a1934_1.pdf QTuH4.pdf Pulse broadening or compression in fast-light pulse propagation through an erbium-doped ﬁber ampliﬁer Heedeuk Shin1 , Aaron Schweinsberg1 , George Gehring1 , Katie Schwertz1 , Hye Jeong Chang1,2 , Q-Han Park3 , Daniel J. Gauthier4 and Robert W. Boyd1 1 The Institute of Optics, University of Rochester, Rochester, New York 14627 Korean Intellectual Property Ofﬁce, DaeJeon 302-791, Korea 3 Department of Physics, Korea University, Seoul, 136-701, Korea 4 Department of Physics, Duke University, Durham, NC 27708, USA firstname.lastname@example.org 2 The Abstract: Pulse broadening or compression in an Er3+-doped ﬁber ampliﬁer is observed, and explained by gain recovery and pulse spectrum broadening effects. Maximal pulse advancement and minimal pulse distortion are obtained by optimizing these competing effects. c 2006 Optical Society of America OCIS codes: (190.5530) Pulse propagation and solitons; (060.5530) Pulse propagation and solitons. Recently, controllable slow- and fast-light pulse propagation with minimal distortion has been of interest to the telecommunications and information processing communities. Several groups have investigated pulse-distortion compensation in slow- and fast-light systems using multiple gain or absorption lines or a simple phase mask in a way that minimizes the second derivative of the absorption coefﬁcient [1, 2]. Recently, we observed pulse broadening or compression in fast-light pulse propagation through erbium-doped ﬁber ampliﬁer (EDFA) [3, 4]. We investigate the mechanisms responsible for pulse broadening or compression, and demonstrate that distortion can be minimized while maximizing the pulse advancement in EDFA. The pulse broadening is interpreted as follows: The gain is saturated by the leading part of the pulse, but the pump mechanism re-excites the atoms from the ground state into the metastable state. This re-excitation can recover the ampliﬁer gain, depending on the lifetime of the metastable state and the pump intensity, and the trailing edge of the pulse can experience the recovered gain, making the pulse broader, when the pulse width is comparable to the lifetime of the metastable state. This mechanism is called “gain recovery” . However, when a pulse is superposed on a continuous-wave background that is larger than the saturation power of the ampliﬁer, a narrow hole in the gain proﬁle of an EDFA is induced due to coherent population oscillation (CPO). Because the center frequency component of a pulse experiences less gain than components of the spectral wings, the pulse transmitted through the EDFA becomes broadened in the frequency domain and experiences pulse compression in the time domain, which we will refer to as “pulse spectrum broadening”. This mechanism competes with gain recovery, making it possible to regulate the output pulse width for a given input pulse. Experimental and theoretical investigations are performed to obtain maximal advancement and minimal pulse distortion. In experiment, a tunable diode laser generates the signal beam at 1550 nm, and an electro-optic modulator (EOM) is used in free space to create a Gaussian pulse on a background. The EDFA is pumped by a co-propagating beam from a 980-nm diode laser. The output pulse is measured after ﬁltering out the pump using a wavelength division multiplexer (WDM). Furthermore, we perform computer simulations of pulse propagation through the EDFA. The 5-level system rate equations for erbium ions in a ﬁber used here have appeared in the literature, and are solved numerically . We deﬁne pulse broadening or compression by the ratio of output pulse FWHM to input pulse FWHM (τout /τin ). In Fig. 1(a), the pulse-width ratio is plotted against the ratio of background-to-pulse power for various pulse widths. The background-to-pulse power ratio (Pbg /Ppulse ) is varied from zero to 2.5. When the power ratio increases, the pulse broadening decreases since the gain is saturated by the background, making the gain recovery effect smaller. In addition, when the input pulse width becomes short, the pulse broadening can decrease since the pulse passes before the gain has time to recover. Fractional advancement, the ratio of pulse advancement to input pulse width, is additionally measured, and it appears to be independent of the power ratio. So we conclude that the background-to-pulse power ratio can be used a free parameter to minimize the pulse distortion without changing the fractional advancement. The degree of pulse distortion can be characterized by the quantity  D= +∞ −∞ ||E (t + ∆t)|2 − |E(t)|2 |dt +∞ −∞ |E 1 2 (t + ∆t)|2 − +∞ 2 2 −∞ ||E(t + δ t)| − |E(t)| |dt +∞ 2 −∞ |E(t + δ t)| 1 2 a1934_1.pdf QTuH4.pdf 1.6 (a) 1.5 Pulse width ratio (τout /τin ) τ in = 2 ms τ in = 5 ms (1) (2) τ in = 10 ms τ in = 40 ms Pulse distortion (D) (b) 0.6 (3) 0.5 0.4 0.3 0.2 0.1 τin = 2 ms τin = 5 ms τin = 10 ms τin = 40 ms 1.4 1.3 1.2 1.1 1 0.9 0.8 0 0.5 1 1.5 2 2.5 0 Power ratio ( P bg / P pulse ) 0.5 1 1.5 2 Power ratio ( Pbg / Ppulse ) 2.5 Fig. 1. (a) Experimentally measured (symbols) and theoretically predicted (lines) pulse-width ratio vs. background-to-pulse power ratio for different pulse widths, and (b) pulse distortion vs. background-to-pulse power ratio for different pulse widths. Insets: (1) Input (dashed line) and output (solid line) pulse waveforms are shown at the power ratio of zero and τin = 40 ms, (2) at the power ratio of 2.5 and τin = 2 ms and (3) at the power ratio of 1.75 and τin = 10 ms. where E (t) and E(t) are the normalized output and input ﬁeld envelope, respectively, ∆t is the time advancement of the pulse, and δ t is the temporal resolution of our detection system. The ﬁrst term represents the distortion caused by pulse reshaping, and the second term is a measure of noise. As shown in Fig. 1(b), both our experimental results and our model’s predictions follow a particular pattern. For small power ratios, an increase in power ratio results in a reduction in distortion until we reach a minimum distortion point. After the minimum distortion point, any increase in power ratio results in an increase in distortion. The minimum distortion point depends on the input pulse width. In addition, the input and output pulse time traces for 40-ms, 2-ms and 10-ms pulse widths are shown in insets (1), (2) and (3) of Fig. 1 at the power ratios of zero, 2.5 and 1.75, respectively. As expected, the trailing parts of output pulse traces are noticeably different. As shown in inset (1) of Fig. 1, the trailing part of the pulse is ampliﬁed more by gain recovery and the pulse becomes broader. In inset (2) of Fig. 1, a dip in the trailing part of the pulse is caused by pulse spectrum broadening and anomalous dispersion, making the pulse compressed. Inset (3) of Fig. 1 shows that the output pulse trace shows pulse advancement and is almost identical to the input trace. These results have a clear conceptual interpretation. At low power ratios, the primary source of distortion is pulse broadening due to gain recovery as shown in inset (1) of Fig. 1. Above the minimum distortion point, however, the distortion is dominated by a recoil effect of pulse spectrum broadening, as shown in inset (2) of Fig. 1. In conclusion, pulse broadening or compression effects in fast-light propagation were observed in an EDFA and explained by gain recovery and pulse spectrum broadening. We observed that distortion depends on pulse width and background-to-pulse power ratio. While increasing pulse width causes pulse broadening, our results show that the addition of a background can offset this distortion effect. Under our experimental condition for various pulse widths, the pulse-width ratio was varied from 0.84 to 1.43. Thus, obtaining pulse advancement with minimal distortion requires proper selection of power ratio for a particular pulse width. References        D. Eliyahu, R. A. Salvatore, J. Rosen, A. Yariv, and J. Drolet, Opt. Lett. 20, 12, 1412 (1995). 20, 12, 1412 (1995). M.D. Stenner and M.A. Neifeld, Z. Zhu, A.M.C. Dawes, and D.J. Gauthier, Opt. Express 13, 9995 (2005). A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and Sl. Jarabo, Europhys. Lett. 73 (2), 218 (2006). G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, Science 312, 895 (2006). G. P. Agrawal, and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989). P. F. Wysocki, J. L. Wagener, M. J. F. Digonnet, and H. J. Shaw, Proc. SPEI, Fiber Laser Sources and Ampliﬁers IV 1789, 66 (1992). M. S. Bigelow, N. N. Lepeshkin, H. Shin, and R. W. Boyd, J. Phys.: Condens. Matter 18, 3117 (2006).
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