Chebyshev center

Electromagnetically induced grating (EIG) is an optical interference phenomenon where an interference pattern is used to build a dynamic spatial diffraction grating in matter. EIGs are dynamically created by light interference on optically resonant materials and rely on population inversion and/or optical coherence properties of the material. They were first demonstrated with population gratings on atoms. EIGs can be used for purposes of atomic/molecular velocimetry, to probe the material optical properties such as coherence and population life-times, and switching and routing of light. Related but different effects are thermally induced gratings and photolithography gratings.

Writing, Reading and Phase matching conditions for EIG diffraction

Figure 1 shows a possible beam configuration to write and read an EIG. The period of the grating is controlled by the angle $\theta$. The writing and reading frequencies are not necessarily the same. E_{_B} is referred as the "backward" reading beam and E_R is the signal obtained by diffraction on the grating.

File:Write-Read EIG color.jpg

Figure 1: Writing and reading an EIG

The phase-matching conditions for the EIG for the plane-wave approximation is given by the simple geometric relation:

$\sin \beta =n{\Bigl (}{\frac {\omega _{1}}{\omega _{2}}}{\Bigr )}\sin(\theta /2)$,

where the angles are given according to Fig. 2, $\omega _{1}$ and $\omega _{2}$ are the frequencies of the writing (W, W') and reading beam (R), respectively, and n is the effective index of refraction of the medium.

Figure 2: Phase matching conditions for EIG diffraction

Types of EIG

File:Grating-types.jpg

Figure 3: Difference between a "matter grating" a "population grating". The smileys :-( and :-) represent ground and optically excited atoms, respectively.

Matter Gratings: The writing lasers form a grating by modulating density of matter or by localizing matter (trapping) on the regions of maxima (or minima) of the writing interference fields. A thermal grating is an example. Matter gratings have slow dynamics (milliseconds) compared to population and phase gratings (potentially nanoseconds and faster).

Population Gratings: The writing lasers are resonant with optical transitions in the matter and the grating is formed by optical pumping. (See Fig. 3)

Coherence Gratings: A grating where the writing lasers form a coherent matter pattern. An example is a pattern of electromagnetically induced transparency

Applications

Usually two lasers at an angle are used to build an EIG. The EIG is used to diffract a third laser, to monitor the behavior of the underlying substrate where the EIG was written or to serve as a switch for one of the lasers involved in the process.

See also

• Atomic coherence
• Electromagnetically induced transparency
• Bragg's law
• Optical lattice

Notes

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References

• Laser-induced thermal grating effects in flames, S Williams,La Rahn, Ph Paul, JW Forsman, RN Zare Opt. Lett. 19:2121, 1681–1683, 1994
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