# Electromagnetically induced grating

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.[1] EIGs can be used for purposes of atomic/molecular velocimetry,[2] to probe the material optical properties such as coherence and population life-times,[3] and switching and routing of light.[4] 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 ${\displaystyle \theta }$. The writing and reading frequencies are not necessarily the same. E_B is referred as the "backward" reading beam and ER is the signal obtained by diffraction on the grating.

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:

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

where the angles are given according to Fig. 2, ${\displaystyle \omega _{1}}$ and ${\displaystyle \omega _{2}}$ 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

Figure 3: Difference between a "matter grating" and 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.