Definitions

# Slow light

Slow light is the literal slowing of the speed of light. It is the propagation of an optical pulse or other modulation of an optical carrier at a very low group velocity. The term is usually only applied when the velocity is at least hundreds of times slower than the speed of light in a vacuum.

Researchers at the Rowland Institute for Science slowed light to 38 miles per hour in 1999, and researchers at UC Berkeley slowed the speed of light traveling through a semiconductor to 6 miles per second in 2004. This was in an effort to develop computers that will use only a fraction of the energy of today's machines.

In 2005, IBM created a microchip that can slow down light, claiming that its light-slowing device is the first to be fashioned out of fairly standard materials, potentially paving the way toward commercial adoption.

## Background

When light propagates through a material, it travels slower than the vacuum speed. This is a change in the phase velocity of the light and is manifested in physical effects such as refraction. This reduction in speed is quantified by the ratio between c and the phase velocity. This ratio is called the refractive index of the material. Slow light is a dramatic reduction in the group velocity of light, not the phase velocity. Slow light effects are not due to abnormally large refractive indexes, as explained below.

The simplest picture of light given by classical physics is of a wave or disturbance in the electromagnetic field. In a vacuum, Maxwell's equations predict that these disturbances will travel at a specific speed, denoted by the symbol c. This well-known physical constant is commonly referred to as the speed of light. The postulate of the constancy of the speed of light in all inertial reference frames lies at the heart of special relativity and has given rise to a popular notion that the "speed of light is always the same." However, in many situations light is more than a disturbance in the electromagnetic field.

In addition to propagating through a vacuum, light may also propagate through many types of matter, denoted as the medium. Light traveling within a medium is no longer a disturbance solely of the electromagnetic field, but rather a disturbance of the field and the positions and velocities of the charged particles (electrons) within the material. The motion of the electrons is determined by the field (due to the Lorentz force) but the field is determined by the positions and velocities of the electrons (due to Gauss' law and Ampere's law)). The behavior of a disturbance of this combined electromagnetic-charge density field (i.e. light) is still determined by Maxwell's equations, but the solutions are complicated due to the intimate link between the medium and the field.

Understanding the behavior of light in a material is simplified by limiting the types of disturbances studied to sinusoidal functions of time. For these types of disturbances Maxwell's equations transform into algebraic equations and are easily solved. These special disturbances propagate through a material at a speed slower than c called the phase velocity. The ratio between the phase velocity and c is called the refractive index or index of refraction of the material. The index of refraction is not a constant for a given material, but depends on temperature, pressure, and upon the frequency of the (sinusoidal) light wave. This is called dispersion.

A human perceives the amplitude of the sinusoidal disturbance as the brightness of the light and the frequency as the color. If a light is turned on or off at a specific time or otherwise modulated, then the amplitude of the sinusoidal disturbance is also time-dependent. The time-varying amplitude does not propagate at the phase velocity but rather at the group velocity. The group velocity depends not only on the refractive index of the material, but also the way in which the refractive index changes with frequency (i.e. the derivative of refractive index with respect to frequency).

Slow light refers to a large reduction in the group velocity of light. If the dispersion relation of the refractive index is such that the index changes rapidly over a small range of frequencies, then the group velocity might be very low, thousands or millions of times less than c, even though the index of refraction is still a typical value (between 1.5 and 3.5 for glasses and semiconductors).

## Procedure

There are many mechanisms which can generate slow light, all of which create narrow spectral regions with high dispersion, i.e. peaks in the dispersion relation. Schemes are generally grouped into two categories: material dispersion and waveguide dispersion. Material dispersion mechanisms such as Electromagnetically Induced Transparency (EIT), Coherent Population Oscillation (CPO), and various Four Wave Mixing (FWM) schemes produce a rapid change in refractive index as a function of optical frequency, i.e. they modify the temporal component of a propagating wave. This is done by using a nonlinear effect to modify the dipole response of a medium to a signal or "probe" field. Waveguide dispersion mechanisms such as photonic crystals, Coupled Resonator Optical Waveguides (CROW), and other micro-resonator structures modify the spatial component (k-vector) of a propagating wave.

A predominant figure of merit of slow light schemes is the Delay-Bandwidth Product (DBP). Most slow light schemes can actually offer an arbitrarily long delay for a given device length (length/delay = signal velocity) at the expense of bandwidth. The product of the two is roughly constant. A related figure of merit is the fractional delay, the time a pulse is delayed divided by the total time of the pulse.

## Potential use

Slow light could be used to greatly reduce noise, which could allow all types of information to be transmitted more efficiently. Also, optical switches controlled by slow light could cut power requirements a million-fold compared to switches now operating everything from telephone equipment to supercomputers. Slowing light could lead to a more orderly traffic flow in networks. Meanwhile, slow light can be used to build interferometers that are far more sensitive to frequency shift as compared to conventional interferometers. This property can be used to build better, smaller frequency sensor and compact high resolution spectrometers.

## Slow light in fiction

Slow glass is a fictional material in Bob Shaw's short story " Light of other days" (Analog, 1966), and several subsequent stories. The glass, which delays the passage of light by years or decades, is used to construct windows, called scenedows, that enable city dwellers, submariners and prisoners to watch "live" countryside scenes. In the original story, Shaw implied that "slow glass" simply was a material with an enormously high index of refraction. In a later story, though, he replaced this with a convoluted explanation where the delay light takes in passing through the glass is attributed to photons passing "...through a spiral tunnel coiled outside the radius of capture of each atom in the glass." The simple "high refractive index" explanation wouldn't work for a simple reason; with a refractive index somewhere in the quadrillions, Fresnel reflection would result in a surface that would be almost perfectly reflective.

Bob Shaw later reworked the stories into the novel Other Days, Other Eyes (1972).

The slow light experiments are mentioned in Dave Eggers' novel You Shall Know Our Velocity. In the novel, the speed of light is described as a "Sunday crawl".

On Discworld, where Terry Pratchett's novel series takes place, light travels only a few hundred miles per hour due to Discworld's high magic field.

## References

• Lene Vestergaard Hau, S.E. Harris, Zachary Dutton, Cyrus H. Behroozi, Nature v.397, p.594 (1999).
• "IBM's new photonic wave-guide". Nature, November 2004.
• Slow and Fast Light Topical Meeting

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