Abstract

Chirped quasi-phase-matched optical parametric amplifiers (chirped QPM OPAs) are investigated experimentally. The measured collinear gain is constant over a broad bandwidth, which makes these devices attractive candidates for use in femtosecond amplifier systems. The experiment also shows that chirped QPM OPAs support noncollinear gain-guided modes. These modes can dominate the desired collinear gain and generate intense parametric fluorescence. Design guidelines to mitigate these parasitic processes are discussed.

© 2008 Optical Society of America

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References

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  1. C. G. Durfee, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Design and implementation of a TW-class high-average power laser system,” IEEE J. Sel. Top. Quantum Electron. 4, 395-406 (1988).
    [CrossRef]
  2. S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207-1223 (1998).
    [CrossRef]
  3. P. Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, “Generation of ultrahigh peak power pulses by chirped pulse amplification,” IEEE J. Quantum Electron. 24, 398-403 (1988).
    [CrossRef]
  4. A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437-440 (1992).
    [CrossRef]
  5. I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, “The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplifiers,” Opt. Lett. 144, 125-133 (1997).
  6. J. Collier, C. Hernandez-Gomez, I. N. Ross, P. Matousek, C. N. Danson, and J. Walczak, “Evaluation of an ultrabroadband high-gain amplification technique for chirped pulse amplification facilities,” Appl. Opt. 36, 7486-7493 (1999).
    [CrossRef]
  7. I. Jovanovic, B. J. Comaskey, C. A. Ebbers, R. A. Bonner, D. M. Pennington, and E. C. Morse, “Optical parametric chirped-pulse amplifier as an alternative to Ti:sapphire regenerative amplifiers,” Appl. Opt. 41, 2923-2929 (2002).
    [CrossRef] [PubMed]
  8. T. Kobayashi and A. Baltuska, “Sub-5-fs pulse generation from a noncollinear optical parametric amplifier,” Meas. Sci. Technol. 13, 1671-1682 (2002).
    [CrossRef]
  9. C.-W. Hsu and C. C. Yang, “Broadband infrared generation with noncollinear optical parametric processes on periodically poled LiNbO3,” Opt. Lett. 26, 1412-1414 (2001).
    [CrossRef]
  10. A. Fragemann, V. Pasiskeviclus, and F. Laurell, “Broadband nondegenerate optical parametric amplification in the mid infrared with periodically poled KTiOPO4,” Opt. Lett. 30, 2296-2298 (2005).
    [CrossRef] [PubMed]
  11. K. L. Baker, “Single-pass gain in a chirped quasi-phase-matched optical parametric oscillator,” Appl. Phys. Lett. 82, 3841-3843 (2003).
    [CrossRef]
  12. M. Charbonneau-Lefort, M. M. Fejer, and B. Afeyan, “Tandem chirped quasi-phase-matching grating optical parametric amplifier design for simultaneous group delay and gain control,” Opt. Lett. 30, 634-636 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
  14. M. Charbonneau-Lefort, B. Afeyan, and M. M. Fejer, “Optical parametric amplifiers using chirped quasi-phase-matching gratings II: space-time evolution of light pulses,” J. Opt. Soc. Am. B 25, 683-700 (2008).
    [CrossRef]
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    [CrossRef]
  16. M. Charbonneau-Lefort, “Optical parametric amplifiers using chirped quasi-phase-matching gratings,” Ph.D. dissertation (Stanford University, 2007).
  17. M. N. Rosenbluth, “Parametric instabilities in inhomogeneous media,” Phys. Rev. Lett. 29, 565-567 (1972).
    [CrossRef]
  18. J. Huang, X. P. Xie, C. Langrock, R. V. Roussev, D. S. Hum, and M. M. Fejer, “Amplitude modulation and apodization of quasi-phase-matched interactions,” Opt. Lett. 31, 604-606 (2006).
    [CrossRef] [PubMed]
  19. M. M. Sushchik and G. I. Freidman, “The effect of nonuniformity of the amplitude and phase distribution of the pumping radiation on the spatial locking of parametrically amplified waves,” Radiophys. Quantum Electron. 13, 1043-1047 (1970).
    [CrossRef]
  20. A. M. Schober, “Parametric interactions of short optical pulses in quasi-phase-matched nonlinear devices,” Ph.D. dissertation (Stanford University, 2005).
  21. R. L. Byer and S. E. Harris, “Power and bandwidth of spontaneous parametric emission,” Phys. Rev. 168, 1064-1068 (1968).
    [CrossRef]

2008 (2)

2006 (1)

2005 (2)

2003 (1)

K. L. Baker, “Single-pass gain in a chirped quasi-phase-matched optical parametric oscillator,” Appl. Phys. Lett. 82, 3841-3843 (2003).
[CrossRef]

2002 (2)

2001 (1)

1999 (1)

J. Collier, C. Hernandez-Gomez, I. N. Ross, P. Matousek, C. N. Danson, and J. Walczak, “Evaluation of an ultrabroadband high-gain amplification technique for chirped pulse amplification facilities,” Appl. Opt. 36, 7486-7493 (1999).
[CrossRef]

1998 (1)

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207-1223 (1998).
[CrossRef]

1997 (1)

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, “The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplifiers,” Opt. Lett. 144, 125-133 (1997).

1992 (2)

A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437-440 (1992).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

1988 (2)

C. G. Durfee, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Design and implementation of a TW-class high-average power laser system,” IEEE J. Sel. Top. Quantum Electron. 4, 395-406 (1988).
[CrossRef]

P. Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, “Generation of ultrahigh peak power pulses by chirped pulse amplification,” IEEE J. Quantum Electron. 24, 398-403 (1988).
[CrossRef]

1972 (1)

M. N. Rosenbluth, “Parametric instabilities in inhomogeneous media,” Phys. Rev. Lett. 29, 565-567 (1972).
[CrossRef]

1970 (1)

M. M. Sushchik and G. I. Freidman, “The effect of nonuniformity of the amplitude and phase distribution of the pumping radiation on the spatial locking of parametrically amplified waves,” Radiophys. Quantum Electron. 13, 1043-1047 (1970).
[CrossRef]

1968 (1)

R. L. Byer and S. E. Harris, “Power and bandwidth of spontaneous parametric emission,” Phys. Rev. 168, 1064-1068 (1968).
[CrossRef]

Afeyan, B.

Backus, S.

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207-1223 (1998).
[CrossRef]

C. G. Durfee, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Design and implementation of a TW-class high-average power laser system,” IEEE J. Sel. Top. Quantum Electron. 4, 395-406 (1988).
[CrossRef]

Bado, P.

P. Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, “Generation of ultrahigh peak power pulses by chirped pulse amplification,” IEEE J. Quantum Electron. 24, 398-403 (1988).
[CrossRef]

Baker, K. L.

K. L. Baker, “Single-pass gain in a chirped quasi-phase-matched optical parametric oscillator,” Appl. Phys. Lett. 82, 3841-3843 (2003).
[CrossRef]

Baltuska, A.

T. Kobayashi and A. Baltuska, “Sub-5-fs pulse generation from a noncollinear optical parametric amplifier,” Meas. Sci. Technol. 13, 1671-1682 (2002).
[CrossRef]

Bonner, R. A.

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

R. L. Byer and S. E. Harris, “Power and bandwidth of spontaneous parametric emission,” Phys. Rev. 168, 1064-1068 (1968).
[CrossRef]

Charbonneau-Lefort, M.

Collier, J.

J. Collier, C. Hernandez-Gomez, I. N. Ross, P. Matousek, C. N. Danson, and J. Walczak, “Evaluation of an ultrabroadband high-gain amplification technique for chirped pulse amplification facilities,” Appl. Opt. 36, 7486-7493 (1999).
[CrossRef]

Collier, J. L.

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, “The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplifiers,” Opt. Lett. 144, 125-133 (1997).

Comaskey, B. J.

Danson, C. N.

J. Collier, C. Hernandez-Gomez, I. N. Ross, P. Matousek, C. N. Danson, and J. Walczak, “Evaluation of an ultrabroadband high-gain amplification technique for chirped pulse amplification facilities,” Appl. Opt. 36, 7486-7493 (1999).
[CrossRef]

Dubietis, A.

A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437-440 (1992).
[CrossRef]

Durfee, C. G.

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207-1223 (1998).
[CrossRef]

C. G. Durfee, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Design and implementation of a TW-class high-average power laser system,” IEEE J. Sel. Top. Quantum Electron. 4, 395-406 (1988).
[CrossRef]

Ebbers, C. A.

Fejer, M. M.

Fragemann, A.

Freidman, G. I.

M. M. Sushchik and G. I. Freidman, “The effect of nonuniformity of the amplitude and phase distribution of the pumping radiation on the spatial locking of parametrically amplified waves,” Radiophys. Quantum Electron. 13, 1043-1047 (1970).
[CrossRef]

Harris, S. E.

R. L. Byer and S. E. Harris, “Power and bandwidth of spontaneous parametric emission,” Phys. Rev. 168, 1064-1068 (1968).
[CrossRef]

Hernandez-Gomez, C.

J. Collier, C. Hernandez-Gomez, I. N. Ross, P. Matousek, C. N. Danson, and J. Walczak, “Evaluation of an ultrabroadband high-gain amplification technique for chirped pulse amplification facilities,” Appl. Opt. 36, 7486-7493 (1999).
[CrossRef]

Hsu, C.-W.

Huang, J.

Hum, D. S.

Jonusauskas, G.

A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437-440 (1992).
[CrossRef]

Jovanovic, I.

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Kapteyn, H. C.

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207-1223 (1998).
[CrossRef]

C. G. Durfee, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Design and implementation of a TW-class high-average power laser system,” IEEE J. Sel. Top. Quantum Electron. 4, 395-406 (1988).
[CrossRef]

Kobayashi, T.

T. Kobayashi and A. Baltuska, “Sub-5-fs pulse generation from a noncollinear optical parametric amplifier,” Meas. Sci. Technol. 13, 1671-1682 (2002).
[CrossRef]

Langley, A. J.

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, “The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplifiers,” Opt. Lett. 144, 125-133 (1997).

Langrock, C.

Laurell, F.

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Maine, P.

P. Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, “Generation of ultrahigh peak power pulses by chirped pulse amplification,” IEEE J. Quantum Electron. 24, 398-403 (1988).
[CrossRef]

Matousek, P.

J. Collier, C. Hernandez-Gomez, I. N. Ross, P. Matousek, C. N. Danson, and J. Walczak, “Evaluation of an ultrabroadband high-gain amplification technique for chirped pulse amplification facilities,” Appl. Opt. 36, 7486-7493 (1999).
[CrossRef]

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, “The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplifiers,” Opt. Lett. 144, 125-133 (1997).

Morse, E. C.

Mourou, G.

P. Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, “Generation of ultrahigh peak power pulses by chirped pulse amplification,” IEEE J. Quantum Electron. 24, 398-403 (1988).
[CrossRef]

Murnane, M. M.

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207-1223 (1998).
[CrossRef]

C. G. Durfee, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Design and implementation of a TW-class high-average power laser system,” IEEE J. Sel. Top. Quantum Electron. 4, 395-406 (1988).
[CrossRef]

Pasiskeviclus, V.

Pennington, D. M.

Pessot, M.

P. Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, “Generation of ultrahigh peak power pulses by chirped pulse amplification,” IEEE J. Quantum Electron. 24, 398-403 (1988).
[CrossRef]

Piskarskas, A.

A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437-440 (1992).
[CrossRef]

Rosenbluth, M. N.

M. N. Rosenbluth, “Parametric instabilities in inhomogeneous media,” Phys. Rev. Lett. 29, 565-567 (1972).
[CrossRef]

Ross, I. N.

J. Collier, C. Hernandez-Gomez, I. N. Ross, P. Matousek, C. N. Danson, and J. Walczak, “Evaluation of an ultrabroadband high-gain amplification technique for chirped pulse amplification facilities,” Appl. Opt. 36, 7486-7493 (1999).
[CrossRef]

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, “The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplifiers,” Opt. Lett. 144, 125-133 (1997).

Roussev, R. V.

Schober, A. M.

A. M. Schober, “Parametric interactions of short optical pulses in quasi-phase-matched nonlinear devices,” Ph.D. dissertation (Stanford University, 2005).

Strickland, D.

P. Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, “Generation of ultrahigh peak power pulses by chirped pulse amplification,” IEEE J. Quantum Electron. 24, 398-403 (1988).
[CrossRef]

Sushchik, M. M.

M. M. Sushchik and G. I. Freidman, “The effect of nonuniformity of the amplitude and phase distribution of the pumping radiation on the spatial locking of parametrically amplified waves,” Radiophys. Quantum Electron. 13, 1043-1047 (1970).
[CrossRef]

Towrie, M.

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, “The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplifiers,” Opt. Lett. 144, 125-133 (1997).

Walczak, J.

J. Collier, C. Hernandez-Gomez, I. N. Ross, P. Matousek, C. N. Danson, and J. Walczak, “Evaluation of an ultrabroadband high-gain amplification technique for chirped pulse amplification facilities,” Appl. Opt. 36, 7486-7493 (1999).
[CrossRef]

Xie, X. P.

Yang, C. C.

Appl. Opt. (2)

J. Collier, C. Hernandez-Gomez, I. N. Ross, P. Matousek, C. N. Danson, and J. Walczak, “Evaluation of an ultrabroadband high-gain amplification technique for chirped pulse amplification facilities,” Appl. Opt. 36, 7486-7493 (1999).
[CrossRef]

I. Jovanovic, B. J. Comaskey, C. A. Ebbers, R. A. Bonner, D. M. Pennington, and E. C. Morse, “Optical parametric chirped-pulse amplifier as an alternative to Ti:sapphire regenerative amplifiers,” Appl. Opt. 41, 2923-2929 (2002).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

K. L. Baker, “Single-pass gain in a chirped quasi-phase-matched optical parametric oscillator,” Appl. Phys. Lett. 82, 3841-3843 (2003).
[CrossRef]

IEEE J. Quantum Electron. (2)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

P. Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, “Generation of ultrahigh peak power pulses by chirped pulse amplification,” IEEE J. Quantum Electron. 24, 398-403 (1988).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

C. G. Durfee, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Design and implementation of a TW-class high-average power laser system,” IEEE J. Sel. Top. Quantum Electron. 4, 395-406 (1988).
[CrossRef]

J. Opt. Soc. Am. B (2)

Meas. Sci. Technol. (1)

T. Kobayashi and A. Baltuska, “Sub-5-fs pulse generation from a noncollinear optical parametric amplifier,” Meas. Sci. Technol. 13, 1671-1682 (2002).
[CrossRef]

Opt. Commun. (1)

A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437-440 (1992).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. (1)

R. L. Byer and S. E. Harris, “Power and bandwidth of spontaneous parametric emission,” Phys. Rev. 168, 1064-1068 (1968).
[CrossRef]

Phys. Rev. Lett. (1)

M. N. Rosenbluth, “Parametric instabilities in inhomogeneous media,” Phys. Rev. Lett. 29, 565-567 (1972).
[CrossRef]

Radiophys. Quantum Electron. (1)

M. M. Sushchik and G. I. Freidman, “The effect of nonuniformity of the amplitude and phase distribution of the pumping radiation on the spatial locking of parametrically amplified waves,” Radiophys. Quantum Electron. 13, 1043-1047 (1970).
[CrossRef]

Rev. Sci. Instrum. (1)

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207-1223 (1998).
[CrossRef]

Other (2)

M. Charbonneau-Lefort, “Optical parametric amplifiers using chirped quasi-phase-matching gratings,” Ph.D. dissertation (Stanford University, 2007).

A. M. Schober, “Parametric interactions of short optical pulses in quasi-phase-matched nonlinear devices,” Ph.D. dissertation (Stanford University, 2005).

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Figures (15)

Fig. 1
Fig. 1

Noncollinear phase-matching.

Fig. 2
Fig. 2

Normalized growth rate, K γ 0 , as a function of normalized angle, k s k i tan θ s γ 0 w 0 , where w 0 is the half-width of the pump beam, for various values of the inverse Rosenbluth gain parameter κ γ 0 2 = 1 λ R . This plot was obtained numerically as described in [16] assuming a single transverse dimension and a Gaussian pump profile, for the case θ i 2.1 θ s corresponding to the experiment.

Fig. 3
Fig. 3

Illustration of noncollinear interactions in chirped QPM gratings. A signal wave with incidence angle θ inc is phase-matched at position z p m . Depending on the angle a gain-guided mode can be supported, with growth rate K ( θ inc ) . This mode grows until the collinear PPMP is reached, in the case of positive chirp rate, or indefinitely in the case of negative chirp rate.

Fig. 4
Fig. 4

Experimental setup.

Fig. 5
Fig. 5

Measured gain spectrum of gratings with positive chirp rate, compared to that of a shorter uniform grating. The lines are a guide to the eye.

Fig. 6
Fig. 6

Long-wavelength portion of the gain spectrum of a positively chirped grating seeded with an EDFA in order to dominate the fluorescence. The 5 cm long QPM grating was chirped in order to achieve a bandwidth of 80 nm around 1520 nm .

Fig. 7
Fig. 7

Gain spectrum of a chirped QPM grating ( 5 cm long, designed to offer a bandwidth of 110 nm ), with a pump intensity sufficiently low ( 15 μ J per pulse) to cause negligible parametric fluorescence. The gain spectrum of a uniform grating is shown for comparison to illustrate the bandwidth increase due to the chirped QPM grating.

Fig. 8
Fig. 8

(a) Gain versus pump pulse energy for two chirped gratings, measured at a signal wavelength of 1540 nm . (b) Gain versus chirp rate, measured at a signal wavelength of 1540 nm and a pump pulse energy of 25 μ J .

Fig. 9
Fig. 9

Experimentally observed parametric gain, compared with theoretical values for peak and average Rosenbluth gain, as well as numerical simulations including diffraction, for (a) a 1.5 cm long uniform QPM grating and (b) a 5 cm long chirped QPM grating designed to achieve a bandwidth of 120 nm . The pump pulse energy was 25 μ J .

Fig. 10
Fig. 10

Gain spectra of linearly chirped gratings with positive and negative chirp rate, seeded collinearly. The three cases correspond to chirp rates designed to phase match bandwidths of 20, 40, and 60 nm .

Fig. 11
Fig. 11

Far-field pattern of the amplified signal produced by negatively chirped QPM gratings. The bright inner circle in each figure is the seeded noncollinear mode, while the weaker outer ring is the amplified parametric fluorescence. The dark line is the shadow of a wedge used to block the cw seed. The wavelength of the seed is indicated in the figure. The angle of the center of the ring for 1570 nm is approximately 2°.

Fig. 12
Fig. 12

Parametric fluorescence spectrum of gratings with chirp rate of equal magnitude but opposite signs. The gratings were designed to phase match wavelengths ranging from 1520 to 1570 nm . The reference level for the spectral energy density is 0.2 pJ nm .

Fig. 13
Fig. 13

Far-field parametric fluorescence patterns: (a) uniform grating, (b) positive chirp, (c) negative chirp.

Fig. 14
Fig. 14

Measured gain of uniform and chirped QPM gratings as a function of the incidence angle. The dashed line represents the contribution from the uniform grating segment.

Fig. 15
Fig. 15

Normalized growth rate, K γ 0 , versus normalized angle, θ s k s k i γ 0 w 0 , for various values of κ γ 0 2 , with k s k i 2.1 . Data are replotted from Fig. 14.

Equations (21)

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

κ = κ ( z z pm ) ,
z pm = z pm 0 + ( 1 v s 1 v i ) δ ω κ ,
γ 0 = ω s ω i n s n i d eff c E p .
G R = exp ( 2 π γ 0 2 κ ) .
Δ ω = Δ K g 1 v s 1 v i .
γ 0 = λ R Δ K g L .
θ s ( ω s , z ) = 2 κ ( ω s , z ) k s ( 1 + k s k i ) ,
G = 1 + ( U amplified U seed ) T pump U seed T int ,
U amplified = I s ( x , y , t ) exp [ 2 π γ 0 2 ( x , y , t ) κ ] d x d y d t ,
U seed = I s ( x , y , t ) d x d y d t ,
K * ( λ R ) = K max γ 0 ,
d 2 I i n = ω s 0 3 n s 0 2 4 π 2 c 2 θ d θ d ω .
P out ω s 0 3 n s 0 2 π w 0 2 16 π 2 c 2 θ min θ max 0 Δ ω B W exp [ 2 K ( θ ) L δ ω Δ ω B W ] θ d δ ω d θ ,
ω s 0 3 n s 0 2 π w 0 2 16 π 2 c 2 θ min θ max Δ ω B W 2 K ( θ ) L e 2 K ( θ ) L d θ ,
ω s 0 3 n s 0 2 π w 0 2 16 π 2 c 2 Δ ω B W θ max Δ θ 2 K max L e 2 K max L ,
= 1 4 P noise e 2 K max L ,
P noise ω s 0 3 n s 0 2 4 π 2 c 2 π w 0 2 θ max Δ θ Δ ω B W 2 K max L .
P input P noise G N C , max G R ,
G N C , max = 1 4 exp [ 2 K * ( λ R ) λ R Δ K g L ] .
L th = k s w 0 2 4 λ R 2 .
w 0 2 λ R L k s .

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