June 15, 1994 / Vol. 19, No. 12 / OPTICS LETTERS
`
`877
`
`Experimental demonstration of compression of dispersed
`optical pulses by reflection from
`self-chirped optical fiber Bragg gratings
`
`Benjamin J. Eggleton, Peter A. Krug, and L. Poladian
`
`Optical Fibre Technology Centre, University of Sydney, Sydney, NSW 2006, Australia
`
`K. A. Ahmed and H.-F. Liu
`
`Photonics Research Laboratories, Electrical and Electronic Engineering Department,
`University of Melbourne, Parkville, Victoria 3052, Australia
`
`Received January 28, 1994
`Dispersion compensation is demonstrated experimentally by pulse compression with the use of chirped optical fiber
`Bragg gratings. The gratings chirp is self-induced by the Gaussian intensity profile of the 240-nm wavelength
`beam used for holographic sidewriting of the grating. Chirped pulses generated by a 1.55-pum gain-switched
`distributed-feedback laser with an initial pulse duration of 21 ps and a spectral width of 0.7 nm are compressed
`to 13 ps, in good agreement with theory.
`
`Group-velocity dispersion in optical fibers causes
`temporal broadening of optical pulses and therefore
`limits the bit-rate-distance product of optical com-
`munication systems at wavelengths where the group-
`velocity dispersion is nonzero. Dispersion-induced
`pulse broadening can, in principle, be eliminated by
`introduction of a dispersive element having disper-
`sion of the same magnitude as, and opposite sign of,
`that of the fiber link.1 -3 Ouellette4 proposed that
`reflection from a linearly chirped optical fiber Bragg
`grating (OFBG) be used as a dispersion compensator.
`The principle of operation of such a compensator is
`that in a chirped grating the resonant frequency is a
`linear function of axial position, z, along the grating
`so that different frequencies present in the pulse are
`reflected at different points and thus acquire differ-
`ent delays. A linear chirp (and consequent temporal
`broadening) acquired by a short pulse propagating
`through a linearly dispersive optical fiber can be com-
`In
`pensated and the original pulse shape restored.
`this Letter we describe the holographic fabrication of
`chirped OFBG's and their use to compress linearly
`chirped, 21-ps optical pulses at 1.55 1Am and compare
`the results with theoretical calculations.
`The Bragg wavelength AB at axial position z of an
`OFBG5 is given by
`AB(z) = 2M(z)A(z),
`(1)
`where Th(z) is the mean refractive index (averaged
`over the grating period) at position z and A(z) is
`the grating period at position z. One can therefore
`achieve chirp by axially varying either A (Ref. 6) or
`7i (Ref. 7) (or both). We use the wave-front-splitting
`prism interferometer described below to holographi-
`cally write OFBG's that have constant A and a mono-
`tonic axial variation of grating strength, and hence of
`7i and AB. The grating chirp is an automatic conse-
`quence of the transverse intensity profile of the ul-
`
`traviolet writing beam, so we refer to the grating as
`being self-chirped.
`The use of a prism interferometer 8 to sidewrite
`OFBG's by ultraviolet holography has been described
`by Legoubin et al.9 We employ a modified prism de-
`sign that incorporates refractive beam expansion at
`the input face of the prism to increase the exposed
`length of the fiber. Figure 1 shows the holographic
`interferometer used to write self-chirped OFBG's.
`is fabricated from high-homogeneity
`The prism
`ultraviolet-grade fused silica (Corning 7940). The
`writing beam, which is generated by a frequency-
`doubled dye laser pumped by an excimer laser, is
`expanded laterally by refraction at the input face of
`the prism. The expanded beam is then spatially bi-
`sected by prism edge X, and one half-beam is spatially
`reversed by total internal reflection from prism face
`Y. The two half-beams are then combined at the
`output face of the prism, parallel to which the fiber
`is mounted. The measured transverse intensity dis-
`tribution of the frequency-doubled output beam of
`the dye laser is monomodal, with an approximately
`
`Input Beam
`
`Prism Interferometer
`
`Y
`
`Spectrum Analyzer
`
`Broadband Source
`
`r
`
`Fib
`
`Writing Beams
`Fig. 1. Prism interferometer for ultraviolet holographic
`sidewriting of self-chirped fiber gratings. The broadband
`source and the spectrum analyzer permit transmission
`spectra to be observed in real time.
`
`0146-9592/94/120877-03$6.00/0
`
`© 1994 Optical Society of America
`
`Page 1
`
`

`
`a length of dispersive optical fiber. This means that
`the pulse compression demonstrated here is equiva-
`lent to a demonstration of dispersion compensation.
`An erbium-doped fiber amplifier amplified the
`chirped pulses before they were injected into the
`self-chirped grating. Autocorrelation measurements
`performed before and after amplification showed
`that
`the optical amplifier does not change the
`pulse duration. The grating was heated
`in a
`thermostatically controlled oven to tune its reflection
`band into optimum coincidence with the spectrum
`of the optical pulses. Use of a 50:50 fiber coupler
`permitted pulses incident upon, and reflected by,
`the grating to be observed on an autocorrelator.
`Autocorrelation traces are presented in Figs. 3(a)
`and 3(b), which show, respectively, the 21-ps input
`pulse and the reflected pulse, which is compressed
`to 13 ps. To show that the observed compression
`is not due to truncation of the pulse spectrum by
`the grating, we reversed the direction of the grating,
`resulting in pulse stretching to 40 ps, as shown in
`Fig. 3(c). Pulse stretching arises because the sign
`of the dispersion of the grating is, in this case, such
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`Delay Time (ps)
`traces of the optical pulses:
`Fig. 3. Autocorrelator
`(a) the initial chirped gain-switched pulse (duration,
`21 ± 1 ps), (b) reflection from the grating (duration,
`13 ± 1 ps), (c) after
`reflection
`from the
`reversed
`grating (duration, 40 ± 1 ps). SHG, second-harmonic
`generation.
`
`878
`
`OPTICS LETTERS / Vol. 19, No. 12 / June 15, 1994
`
`Spectrum Analyzer
`Fig. 2. Experimental setup for measurement of pulse
`compression.
`Gaussian profile. Because this beam is bisected and
`folded onto itself by the prism, the transverse inten-
`sity profile of each of the half-beams that illuminate
`the fiber is therefore approximately half-Gaussian.
`With the assumption that the local index increase
`is proportional to the local intensity of the writing
`beam I(z), the average index is
`7i(z) = no + An exp(-z2 /L2 )
`(z 2 0),
`(2)
`where z = 0 at the peak of the intensity distribution,
`no is the unexposed core index, An is the mean index
`increase at z = 0, and L is the le width of the half-
`Gaussian intensity distribution of each writing beam.
`We refer to L as the grating length. From Eq. (1)
`there will be a half-Gaussian variation of AB along
`the grating.
`The OFBG used in the experiment was written in
`single-mode boron-codoped germanosilicate core fiber
`that had been soaked in hydrogen at 40-atm pres-
`sure at 100'C for five days to enhance its ultravi-
`olet photosensitivity.10
`50,000 shots at an approxi-
`mate energy density of 500 mJ/cm2 at A = 240 nm
`were used to fabricate the Bragg grating. Measure-
`ment of the shift of the peak Bragg wavelength during
`writing of the grating gives An = (2.0 + 0.1) X 10-3.
`The measured reflection spectrum indicates that the
`grating is more than 90% reflective over a wave-
`length range of 1 nm and more than 99% reflective
`over 0.8 nm. The shape of the spectrum is in close
`agreement with coupled-mode calculations, assuming
`a half-Gaussian index profile as given by Eq. (2), with
`a grating length L = 7.2 mm.
`Figure 2 shows the experimental setup in which
`pulse compression measurements were performed
`with a 2-GHz train of 21-ps-long pulses gener-
`ated by a gain-switched buried heterostructure
`distributed-feedback (DFB) laser.1 ' The measured
`spectral width of the pulses was 0.7 nm, yield-
`ing a time-bandwidth product of 1.8 and a chirp
`parameters of C = -5. The pulse chirp, which re-
`sults from the gain-switched modulation of the laser,
`is known to be almost linear because in a sepa-
`rate experiment Liu et al.'3 showed that the pulses
`were able to be compressed to near the transform
`limit by transmission through a suitable length of
`dispersion-shifted single-mode optical fiber. The
`chirp of the laser pulses is, therefore, nearly iden-
`tical to the chirp acquired by dispersion of an ini-
`tially transform-limited pulse after passage through
`
`Page 2
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`

`
`Table 1. Measured and Calculated Pulse Durations
`
`Pulse
`
`Theoretical
`Experimental
`Duration (ps) Duration (ps)
`
`Input
`Reflected (compression)
`Reflected (stretching)
`
`21 ± 1
`13 ± 1
`40 ± 1
`
`21P+ 1
`14 ± 1
`47 ± 3
`
`that it adds to the dispersion of the optical pulse.
`The pulse energy loss on reflection from the chirped
`grating was slightly more than 6 dB and was due
`mostly to the two passes of the pulse through the
`3-dB coupler. The results are summarized
`in
`Table 1.
`We theoretically model the response of the self-
`chirped OFBG with coupled-mode analysis.'4"15 The
`coupled-mode equations for nonuniform gratings are
`identical to those for a uniform grating, except that
`the coupling strength and detuning are now functions
`of position. The coupling strength K = wrAn'7/AB,
`where 77 is the fraction of the power guided in the
`core, and the wave-number detuning 8 are given by16
`
`K(Z) = KO exp(-z2 /L2),
`
`8(z) = 80 + 2 Ko exp(-z 2 /L 2 ),
`
`(3)
`
`(4)
`
`,
`
`(5)
`
`so=
`
`-
`
`where KO is the coupling strength at the peak
`of the half-Gaussian and 80 is given by
`2ir
`2ir
`A
`AB
`where A is the signal wavelength. The second term
`in Eq. (4) is the self-induced chirp. The coupled-
`mode equations are solved numerically to yield the
`complex amplitude reflectance r(A) and thus the
`intensity reflectance Ir(A)12 and phase 0 (A). The dis-
`persion of the grating (ignoring the negligible contri-
`butions from material and waveguide dispersion) iS4
`
`(6)
`
`DL = a = 2rc a2 0(W)
`aA
`aow2
`A 2
`where D is the grating dispersion per unit grating
`length, r(A) is the delay experienced by light of wave-
`length A, c is the optical frequency, and c is the veloc-
`ity of light in vacuuo. Numerical results with esti-
`mates of values of experimental parameters for 21-ps,
`linearly chirped input pulses give the compressed and
`broadened pulse durations shown in Table 1. The
`uncertainties in the theoretical values result from the
`uncertainty in the spectral positioning of the grating
`spectrum with respect to the input pulse spectrum.
`The theoretical compressed pulse duration is in very
`good agreement with the experimental value. We
`postulate that the small discrepancy between the cal-
`culated and measured values for the stretched pulses
`may be explained by a combination of (i) nonuniform
`chirp components in the input pulse, (ii) saturation of
`the index increase during grating writing, causing de-
`parture from the Gaussian variation of i(z), and (iii)
`chirp in the grating period caused by optical aberra-
`tions and divergence in the ultraviolet writing beams.
`We next consider the theoretical characteristics
`of a half-Gaussian dispersion-compensating grating
`
`June 15, 1994 / Vol. 19, No. 12 / OPTICS LETTERS
`
`879
`
`that is better optimized for compression of 21-ps lin-
`early chirped pulses with chirp parameter C = -5.
`Coupled-mode calculations show that, for a grating of
`length L = 7.2 mm, An = 3.8 x 10-3 (compared with
`An = 2.0 x 10-3 for the grating used in the exper-
`iment) gives an almost constant grating dispersion,
`DL = 30 ps/nm, over the entire spectral width of the
`pulse. The resulting compression factor of 4.6 to a
`pulse width of 4.5 ps is close to the transform limit
`of 4.0 ps. The pulse is not perfectly regenerated be-
`cause of the small deviations from constancy of the
`dispersion spectrum.
`In conclusion, we have demonstrated that disper-
`sion compensation can be achieved by compression of
`chirped optical pulses with self-chirped optical fiber
`Bragg gratings. The observed compression factor of
`1.6 (and also pulse stretching by a factor of 1.9 for a
`reversed grating) are in good agreement with calcu-
`lations based on the coupled-mode formalism. It is
`shown that an optimized self-chirped grating could
`produce almost perfect dispersion compensation of
`linearly chirped pulses.
`The authors acknowledge valuable discussions
`with Martijn de Sterke, Peter Hill, and Patrice
`Coll. The authors also acknowledge the support
`of Telstra Corporation Limited, the Australian Re-
`search Council, and the Australian Postgraduate
`Research Awards. The Optical Fibre Technology
`Centre and the Photonics Research Laboratory are
`members of the Australian Photonics Cooperative
`Research Centre.
`Benjamin J. Eggleton is also with the School of
`Physics, University of Sydney.
`
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`
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