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Science

Observation of Backward Pulse Propagation Through a Medium with a Negative Group Velocity

George M. Gehring, Aaron Schweinsberg, Christopher Barsi, Natalie B. Kostinski, Robert W. Boyd

Published May 12, 2006• 273 citations
Publisher

Abstract

The nature of pulse propagation through a material with a negative value of the group velocity has been mysterious, as simple models seem to predict that pulses will propagate "backward" through such a material. Using an erbium-doped optical fiber and measuring the time evolution of the pulse intensity at many points within the fiber, we demonstrate that the peak of the pulse does propagate backward inside the fiber, even though the energy flow is always in the forward direction.

DOI
10.1126/science.1124524

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Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text G. M. Gehring, A. Schweinsberg, H. Shin, and R. W. Boyd, "Pulse Propagation with a Negative Group Velocity in Erbium Doped Fiber," in Frontiers in Optics, OSA Technical Digest (CD) (Optica Publishing Group, 2006), paper FThG1. Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

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The group velocity at which light pulses propagate through a dispersive material system is very different from the vacuum speed of light c, One refers to light as being "slow" for v g << c (Boyd & Gauthier, 2009) or "fast" for v g > c or v g <0 (Stenner et al, 2003 ).For v g <0, the pulse envelope appears to travel backward in the material (Gehring et al, 2006), and hence it is sometimes referred to as "backward light."The subject of slow light has caused keen interest in the past decade or more, and it is possible to control the group velocity of light pulses in the dispersive materials.Interest in slow and fast light dates back to the early days of the 20th century.Sommerfeld and Brillouin (Sommerfeld & Brillouin, 1960) were intrigued by the fact that theory predicts that v g can exceed c, which leads to apparent inconsistencies with Einstein's special theory of relativity.Experimental investigations of extreme propagation velocities were performed soon after the invention of the laser (Faxvog and et al, 1970).In 1999, Harris's group research work greatly stimulated researchers' interests, which showed that light could be slowed down to 17m/s.The result was obtained in ultra cold atom clouds with the use of electromagnetically induced transparency (EIT), which induces transparency in a material while allowing it to retain strong linear and nonlinear optical properties (Hau et al, 1999).Slow light can also be obtained through the use of the optical response of hot atomic vapors (Philips et al, 2001).These early research works require hard conditions and the slow light cannot operate in room temperature.Recently, researchers found ways to realize slow light operating in room temperature and solid-state materials, which are more suited for many practical applications, namely slow light via stimulated Brillouin scattering(SBS), slow light via coherent population oscillations (CPO), tunable time delays based on group velocity dispersion or conversion/ dispersion(C/D), slow light in fiber Bragg gratings and so on.In this chapter, we describe some of the physical mechanisms that can be used to induce slow and fast light effects in room-temperature solids (Bigelow et al, 2003) and some of the exotic propagation effects that can thereby be observed.We also survey some applications of slow and fast light within the fields of quantum electronics and photonics. Fundamentals of slow and fast lightSlow and fast light refer to the group velocity of a light wave.The group velocity is the velocity most closely related to the velocity at which the peak of a light pulse moves through an optical dispersive material (Milonni, 2005), and is given by the standard result www.intechopen.comRecent Progress in Optical Fiber Research 82where n is the refractive (phase) index and ω is the angular frequency of the carrier wave of the light field.One refers to light as being slow light for v g << c, fast light for for v g > c, and backwards light for v g <0 or v g is negative.Extreme values of the group velocity invariably rely on the dominance of the second contribution to the group index of Equation ( 1).This contribution of course results from the frequency dependence of the refractive index, and for this reason extreme values of the group velocity are usually associated with the resonant or near-resonant response of material systems.According to this theory, slow light is expected in the wings of an absorption line and fast light is expected near line center, and the spatial dispersion, that is, the non-locality in space of the medium response, is another mechanism that can lead to slow light, as has been predicted (Kocharovskaya et al,2001) and observed (Strekalov et al, 2001).We catalogue the main methods to realize slow light in room temperature solid, namely slow light via stimulated Brillouin scattering(SBS), slow light via coherent population oscillations (CPO), tunable time delays based on group velocity dispersion or conversion/ dispersion(C/D), slow light in fiber Bragg gratings and so on.We will describe CPO and SBS slow light in more details.

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The nature of pulse propagation through a material with a negative value of the group velocity has been mysterious, as simple models seem to predict that pulses will propagate "backward" through such a material. Using an erbium-doped optical fiber and measuring the time evolution of the pulse intensity at many points within the fiber, we demonstrate that the peak of the pulse does propagate backward inside the fiber, even though the energy flow is always in the forward direction.
Recently,there has been interest in modifying the group velocity of optical pulses,resulting in stopped,slow,and fast(superluminal)light.According to the physical theory,fast appears in the anomalous medium,and then it so called light medium.There are many experimeuts to produce fast light,this situation opens up new perspectives for the so called dispersion engineering.For example,signal propagating with a group velocity that exceeds the speed of light in vacuum(c) is intriguing for scientists.And then,the traveling of short wave pulses,microwave pulses and light pulses with group velocity vg,whose values exceed infinity,so called negative group velocity(NGV) propagation.Such circumstance occurs when the peak of a pulse traveling through DUT,exits before the peak of the input pulse has reached the beginning of DUT.This effect is counterintuitive,but it is a discover under the experimental basis.When the group velocity of light in a material is negative,it is the NGV medium. Although NGV are possible particularly in gain systems,there have been some experimental demonstrations of that phenomenon in passive systems,such as the coaxial cables,waveguides,micro-strip lines,and optical fibers,etc.If the experimental configuration used with a higher impedance mismatch,then it permits larger group delays,and a corresponding NGV.If n is the effective refraction index of the medium,we wantfn |f/ndn/df|1 to obtain the NGV. Many experiments showed the group velocity can surpass the light speed c,but scientists still lack the further understanding of the results.In 2001,Scientists obtained the formula v-e=|T|2vg,where v-e is average energy velocity,T is transmission coeficient of the system.If we want v-ec,the condition is vgc|T|-2.Hence it can be concluded that only vg/c is very large,the energy velocity can surpass c.This demonstration opens the door to interesting possibilities. The definition of signal velocity by Brillouin,mathemalical meaning exceeds physical meaning.We argue that undistorted wave group(wave packet) propagation are the first consideration.According to this viewpoint,the theoretical analysis show that superluminal propagation(i.e.superluminal communication) was observed by authors of many NGV researchers.……The superluminal group velocity wave propagation,the negative group velocity wave propagation——each of the two cases has its own use.Now,scientists do research works in these fields: such as optical communication,squeezed light and quantum entanglement.The condusion tell us that,a hight efficiency and low-loss fast light scheme may explore potential applications.
The group velocity at which light pulses propagate through a dispersive material system is very different from the vacuum speed of light c, One refers to light as being "slow" for v g << c (Boyd & Gauthier, 2009) or "fast" for v g > c or v g <0 (Stenner et al, 2003 ).For v g <0, the pulse envelope appears to travel backward in the material (Gehring et al, 2006), and hence it is sometimes referred to as "backward light."The subject of slow light has caused keen interest in the past decade or more, and it is possible to control the group velocity of light pulses in the dispersive materials.Interest in slow and fast light dates back to the early days of the 20th century.Sommerfeld and Brillouin (Sommerfeld & Brillouin, 1960) were intrigued by the fact that theory predicts that v g can exceed c, which leads to apparent inconsistencies with Einstein's special theory of relativity.Experimental investigations of extreme propagation velocities were performed soon after the invention of the laser (Faxvog and et al, 1970).In 1999, Harris's group research work greatly stimulated researchers' interests, which showed that light could be slowed down to 17m/s.The result was obtained in ultra cold atom clouds with the use of electromagnetically induced transparency (EIT), which induces transparency in a material while allowing it to retain strong linear and nonlinear optical properties (Hau et al, 1999).Slow light can also be obtained through the use of the optical response of hot atomic vapors (Philips et al, 2001).These early research works require hard conditions and the slow light cannot operate in room temperature.Recently, researchers found ways to realize slow light operating in room temperature and solid-state materials, which are more suited for many practical applications, namely slow light via stimulated Brillouin scattering(SBS), slow light via coherent population oscillations (CPO), tunable time delays based on group velocity dispersion or conversion/ dispersion(C/D), slow light in fiber Bragg gratings and so on.In this chapter, we describe some of the physical mechanisms that can be used to induce slow and fast light effects in room-temperature solids (Bigelow et al, 2003) and some of the exotic propagation effects that can thereby be observed.We also survey some applications of slow and fast light within the fields of quantum electronics and photonics. Fundamentals of slow and fast lightSlow and fast light refer to the group velocity of a light wave.The group velocity is the velocity most closely related to the velocity at which the peak of a light pulse moves through an optical dispersive material (Milonni, 2005), and is given by the standard result www.intechopen.comRecent Progress in Optical Fiber Research 82where n is the refractive (phase) index and ω is the angular frequency of the carrier wave of the light field.One refers to light as being slow light for v g << c, fast light for for v g > c, and backwards light for v g <0 or v g is negative.Extreme values of the group velocity invariably rely on the dominance of the second contribution to the group index of Equation ( 1).This contribution of course results from the frequency dependence of the refractive index, and for this reason extreme values of the group velocity are usually associated with the resonant or near-resonant response of material systems.According to this theory, slow light is expected in the wings of an absorption line and fast light is expected near line center, and the spatial dispersion, that is, the non-locality in space of the medium response, is another mechanism that can lead to slow light, as has been predicted (Kocharovskaya et al,2001) and observed (Strekalov et al, 2001).We catalogue the main methods to realize slow light in room temperature solid, namely slow light via stimulated Brillouin scattering(SBS), slow light via coherent population oscillations (CPO), tunable time delays based on group velocity dispersion or conversion/ dispersion(C/D), slow light in fiber Bragg gratings and so on.We will describe CPO and SBS slow light in more details.
For a pulse with carrier frequency detuned less than an atomic plasma frequency but outside a narrow Lorentzian gain line, the group velocity will be negative. Unlike propagation at the center of an absorption line, the energy velocity is approximately equal to the group velocity, and is also negative. We show that a classical Gaussian pulse with such a carrier frequency will propagate at the negative group velocity for many atomic plasma wavelengths, before dispersion deforms the pulse shape. The peak of the transmitted pulse leaves the gain medium before the peak of the incident pulse enters, i.e., the pulse is transmitted superluminally. For a sufficiently long medium the exit pulse is well resolved from a comparison pulse traveling through an equal distance of vacuum. There is no conflict with causality, as numerical simulations with a switched-on Gaussian demonstrate. We propose an experiment to observe this kind of propagation by sending a pulsed probe beam through a Xe gas cell pumped to achieve inversion.