Supplementary Information
Title: Concealing with Structured Light
Authors: Jingbo Sun1, Jinwei Zeng1, Xi Wang1, Alexander N. Cartwright1, and Natalia M.
Litchinitser1*
*Correspondence and requests for materials should be addressed:
E-mail: natashal@buffalo.edu
I) Generation and annihilation of optical vortices
A spiral phase plate with a single turn step of h is shown schematically in Fig. S1. Assuming an
incident plane wave described by the complex amplitude u0  ,  , z  passing though the spiral
phase plate, the output amplitude u1 is given by
u1  u0 e x p il  ,
(S1)
where  is the azimuthal angle of the plate given by arctan  y x  , and l is the height of the step
normalized to a wavelength given by:
l  nh 
(S2)
where n is the difference in refractive index between the plate and the surrounding medium,
and is the wavelength. If we choose h such that l  m (m is any integer), the beam directly
after the plate is transformed into a vortex beam with topological charge of m, which specifies
that the phase rotates m times 2π in a single wavelength. The sign of m can be determined by the
direction of rotation.
If such a vortex beam u1 passes through another spiral phase plate with exactly the same step size
(h) but an opposite rotation direction (), the amplitude of u2 at the output of the second plate
can be written as:
u 2  u1 exp  il     u0 exp  il exp  il     u0 ,
(S3)
which indicates that the input beam shape can be perfectly reconstructed.
Figure S1. The structure of the spiral phase plate.
II) Materials and fabrication
Two spiral phase plates with the diameter of 22mm with opposite helicity were fabricated using a
standard machine tool (Handan Exotic Device Ltd. China). A milling tool was used to cut a spiral
ramp surface on the PMMA bulk sample with refractive index of 1.4872 by removing material
around the axis circle by circle, from the center to the edge. Each circle cutting was done in 72
steps and finally, resulted in a step size of h=1.06mm, or l=815 over a full turn.
In order to produce a vortex with charge ±1, these two spiral phase plate were immersed in a
refraction index matching fluid with refractive index n0=1.4878. The phase plates and immersion
fluid were chosen to produce a vortex beam with a topological charge of ±1 corresponding to the
difference in the refraction index n-n0=-0.0006.
Figure S2. PMMA spiral phase plate immersed in the refractive index matching fluid.
III) What is inside the darkness?
In the center of optical vortex, the phase in undefined, resulting in a dark core, where the
intensity is zero due to destructive interference. In our experiment, an elongated object (a needle)
is placed between the two vortex plates and inside the dark core of the vortex.
In order to visualize “the darkness,” we use a thin screen to “cut” the vortex and show its
cross-section along the propagation direction, as shown in Fig. S3. Indeed, Fig. S3 clearly shows
the central dark line corresponding to the vortex core or the singularity region.
Figure S3. The cross section of the vortex beam along its propagation direction.
IV) Experimental setup
Two spiral phase plates are placed in the light path with their central point in the middle of the
incident beam (that is large enough to be considered as a plane wave). A metal rod held by a thin
transparent slab is mounted on a stage which can translate and rotate laterally and vertically. In
the experiment, we tune the position and the orientation of the stage so that the axis of the metal
rod is contained inside the singularity of the vortex beam.
Figure S4. Experimental setup.
IV) Working bandwidth of the vortex based concealing device
As we show below, the proposed device above is robust and can operate over a wide range of
wavelengths. Since the charge imparted on the beam is a function of wavelength, the value of the
topological charge m can be a value of not an integer over the wavelength range. However, over
a certain range around it closest integer, e.g. m±0.1, the phase of the light rotates slightly more or
less than m full rotations. In this case, the light is in a metastable state and over propagation over
a certain distance may degenerate to its closest stable state, which would be a non-vortex beam if
m is close to 0 or a vortex beam with integer m. However, if the value of m is far from an integer,
the beam will not degenerate and may keep an altered doughnut shape pattern. Such tolerance of
the vortex beam generated using a spiral phase plate ensures a relatively wide working
bandwidth of the proposed concealing device.
We performed detailed numerical studies of the vortex behavior at different wavelengths to
quantify the working bandwidth of the concealing device. These studies suggest that the working
band ranges from 560nm to 700nm for the experimental conditions discussed in the text, as
shown in Fig. S5. For 545nm and 720nm, the beams produced by the spiral phase plate deviates
too much from m=1 and thus can not conceal the object any more.
Figure S5. Electric field distribution in the computation area and the intensity distribution
between the two spiral phase plates (right column), marked by the blue dashed line for different
wavelengths: (a) 720nm; (b) 700nm; (c) 633nm; (d) 560nm; (e) 545nm.
V) Image processing
We used Image J software to extract line plots shown in Figure 4. Yellow color in images shown
in Fig. 4 suggest that red channel of digital camera sensor was oversaturated (for the same reason
bright red sunset appears yellow or orange on photo). Therefore, we used Image J to extract the
information from a green channel of digital image that was not saturated.