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Quantum Electronics and Laser Science Conference

Light slowing down in moire fiber gratings and its implications for nonlinear optics

Jacob B. Khurgin, Jeeun Kang

Published Nov 13, 2002• 4 citations
Publisher

Abstract

Summary form only given. While the reflection and transmission properties of moire fiber grating (MFG) are well known, the analysis of their dispersion is more involved, since the number of coupled Bloch waves propagating in MFG is actually infinite. Here we report, for the first time to the best of our knowledge, the detailed analysis of the dispersion in MFG, show the analogy between the MFG and electromagnetically induced transparency (EIT) media, and its practical applications to linear and nonlinear processes.

DOI
10.1109/qels.2001.961995

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Light slowing down in Moiré fiber gratings and its implications for nonlinear optics

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A theory of the dispersion in the Moir\'e gratings is developed and it is shown that the group velocity of light in them can be reduced by up to three orders of magnitude. A conceptual similarity between Moir\'e grating and the electro-magnetic-induced transparency medium is demonstrated, and it is argued that for some applications the Moir\'e gratings present a simple viable alternative to electromagnetically induced transparency.

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Slow and Stopped Light in a Time-Dependent Moiré Grating

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The reduction in the group velocity of a light pulse due to a resonance is termed slow light. A velocity reduction to 17 m/s was demonstrated using electromagnetically induced transparency (EIT) [1]. It was later demonstrated that light could be stopped completely [2-3]. Whilst slow light EIT experiments have been ground breaking, they require a vapour cloud cooled close to 0 K. Here we present a possible alternative using gratings and a time-dependent refractive index.

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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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Superluminal pulse propagation in linear and nonlinear photonic grating structures

Stefano Longhi, Marcello Marano, M. Belmonte +1 more

Optical pulse propagation in photonic grating structures can show anomalous (i.e., superluminal or negative) group velocities under certain circumstances owing to the anomalous dispersive properties induced by the periodic grating structure. Such phenomena can be observed for either linear pulse propagation in passive dielectric grating structures, such as in fiber Bragg gratings (FBGs), as well as in frequency-conversion processes exploiting second-order cascading effects in quasi-phase-matched (QPM) nonlinear crystals. Engineering of the grating structure can be exploited to observe a wide variety of anomalous pulse transmission and reflection behaviors. In this article, we review the main recent experimental and theoretical achievements obtained by our group in this field. In particular, we report on superluminal propagation of picosecond optical pulses at the 1.5-μm wavelength of optical communications in FBGs, both in transmission and reflection configurations, with the observation of group velocities as large as ∼5c/sub 0/. We also show that the phenomenon of transparent pulse propagation at a negative group velocity in a gain doublet atomic amplifier, recently observed in cesium vapor by Wang and co-workers (L. J. Wang, A. Kuzmich, and A. Dogariu, Nature vol.406, p.277-9, 2000), can be achieved as well in a photonic parametric amplifier by exploiting the anomalous dispersive properties of the amplifier induced by a suitably designed QPM grating profile.

IEEE Journal of Selected Topics in Quantum Electronics•Jan 1, 2003•37 citations
Summary form only given. While the reflection and transmission properties of moire fiber grating (MFG) are well known, the analysis of their dispersion is more involved, since the number of coupled Bloch waves propagating in MFG is actually infinite. Here we report, for the first time to the best of our knowledge, the detailed analysis of the dispersion in MFG, show the analogy between the MFG and electromagnetically induced transparency (EIT) media, and its practical applications to linear and nonlinear processes.
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 investigate a theoretical model for a dynamic Moir\'e grating which is capable of producing slow and stopped light with improved performance when compared with a static Moir\'e grating. A Moir\'e grating superimposes two grating periods, which creates a narrow slow light resonance between two band gaps. A Moir\'e grating can be made dynamic by varying its coupling strength in time. By increasing the coupling strength the reduction in group velocity in the slow light resonance can be improved by many orders of magnitude while still maintaining the wide bandwidth of the initial, weak grating. We show that for a pulse propagating through the grating this is a consequence of altering the pulse spectrum, and therefore the grating can also perform bandwidth modulation. Finally we present a possible realization of the system via an electro-optic grating by applying a quasistatic electric field to a poled ${\ensuremath{\chi}}^{(2)}$ nonlinear medium.
Optical pulse propagation in photonic grating structures can show anomalous (i.e., superluminal or negative) group velocities under certain circumstances owing to the anomalous dispersive properties induced by the periodic grating structure. Such phenomena can be observed for either linear pulse propagation in passive dielectric grating structures, such as in fiber Bragg gratings (FBGs), as well as in frequency-conversion processes exploiting second-order cascading effects in quasi-phase-matched (QPM) nonlinear crystals. Engineering of the grating structure can be exploited to observe a wide variety of anomalous pulse transmission and reflection behaviors. In this article, we review the main recent experimental and theoretical achievements obtained by our group in this field. In particular, we report on superluminal propagation of picosecond optical pulses at the 1.5-μm wavelength of optical communications in FBGs, both in transmission and reflection configurations, with the observation of group velocities as large as ∼5c/sub 0/. We also show that the phenomenon of transparent pulse propagation at a negative group velocity in a gain doublet atomic amplifier, recently observed in cesium vapor by Wang and co-workers (L. J. Wang, A. Kuzmich, and A. Dogariu, Nature vol.406, p.277-9, 2000), can be achieved as well in a photonic parametric amplifier by exploiting the anomalous dispersive properties of the amplifier induced by a suitably designed QPM grating profile.