Abstract

We present numerical investigations of parametric transfer in synchronously pumped optical parametric oscillators (SPOPOs) used for indirect mid-infrared pulse shaping. The introduction of an optical bandpass filter in the resonator results in transfer of intensity and phase profile of the input pump onto the output idler pulse. We investigate the effect of resonator parameters, process nonlinearity, and chromatic dispersion of the nonlinear crystal, on the SPOPO behavior and the transfer fidelity. We show numerically that parametric transfer from a broad-bandwidth pump pulse can be achieved with good fidelity and high efficiency for a broad range of parameters in a periodically poled lithium niobate SPOPO.

© 2007 Optical Society of America

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  1. H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, "Whither the future of controlling quantum phenomena?" Science 288, 824-828 (2000).
    [CrossRef] [PubMed]
  2. R. N. Zare, "Laser control of chemical reactions," Science 279, 1875-1879 (1998).
    [CrossRef] [PubMed]
  3. V. D. Kleiman, S. M. Arrivo, J. S. Melinger, and E. J. Heilweil, "Controlling condensed-phase vibrational excitation with tailored infrared pulses," Chem. Phys. 233, 207-215 (1998).
    [CrossRef]
  4. L. Windhorn, T. Witte, J. S. Yeston, D. Proch, M. Motzkus, K. L. Kompa, and W. Fuß, "Molecular dissociation by mid-IR femtosecond pulses," Chem. Phys. Lett. 357, 85-90 (2002).
    [CrossRef]
  5. L. Windhorn, J. S. Yeston, T. Witte, W. Fuß, M. Motzkus, D. Proch, and K. L. Kompa, "Getting ahead of IVR: a demonstration of mid-infrared induced molecular dissociation on a substatistical time scale," J. Chem. Phys. 119, 641-645 (2003).
    [CrossRef]
  6. A. M. Weiner, D. E. Leaird, J. S. Patel, and I. J. R. Wullert, "Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator," IEEE J. Quantum Electron. 28, 908-920 (1992).
    [CrossRef]
  7. E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane, G. Mourou, H. Kapteyn, and G. Vdovin, "Pulse compression by use of deformable mirrors," Opt. Lett. 24, 493-495 (1999).
    [CrossRef]
  8. F. Verluise, V. Laude, Z. Cheng, C. Spielmann, and P. Tournois, "Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter: pulse compression and shaping," Opt. Lett. 25, 575-577 (2000).
    [CrossRef]
  9. S. H. Shim, D. B. Strasfeld, E. C. Fulmer, and M. T. Zanni, "Femtosecond pulse shaping directly in the mid-IR using acousto-optic modulation," Opt. Lett. 31, 838-840 (2006).
    [CrossRef] [PubMed]
  10. H. S. Tan, W. Schreiber, and W. S. Warren, "High-resolution indirect pulse shaping by parametric transfer," Opt. Lett. 27, 439-441 (2002).
    [CrossRef]
  11. T. Witte, D. Zeidler, D. Proch, K. L. Kompa, and M. Motzkus, "Programmable amplitude- and phase-modulated femtosecond laser pulses in the mid-infrared," Opt. Lett. 27, 131-133 (2002).
    [CrossRef]
  12. T. Witte, K. L. Kompa, and M. Motzkus, "Femtosecond pulse shaping in the mid-infrared by difference-frequency mixing," Appl. Phys. B 76, 467-471 (2003).
    [CrossRef]
  13. W. S. Tan and W. S. Warren, "Mid-infrared pulse shaping by optical parametric amplification and its application to optical free induction decay measurement," Opt. Express 11, 1021-1028 (2003).
    [CrossRef] [PubMed]
  14. H. S. S. Hung, N. A. Naz, J. Prawiharjo, D. P. Shepherd, and D. C. Hanna, "Parametric transfer in a synchronously pumped optical parametric oscillator," presented at CLEO/QELS Long Beach, California, USA, 21-25 May (2006).
  15. N. A. Naz, H. S. S. Hung, M. V. O'Connor, D. C. Hanna, and D. P. Shepherd, "Adaptively shaped mid-infrared pulses from a synchronously pumped optical parametric oscillator," Opt. Express 13, 8400-8405 (2005).
    [CrossRef] [PubMed]
  16. J. Prawiharjo, H. S. S. Hung, D. C. Hanna, and D. P. Shepherd, "Theoretical and numerical investigations of parametric transfer via difference-frequency generation for indirect mid-infrared pulse shaping," J. Opt. Soc. Am. B 24, 895-905 (2007).
    [CrossRef]
  17. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
  18. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, and M. A. Krumbügel, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
    [CrossRef]
  19. D. Jundt, "Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate," Opt. Lett. 22, 1553-1555 (1997).
    [CrossRef]
  20. K. S. Abedin and H. Ito, "Temperature-dependent dispersion relation of ferroelectric lithium tantalate," J. Appl. Phys. 80, 6561-6563 (1996).
    [CrossRef]
  21. K. Kato, E. Takaoka, and N. Umemura, "Thermo-optic dispersion formula for RbTiOAsO4," Jpn. J. Appl. Phys., Part 1 42, 6420-6423 (2003).
    [CrossRef]
  22. L. E. Myers, G. D. Miller, R. C. Eckardt, M. M. Fejer, R. L. Byer, and W. R. Rosenberg, "Quasi-phase-matched 1.064 μm-pumped optical parametric oscillators in bulk periodically poled LiNbO3," Opt. Lett. 20, 52-54 (1995).
    [CrossRef] [PubMed]
  23. T. Hatanaka, K. Nakamura, T. Taniuchi, H. Ito, Y. Furukawa, and K. Kitamura, "Quasi-phase-matched optical parametric oscillation with periodically poled stoichiometric LiTaO3," Opt. Lett. 25, 651-653 (2000).
    [CrossRef]
  24. D. T. Reid, Z. Penman, M. Ebrahimzadeh, W. Sibett, H. Karlsson, and F. Laurell, "Broadly tunable infrared femtosecond optical parametric oscillator based on periodically poled RbTiOAsO4," Opt. Lett. 22, 1397-1399 (1997).
    [CrossRef]
  25. B. J. Pearson, J. L. White, T. C. Weinacht, and P. H. Bucksbaum, "Coherent control using adaptive learning algorithms," Phys. Rev. A 63, 063412 (2001).
    [CrossRef]
  26. http://www.iss.soton.ac.uk/research/iridis.

2007 (1)

2006 (1)

2005 (1)

2003 (4)

T. Witte, K. L. Kompa, and M. Motzkus, "Femtosecond pulse shaping in the mid-infrared by difference-frequency mixing," Appl. Phys. B 76, 467-471 (2003).
[CrossRef]

W. S. Tan and W. S. Warren, "Mid-infrared pulse shaping by optical parametric amplification and its application to optical free induction decay measurement," Opt. Express 11, 1021-1028 (2003).
[CrossRef] [PubMed]

L. Windhorn, J. S. Yeston, T. Witte, W. Fuß, M. Motzkus, D. Proch, and K. L. Kompa, "Getting ahead of IVR: a demonstration of mid-infrared induced molecular dissociation on a substatistical time scale," J. Chem. Phys. 119, 641-645 (2003).
[CrossRef]

K. Kato, E. Takaoka, and N. Umemura, "Thermo-optic dispersion formula for RbTiOAsO4," Jpn. J. Appl. Phys., Part 1 42, 6420-6423 (2003).
[CrossRef]

2002 (3)

2001 (1)

B. J. Pearson, J. L. White, T. C. Weinacht, and P. H. Bucksbaum, "Coherent control using adaptive learning algorithms," Phys. Rev. A 63, 063412 (2001).
[CrossRef]

2000 (3)

1999 (1)

1998 (2)

R. N. Zare, "Laser control of chemical reactions," Science 279, 1875-1879 (1998).
[CrossRef] [PubMed]

V. D. Kleiman, S. M. Arrivo, J. S. Melinger, and E. J. Heilweil, "Controlling condensed-phase vibrational excitation with tailored infrared pulses," Chem. Phys. 233, 207-215 (1998).
[CrossRef]

1997 (3)

1996 (1)

K. S. Abedin and H. Ito, "Temperature-dependent dispersion relation of ferroelectric lithium tantalate," J. Appl. Phys. 80, 6561-6563 (1996).
[CrossRef]

1995 (1)

1992 (1)

A. M. Weiner, D. E. Leaird, J. S. Patel, and I. J. R. Wullert, "Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator," IEEE J. Quantum Electron. 28, 908-920 (1992).
[CrossRef]

Appl. Phys. B (1)

T. Witte, K. L. Kompa, and M. Motzkus, "Femtosecond pulse shaping in the mid-infrared by difference-frequency mixing," Appl. Phys. B 76, 467-471 (2003).
[CrossRef]

Chem. Phys. (1)

V. D. Kleiman, S. M. Arrivo, J. S. Melinger, and E. J. Heilweil, "Controlling condensed-phase vibrational excitation with tailored infrared pulses," Chem. Phys. 233, 207-215 (1998).
[CrossRef]

Chem. Phys. Lett. (1)

L. Windhorn, T. Witte, J. S. Yeston, D. Proch, M. Motzkus, K. L. Kompa, and W. Fuß, "Molecular dissociation by mid-IR femtosecond pulses," Chem. Phys. Lett. 357, 85-90 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. M. Weiner, D. E. Leaird, J. S. Patel, and I. J. R. Wullert, "Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator," IEEE J. Quantum Electron. 28, 908-920 (1992).
[CrossRef]

J. Appl. Phys. (1)

K. S. Abedin and H. Ito, "Temperature-dependent dispersion relation of ferroelectric lithium tantalate," J. Appl. Phys. 80, 6561-6563 (1996).
[CrossRef]

J. Chem. Phys. (1)

L. Windhorn, J. S. Yeston, T. Witte, W. Fuß, M. Motzkus, D. Proch, and K. L. Kompa, "Getting ahead of IVR: a demonstration of mid-infrared induced molecular dissociation on a substatistical time scale," J. Chem. Phys. 119, 641-645 (2003).
[CrossRef]

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

Jpn. J. Appl. Phys., Part 1 (1)

K. Kato, E. Takaoka, and N. Umemura, "Thermo-optic dispersion formula for RbTiOAsO4," Jpn. J. Appl. Phys., Part 1 42, 6420-6423 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (9)

D. Jundt, "Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate," Opt. Lett. 22, 1553-1555 (1997).
[CrossRef]

L. E. Myers, G. D. Miller, R. C. Eckardt, M. M. Fejer, R. L. Byer, and W. R. Rosenberg, "Quasi-phase-matched 1.064 μm-pumped optical parametric oscillators in bulk periodically poled LiNbO3," Opt. Lett. 20, 52-54 (1995).
[CrossRef] [PubMed]

T. Hatanaka, K. Nakamura, T. Taniuchi, H. Ito, Y. Furukawa, and K. Kitamura, "Quasi-phase-matched optical parametric oscillation with periodically poled stoichiometric LiTaO3," Opt. Lett. 25, 651-653 (2000).
[CrossRef]

D. T. Reid, Z. Penman, M. Ebrahimzadeh, W. Sibett, H. Karlsson, and F. Laurell, "Broadly tunable infrared femtosecond optical parametric oscillator based on periodically poled RbTiOAsO4," Opt. Lett. 22, 1397-1399 (1997).
[CrossRef]

E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane, G. Mourou, H. Kapteyn, and G. Vdovin, "Pulse compression by use of deformable mirrors," Opt. Lett. 24, 493-495 (1999).
[CrossRef]

F. Verluise, V. Laude, Z. Cheng, C. Spielmann, and P. Tournois, "Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter: pulse compression and shaping," Opt. Lett. 25, 575-577 (2000).
[CrossRef]

S. H. Shim, D. B. Strasfeld, E. C. Fulmer, and M. T. Zanni, "Femtosecond pulse shaping directly in the mid-IR using acousto-optic modulation," Opt. Lett. 31, 838-840 (2006).
[CrossRef] [PubMed]

H. S. Tan, W. Schreiber, and W. S. Warren, "High-resolution indirect pulse shaping by parametric transfer," Opt. Lett. 27, 439-441 (2002).
[CrossRef]

T. Witte, D. Zeidler, D. Proch, K. L. Kompa, and M. Motzkus, "Programmable amplitude- and phase-modulated femtosecond laser pulses in the mid-infrared," Opt. Lett. 27, 131-133 (2002).
[CrossRef]

Phys. Rev. A (1)

B. J. Pearson, J. L. White, T. C. Weinacht, and P. H. Bucksbaum, "Coherent control using adaptive learning algorithms," Phys. Rev. A 63, 063412 (2001).
[CrossRef]

Rev. Sci. Instrum. (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, and M. A. Krumbügel, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

Science (2)

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, "Whither the future of controlling quantum phenomena?" Science 288, 824-828 (2000).
[CrossRef] [PubMed]

R. N. Zare, "Laser control of chemical reactions," Science 279, 1875-1879 (1998).
[CrossRef] [PubMed]

Other (3)

http://www.iss.soton.ac.uk/research/iridis.

H. S. S. Hung, N. A. Naz, J. Prawiharjo, D. P. Shepherd, and D. C. Hanna, "Parametric transfer in a synchronously pumped optical parametric oscillator," presented at CLEO/QELS Long Beach, California, USA, 21-25 May (2006).

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

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Figures (13)

Fig. 1
Fig. 1

Illustration of indirect pulse shaping via parametric transfer in an SPOPO.

Fig. 2
Fig. 2

(a) Temporal intensity and instantaneous frequency, and (b) spectral intensity and group delay of the input pump pulse.

Fig. 3
Fig. 3

Representative examples of good and bad transfer fidelities. Curves show overlays of spectral intensity and group delay of the generated idler (solid curves) and of the input pump pulses (dashed curves), for an SPOPO (a) with an OBPF having a FWHM δ f = 0.5 THz , and (b) without an OBPF. The calculated transfer fidelities were (a) Z = 2.49 × 10 4 , and (b) Z = 2.34 × 10 1 .

Fig. 4
Fig. 4

Pump depletion and transfer fidelity as functions of input pump peak intensity for SPOPO without and with OBPF having various FWHM δ f , as indicated by the legend. In this calculation, no chromatic dispersion in the nonlinear crystal was present, while the resonator reflectivity was R = 95 % .

Fig. 5
Fig. 5

Pump depletion and transfer fidelity as functions of input pump peak intensity for different resonator reflectivities R, as indicated by the legend. In this calculation, no chromatic dispersion was present, while the OBPF’s FWHM was δ f = 0.5 THz .

Fig. 6
Fig. 6

Pump depletion and transfer fidelity as functions of input pump peak intensity for temporal walk-off between the idler and pump pulses δ ν i p L , as indicated by the legend, at zero round-trip mismatch ( τ = 0 ) . The resonator reflectivity was R = 95 % , the OBPF’s FWHM was δ f = 0.5 THz , and there was no GVD or temporal walk-off between the pump and signal pulses.

Fig. 7
Fig. 7

Pump depletion (top), transfer fidelity (middle), and temporal and spectral rms widths of the signal pulse at steady-state condition at the entrance of the nonlinear crystal (bottom) as functions of round-trip mismatch τ for different temporal walk-offs between signal and pump pulses in the nonlinear crystal ( δ ν s p L ) , as indicated by the legend. Input pump peak intensity was I p , 0 = 5 MW cm 2 , the resonator reflectivity was R = 95 % , the OBPF’s FWHM was δ f = 0.5 THz , and there were no GVD and temporal walk-off between the idler and pump pulses.

Fig. 8
Fig. 8

Pump depletion and transfer fidelity as functions of round-trip mismatch τ for different GDD, β p L , due to the pump pulse GVD. The input pump peak intensity was I p , 0 = 5 MW cm 2 , the resonator reflectivity was R = 95 % , the OBPF’s FWHM was δ f = 0.5 THz , and the temporal walk-off between pump and signal was δ ν s p L = 1 ps , while there was no temporal walk-off between the idler and pump pulses.

Fig. 9
Fig. 9

Pump depletion and transfer fidelity as functions of round-trip mismatch τ for different GDD, β i L , due to the idler pulse GVD. Input pump peak intensity was I p , 0 = 5 MW cm 2 , the resonator reflectivity was R = 95 % , the OBPF’s FWHM was δ f = 0.5 THz , and the temporal walk-off between pump and signal was δ ν s p L = 1 ps , while there was no temporal walk-off between the idler and pump pulses.

Fig. 10
Fig. 10

(a) Group velocity (solid curve) and GVD (dashed curve) of congruent lithium niobate at a temperature T = 120 ° C as calculated from the Sellmeier equation for its extraordinary refractive index [19]. (b) Temporal walk-off between idler and pump pulses ( δ ν i p ) and that between signal and pump pulses ( δ ν s p ) as functions of the idler carrier wavelength for different pump carrier wavelengths, as indicated by the legend.

Fig. 11
Fig. 11

Pump depletion and transfer fidelity of a PPLN SPOPO, with and without the OBPF in the resonator, as functions of input pump peak intensity for different PPLN lengths L, as indicated by the numbers, at zero round-trip mismatch ( τ = 0 ) . Input pump wavelength was λ p = 1.05 μ m , and the output idler wavelength was selected to be λ i = 3.467 μ m , such that δ ν i p = 0 . The resonator reflectivity was R = 95 % , and the OBPF’s FWHM was δ f = 0.5 THz .

Fig. 12
Fig. 12

Pump depletion and transfer fidelity of a PPLN SPOPO as functions of round-trip mismatch for different wavelength shifts, as indicated by the legend, from λ i = 3.467 μ m that satisfies δ ν i p = 0 with input pump wavelength λ p = 1.05 μ m . The input pump peak intensity was I p , 0 = 69 MW cm 2 , the PPLN length was L = 2.5 mm , the resonator reflectivity was R = 95 % , and the OBPF’s FWHM was δ f = 0.5 THz .

Fig. 13
Fig. 13

(a) Pump depletion and (b) transfer fidelity of a PPLN SPOPO as functions of round-trip mismatch for different wavelength shifts, as indicated by the numbers. The pump depletion curves (a) show the wavelength shift from λ i = 3.467 μ m , while the transfer fidelity curves (b) are from λ i = 3.627 , 3.467, and 3.320 μ m that satisfies δ ν i p = 0 with input pump wavelengths λ p = 1.00 , 1.05, and 1.10 μ m , respectively, as indicated by the legend. The input pump peak intensity was I p , 0 = 5 MW cm 2 , the PPLN length was L = 10 mm , the resonator reflectivity was R = 95 % , and the OBPF’s FWHM was δ f = 0.5 THz .

Equations (15)

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E j ( z , t ) = A j ( z , t ) exp [ i k ( ω j ) z i ω j t ] ,
A j ( z , t ) = Ψ j ( z , t ) exp [ i ϕ j ( z , t ) ] ,
E ̂ j ( z , Ω j ) = F [ E ( z , t ) ] = A ̂ j ( z , Ω j ) exp [ i k ( ω j + Ω j ) z ] ,
A p z + i β p 2 2 A p t 2 = i γ p A s A i exp ( i Δ k 0 z ) ,
A s z + δ ν s p A s t + i β s 2 2 A s t 2 = i γ s A p A i * exp ( i Δ k 0 z ) ,
A i z + δ ν i p A i t + i β i 2 2 A i t 2 = i γ i A p A s * exp ( i Δ k 0 z ) ,
A p ( q ) ( 0 , t ) = A p ( t ) ,
A s ( q ) ( 0 , t ) = M [ A s ( q 1 ) ( L , t ) ] ,
A i ( q ) ( 0 , t ) = 0 ,
M [ A s ( L , t ) ] = R F 1 { G ( Ω s ) exp [ i Ω s ( δ ν s p L + τ ) ] A ̂ s ( L , Ω s ) } ,
G ( Ω s ) = exp [ 4 ln 2 ( Ω s 2 π δ f ) 2 ] .
A p ( t ) = A p , 0 g ( t ) exp ( i 10 g ( t ) 2 ) ,
g ( t ) = exp [ 2 ln 2 ( t δ t p ) 2 ] ;
Z = 1 S p ( Ω , τ ; z = 0 ) S i ( Ω , τ ; z = L ) d Ω d τ [ S p 2 ( Ω , τ ; z = 0 ) d Ω d τ S i 2 ( Ω , τ ; z = L ) d Ω d τ ] 1 2 ,
S j ( Ω , τ ; z ) = A j ( z , t ) A j ( z , t τ ) 2 exp ( i Ω t ) d t 2 .

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