Nanfang Yu, Patrice Genevet, Mikhail A. Kats, Francesco Aieta,Jean-Philippe Tetienne, Federico Capasso, Zeno Gaburro

Light Propagation with Phase

Discontinuities: Generalized Laws of

Reflection and Refraction

Xing Zhenping

Department of Optical Engineering

Zhejiang University

Page 2

Shape the wavefront

• conventional optical component

Lens and wavefront- Wikipedia

Gradual phase shift

accumulated during

propagation

Lack of freedom

• abnormal refraction & reflection

Metarefraction - Wikipedia

How to manipulate the

refraction angle when

the incident angle is

fixed ?

Page 3

Light propagation with phase discontinuities

Fermat's principle - the principle of the stationary phase

QED：光和物质的奇妙理论

Reflection:

Page 4

How to inprint phase discontinuities

•V - antenna

•2 modes - polarization

•B and C have a π phace difference

•scattered light from a

straight rod antenna

first-order antenna resonance

S: h ≈λeff/2 A: 2h ≈ λeff/2

brighter color - large currents

colored gradiant - directions of the currents

When the angle between the incident polarizationand the antenna symmetry axis is 45°

Page 5

Changing the angles

Analytically calculated amplitude and phase shift cross-polarized scattered light for V-antennas

gold rods with a circular cross section

λ=8 um

Page 6

V- antenna array

Γ

|dΦ/dx|= 2π/Γ

(G) FDTD simulations of the scattered electric field for the individual antennas

composing the array in (F)

Page 7

From materials to the 2-dimentional structures

A two-dimensional array of optical resonators

Spatially varying phase response

Subwavelength separation

Page 8

Experimental results

red curves: measured with a polarizer (magnified by a factor

of two for clarity)

black curves : measured with a polarizer

grey arrows: calculated results from EQU 6

Page 9

negative refraction & reflection

blue arrow: critical angle

Page 10

Discussion

• Gratings? Diffraction?

subwavelength spacing between the antennas

provide efficient scattering

prevent the occurrence of grating diffraction.

not too near - avoid the near-field coupling phenomena

Page 11

Discussion(2)

Fresnel lens ?

When can we apply the generalized laws of refraction & reflection?

deeply subwavelength thickness of the array

abrupt phase changes with no contribution from propagation

Fresnel lens - Wikipedia

Reference

Yu, Nanfang, et al. "Light propagation with phase discontinuities: generalized

laws of reflection and refraction." Science 334.6054 (2011): 333-337.

Further reading: Biagioni, Paolo, Jer-Shing Huang, and Bert Hecht. "Nanoantennas for visible

and infrared radiation." Reports on Progress in Physics 75.2 (2012): 024402.

Special thanks to lens(optics) - Wikipedia

meta material - Wikipedia

fresnel lens - Wikipedia