'Invisibility Cloak' Realized in Theory

Apr 18, 2008
Tetsuo Nozawa, Nikkei Electronics
Fig.1: Cross sectional view of columnar invisible cloak: The yellow lines are the trajectories of light. The lines in other colors represent the boundaries between five media that constitute the invisible cloak. The region outside the boundary of radius 1 is the medium w1 (refractive index n > 0), the region surrounded by the red and blue lines and the x-axis is the medium R1 (refractive index n > 0), the region surrounded by the blue and brown lines is the medium R2 (refractive index n < 0), the region surrounded by the brown and green lines is R3 (refractive index n > 0) and the region surrounded by the purple and green lines and the x-axis is the medium R4 (refractive index n < 0). Diagram courtesy of Ochiai, Toyama Prefectural University
Fig.1: Cross sectional view of columnar invisible cloak: The yellow lines are the trajectories of light. The lines in other colors represent the boundaries between five media that constitute the invisible cloak. The region outside the boundary of radius 1 is the medium w1 (refractive index n > 0), the region surrounded by the red and blue lines and the x-axis is the medium R1 (refractive index n > 0), the region surrounded by the blue and brown lines is the medium R2 (refractive index n < 0), the region surrounded by the brown and green lines is R3 (refractive index n > 0) and the region surrounded by the purple and green lines and the x-axis is the medium R4 (refractive index n < 0). Diagram courtesy of Ochiai, Toyama Prefectural University
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Fig.2: Enlarged view of central portion: Only the trajectories of light are shown in different colors. The central portion impenetrable to light is where an object can be hidden.
Fig.2: Enlarged view of central portion: Only the trajectories of light are shown in different colors. The central portion impenetrable to light is where an object can be hidden.
[ If it clicks, the expanded picture will open ]

Researchers at Toyama Prefectural University and other institutions announced that they theoretically formulated a "perfect invisible cloak."

The invisible cloak generates no reflection or phase delay at all even when an electromagnetic wave passes through it. It was developed with the use of an artificial dielectric material called "left-handed metamaterial," which has a negative refractive index n. It can be said that the researchers created a sort of blueprint of the perfect invisible cloak.

It is predicted that the use of left-handed metamaterials makes electromagnetic control devices available. Some examples of such devices are a lens that reflects no light and a lens that can provide a perfect focal point. They are believed to be difficult to produce with the existing materials. The latest development relates to one of these control devices.

The invisible cloak was designed by Tomoshiro Ochiai, a lecturer of Department of Information Systems Engineering of Faculty of Engineering at Toyama Prefectural University and two other researchers from University of St Andrews in Scotland, UK and Future University-Hakodate. A coauthored paper titled "A Novel Design of Dielectric Perfect Invisibility Devices" was published in a theoretical physics journal, "Journal of Mathematical Physics."

Here, an invisible cloak refers to a columnar or block object with a void in the core or center, which is designed such that a plane electromagnetic wave with a certain frequency irradiated at this object goes around the void and reaches behind the object. In particular, the object may be called "the perfect visible cloak" when the electromagnetic wavefront becomes planar again after passing through the object and the amplitude and the phase of the resultant plane wave completely coincide with those of the wavefront obtained when there is no object.

The cloak is named after the fact that it generates no reflection or phase delay when an electromagnetic wave with a given frequency is irradiated and the view behind the cloak can be seen as it is. Thus, taking into account an electromagnetic wave with a specific frequency, it appears as though anything hidden in the void portion of such an object will disappear together with the invisible cloak.

Five media attached together

The following describes the design of the latest invisible cloak (hereafter referred to as "the cloak"). The cloak has is substantially columnar in shape. Fig. 1 is a cross sectional view of the cloak. Note that yellow lines represent the trajectories of light that pass through the cloak, not the shape of the cloak itself. The scale indicates the space coordinates from the center. The unit of distance is arbitrary.

The cloak is composed of five metamaterials (artificial dielectric materials) with different values of refractive indices n and different index distributions, which are combined with one another like building blocks. In Fig.1, red purple green and blue lines illustrate the boundaries between these media.

The outermost medium w1 extends outside of the circle indicated by the red and purple lines. As a matter of fact, the outer side of this cloak cannot be clearly defined because the cloak extends towards infinity like gas. In Fig. 1, however, "it is appropriate to regard the vicinity of radius 5 as the practical outer borer," said Ochiai.

Designing "a green where the ball won't go in the hole"

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When the cloak is irradiated with "light" from a distance, the light starts to meander greatly from the vicinity of radius 3 and passes through a surface with a discontinuous refractive index n off into the distance again (Fig. 2). At the surfaces with discontinuous index n, light is either refracted in the shape of a left angle bracket or is not refracted at all.

The core portion of the cloak is impenetrable to light coming from any angle. Thus, anything placed in that portion becomes invisible when seen from a distance. The radius of the core region in the figure is approximately 0.12, although it differs depending on the maximum value of n and the distribution of index. The cloak is considerably thick, assuming that the radius 5 is the outer edge of the cloak.

Here, the distribution of refractive index n plays an important role for the cloak to be invisible. Light goes around the core portion because the distribution of refractive index in the media is designed such that the squared value of index n becomes greater in the direction of the core.

To the incident light, the squared value of the refractive index n is like bumps on a green to a golf ball. When a ball is hit with the same amount of force, there will be some places where the ball cannot reach depending on the height of bumps on the green.

No reflection or phase delay

The researchers set the following conditions for designing the media. (1) No light reflections occur at the boundaries between the media, (2) No phase delay generated in the light that passes through the media, with regard to the light that passes in the distance and (3) No variation between the direction of light approaching the cloak and the direction of light going away from the cloak.

Omitting the detailed description of how to satisfy these requirements, conditions (1)-(3) are met simultaneously by formulating the structure shown in Fig. 1, which consists of general materials combined with left-handed metamaterials with a negative index n.

The outermost medium w1 has a positive refractive index n, and the medium w1 merges continuously with the general space as it goes farther away from the core, that is, n =1. In contrast, the index n of the medium w1 slowly changes from 1 when it comes closer in the direction of the cloak core from the distance.

The deviation from n = 1 is smaller at positions distant from the cloak core, but suddenly varies at positions somewhat closer to the core.

The other four media are located inside radius 1. Media R1 and R3 both have a positive value for the index n, whereas media R2 and R4 have a negative value for the index n. The surfaces obtained by attaching the media R1-R4 with one another all have the same absolute value for the index n, only with the inverted signs.

The media R1 and w1 are attached together in such a manner that the index n of both media is continuous, whereas the medium R4 is attached with the medium w1 so that the signs of the indices n are inverted with respect to each other.

Easier to produce than existing cape?

The invisible cloak has been studied by a number of researchers since around 2006. A practical prototype targeted at the microwave has already been developed. But the existing cloaks are not "perfect" because they are designed without giving due consideration to the reflection.

Moreover, the refractive indices n are positive values. According to a mathematical theory called "Nachman's theory," it has been known that, when only using materials with a positive refractive index, "a perfect invisible cloak cannot be produced unless the materials that induce birefringence are used."

Birefringence is a phenomenon where the refractive index at one point of a medium varies depending on the incident direction of light and the wavefront direction. It is extremely complicated to artificially design such a medium.

Meanwhile, the latest cloak overcame the mathematical constraint by combining the left-handed metamaterial media with a negative refractive index n. Thus, it is no longer necessary to develop a birefringent medium. It is highly possible to develop a truly perfect invisible cloak if a left-handed metamaterial whose refractive index n becomes a negative value in the entire visible light range may be produced and combined in accordance with the latest design.