1048 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 11, NO. 8, AUGUST 1999 A New Wide-Band Pulse-Restoration Technique for Digital Fiber-Optic Communication Systems Using Temporal Gratings H. Hakimi, F. Hakimi, Member, IEEE, K. L. Hall, Senior Member, IEEE, and K. A. Rauschenbach, Member, IEEE Abstract— We demonstrate a new wide-band (over 20 nm) pulse-restoration technique, based on real-time Fourier transformation of an array of pulses acting as a temporal grating in a dispersive medium. A compression factor of 48 is demonstrated using an array of 16 coherent pulses. This method can be adapted for long-distance digital high-data rate, dense wavelength-division-multiplexed and time-division-multiplexed communication over single-mode fibers. We anticipate the pulse compression factor will vary by less than 10% over a bandwidth of 100 nm. Index Terms—Dispersion compensation, optical fiber commu- nication, optical fiber dispersion, optical processing, time-division multiplexing, wavelength-division multiplexing. D ISPERSION compensation or management is utilized in almost every high-data-rate transmission experiment to minimize input signal distortion and to extend communication length. To date, several optical techniques to compensate chromatic dispersion have been demonstrated including the use of interferometers [1], mid-span phase conjugation [2], dispersion compensating fibers [3], waveguide ring resonators [4] and chirped fiber gratings [5]. However, all of these techniques generally suffer from a narrow wavelength band of operation. In this letter, we demonstrate a new wide- band pulse-restoration technique that takes advantages of the analogy between diffraction in space and dispersion in time [6]–[8]. The parallelism of time and space is a useful concept since one can solve problems in one domain when the solutions are known in the other domain. Some examples of time–space analogies include spatial diffraction and temporal dispersion, and self-focusing acting as a spatial lens and self- phase modulation (SPM) in fibers acting as a time lens [8]. In the same spirit, short optical pulses can be considered as “slits” in time and a series of appropriately delayed optical pulses as a temporal grating (TG). In this letter, we show that a TG or an array of coherent pulses can be used to achieve wide-band pulse restoration in a fiber-optic link. In our initial experiment, we demonstrated a pulse compression factor of 48, limited by our 16-pulse array. Higher compression factors are possible using more pulses in the TG. In order to understand this new method, we invoke the analogy between spatial diffraction and temporal dispersion. Manuscript received March 15, 1999; revised May 12, 1999. The authors are with the MIT Lincoln Laboratory, Lexington, MA 02420- 9108 USA. Publisher Item Identifier S 1041-1135(99)05994-7. Fig. 1. (a) Experimental setup. (b) The 2-ps input pulse, and (c) the 240-ps dispersed pulses after propagation through 10.6 km of SMF-28 fiber, as measured on a 40-GHz 3-dB bandwidth oscilloscope. An optical pulse disperses and broadens as a result of chro- matic dispersion in a fiber, in the same manner that light from a spatial slit is diffracted into a far-field region. In both cases, within second order dispersion, the far-field patterns are the Fourier transform of the near-fields, namely, the original spatial slit illuminated by a flat phase front plane wave or the original Fourier transform limited temporal pulse. This concept has been discussed and analyzed previously by Akhmanov et al. and later by Jannson for a single pulse in a dispersive medium [9], [10]. Here, we expand on this concept to utilize the interference aspect of a train of coherent pulses in a dispersive medium for pulse restoration. Since diffraction from a series of spatial slits generates a far-field pattern which is the product of single-slit diffraction pattern and a multislit interference pattern, in direct analogy, we assert that dispersion of a coherent array of optical pulses, when acted on by chromatic dispersion, results in a temporal pattern which is the product of the single dispersion pulse pattern times the multipulse interference pattern [11]. Consequently, one may borrow from the whole arsenal of phase array antenna techniques to construct desirable far-field temporal patterns using the TG method in a variety of applications. In the case of diffraction from a series of slits, one can tailor the width and the intensity of the central maximum, in the far field region, by varying the slit spacing and the individual slit 1041–1135/99$10.00  1999 IEEE