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 $\theta$. 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.

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

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.

See also

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

Notes

1. Mitsunaga et al., Phys. Rev. A 59, 4773 (1999)
2. Tabosa, J (1999). "Transient Bragg diffraction by a transferred population grating: application for cold atoms velocimetry". Optics Communications 165: 59. Bibcode:1999OptCo.165...59T. doi:10.1016/S0030-4018(99)00228-X.
3. G.C.Cardoso, Phys. Rev. A 65, 033803 B (2002).
4. Brown AW, Xiao, M, Opt. Lett. 30, 699 2005 ; Su XM, Ham BS, Dynamic control of the photonic band gap using quantum coherence Phys. Rev. A 71, 013821 (2005)

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
• Cardoso, G. C.; Tabosa, J. (2002). "Electromagnetically induced gratings in a degenerate open two-level system". Physical Review A 65 (3): 033803. Bibcode:2002PhRvA..65c3803C. doi:10.1103/PhysRevA.65.033803.