Dispersionless slow light with 5-pulse-width delay in fibre Bragg grating J.T. Mok, M. Ibsen, C. Martijn de Sterke and B.J. Eggleton The excitation of gap solitons in a 30 cm fibre Bragg grating using 0.68 ns pulses, which emerge with a tunable delay of up to 3.2 ns, cor- responding to almost five pulse widths, and without broadening, are observed. This delay is an improvement by a factor of 2 from previous experiments. Introduction: The increasing interest in slow light research has been spurred partly by its potential to benefit numerous fields in optics. For instance, slow light has recently been applied to strengthen the nonlinear interaction between the light and medium [1], and to shorten the required optical path length in an interferometric device [2]. Other proposed applications of slow light include optical delay lines and buffers, and channel synchronisation. The Kramers-Kronig relations, however, lead to the inevitable broadening of the delayed pulses owing to group vel- ocity dispersion (GVD) in slow light media that rely only on their linear properties [3]. The broadening increases with propagation dis- tance, making longer devices unattractive, and thereby limiting the delay that can be obtained. Although the linear properties of slow light systems can be engineered to reduce dispersive effeects, some are difficult to implement [4], while others eliminate dispersion only to a finite order [5]. Tunability is also reduced when pulse broadening is minimised by flattening the dis- persion relation. In contrast, by exploiting the nonlinear response of a system to balance the dispersion, pulse broadening can be completely eliminated. In such schemes solitons are formed [6], and the propagation distance is not limited by dispersion, as we show here. Tunability is also maintained since the dispersion relation does not need to be manipulated otherwise. Principle: Within the bandgap of a fibre Bragg grating (FBG), centred at the Bragg wavelength l B ¼ 2nL, where n is the refractive index and L is the period of the grating, most of the light is reflected and the trans- mission is low. Just outside the bandgap, light propagation is affected in that the group velocity v g varies smoothly but rapidly from v g ¼ 0 at the band-edge to v g ¼ c/n for wavelengths far from the bandgap, as illustrated in Fig. 1a, where c is the velocity of light in vacuum. Though at wavelengths just outside the gap the light propagates slowly, a strongly wavelength-dependent group velocity implies large GVD, which causes temporal broadening. Fig. 1 Measured transmission and simulated group velocity of 30 cm FBG against wavelength (dynamic range 20 dB), and illustration of bandgap shift at high intensity a Measured transmission and simulated group velocity of 30 cm FBG against wavelength — measured transmission - - - simulated group velocity b Illustration of bandgap shift at high intensity At high intensities I, the refractive index increases as n ¼ n 0 þ n 2 I owing to the nonlinear Kerr effect, and since l B ¼ 2nL, the bandgap shifted to a longer wavelength (Fig. 1b). Pulses launched within the linear bandgap but close to the band-edge are switched out of the bandgap and are transmitted as gap solitons [7]. The GVD now being anomalous on the short wavelength side of the bandgap is balanced by the Kerr nonlinearity. The gap soliton velocity depends on the bandgap shift, which in turn depends on the intensity. The velocity, and hence the delay of the output pulse, can therefore be controlled by the input power. The pulse delay increases with the grating length or coupling strength [8]. Nonlinear pulse propagation in FBGs can be described by the non- linear coupled mode equations [7] +i @A + @z þ i n c @A + @t þ dA + þ kA + þ gðjA + j 2 þ 2jA + j 2 ÞA + ¼ 0 ð1Þ where A + (z, t ) are the field envelopes of the forward (backward) modes as a function of position z and time t, g is the fibre nonlinearity, defined such that jA + j 2 is the power in the modes, k¼ pDn/l B is the grating’s coupling strength, and Dn is the amplitude of the refractive index modulation. The detuning d ¼2pn(l 21 2 l B 21 ) relates to the difference between l B and the laser wavelength l. All simulations shown below are performed by solving (1(1)) using a collocation method [9]. Experimental setup: Fig. 2 shows the schematic of the experimental setup [10]. 0.68 ns pulses at a fixed wavelength of 1064 nm are sent into an L ¼ 30 cm uniform FBG apodised for the first and last 2 cm. The FBG is fabricated using a CW light at 244 nm in a germanosilicate fibre with an N.A. of 0.12 and cutoff wavelength at 950 nm. We estimate the broadband loss induced by the UV processing to be 0.1–0.2 dB/m. The bandgap as shown in Fig. 1a is 0.215 nm wide, implying k 0 ’ 8.2 cm 21 and Dn ’ 3.5  10 24 . The power meter monitors the pulse transmission. Both the pulse shape and pulse arrival time are measured with a sampling oscilloscope. d is tuned by strain. Fig. 2 Schematic of experimental setup Results: Fig. 3 shows the transmission of the FBG against input peak power. We first strain-tune the grating such that the transmission in the linear regime is 225 dB, corresponding to d ’ 8.0 cm 21 . After an initial drop, the transmission increases with input power, indicating a bandgap shift. The transmission saturates around 23 dB, with the remaining light being reflected. The deviation from the simulation par- ticularly in the vertical part of the curve could be due to a drift in d caused by room temperature changes, whereby 0.18C is sufficient to produce a noticeable effect. Fig. 3 Measured (dynamic range 30 dB) and simulated transmission of FBG against input peak power Fig. 4 shows the transmitted pulse and reference pulse at various power levels. The reference pulse is measured by tuning the grating so that the pulse is detuned far (d & 3k); from the bandgap, where the effect of the grating is negligible. The largest delay of 3.2 ns, or equiva- lently 4.7 the input pulse width, corresponding to v g ¼ 0.32c/n, was obtained at a peak power of 810 W. The pulse measurement at this power level appears noisy partly due to instrument sensitivity. The delay of the output pulse decreases with power, down to 1.2 ns, since the group velocity increases towards v g ¼ c/n as the bandgap shifts ELECTRONICS LETTERS 6th December 2007 Vol. 43 No. 25