. The colour scale for the pulse quality runs from 1 to 10, as in Fig. 3(b).

Fig. 5.
Fig. 5.

Conversion efficiency as a function of n g,3 for T=200 fs. The vertical lines mark n g,1 =1.6 and n g,2 = 1.66 and the legend shows the position in the crystal, in mm.

Fig. 6.
Fig. 6.

Conversion efficiency and pulse quality with seed intensity 10 W/cm2 (1000 times greater than in Figs. 3–4). (a,b) n g,3 = 1.63 (as in Fig. 3), (c,d) n g,3 = 2.0 (as in Fig. 4(i,j)). The colour scale for the pulse quality runs from 1 to 10, as in Fig. 3(b).

Fig. 7.
Fig. 7.

Conversion efficiency and pulse quality from OPGs, as functions of crystal length and pump pulse length. (a,b) n g,3 = 1.63 (as in Fig. 3), (c,d) n g,3 = 1.66 (as in Fig. 4(c,d)), and (e,f) n g,3 = 1.80 (as in Fig. 4(g,h)).

Fig. 8.
Fig. 8.

Conversion efficiency (blue), pulse quality (black) and beam quality (red) as functions of crystal length z. In order to show all quantities conveniently in the same graph, pulse and beam quality are plotted as the inverse of the time-bandwidth product and M 2, respectively. n g,3 = 1.63 in the top row (a–d) and 1.80 in the bottom row (e–h). The pump pulse length (in ps) and pump beam waist radius (in μm) are given on each graph.

Fig. 9.
Fig. 9.

(a) Signal intensity vs. radial position and time for n g,3 = 1.63, T = 3ps, w 0 = 200 μm, and position z = 7 mm. The movie shows the evolution of all three pulses along z (520 kB). (b) Normalised signal power at z = 7 mm. (c) Normalised signal fluence at z = 7 mm. [Media 2]

Tables (2)

Tables Icon

Table 1. Physical parameters assumed in the simulations. Exceptions are noted in the text or figure captions. The normalised pump amplitude corresponding to these parameters is up = 3.84·103 m-1. n g,3 takes the values 1.63, 1.645, 1.66, 1.69, 1.72, 1.8 and 2, and results for n g,3 < (n g,1 + n g,2)/2 follow from symmetry.

Tables Icon

Table 2. Parameters, scaling factors and relevant figure for various examples. The beams have been ordered so that n g,1 < n g,2. In the polarization row, F indicates fast and S indicates slow. of-elem. shows the value used for the relevant element of the nonlinear tensor. T′ and L c are a pair of suitable parameters selected from the figure, and T and Lc are the corresponding scaled parameters for the example.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

I j = 2 n j e j 2 Z 0 ,
e 1 z + n g , 1 c e 1 t = i ω 1 χ eff n 1 c e 3 e 2 * exp ( i Δ kz )
e 2 z + n g , 2 c e 2 t = i ω 2 χ eff n 2 c e 3 e 1 * exp ( i Δ kz )
e 3 z + n g , 3 c e 3 t = i ω 3 χ eff n 3 c e 1 e 2 exp ( i Δ kz ) ,
u j = e j χ eff c ( ω 1 ω 2 ω 3 n j n 1 n 2 n 3 ω j ) 1 2 .
u 1 z = iu 3 u 2 *
u 2 z + δn g , 2 c u 2 t = iu 3 u 1 *
u 3 z + δn g , 3 c u 3 t = iu 1 u 2 ,
u 1 z δn g , 2 c u 1 t = iu 3 u 2 *
u 2 z = iu 3 u 1 *
u 3 z + n g , 3 n g , 2 c u 3 t = iu 1 u 2 ,
L e ( T ) = KcT δn g , p ,
T min = gδn g , p ( Kcu p ) .
u p = χ eff c ( I p Z 0 2 n 3 ) 1 2 ( ω 1 ω 2 ω 3 n j n 1 n 2 n 3 ω j ) 1 2 .

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