Abstract

It is shown that the combination of pulse-front slant, k-vector tilt, and crystal birefringence often permits exact matching of both phase and group velocities for three-wave mixing in birefringent crystals. This exact match makes possible more-efficient mixing of short light pulses, and it permits efficient mixing of chirped or broadband light. I analyze this process and present examples.

© 2001 Optical Society of America

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References

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  1. E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
    [CrossRef]
  2. A. Shirakawa, I. Sakane, M. Takasaka, and T. Kobayashi, Appl. Phys. Lett. 74, 2268 (1999).
    [CrossRef]
  3. G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, G. Tempea, F. Krausz, and K. Ferencz, Appl. Phys. B Suppl. 70, S253 (2000).
    [CrossRef]
  4. A. Andreoni and M. Bondani, Appl. Opt. 37, 2414 (1998).
    [CrossRef]
  5. A. Dubietis, G. Valiulis, R. Danielius, and A. Piskarskas, Pure Appl. Opt. 7, 271 (1998).
    [CrossRef]
  6. R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, Opt. Lett. 21, 973 (1996).
    [CrossRef] [PubMed]
  7. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, New York, 1996).
  8. B. A. Richman, S. E. Bisson, R. Trebino, E. Sidick, and A. Jacobson, Opt. Lett. 23, 497 (1998).
    [CrossRef]
  9. Function GVM in SNLO versions 22 and higher. SNLO nonlinear optics software is available from the author as a free download at http://www.sandia.gov/imrl/XWEB1128/xxtal.htm .

2000 (2)

G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, G. Tempea, F. Krausz, and K. Ferencz, Appl. Phys. B Suppl. 70, S253 (2000).
[CrossRef]

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

1999 (1)

A. Shirakawa, I. Sakane, M. Takasaka, and T. Kobayashi, Appl. Phys. Lett. 74, 2268 (1999).
[CrossRef]

1998 (3)

1996 (1)

Andreoni, A.

Beutter, M.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

Bisson, S. E.

Bondani, M.

Cerullo, G.

G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, G. Tempea, F. Krausz, and K. Ferencz, Appl. Phys. B Suppl. 70, S253 (2000).
[CrossRef]

Danielius, R.

De Silvestri, S.

G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, G. Tempea, F. Krausz, and K. Ferencz, Appl. Phys. B Suppl. 70, S253 (2000).
[CrossRef]

Di Trapani, P.

Diels, J.-C.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, New York, 1996).

Dubietis, A.

A. Dubietis, G. Valiulis, R. Danielius, and A. Piskarskas, Pure Appl. Opt. 7, 271 (1998).
[CrossRef]

Ferencz, K.

G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, G. Tempea, F. Krausz, and K. Ferencz, Appl. Phys. B Suppl. 70, S253 (2000).
[CrossRef]

Foggi, P.

Jacobson, A.

Kobayashi, T.

A. Shirakawa, I. Sakane, M. Takasaka, and T. Kobayashi, Appl. Phys. Lett. 74, 2268 (1999).
[CrossRef]

Krausz, F.

G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, G. Tempea, F. Krausz, and K. Ferencz, Appl. Phys. B Suppl. 70, S253 (2000).
[CrossRef]

Lochbrunner, S.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

Nisoli, M.

G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, G. Tempea, F. Krausz, and K. Ferencz, Appl. Phys. B Suppl. 70, S253 (2000).
[CrossRef]

Piel, J.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

Piskarskas, A.

Richman, B. A.

Riedle, E.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

Rudolph, W.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, New York, 1996).

Sakane, I.

A. Shirakawa, I. Sakane, M. Takasaka, and T. Kobayashi, Appl. Phys. Lett. 74, 2268 (1999).
[CrossRef]

Schenkl, S.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

Shirakawa, A.

A. Shirakawa, I. Sakane, M. Takasaka, and T. Kobayashi, Appl. Phys. Lett. 74, 2268 (1999).
[CrossRef]

Sidick, E.

Solcia, C.

Sporlein, S.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

Stagira, S.

G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, G. Tempea, F. Krausz, and K. Ferencz, Appl. Phys. B Suppl. 70, S253 (2000).
[CrossRef]

Takasaka, M.

A. Shirakawa, I. Sakane, M. Takasaka, and T. Kobayashi, Appl. Phys. Lett. 74, 2268 (1999).
[CrossRef]

Tempea, G.

G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, G. Tempea, F. Krausz, and K. Ferencz, Appl. Phys. B Suppl. 70, S253 (2000).
[CrossRef]

Trebino, R.

Valiulis, G.

A. Dubietis, G. Valiulis, R. Danielius, and A. Piskarskas, Pure Appl. Opt. 7, 271 (1998).
[CrossRef]

Zinth, W.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

Appl. Phys. B Suppl. (1)

G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, G. Tempea, F. Krausz, and K. Ferencz, Appl. Phys. B Suppl. 70, S253 (2000).
[CrossRef]

Appl. Phys. Lett. (1)

A. Shirakawa, I. Sakane, M. Takasaka, and T. Kobayashi, Appl. Phys. Lett. 74, 2268 (1999).
[CrossRef]

Opt. Lett. (2)

Pure Appl. Opt. (1)

A. Dubietis, G. Valiulis, R. Danielius, and A. Piskarskas, Pure Appl. Opt. 7, 271 (1998).
[CrossRef]

Other (2)

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, New York, 1996).

Function GVM in SNLO versions 22 and higher. SNLO nonlinear optics software is available from the author as a free download at http://www.sandia.gov/imrl/XWEB1128/xxtal.htm .

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Figures (2)

Fig. 1
Fig. 1

Phase-matching diagram of noncollinear mixing. Vectors ks, ki, and kp are the signal, the idler, and the pump propagation vectors, respectively. The thick bold line represents the parallel envelopes of all three pulses.

Fig. 2
Fig. 2

Diagram for calculation of the group velocity of a slanted pulse along z^. The propagation vector is tilted by δ relative to z^, and v is the group velocity of an unslanted pulse. The birefringent walk-off angle is ρ, and ϕ is the slant angle of the pulse front relative to the normal to z^. The velocity at which point a sweeps along the z^ axis is vz. The grating is shown for heuristic purposes only.

Tables (1)

Tables Icon

Table 1 Examples of Group-Velocity-Matched Mixing of Three Interacting Waves at 800, 1400, and 1867  nm

Equations (15)

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v=v/cosρ,h=vsinδ-ρ,
vz=vcosδ-ρ-htanϕ=vcosδ-ρ-tanϕsinδ-ρcosρ.
vz=vcosδ-tanϕsinδ+ρsinδ+tanϕcosδ.
1vz=dkzdω=dkcosδdω=dkdωcosδ-ksinδdδdω.
1vz=kω+kδdδdωcosδ-ksinδdδdω.
1vz=1v+kρdδdωcosδ-ksinδdδdω.
kω,ψsinψ=kg,
kψdψdω+kωsinψ+kcosψdψdω=0.
dψdω=-1kvsinψρsinψ+cosψ.
dδdω=-1kvsinϕ+δρsinϕ+δ+cosϕ+δ.
Δkz1=dkzpdωΔωp-dkzsdωΔωs-dkzidωΔωi,
Δkz1=1vzΔωp-Δωs-Δωi,
Δkz2=12d2kzpdω2Δωp2-12d2kzsdω2Δωs2-12d2kzidω2Δωi2.
d2kzdω2=ddω1vz=-1vz2dvzdω
d2kzdω2=-GVDvvz+1kvvztanϕ+δ1+ρtanϕ+δ×ρ-tanϕ+δ1+ρtanϕ+δ,

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