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On the Mathematics of Slow Light

Aaron Welters

Published Dec 1, 2011• 5 citations
OpenAlex

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In early 1999, a news article in the prestigious journal Nature led off with the announcement, "€œAn experiment with atoms at nanokelvin temperatures has produced the remarkable observation of light pulses traveling at velocities of only 17 m/s."€ The review continued with the understatement, "Observation of light pulses propagating at a speed no faster than a swiftly moving bicycle...comes as a surprise."€ These findings (and their review) marked the beginning of the current wave of interest in the field that has come to be called "€œslow light.â€" When we refer to "the speed of light," we typically mean c, the phase velocity of light in a vacuum, or the speed of propagation of the phase fronts of monochromatic light. The phase fronts travel more slowly through a material, propagating at the speed c/n, where n is the index of refraction of the medium. However, this ordinary slowing of the phase velocity is not slow light. "€œSlow light"€ and "€œfast light"€ refer to changes in the group velocity of light in a medium. A pulse of light can be decomposed mathematically into a group of monochromatic waves at slightly different frequencies, as in Fig. 19.1. In a dispersive material, these monochromatic waves travel at different speeds. When one views the propagation of the pulse as a whole, its apparent velocity depends on the extent of the spread of individual monochromatic-wave velocities. Each monochromatic wave travels at its own phase velocity, while the pulse travels at the group velocity. Of course, the group velocity of a pulse of light is not a new concept. The field of slow and fast light has drawn on theory and developments from the work of Sommerfeld and Brillouin from 1907 to 1914, experiments with early laser amplifiers in 1966, and other work done through the end of the 20th century. (For more of the history behind slow and fast light, see Refs. 8 and 9.)

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Theoretical analysis and experiment performance of slow-light based on stimulated Brillouin scattering (SBS)

Hongyan Zhou, Kun Hua Zhong, Ru Zhang +1 more

Slow light technology will play a key role in future all-optical communication. The slow-light technology based on stimulated Brillouin scattering has become a research highlight because of its additional advantages, such as compatibility of the devices with existing telecommunication systems, room-temperature operation, and tunable at arbitrary wavelengths. According to the propagation of a cw pulse through a Brillouin fiber amplifier, whose frequency is near the Stokes resonance, via three-wave coupling equations, both pump depletion and fiber losses taken into consideration, the principle of how slow-light effect based on stimulated Brillouin scattering produced and the mathematical expression of time delay are strictly deduced. A delay of 8 ns is obtained when the input Stokes pulse is 200ns and the SBS (stimulated Brillouin scattering) gain G is ~18 in our designed experiment of SBS slow-light system. Then the extent of transformation from pump waves to Stokes waves is measured using MATLAB numerical simulation according to the experiment dates, based on the relation between output pump light power and input pump light power and also the relation between output Stokes light power and input pump light power. And the relation between the input light power and propagation distance is discussed as well. Finally the relation between slow light pulse delay and SBS gain is also obtained.

Journal of Physics Conference Series•Feb 1, 2011•0 citations

Application of Slow Light Physics

Marlan O. Scully

Bulletin of the American Physical Society•Oct 7, 2006•0 citations
In early 1999, a news article in the prestigious journal Nature led off with the announcement, "€œAn experiment with atoms at nanokelvin temperatures has produced the remarkable observation of light pulses traveling at velocities of only 17 m/s."€ The review continued with the understatement, "Observation of light pulses propagating at a speed no faster than a swiftly moving bicycle...comes as a surprise."€ These findings (and their review) marked the beginning of the current wave of interest in the field that has come to be called "€œslow light.â€" When we refer to "the speed of light," we typically mean c, the phase velocity of light in a vacuum, or the speed of propagation of the phase fronts of monochromatic light. The phase fronts travel more slowly through a material, propagating at the speed c/n, where n is the index of refraction of the medium. However, this ordinary slowing of the phase velocity is not slow light. "€œSlow light"€ and "€œfast light"€ refer to changes in the group velocity of light in a medium. A pulse of light can be decomposed mathematically into a group of monochromatic waves at slightly different frequencies, as in Fig. 19.1. In a dispersive material, these monochromatic waves travel at different speeds. When one views the propagation of the pulse as a whole, its apparent velocity depends on the extent of the spread of individual monochromatic-wave velocities. Each monochromatic wave travels at its own phase velocity, while the pulse travels at the group velocity. Of course, the group velocity of a pulse of light is not a new concept. The field of slow and fast light has drawn on theory and developments from the work of Sommerfeld and Brillouin from 1907 to 1914, experiments with early laser amplifiers in 1966, and other work done through the end of the 20th century. (For more of the history behind slow and fast light, see Refs. 8 and 9.)
Slow light technology will play a key role in future all-optical communication. The slow-light technology based on stimulated Brillouin scattering has become a research highlight because of its additional advantages, such as compatibility of the devices with existing telecommunication systems, room-temperature operation, and tunable at arbitrary wavelengths. According to the propagation of a cw pulse through a Brillouin fiber amplifier, whose frequency is near the Stokes resonance, via three-wave coupling equations, both pump depletion and fiber losses taken into consideration, the principle of how slow-light effect based on stimulated Brillouin scattering produced and the mathematical expression of time delay are strictly deduced. A delay of 8 ns is obtained when the input Stokes pulse is 200ns and the SBS (stimulated Brillouin scattering) gain G is ~18 in our designed experiment of SBS slow-light system. Then the extent of transformation from pump waves to Stokes waves is measured using MATLAB numerical simulation according to the experiment dates, based on the relation between output pump light power and input pump light power and also the relation between output Stokes light power and input pump light power. And the relation between the input light power and propagation distance is discussed as well. Finally the relation between slow light pulse delay and SBS gain is also obtained.