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Abstract
Considering that previous invisible gateways (an open entrance that only blocks electromagnetic waves) based on super-scatters designed by transformation optics cannot effectively work for narrow beams and light rays that do not touch negative refractive index material, we explore a new way to realize an improved invisible gateway that can give a good performance for both light waves and rays. In all previous invisible gateways, they require a finite thickness of the wall and the gateway. For the improved invisible gateway proposed in this study, there is no requirement on the thickness of the wall and gateway, i.e. the wall and gateway can be infinitely thin. Our study will go a further step to realize the invisible gateway in fiction.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Invisible gateway is a special entrance that allows all other kinds of entities except electromagnetic waves. It can be treated as a concealed entrance within a background wall, i.e. a hidden portal mentioned in fiction [1]. In 2009, Luo et al, proposed a method to achieve such an invisible gateway using a super-scatter designed by transformation optics (TO) [2]. The basic schematic diagram of an invisible gateway designed by TO is shown in Fig. 1(a). TO is a theoretical tool that can design novel electromagnetic devices by a coordinate transformation method [3–10], which has been invested many researches in recent years. Many new topics are still emerging from TO, including illusions for magnets [11], time travel [12, 13], polarization manipulation [14], optical surface transformation [15, 16], surface waves devices [17, 18], novel lenses [19, 20], transforming emissions [21], remote cloakings [22]. To design a super-scatter, it requires a spatial folding coordinate transformation, i.e. some double negative refractive index materials are unavoidable [5], which often limits its working frequency. Chen et al, theoretically designed a magnetic photonic crystal structure to realize a broadband invisible gateway by TO [23]. Later, an ‘invisible gateway’ has been experimentally demonstrated by a transmission medium, i.e. not a true invisible gateway in free space [24]. In 2015, a reduced invisible gateway has been realized by crossed split-ring resonator and wire unit cells around 11GHz for single polarized wave [25]. Our group tried to use classic waveguide theory to understand the working mechanism of the invisible gateway [26]. The gate can be treated as a waveguide for electromagnetic wave. If we set some scatters inside this waveguide, it can block the incident electromagnetic wave at certain frequency (i.e. the corresponding mode at this frequency in the waveguide is prevented by the scatter). We can also broaden the working bandwidth of this invisible gateway by setting more scatters inside the gate without using any negative refractive index materials.
Fig. 1 (a) The basic schematic diagram of an invisible gateway designed by TO (Left) and a real gateway (Right). The red regions are PECs (i.e. the walls that electromagnetic waves cannot go through). The yellow and white regions are negative refractive index materials (μr = εr = −1) and free space, respectively, which are complementary medium pairs. The invisible gateway blocks electromagnetic waves produced by a source on the right side. Other materials, e.g. a human from left, can go through this gateway. However, for a real gateway, both electromagnetic waves and other materials (e.g. a human) cannot go through it. (b) Full-wave 2D simulations for the normalized amplitude of electric field distributions when a unit line current on the right side of the invisible gateway (Left) and real gateway (Right). Since the wave touches the negative refractive index materials in the invisible gateway, some surface plasmon polaritons are excited. In this case, no electromagnetic waves enter into the other side of the wall. (c) Full wave 2D simulations (Left) and ray optic simulations (Right), when a narrow beam/ray impinges onto the air region of the invisible gateway. In this case, nearly no beam/ray touches negative refractive index materials of the invisible gateway, and hence, no invisible gateway effect (i.e. narrow beam/ray passes through the wall). The ray propagates with time is given in Visualization 1. The black arrow indicates the direction of the incident light. The invisible gateway we use here is from Ref. 18.
However, there are still some limitations on all previous proposed invisible gateways: i) In real sense of invisible gateway, the wavelength of incident electromagnetic wave is often much smaller than the size of the gateway (geometrical optic approximation works), which makes it much tougher to achieve such an invisible gateway by setting some scatters inside the waveguide. For invisible gateways designed by TO [2, 23–25], they cannot work either when a light ray directly impinges onto the free space region of the gateway (i.e. the light does not touch the negative refractive medium). As shown in Fig. 1(b), the invisible gateway can work very well for the case that the wave touches the negative refractive index materials (it excites the surface plasmon polaritons). However, it will lose its performance for an infinitely narrow beam or a light ray that does not touch the double negative refractive index materials (surface plasmon polaritons cannot be excited) in Fig. 1(c). This is the most serious problem of all current invisible gateways. ii) The effect of all previous methods requires a finite thickness of the wall. If the thickness of the wall is extremely thin, it cannot be treated as a waveguide, and there is no place to put the negative refractive index materials inside the wall. Previous theoretical studies on invisible gateway are mainly focused on how to choose a proper coordinate transformation for a spatial folding transformation to design a super-scatter and to calculate the required transformation medium by transformation optics. There is no strict mathematics analysis on the light trace when light rays do not touch the super-scatters (directly incident onto the free space region between the walls; especially, for the case when the beam is extremely narrow, and the wavelength is very small). Physically, it is reasonable that the light trace is virtually a straight line when the light ray propagates in free space. The light trace will be influenced little by the medium far away from the beam (i.e. the size of the gate can be arbitrarily large theoretically).
The starting point of this study is trying to explore some other way to realize an improved invisible gateway that is much closer to the hidden portal in fiction. For an invisible gateway in the real sense, for the light rays that directly go through the free space region at the middle opening of the wall, they can still be guided back, creating an illusion that these light rays are directly reflected from a virtual “gateway” at the middle of the wall. Even if the thickness of the wall is infinitely thin, the improved invisible gateway can still work. The purpose of this study is to continue previous studies on invisible gateway and make one further step towards some real application, and explore some other ways (without using transformation optics and super-scatters) to design an invisible gateway. This is not a comment on previous studies of invisible gateway.
2. Method and results
Our method is not based on TO, in which a super-scatter is often required to produce a virtual magnified PEC that fits the size of the gateway. Super-scatter (spatial scaling and folding transformations) is not a necessary condition to achieve such an invisible gateway effect. Once the real gateway is not located at the air region at the middle opening of the wall, and its virtual image is exactly in the right position at the middle opening of the wall, such an invisible gateway effect can be achieved. We can design some optical lenses that can shift the real gateway to form an image exactly located at the air region at the middle opening of the wall as shown in Fig. 2(a). We do need to shrink/magnify the size of the real gateway, and only need to make an image of equal size. There are many ways to achieve this effect, e.g. a novel optical translational projector [27], a super-lens [28] and some absolute optical instruments designed by geometrical optics [29–32].
Fig. 2 (a) The basic schematic diagram of our method to realize an invisible gateway. The purple region indicates the lens that can produce an image of the real gateway, i.e. the virtual gateway, at the center air region of the wall. (b) The composite lens we use in this study: an inside-out Eaton lens (colored green) and a super-lens (negative refractive index material slab) μr = εr = −1 (colored yellow). The red long lines and the red short line indicate the wall and the real gateway, respectively, which are both metals (modeled by extremely thin PEC boundaries in our later numerical simulations). All white regions are air. Note that there is an opening in the middle of the wall. H and d indicate the height and thickness of this opening air region. The function of the composite structure is to form an image of the real gateway exactly at the middle of the wall (i.e. the location of the opening). The thickness of the wall and real gateway can be infinitely thin in our method.
In this study, we use a composite lens, i.e. an inside-out Eaton lens combined with a super-lens (a negative refractive index slab) to realize an invisible gateway, which can work very well for both light waves and rays. Our method does not have the problem of previous methods shown in Fig. 1(c). The structure of our composite lens is shown in Fig. 2(b), in which the refractive index of inside-out Eaton lens (colored green) is given by:
where a is the inner radius of the lens, and r2 = x2 + y2. Note that we only use half of inside-out Eaton lens whose center is exactly at the center air region of the wall, which is colored red lines in Fig. 2(b). The function of inside-out Eaton lens is to form a sharp image of the real gateway, which is denoted by the red short line aside to the yellow region in Fig. 2(b); the red short line is also a metal, like a part of metal wall) at the center air region of the wall. The yellow region aside to the real gateway is a super-lens (a slab with negative refractive index μr = εr = −1), which can also form an image of the real gateway at the center air region of the wall and recover the phase delay for light rays that directly incident onto the real gateway. The inside-out Eaton lens is designed by geometrical optics [32], which is similar to the method to design surface wave cloaking [17]. The super-lens is designed by transformation optics [19] and can be explained from the perspective of wave optics [18, 28]. Our composite lens is designed by a mixed method (both wave optics and geometrical optics). Next, we give the detailed explanations why the composite lens given in Fig. 2(b) can achieve an invisible gateway effect for both light waves and rays.From the perspective of ray optics, we can classify light rays incidents from right side to the wall into three types as shown in Fig. 3(a). Type A rays directly incident onto the real wall, which will be reflected by the Snell’s law. Type B rays directly incident onto the super-lens and real gateway, whose path of propagation can also be determined by Snell’s law as shown in Fig. 3(a). For the outside viewers, the reflected type B rays have the same trajectory with the type A rays (looks like reflected by a virtual gateway indicated by the dash red line). Type C rays can pass through the air region inside the wall and does not touch any of the real gateway and super-lens. The function of inside-out Eaton lens is to redirect type C rays back from the air region inside the walls, and makes them look like directly reflected from a virtual gateway inside the wall as shown in Fig. 3(b) and Visualization 2. Therefore, the reflected type C rays still look like directly reflected from the virtual gateway indicated by the red dash line as the type B rays. In short, the inside-out Eaton lens and super-lens work for type B and C rays, respectively. For the outside viewers whose eyes cannot sense any phase information of light, all incident rays look like being reflected from a real flat wall without any air gap in the middle.
Fig. 3 (a) Three types of light rays. Type A rays directly incident onto the real PEC wall and are reflected by Snell’s law. The type B rays are guided by superlens (colored by yellow) and reflected, which look like directly reflected by a virtual PEC wall (indicated by the dash red line). Type C rays are redirected by the inside-out Eaton lens (not shown here), which also look like directly reflected by the virtual PEC wall (the dash red line). (b) 2D ray tracing numerical simulation result when type C ray incidents onto the air hole between two walls. Inside-out Eaton lens can redirect the type C ray back even if the ray does not touch either the real gateway or super-lens. The color of the ray trace indicates different time.
Full wave numerical simulations also show that our composite lens can also be a good invisible gateway for light waves as shown in Fig. 4. The function of negative refractive index material in our composite structure is mainly to recover the phase delay, which can also be treated as a super-lens that images the real gateway to the air region at the middle opening of the wall. The function of inside-out Eaton lens is to redirect the light rays that do not touch any of the super-lens and the real gateway, which is also an imaging device of a common image with super-lens. Note that in all simulations of our composite lens, the thickness of the wall is assumed as an infinitely thin PEC, which cannot be utilized by all previous methods to realize an invisible gateway effect [2, 23–25].
Fig. 4 2D full wave numerical simulations for the normalized amplitude of electric field distributions. (a) and (c): a line source in front of a real gateway. (b) and (d): a line source in front of an invisible gateway achieved by our composite lens.
In above simulations, the left side of the wall is entirely enclosed by the inside-out Eaton lens as shown in Fig. 2(b), i.e. it is a closed room unlike the right side of the wall (with an open corridor). Considering that nearly no light is guided through the middle part of the inside-out Eaton lens, i.e. the region behind the super-lens in Fig. 3(b), we try to remove this part and create an open corridor on the left side of the wall as shown in Fig. 5(a). Note that we set the height of the gateway H = 0.2m and the distance between the super-lens and the wall d = 0.05m unchanged in all our simulations, and choose the wavelengths of incident waves and rays as λ0 = 0.3m (full wave simulations in Figs. 4 and 5, i.e. H = 2λ0/3 and d = λ0/6) and λ0 = 660nm (ray tracing simulations in Fig. 3(b) and Visualization 2, i.e. H≈3 × 105λ0 and d≈7 × 104λ0), respectively. As shown in Figs. 5(b) and 5(c), the electric field distributions on the right side of the wall are nearly the same as the field distributions for the case of original gateway in Figs. 4(a) and 4(c), respectively. The amount of energies leaking into the air corridor is very small. To study how much energy leaks into the air corridor, we make the integral of energy flow density on the boundary of the air corridor as plotted in Fig. 5(d). As the position of the line current source gets closer to the air hole inside the wall, more energies leak into the air corridor. However, compared with the case without our composite lens (only PEC wall), the leaked energies are greatly reduced when the invisible gateway is applied. The small amount of leaked energies may have some other applications, e.g. detectors (cannot be seen from the right side of the wall) on the left side of the wall can still receive very weak electromagnetic signal from the outside world (seeing without being seen).
Fig. 5 (a) The proposed invisible gateway with an air corridor at the middle of the inside-out Eaton lens. (b) and (c) are 2D full wave numerical simulations for the normalized amplitude of electric field distributions. The positions of the line current source in (b) and (c) are the same as the ones in Fig. 4(b) and (d), respectively. (d) The integral of power flow density on the boundary of the air corridor when the position of the line current source changes along the y direction for the cases when our composite lens is applied (blue line) or only PEC wall (red line) is used.
3. Summary
There are still related topics need to be studied in the future, which can be summarized as: i) the time domain response of invisible gateways. In recent studies by Qian et al, they find the time delay effect of super-scatter in the time domain [33]. It would be interesting to choose some special lenses without dispersion or low dispersion to design the invisible gateway. ii) The wall is modeled as PEC in our studies and all previous studies. The wall can be other kinds of media (e.g. wood, glass, cement) in some practical situations. How to design an invisible gateway for other kinds of wall is another follow-up study on this topic. iii) the most critical problem of most invisible gateways is that some negative refractive media are required, which limit the performance of invisible gateways in practice due to the loss. To achieve an invisible gateway without any negative refractive media will promote the application of invisible gateway. This problem may also be solved as the development of advanced artificial materials. There are many new kinds of artificial materials in recent years, such as super-thin surface materials (graphene [34] and metasurfaces [35]), graded index metamaterials [36], zero refractive index materials [37], etc.
There are some limitations of our method to achieve an invisible gateway. Firstly, our composite lens still requires negative refraction index materials, which may limit its bandwidth. Secondly, the invisible gateway will lose its performance when there is a person/object entering the open hole inside the wall, which is also a common problem for all previous invisible gateways.
We can envisage some applications of such a technology. For example, we can cloak the entrance of some important regions by the proposed invisible gateway, and set some special devices behind the wall (e.g. some laser weapons). Another application of such an invisible gateway is to create an electromagnetic protection region behind the metal wall with an open hole (for air circulation to outside world). Traditional electromagnetic protection is to enclose the whole protected region by metal wall without any circulation channel to the outside world.
To achieve an invisible gateway effect much closer to a hidden portal in fiction, we proposed a composite lens by an inside-out Eaton lens and super-lens together to realize an improved invisible gateway. Two main problems of previous methods have been tackled very well by our composite lens. In all previous methods, they cannot deal with light rays (or extremely narrow beams) that directly incident onto the air region inside the wall (see Fig. 1(c)). Our composite lens can redirect light rays (or extremely narrow beams) that do not touch either super-lens or the real gateway and make it looks like directly being reflected from a virtual gateway inside the wall. Unlike previous methods in which the wall should have a finite thickness, our composite lens can still work very well even if the thickness of the wall is infinite thin. The idea and method delivered in this study will produce new insights on invisible gateway and pave the way for realizing an invisible gateway in the real sense.
Funding
This work is partially supported by the National Natural Science Foundation of China (Nos. 11604292, 11621101, 91233208 and 60990322), the National Key Research and Development Program of China (No. 2017YFA0205700), the Postdoctoral Science Foundation of China (No.2017T100430), the fundamental research funds for the central universities (No. 2017FZA5001), the National High Technology Research and Development Program (863 Program) of China (No. 2012AA030402), the Program of Zhejiang Leading Team of Science and Technology Innovation, the Preferred Postdoctoral Research Project Funded by Zhejiang Province (No. BSH1301016) and AOARD.
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