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Photonics North (PN)

Experimental observation of subluminal light carrying orbital angular momentum in vacuum

Frédéric Bouchard, Jérémie Harris, Harjaspreet Mand, Ebrahim Karimi, Robert W. Boyd

Published Jun 1, 2015• 2 citations
Publisher

Abstract

Einstein's theory of relativity establishes the speed of light in vacuum, c, as a fundamental constant. However, in optically dense media, light can be made to travel at speeds lower than c, e.g. light in water propagates at 3/4c. More dramatically, the speed of light pulses can be altered by orders of magnitude in dispersive media such as cold atomic clouds [1], atomic vapours [2] and structurally engineered materials [3]. Under exotic conditions, the velocity of these pulses can be rendered greater or smaller than c, or even negative [4]. While significant control can be exerted over the speed of light in dispersive media, no experimental demonstration of altered light speed has hitherto been achieved in vacuum for propagating physical beams of finite energy. Here we show that pulsed beams of twisted light can exhibit sub-luminal velocities upon vacuum propagation. Our experiment reveals changes in the range of 0.1% in the velocity of propagating twisted pulsed beams relative to c. Though our work poses no challenge to relativity theory, it experimentally confirms a counterintuitive body of theoretical work on the group velocity of structured pulses in vacuum, and introduces a novel theory of pulse velocity for twisted light. Our results are particularly important given the recent surge of interest in the application of structured beams to telecommunication [5], quantum key distribution [6] and quantum information [7].

DOI
10.1109/pn.2015.7292539

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Einstein's theory of relativity establishes the speed of light in vacuum, c, as a fundamental constant. However, in optically dense media, light can be made to travel at speeds lower than c, e.g. light in water propagates at 3/4c. More dramatically, the speed of light pulses can be altered by orders of magnitude in dispersive media such as cold atomic clouds [1], atomic vapours [2] and structurally engineered materials [3]. Under exotic conditions, the velocity of these pulses can be rendered greater or smaller than c, or even negative [4]. While significant control can be exerted over the speed of light in dispersive media, no experimental demonstration of altered light speed has hitherto been achieved in vacuum for propagating physical beams of finite energy. Here we show that pulsed beams of twisted light can exhibit sub-luminal velocities upon vacuum propagation. Our experiment reveals changes in the range of 0.1% in the velocity of propagating twisted pulsed beams relative to c. Though our work poses no challenge to relativity theory, it experimentally confirms a counterintuitive body of theoretical work on the group velocity of structured pulses in vacuum, and introduces a novel theory of pulse velocity for twisted light. Our results are particularly important given the recent surge of interest in the application of structured beams to telecommunication [5], quantum key distribution [6] and quantum information [7].
The propagation of light in dispersive media is a subject of fundamental as well as practical importance. In recent years attention has focused in particular on how refractive index can vary with frequency in such a way that the group velocities of optical pulses can be much greater or much smaller than the speed of light in vacuum, or in which the refractive index can be negative. Treating these topics at an introductory to intermediate level, Fast Light, Slow Light and Left-Handed Light focuses on the basic theory and describes the significant experimental progress made during the past decade. The book pays considerable attention to the fact that superluminal group velocities are not in conflict with special relativity and to the role of quantum effects in preventing superluminal communication and violations of Einstein causality. It also explores some of the basic physics at the opposite extreme of very slow group velocities as well as stopped and regenerated light, including the concepts of electromagnetically induced transparency and dark-state polaritons. Another very active aspect of the subject discussed concerns the possibility of designing metamaterials in which the refractive index can be negative and propagating light is left-handed in the sense that the phase and group velocities are in opposite directions. The last two chapters are an introduction to some of the basic theory and consequences of negative refractive index, with emphasis on the seminal work carried out since 2000. The possibility that "perfect" lenses can be made from negative-index metamaterials-which has been perhaps the most controversial aspect of the field-is introduced and discussed in some detail.
In a dispersive medium, different monochromatic modes of light have different phase velocities. Under special circumstances, a superposition of these modes results in an interesting effect wherein the group velocity (the velocity at which the peak of the wavepacket propagates) could be greater than c or even negative although the phase velocities of the modes are all less than c . Can this superluminal group velocity be used for information transfer? We show here that the `superluminal' effect is due to a coherent optical wave superposition effect. Whatever the velocity of the `peak', the whole pulse cannot travel with a speed greater than the fastest phase velocity of its component modes. Thus the maximum speed for information transfer, which involves the sending of a finite pulse, cannot be greater than the maximum phase velocity in the medium.
The propagation of light in dispersive media is a subject of fundamental as well as practical importance. In recent years attention has focused in particular on how refractive index can vary with frequency in such a way that the group velocities of optical pulses can be much greater or much smaller than the speed of light in vacuum, or in which the refractive index can be negative. Treating these topics at an introductory to intermediate level, Fast Light, Slow Light and Left-Handed Light focuses on the basic theory and describes the significant experimental progress made during the past decade. The book pays considerable attention to the fact that superluminal group velocities are not in conflict with special relativity and to the role of quantum effects in preventing superluminal communication and violations of Einstein causality. It also explores some of the basic physics at the opposite extreme of very slow group velocities as well as stopped and regenerated light, including the concepts of electromagnetically induced transparency and dark-state polaritons. Another very active aspect of the subject discussed concerns the possibility of designing metamaterials in which the refractive index can be negative and propagating light is left-handed in the sense that the phase and group velocities are in opposite directions. The last two chapters are an introduction to some of the basic theory and consequences of negative refractive index, with emphasis on the seminal work carried out since 2000. The possibility that "perfect" lenses can be made from negative-index metamaterials-which has been perhaps the most controversial aspect of the field-is introduced and discussed in some detail.
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.
We were able to arbitrarily control the speed of a light pulse from subluminal to superluminal velocity by changing only the power of the laser for coupling coherently the single transition between 62S1/2F=46{}^{2}{S}_{1/2}F=462S1/2​F=4 and $6{}^{2}{P}_{3/2}{F}^{\ensuremath{'}}=5$ in the D2{D}_{2}D2​ line of a Cs atomic vapor system. With weak coupling power, a Gaussian light pulse was propagated superluminally with a negative group velocity ${v}_{g}=\ensuremath{-}c/14400,$ which is caused by a highly anomalous dispersion related to an electromagnetically induced absorption. By increasing the coupling power at the same laser frequency, the pulses were propagated with a vacuum speed at the middle power and a subluminal group velocity vg=c/3000{v}_{g}=c/3000vg​=c/3000 at high power, which is caused by a normal dispersion related to an electromagnetically induced transparency. It was also found that group velocities depend largely on polarization combinations.