Negative refraction in photonic crystals Mike Kaliteevski Durham University

Outine Photonic Crystals: Introduction Negative refraction in left-handed material Non-diffracting beams Electromagnetic wiggler

Bragg reflector r n1n1 n2n2 t

n1n1 r n1n1 d2d2 n2n2

r n1n1 n2n2 n1n1 n2n2 d2d2 d2d2 Periodic sequence of the pairs of quarterwave layers is the Bragg reflector. The waves, reflected from different boundaries experience positive interference (enforce each other).

Bragg reflector

Bloch theorem. Dispersion relations

 BR =  c/(n 1 d 1 +n 2 d 2 )  BR   Formation of the photonic band gap in periodic structures

Probability of spontaneous emission

L

Microcavity

Electric field Magnetic field

Probability of spontaneous emission L L

2D Photonic crystal

1D photonic crystal

2D photonic crystal

Dispersion relations in 2D photonic crystal

Plane waves method Bloch theorem Wave equation Lattice vector Reciprocal lattice vector

Plane waves method Wave equation Reciprocal lattice vector

2D photonic crystals HE

Disperison relations H E

Complete PBG

Transmissiom of light Experiment Modelling

PC spectral filter

Defects in photonic crystals m = 1 m = 2 m = 0m = 3

Photonic crystal waveguide

PC Waveguide

OE_15_ D Photonic crystals

Transmission of light and bandstructure in opals and inverse opals.

Photonic microstructures in nature

Negative refraction in left-handed material

Right - hand materials Usual electromagnetic word

Left - hand materials V.G.Veselago, Electrodinamics of the materials with negative dielectric and magnetic constant (1967) Inversed Doppler effect Inversed Vavilov – Cherenkov effect Negative refraction

Refraction  KτKτ KτKτ

 KτKτ KτKτ Positive refraction

 KτKτ KτKτ Negative refraction

Left - hand materials Negative refraction Flat Lense

L n1n1 n2n2  A D Flat lence n1n1 n 2 =-n 1

Superlence ??? Comment: John Michael Williams, Some Problems with Negative Refraction, Phys. Rev. Lett. 87, (2001)Phys. Rev. Lett. 87, (2001) Comment: G. W. 't Hooft, Comment on “Negative Refraction Makes a Perfect Lens”, Phys. Rev. Lett. 87, (2001)Phys. Rev. Lett. 87, (2001) Reply: M. Nieto-Vesperinas and N. Garcia, Nieto- Vesperinas and Garcia Reply:, Phys. Rev. Lett. 91, (2003)Phys. Rev. Lett. 91, (2003) J. B. PendryJ. B. Pendry, Negative Refraction Makes a Perfect Lens, Phys. Rev. Lett. 85, (2000) Автор ввел понятие "суперлинза",...утверждая, что для этого устройства отсутсвует дифракционный предел. Наверное, наиболее убедительное доказательство ошибочности подобного рода утверждений можно найти в... [ В.Г.Веселаго, УФН, 173 (7) 790 (2003) ] With a conventional lens sharpness of the image is always limited by the wavelength of light. An unconventional alternative to a lens, a slab of negative refractive index material, has the power to focus all Fourier components of a 2D image, even those that do not propagate in a radiative manner. Such “superlenses”.....

Realization of left-hand materials Metamaterials Photonic crystals

Negative refraction in photonic crystals v gr <0 v gr >0 2D hexagonal metallic PC, D =200 microns, d = 60 microns

Negative refraction in 2D hexagonal photonic crystals

Refraction of wave in photonic crystal prism v gr <0 v gr >0

Refraction of wave in photonic crystal prism

Experimental study of negative refraction

Experimental study of negative refraction of THz using QCL

SIGNAL WITHOUT SAMPLE Negatively refracted beam

Non-diffracting beams W 

L l1l1 l2l2    A D n1n1 n2n2 n1n1

Negative refraction in 1D photonic crystals n1 n2 d 1 d 2

Problem: Veselago lens based on 1D PC Bragg reflector does not work. Because system is anisotropic: negative effective mass is required for negative refraction, and for 2 nd, 4 th, etc bands m z 0

n1n2 d 1 d 2 x z K 0 Field of the wave in the structure

Modes in Bragg reflector

Amplitude of waves

High contrast: n 1 =3.7 n 2 =1 Low contrast: n 1 =1.4 n 2 =1.8

Negative refraction

Normal channelling

Low contrast: n 1 =1.4 n 2 =1.8 Electromagnetic wiggler

Electromagnetic wggler

Conclusion: One can hardly make Veselago lense based 1D photonic crystal But there are some interesting effects like “electromagnetic snake”, normal channeling, etc.