Observation of superluminal and slow light propagation in erbium-doped optical fiber

– We observe both extremely slow and superluminal pulse propagation speeds at room temperature in an erbium-doped fiber (EDF). A signal at 1550 nm is sent through an erbium-doped fiber with varying powers of a 980 nm pump. The degree of signal delay or advancement is found to depend significantly on the pump intensity. We observe a maximum fractional advancement of 0.124 and a maximum fractional delay of 0.089. The effect is demonstrated both for a sinusoidally modulated signal and for Gaussian pulses. The ability to control the sign and magnitude of the pulse velocity could have important implications for applications in photonics. There has recently been much interest in optical processes that can lead to unusually small or unusually large group velocities of propagation through material systems. Such situations can lead to many possible applications, such as the development of variable optical delay lines for use in telecommunication systems. As the expression for the group velocity of light is given by vg = c/(n+ ω ∂n ∂ω ), where n is the phase index, materials with highly dispersive regions can exhibit group velocities that are very low, very large, or even negative [1– 3]. As regions of high dispersion are coupled to sharp absorption peaks according to the Kramers-Kronig relations, studies have focused on techniques that are capable of producing these features in the absorption spectrum. Electromagnetically induced transparency (EIT), a technique that creates a narrow transparency window for a probe pulse via the application of a strong pump field at a different frequency, has been shown to produce slow light in several material systems [4–7]. Additionally, by making use of the phenomenon of coherent population oscillations (CPO), researchers have produced slow or fast pulse propagation effects in ruby [8], alexandrite [9], and low-temperature semiconductor quantum wells [10]. c © EDP Sciences Article published by EDP Sciences and available at http://www.edpsciences.org/epl or http://dx.doi.org/10.1209/epl/i2005-10371-0 A. Schweinsberg et al.: Superluminal and slow light in EDF 219 Still another procedure for slowing the velocity of light is to make use of the rapid variation of refractive index that accompanies the gain associated with the processes of stimulated Brillouin scattering [11–13] and stimulated Raman scattering [14]. In the present work, we show that both slow and fast light propagation can occur in erbium-doped optical fiber, occurring through the process of coherent population oscillations. The widespread use of erbium-doped fiber amplifiers at the 1550 nm signal wavelength used in the telecommunications industry suggests that slow and fast light effects in this system could lead to important applications. The technique described here works at room temperature. Additionally, the fiber system has a very simple experimental setup and allows for the possibility of long interaction lengths and high intensities, both of which can lead to large time delays. Moreover, while pulses can be delayed without a separate pump field, the easy integration of a pump at 980 nm enables the propagation speed to be tuned continuously, leading to either significant delay or significant advancement for appropriate pulse widths. Previous workers had observed phase delays of modulated light fields in EDFA’s [15–17]. The present research extends this work by showing that both delays and advancement are possible for either modulated or pulsed light fields. We also develop a theoretical model that describes our experimental results with high accuracy. Coherent population oscillations occur when the ground state population of a saturable medium oscillates at the beat frequency between two applied optical fields. The oscillation creates a narrow hole in the absorption spectrum having a linewidth on the order of the inverse of the excited-state lifetime; this hole is susceptible to power broadening. The original theoretical prediction of spectral holes from CPO was made in 1967 by Schwartz and Tan [18], and was based upon an analysis of the density matrix equations of motion. Some additional insight may be gained by considering the problem in the time domain, where the slow light effect of a CPO hole can be seen as the saturation of the medium by the leading edge of the pulse, allowing the remainder to be transmitted with less attenuation. The resulting pulse in this case would be delayed, but reduced in overall intensity. Oppositely, a medium exhibiting saturable gain produces an advanced pulse. The ground state recovery time of the system is determined by the lifetime of the metastable state, which places a lower bound on the pulse duration for which anomalous propagation effects can be observed. This explanation of the effect was first used by Basov et al. in 1965 [19] and was explored in more theoretical detail by Selden in following years [20,21]. We can model the propagation of intensity-modulated 1550 nm light through an erbiumdoped fiber in the presence of a 980 nm pump using a rate equation analysis [16]. The energy levels in erbium can be approximated as a three-level system, and under the additional approximation of rapid decay from the upper pumping state to the metastable state, we obtain the rate equation for the ground state population density n: