Abstract

Light-pulse propagation in angularly dispersive systems is explored in the context of a center-of-mass definition of energy arrival time. In this context the time of travel is given by a superposition of group delays weighted by the spectral content of the pulse. With this description the time of travel from one point to the next for a pulse is found to be completely determined by the spectral content, independent of the state of chirp. The effect of sensor orientation on arrival time is also considered.

© 2001 Optical Society of America

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References

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  1. M. Pessot, P. Maine, and G. Mourou, “1000 times expansion/compression of optical pulses for chirped pulse amplification,” Opt. Commun. 62, 419–421 (1987).
    [CrossRef]
  2. D. N. Fittinghoff, B. C. Walker, J. A. Squier, C. S. Toth, C. Rose-Petruck, and C. P. J. Barty, “Dispersion considerations in ultrafast CPA systems,” IEEE J. Sel. Top. Quantum Electron. 4, 430–440 (1998).
    [CrossRef]
  3. C. G. Durfee III, 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, 395–405 (1998).
    [CrossRef]
  4. S. D. Brorson and H. A. Haus, “Diffraction gratings and geometric optics,” J. Opt. Soc. Am. B 5, 247–248 (1988).
    [CrossRef]
  5. J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370–2373 (2000).
    [CrossRef] [PubMed]
  6. O. E. Martinez, “Grating and prism compressors in the case of finite beam size,” J. Opt. Soc. Am. B 3, 929–934 (1986).
    [CrossRef]
  7. O. E. Martinez, J. P. Gordon, and R. L. Fork, “Negative group-velocity dispersion using refraction,” J. Opt. Soc. Am. A 1, 1003–1006 (1984).
    [CrossRef]
  8. E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
    [CrossRef]
  9. C. H. Brito Cruz, P. C. Becker, R. L. Fork, and C. V. Shank, “Phase correction of femtosecond optical pulses using a combination of prisms and gratings,” Opt. Lett. 13, 123–125 (1988).
    [CrossRef] [PubMed]
  10. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, U.K., 1999), pp. 117–119.
  11. R. L. Fork, O. E. Martinez, and J. P. Gordon, “Negative dispersion using pairs of prisms,” Opt. Lett. 9, 150–152 (1984).
    [CrossRef] [PubMed]

2000 (1)

J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370–2373 (2000).
[CrossRef] [PubMed]

1998 (2)

D. N. Fittinghoff, B. C. Walker, J. A. Squier, C. S. Toth, C. Rose-Petruck, and C. P. J. Barty, “Dispersion considerations in ultrafast CPA systems,” IEEE J. Sel. Top. Quantum Electron. 4, 430–440 (1998).
[CrossRef]

C. G. Durfee III, 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, 395–405 (1998).
[CrossRef]

1988 (2)

1987 (1)

M. Pessot, P. Maine, and G. Mourou, “1000 times expansion/compression of optical pulses for chirped pulse amplification,” Opt. Commun. 62, 419–421 (1987).
[CrossRef]

1986 (1)

1984 (2)

1969 (1)

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

Backus, S.

C. G. Durfee III, 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, 395–405 (1998).
[CrossRef]

Barty, C. P. J.

D. N. Fittinghoff, B. C. Walker, J. A. Squier, C. S. Toth, C. Rose-Petruck, and C. P. J. Barty, “Dispersion considerations in ultrafast CPA systems,” IEEE J. Sel. Top. Quantum Electron. 4, 430–440 (1998).
[CrossRef]

Becker, P. C.

Brito Cruz, C. H.

Brorson, S. D.

Durfee III, C. G.

C. G. Durfee III, 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, 395–405 (1998).
[CrossRef]

Fittinghoff, D. N.

D. N. Fittinghoff, B. C. Walker, J. A. Squier, C. S. Toth, C. Rose-Petruck, and C. P. J. Barty, “Dispersion considerations in ultrafast CPA systems,” IEEE J. Sel. Top. Quantum Electron. 4, 430–440 (1998).
[CrossRef]

Fork, R. L.

Glasgow, S. A.

J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370–2373 (2000).
[CrossRef] [PubMed]

Gordon, J. P.

Haus, H. A.

Kapteyn, H. C.

C. G. Durfee III, 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, 395–405 (1998).
[CrossRef]

Maine, P.

M. Pessot, P. Maine, and G. Mourou, “1000 times expansion/compression of optical pulses for chirped pulse amplification,” Opt. Commun. 62, 419–421 (1987).
[CrossRef]

Martinez, O. E.

Mourou, G.

M. Pessot, P. Maine, and G. Mourou, “1000 times expansion/compression of optical pulses for chirped pulse amplification,” Opt. Commun. 62, 419–421 (1987).
[CrossRef]

Murnane, M. M.

C. G. Durfee III, 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, 395–405 (1998).
[CrossRef]

Peatross, J.

J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370–2373 (2000).
[CrossRef] [PubMed]

Pessot, M.

M. Pessot, P. Maine, and G. Mourou, “1000 times expansion/compression of optical pulses for chirped pulse amplification,” Opt. Commun. 62, 419–421 (1987).
[CrossRef]

Rose-Petruck, C.

D. N. Fittinghoff, B. C. Walker, J. A. Squier, C. S. Toth, C. Rose-Petruck, and C. P. J. Barty, “Dispersion considerations in ultrafast CPA systems,” IEEE J. Sel. Top. Quantum Electron. 4, 430–440 (1998).
[CrossRef]

Shank, C. V.

Squier, J. A.

D. N. Fittinghoff, B. C. Walker, J. A. Squier, C. S. Toth, C. Rose-Petruck, and C. P. J. Barty, “Dispersion considerations in ultrafast CPA systems,” IEEE J. Sel. Top. Quantum Electron. 4, 430–440 (1998).
[CrossRef]

Toth, C. S.

D. N. Fittinghoff, B. C. Walker, J. A. Squier, C. S. Toth, C. Rose-Petruck, and C. P. J. Barty, “Dispersion considerations in ultrafast CPA systems,” IEEE J. Sel. Top. Quantum Electron. 4, 430–440 (1998).
[CrossRef]

Treacy, E. B.

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

Walker, B. C.

D. N. Fittinghoff, B. C. Walker, J. A. Squier, C. S. Toth, C. Rose-Petruck, and C. P. J. Barty, “Dispersion considerations in ultrafast CPA systems,” IEEE J. Sel. Top. Quantum Electron. 4, 430–440 (1998).
[CrossRef]

Ware, M.

J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370–2373 (2000).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

D. N. Fittinghoff, B. C. Walker, J. A. Squier, C. S. Toth, C. Rose-Petruck, and C. P. J. Barty, “Dispersion considerations in ultrafast CPA systems,” IEEE J. Sel. Top. Quantum Electron. 4, 430–440 (1998).
[CrossRef]

C. G. Durfee III, 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, 395–405 (1998).
[CrossRef]

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

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

Opt. Commun. (1)

M. Pessot, P. Maine, and G. Mourou, “1000 times expansion/compression of optical pulses for chirped pulse amplification,” Opt. Commun. 62, 419–421 (1987).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370–2373 (2000).
[CrossRef] [PubMed]

Other (1)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, U.K., 1999), pp. 117–119.

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Figures (4)

Fig. 1
Fig. 1

(a) Orientation of k(ω) assumed to lie in the xy plane. (b) Displacement Δr between points r0 and r where pulse forms will be examined.

Fig. 2
Fig. 2

(a) Snapshot of the intensity distribution of a Gaussian pulse diffracting from a grating surface. (b) Angle of the Poynting vector, measured from the horizontal x axis, for the pulse illustrated in (a).

Fig. 3
Fig. 3

Pulse delay time from r0 to r as a function of detector orientation, uˆ, for the system illustrated in Fig. 2. The angle is measured from the horizontal x axis.

Fig. 4
Fig. 4

Geometry for (a) diffraction grating pair, (b) material window, and (c) prism pair.

Equations (28)

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ϕ(ω)=k(ω)·Δr.
E(r, t)=12π -E(r0, ω)exp[iϕ(ω)]exp(-iωt)dω,
E(r0, ω)=12π -E(r0, t)exp(iωt)dt.
k(ω)=k[xˆ cos θ(ω)+yˆ sin θ(ω)],
ϕ(ω)=k(ω)·Δr=[ωn(ω)/c][Δx cos θ(ω)+Δy sin θ(ω)],
ϕ(ω)ϕ(ω)|ω¯+ϕ(ω)ωω¯(ω-ω¯)+12 2ϕ(ω)ω2ω¯(ω-ω¯)2+ .
Δx=Δr cos θ(ω),Δy=Δr sin θ(ω).
ϕω ω=Δrc n(ω)+nωω.
truˆ·-tS(r, t)dtuˆ·-S(r, t)dt,
Δt=uˆ·-S(r0, ω) ϕ(ω)ω dωuˆ·-S(r0, ω)dω,
E(ω, r)=Ei(ω, r0)ξ(-sin θxˆ+cos θyˆ)exp[iϕ(ω)],
H(ω, r)=kμ0ωE(ω, r)zˆ,
S(ω, r)E(ω, r)×H*(ω, r)=ξ|Ei(ω, r0)|2  kμ0ω[cos θxˆ+sin θyˆ],
E(r0, t)=E0  exp(-t2/τ2)exp(-iω0t)
θg(ω)=sin-12πcωd-sin θi,
ϕg(ω)=lg  ωc 1-2πcωd-sin θi21/2,
θw(ω)=sin-1sin θin(ω).
ϕw(ω)=lw  ωc[n(ω)2-sin2(θi)]1/2.
θp(ω)=sin-1n(ω)sinα-sin-1sin θin(ω),
ϕp(ω)=lp  ωc cos[θR-θp(ω)].
truˆ·-tS(r, t)dtuˆ·-S(r, t)dt.
-iuˆ·-H(r, ω)dω
×ω -E(r, ω)dω12π -  exp[-i(ω+ω)t]dt.
tr=-iuˆ·-  E(r, ω)ω×H*(r, ω)dωuˆ·-S(r, ω)dω.
E(r, ω)=E(r0, ω)exp[iϕ(ω)],
H(r, ω)=H(r0, ω)exp[iϕ(ω)].
tr=uˆ·--i E(r0, ω)ω+E(r0, ω) ϕ(ω)ω×H*(r0, ω)dωuˆ·-S(r0, ω)dω.
Δttr-tr0=uˆ·-S(r0, ω) ϕ(ω)ω dωuˆ·-S(r0, ω)dω.

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