Abstract

Analytical expressions for the throughput of a direct space-to-time encoder are used to determine possible output distortions and limitations. The interplay of relevant design parameters is analyzed to avoid such distortions and optimize the performance of the encoder. It is proved that the different propagation angles of the beams in the system produce drastic variations in the coupling coefficient to an optical fiber. It is also shown that it is possible to solve this problem when the throughput of the system is reduced.

© 2001 Optical Society of America

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References

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  1. D. E. Leaird and A. M. Weiner, “Femtosecond optical packet generation by a direct space-to-time pulse shaper,” Opt. Lett. 24, 853–855 (1999).
    [CrossRef]
  2. C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1983), Vol. 20, p. 63.
  3. Ph. Emplit, J.-P. Hamaide, and F. Reynaud, “Passive amplitude and phase picosecond pulse shaping,” Opt. Lett. 17, 1358–1360 (1992).
    [CrossRef] [PubMed]
  4. O. E. Martínez, “Gating and prism compressors in the case of finite beam size,” J. Opt. Soc. Am. B 3, 929–934 (1986).
    [CrossRef]
  5. O. E. Martínez, “Matrix formalism for pulse compressors,” IEEE J. Quantum Electron. QE-24, 2530–2536 (1988).
    [CrossRef]
  6. D. E. Leaird and A. M. Weiner, “Chirp control in the direct space-to-time pulse shaper,” Opt. Lett. 25, 850–852 (2000).
    [CrossRef]
  7. D. Marcuse, “Gaussian approximation of the fundamental modes of the graded-index fibers,” J. Opt. Soc. Am. 68, 103–109 (1978).
    [CrossRef]
  8. A. B. Buckman, Guided-Wave Photonics (Saunders, Philadelphia, Pa., 1992), p. 150.

2000 (1)

1999 (1)

1992 (1)

1988 (1)

O. E. Martínez, “Matrix formalism for pulse compressors,” IEEE J. Quantum Electron. QE-24, 2530–2536 (1988).
[CrossRef]

1986 (1)

1978 (1)

Emplit, Ph.

Hamaide, J.-P.

Leaird, D. E.

Marcuse, D.

Martínez, O. E.

O. E. Martínez, “Matrix formalism for pulse compressors,” IEEE J. Quantum Electron. QE-24, 2530–2536 (1988).
[CrossRef]

O. E. Martínez, “Gating and prism compressors in the case of finite beam size,” J. Opt. Soc. Am. B 3, 929–934 (1986).
[CrossRef]

Reynaud, F.

Weiner, A. M.

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Figures (6)

Fig. 1
Fig. 1

Schematic of the space-to-time shaper. Five pixels of width σ are represented.

Fig. 2
Fig. 2

Pixel spot size at the grating is σ, and it becomes R at the slit plane. D is the aperture of the slit.

Fig. 3
Fig. 3

Limited bandwidth of the laser pulse Δω, the dispersion of the grating β, and the focal length of lens f determine the spatial dispersion of the input beam spectrum at the slit plane S.

Fig. 4
Fig. 4

Throughput of the DST shaper as a function of the ratio of pixel time duration and input pulse width (S/R). The ratio of the pixel beam at the slit plane and the aperture (R/D) is an upper bound to the number of pixels. For large S/R, the throughput scales as the ratio of the input pulse width and the temporal window generated by the array of pixels (R/S).

Fig. 5
Fig. 5

Coupling efficiency to a monomode optical fiber of the DST as a function of the ratio of pixel time duration and input pulse width (S/R) for the fourth pixel and ξ=1.5.

Fig. 6
Fig. 6

Coupling coefficient to a monomode optical fiber as a function of D/R for different pixels and S/R=1. When we reduce D/R, the throughput decreases and the intensities of the pixels become balanced.

Equations (18)

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α=-cos(γ)cos(θ),
β=λ22πcd cos(θ),
ag(x, ω)=a exp-ω22Δω2exp-ik (x-hm)22q,
1q=nρ-i 2kσ2,
afocus(x, ω)=a exp-ω22Δω2exp-ik βωhmα×exp-k2σ24f2α2(x-fβω)2×exp-ik hmxfα,
Tslit=exp-x22D2.
T=1+f2(2α2+k2β2Δω2σ2)2D2k2σ2-1/2.
R=|α|f2kσ,
S=βΔωf.
T=1+R22D2 1+S2R2-1/2.
SRΔω βkσ|α|.
fαhm<Dk.
RD>mξ.
Ψ01=1πD exp-(x2+y2)2D2,
a01=-Ψ01(x, y)E(x, y)dxdy,
T=4Ry exp-2 m2ξ21+R2D21+D2R21/21+D2R2+S2R21/21+Ry2D2R,
η>2m2ξ2 D2R21+D2R2.
T<2η exp(-η)Nξ,

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