Qian Li, K. Senthilnathan, K. Nakkeeran, and P. K. A. Wai, "Nearly chirp- and pedestal-free pulse compression in nonlinear fiber Bragg gratings," J. Opt. Soc. Am. B 26, 432-443 (2009)

We demonstrate almost chirp- and pedestal-free optical pulse compression in a nonlinear fiber Bragg grating with exponentially decreasing dispersion. The exponential dispersion profile can be well-approximated by a few gratings with different constant dispersions. The required number of sections is proportional to the compression ratio, but inversely proportional to the initial chirp value. We propose a compact pulse compression scheme, which consists of a linear and nonlinear grating, to effectively compress both hyperbolic secant and Gaussian shaped pulses. Nearly transform-limited pulses with a negligibly small pedestal can be achieved.

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$C(0)$ is the normalized chirp coefficient of the chirped hyperbolic secant or Gaussian input pulse. The normalized chirp coefficients after the linear FBG $[C(0)]$ are determind by fitting the phase of the pulse using $C(0){t}^{2}\u2215{T}^{2}({L}_{\mathrm{LFBG}})\u22152$, where $T({L}_{\mathrm{LFBG}})$ is the pulse width parameter of the hyperbolic secant or Gaussian pulse. Similarly, the chirp coefficient of the compressed pulse, $C(z)$, is determined by fitting the phase of the pulse using $C(z){t}^{2}\u2215{T}^{2}({L}_{\mathrm{NFBG}})\u22152$, where $T({L}_{\mathrm{NFBG}})$ is the pulse width parameter of the compressed pulse.

Table 4

Comparison of the Pedestal Generated for Different Values of the $\text{Ratio}={L}_{D0,\mathrm{Gauss}}\u2215{L}_{N0,\mathrm{Gauss}}$^{
a
}

Ratio

Change of ${\beta}_{20}$

Change of Peak Power

1

6.49%

6.49%

1.2

1.47%

1.47%

$\sqrt{2}$

0.0935%

1.6

1%

1%

1.8

2.42%

2.38%

2

3.69%

3.68%

${L}_{D0,\mathrm{Gauss}}={T}_{\mathrm{Gauss}}^{2}({L}_{\mathrm{LFBG}})\u2215\mid {\beta}_{20}\mid $ and ${L}_{N0,\mathrm{Gauss}}=1\u2215{\gamma}_{g}\u2215{P}_{0}$ are the initial dispersion and nonlinear lengths, respectively, of the ratio. The different values of ${L}_{D0,\mathrm{Gauss}}\u2215{L}_{N0,\mathrm{Gauss}}$ are obtained by either changing the initial dispersion value of NFBG ${\beta}_{20}$ or changing the peak power of the initial pulse. Different lengths of NFBG are used to achieve the same FWHM of the final compressed pulse.

Tables (4)

Table 1

Comparison Between Different Pulse Compression Schemes

Large Compression Ratio

Pedestal-Free

Chirp-Free– Almost Chirp-Free

Avoid Wave Breaking at High Powers

Short Length

Higher-order soliton compression

√

Adiabatic pulse compression in fibers

√

Adiabatic pulse compression in NFBG

√

√

Self-similar pulse compression in fibers

√

√

√

√

Self-similar pulse compression in NFBG

√

√

√

√

√

Table 2

Values of the Constants ${c}_{i}$ in Eq. (12) for Different Choices of the Reduction Methods and Ansatz

$C(0)$ is the normalized chirp coefficient of the chirped hyperbolic secant or Gaussian input pulse. The normalized chirp coefficients after the linear FBG $[C(0)]$ are determind by fitting the phase of the pulse using $C(0){t}^{2}\u2215{T}^{2}({L}_{\mathrm{LFBG}})\u22152$, where $T({L}_{\mathrm{LFBG}})$ is the pulse width parameter of the hyperbolic secant or Gaussian pulse. Similarly, the chirp coefficient of the compressed pulse, $C(z)$, is determined by fitting the phase of the pulse using $C(z){t}^{2}\u2215{T}^{2}({L}_{\mathrm{NFBG}})\u22152$, where $T({L}_{\mathrm{NFBG}})$ is the pulse width parameter of the compressed pulse.

Table 4

Comparison of the Pedestal Generated for Different Values of the $\text{Ratio}={L}_{D0,\mathrm{Gauss}}\u2215{L}_{N0,\mathrm{Gauss}}$^{
a
}

Ratio

Change of ${\beta}_{20}$

Change of Peak Power

1

6.49%

6.49%

1.2

1.47%

1.47%

$\sqrt{2}$

0.0935%

1.6

1%

1%

1.8

2.42%

2.38%

2

3.69%

3.68%

${L}_{D0,\mathrm{Gauss}}={T}_{\mathrm{Gauss}}^{2}({L}_{\mathrm{LFBG}})\u2215\mid {\beta}_{20}\mid $ and ${L}_{N0,\mathrm{Gauss}}=1\u2215{\gamma}_{g}\u2215{P}_{0}$ are the initial dispersion and nonlinear lengths, respectively, of the ratio. The different values of ${L}_{D0,\mathrm{Gauss}}\u2215{L}_{N0,\mathrm{Gauss}}$ are obtained by either changing the initial dispersion value of NFBG ${\beta}_{20}$ or changing the peak power of the initial pulse. Different lengths of NFBG are used to achieve the same FWHM of the final compressed pulse.