Supporting Information for
Dispersionless Phase Discontinuities for Controlling Light
Propagation
Lingling Huang1,2, Xianzhong Chen1, Benfeng Bai2, Qiaofeng Tan2, Guofan Jin2, Thomas
Zentgraf3, Shuang Zhang1
1. School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT, UK
State Key Laboratory of Precision Measurement Technology and Instruments, Department of
Precision Instruments, Tsinghua University, Beijing 100084, China
3. Department of Physics, University of Paderborn, Warburger Straße 100, D-33098 Paderborn,
Germany
4. Department of Physics, Hong Kong Baptist University, Hongkong
2.
Dipole model for deriving phase discontinuity for circular polarizations:
In Fig. S1, a single electric dipole forms an orientation angle  with x axis in x-y
plane (Note the same analysis also applies to a magnetic dipole). When circularly
polarized light excites the electric dipole at normal incidence, the normalized incident
electric field Eσ can be expressed as
Es = Ex e x + E y e y =
1
2
(e
x
+ s ie y
)
(A.1)
where σ = ±1 correspond to right- (RCP) and left-circularly polarized light (LCP), Ex,
Ey, ex, ey represent the electric field components and the unit vectors along x and y
direction, respectively. The amplitude of the induced electric dipole moment can be
expressed as
 px 
 cos2 
sin  cos    Ex 


p 
 
e 
sin 2    E y 
sin  cos 
 y
(A.2)
where px, py are the x- and y- components of the electric dipole moment, and αe is the
electric polarizability of the nanorod.
By substituting Eq. (1) into Eq. (2), the dipole moment p can be written as:
p=
ae
1
i
1
[( e x + s e y ) + e+s i 2j (e x - s ie y )]
2
2
2 2
(A.3)
As shown by Equation A.3, the dipole contains two terms. The first term, which has
the same helicity as that of the incident light, is independent of the rotation angle of
the dipole. On the other hand, the second term shows an opposite helicity to that of
incident beam, and a phase term that is twice the rotation angle of the dipole.
Calculation of the coupling efficiency:
We used Commercial software COMSOL Multiphysics for the simulation of SPP
unidirectional excitation. All the geometric parameters are in consistent with the
fabricated structures and the incident beam are set to be circular polarization which
illuminate from the air side. Periodic boundary condition is set in y direction, with the
others set to scattering boundary. Enough calculation area is included to eliminate the
reflection from the boundaries. The incident power flow across the metasurface area
is normalized to 1, and we calculate the SPP excitation power both in the metal and
substrate domain, by integrating the Poyntin vector over a cross section perpendicular
to the propagation directions. Note that only the components of Ez and Hy contribute
to the power flow of SPP, and are therefore used for the calculation. By such scheme,
the final SPP excitation efficiency is calculated to be 3.78%. We also numerically
simulated another metasurface design consisting of gold nano rods above the metal
surface separated by a dielectric film (MgF2), which exhibits a magnetic resonance
due to the metal-dielectric-metal configuration. The structure is shown in Fig. S1. At
288 THz, the SPP excitation efficiency can be dramatically increased to 14.25%.
y
arra
e
l
c
i
part
Gold
MgF
Go
ld
2
film

s
s
ub
ss S
te
stra
Gla
fil
m
y
z
x
Fig. S1. The configuration of an alternative design to enhance the launching
efficiency of SPP. Each element is a metal nanorod (blue) above the metal film
separted by a continuous dielectric layer (red). The gold nanorod has a thickness of 50
nm. The bottom gold film act as reflector, thus it should be optical thick enough to
prevent the transmission. The width (W) and the length (L) of the resonator are
carefully chosen to be 180 nm and 75 nm, respectively, with thickness of 30 nm. The
spacing between the nanorods is kept to be 550 nm.