# Localization of light in 3D by point scatterers

Sergey E. Skipetrov

► To cite this version:

Sergey E. Skipetrov. Localization of light in 3D by point scatterers. Localisation 2020, Stefan Kette-
mann; Tomi Ohtsuki; Keith Slevin, Aug 2020, Online, Japan. hal-04777528

HAL Id: hal-04777528

https://hal.science/hal-04777528v1

Submitted on 12 Nov 2024

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<figure><img src="image_1.png" /></figure>
# Localization of Light in 3D by Point Scatterers

Serguei E. Skipetrov¹

¹Université Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France

Email: sergey.skipetrov@lpmmc.cnrs.fr

A popular model to study the multiple scattering of waves in disordered media is the point-scatterer model in which resonant point scatterers (impurities) are randomly distributed in space with a uniform average density [1]. This model can be experimentally realized for light scattering by cold atoms [2]. It turns out, however, that Anderson localization of light in 3D cannot be achieved in this model because of near-field dipole-dipole interactions between scatterers – a phenomenon specific for light and absent for scalar waves (Schrödinger waves, sound) or vector elastic waves [3].

<figure><img src="image_2.png" /><figcaption>Fig.1: A diagram summarizing our results for the relation between the optical eigenmode localization and near-field effects in random ensembles of resonant point scatterers.</figcaption></figure>

Dipole-dipole interactions can be partially suppressed by applying a strong external static magnetic or electric field [4–6]. In this case, the optical coupling between two atoms at a distance r reduces to [6]

$$G = \pm \frac{e^{ik_0 r}}{k_0 r} \left\{ \alpha_{\text{far}}(\theta) + \alpha_{\text{near}}(\theta) \left[ \frac{i}{k_0 r} - \frac{1}{(k_0 r)^2} \right] \right\}, \quad (1)$$

where $\alpha_{\text{near}}(\theta)$ quantifies the strength of near-field coupling depending on the angle $\theta$ between the vector r and the external field. Spatially localized states appear in the system only when the magnitude of $\alpha_{\text{near}}(\theta)$ is small (see Fig. 1) [6].

Another way to reduce the near-field coupling is to arrange scatterers in a regular structure – a photonic crystal – where no two atoms are closer than some minimal distance $r_{\min}$. Weak disorder introduces localized states near band edges of the crystal as predicted earlier [7]. The critical properties of the associated localization transition bear signatures of the interplay between the band structure, the disorder, and the dipole-dipole coupling [8].

[1] P. de Vries, D.V. van Coevorden, and A. Lagendijk, Rev. Mod. Phys. **70**, 447 (1998).

[2] G. Labeyrie *et al.*, Phys. Rev. Lett. **83**, 5266 (1999).

[3] S.E. Skipetrov and I.M. Sokolov, Phys. Rev. Lett. **112**, 023905 (2014).

[4] S.E. Skipetrov and I.M. Sokolov, Phys. Rev. Lett. **114**, 053902 (2015).

[5] S.E. Skipetrov, Phys. Rev. Lett. **121**, 093601 (2018).

[6] S.E. Skipetrov and I.M. Sokolov, Phys. Rev. B **99**, 134201 (2019).

[7] S. John, Phys. Rev. Lett. **58**, 2486 (1987).

[8] S.E. Skipetrov, in preparation.