Abstract

A generalized solution of the linear propagation equation is proposed in terms of chirped Gauss–Hermite orthogonal functions. Some well-known special cases are pointed out, and the usefulness of this approach in analyzing arbitrarily shaped chirped pulses in rapidly converging series is discussed.

© 1997 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995), Chap. 3, pp. 63–86.
  2. F. Koyama and Y. Suematsu, IEEE J. Quantum Electron. 21, 292 (1985).
    [Crossref]
  3. A. Takada, T. Sugie, and M. Saruwatari, J. Lightwave Technol. 5, 1525 (1987).
    [Crossref]
  4. D. Marcuse, Appl. Opt. 20, 3573 (1981).
    [Crossref] [PubMed]
  5. P. Lazaridis, G. Debarge, and P. Gallion, Opt. Lett. 20, 1160 (1995).
    [Crossref] [PubMed]
  6. A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), p. 54.

1995 (1)

1987 (1)

A. Takada, T. Sugie, and M. Saruwatari, J. Lightwave Technol. 5, 1525 (1987).
[Crossref]

1985 (1)

F. Koyama and Y. Suematsu, IEEE J. Quantum Electron. 21, 292 (1985).
[Crossref]

1981 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995), Chap. 3, pp. 63–86.

Debarge, G.

Gallion, P.

Koyama, F.

F. Koyama and Y. Suematsu, IEEE J. Quantum Electron. 21, 292 (1985).
[Crossref]

Lazaridis, P.

Marcuse, D.

Saruwatari, M.

A. Takada, T. Sugie, and M. Saruwatari, J. Lightwave Technol. 5, 1525 (1987).
[Crossref]

Suematsu, Y.

F. Koyama and Y. Suematsu, IEEE J. Quantum Electron. 21, 292 (1985).
[Crossref]

Sugie, T.

A. Takada, T. Sugie, and M. Saruwatari, J. Lightwave Technol. 5, 1525 (1987).
[Crossref]

Takada, A.

A. Takada, T. Sugie, and M. Saruwatari, J. Lightwave Technol. 5, 1525 (1987).
[Crossref]

Yariv, A.

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), p. 54.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

F. Koyama and Y. Suematsu, IEEE J. Quantum Electron. 21, 292 (1985).
[Crossref]

J. Lightwave Technol. (1)

A. Takada, T. Sugie, and M. Saruwatari, J. Lightwave Technol. 5, 1525 (1987).
[Crossref]

Opt. Lett. (1)

Other (2)

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), p. 54.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995), Chap. 3, pp. 63–86.

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Figures (1)

Fig. 1
Fig. 1

Relative rms error (Erms) versus number of nonzero basis functions in the approximation of the pulse of Eq.  (11).

Tables (3)

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Table 1 Nonzero Expansion Coefficients and Relative rms Error Erms of the First Four Approximations to the Chirped Hyperbolic Secant Pulse of Eq.  (11)

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Table 2 Number of Nonzero Basis Functions Required for a Predefined Relative rms Error Erms in Approximating the Pulse of Eq.  (11)

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Table 3 Comparison between the Peak Amplitude Computed by the CGH and FFT Methods in the Case of the Pulse of Eq.  (11) with α=-10

Equations (12)

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jφz, tz=122φz, tt2,
Φz, ω=Φ0, ωexpjω2z2.
Φm0, ω=2π-jm1+α21/4exp-ω2/21+jα×exp-jm+1/2arctan αHmω1+α22mm!π1/2,
φmz, t=12π-+Φmz, ωexpjωtdω=hmt1+αz2+z21/21+αz2+z21/4expjm+1/2×arctanz1+αz-j2α+1+α2z1+αz2+z2t2,
hmt=12mm!π1/2exp-t2/2Hmt, with -+hmthntdt=δmn
-+φmz, tφn*z, tdt=12π-+Φm0, ωΦn*0, ωdω=δmn.
uz, t=m=0+cmφmz, t,
cm=-+u0, tφm*0, tdt=-+u0, texpjαt22hmtdt,
Erms2=1-m=0N-1cm2-+u0, t2dt.
u0, t=Atexp-jαt22,
u0, t=sechπ/2texp-jαt22.
Uz, ω=2π1+α21/4exp-jαω2/21+α2expjω2z2×m=0+cm-jm exp-jm+1/2×arctan αhmω/1+α2.

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