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Abstract
Asymmetric optical transmission is fundamental and highly desirable in information processing and full manipulation of lightwave. We here propose an asymmetric optical transmission device consisting of a gradient metasurface and a one-dimensional subwavelength grating. Owing to the unidirectional excitation of surface plasmon polaritons (SPPs) by the gradient metasurface, and SPP-assisted extraordinary optical transmission, forward incident light has much higher transmission than the backward one. We combine temporal coupled mode theory and finite-difference time-domain simulations to verify its operation principle and study the performance. The results indicate that asymmetric transmission with high-contrast and large forward transmittance can be obtained around the 1.3 µm optical communication band.
© 2017 Optical Society of America
1. Introduction
The realization of asymmetric optical transmission has been a thriving research theme owing to its potentially important applications in integrated photonic systems for communications and information processing [1–8]. Analogous to its electronic counterparts, asymmetric optical transmission is characterized by the high contrast between forward transmission (front-side incidence) and backward transmission (back-side incidence). Conventional approaches for asymmetric transmission include using magnetic-optical materials [2,3] or nonlinear materials [4,5]. However, they are difficult to achieve on-chip integration due to their bulky size or the requirement of high operating threshold intensity. Artificial structures can also be used for asymmetric transmissions, such as photonic crystals [6,7], non-symmetric gratings [8–10], chiral metamaterials [11,12], and so on. Nevertheless, the incident electromagnetic (EM) wave usually undergoes cross-polarization conversion in those asymmetric transmission devices based on chiral metamaterials [12], or is transformed into higher diffraction order by the non-symmetric grating [8]. Generally speaking, all these regimes can be explained in terms of one-way mode conversion [10], which relatively limits their practical applications.
Surface plasmon polaritons (SPPs) are highly localized EM wave bounded at metal/dielectric interface, propagating along the interface and decaying exponentially in the vertical direction of the interface [13,14]. Owing to the ability of confining EM waves on the subwavelength scale, SPPs have wide applications in nanophotonics, imaging, biosensing and photonic integrated circuits, etc. However, momentum mismatching problem prevents a free-space light from efficiently coupling into SPPs, or vice versa [15]. Therefore, it is necessary to modify the dispersion relation at the interface to satisfy momentum conservation [13], and a variety of methods have been explored to excite SPPs, such as using bulky prisms [16] or gratings [17], introducing topological defects on surface [14], etc. However, they are usually inefficient and lack the ability to dynamically control the phase or amplitude of the excited SPPs. Recently, metasurfaces have been introduced to control EM waves on the subwavelength scale [18–21] and opened new possibilities for the efficient coupling between propagating waves and SPPs [22–24]. According to the generalized Snell’s law [20], when the induced phase gradient of the metasurface is greater than the wave vector of the incident wave in free space, the incoming wave can be coupled into SPPs even at normal angles of incidence [22].
We here propose a novel scheme for asymmetric optical transmission device by using a gradient metasurface capable of unidirectionally exciting SPPs. By optimally designing the asymmetric device structure, only forward-propagating waves are able to excite SPPs by the gradient metasurface and then transmit through the device, whereas the backward optical waves cannot excite SPPs and most of them are reflected.
The organization of this paper is as follows, section 2 presents device structure and operation principle, section 3 gives the design guidelines for asymmetric optical transmission device, and section 4 shows the results and discussion. Brief conclusions are given in the final section.
2. Device structure and operation principle
Figure 1 schematically shows the configuration of the asymmetric optical transmission device, which consists of an upper gradient metasurface and a bottom one-dimensional (1D) subwavelength grating. The gradient metasurface employs meta-insulator-metal (MIM) configuration, which is composed of gold (Au) cross-shaped antennas and a very thin Au film separated by a SiO2 dielectric layer. And the metasurface is designed such that it provides the incident EM wave with a large enough phase gradient to excite SPPs on the metal/dielectric interface. Specially, in order to ensure the SPPs to efficiently tunnel through the Au film and then enter into the bottom grating layer, the thickness of the Au thin film is chosen to be smaller than the penetration depth of the SPPs in the metal layer [25,26]. The bottom grating, consisting of Au wires along the y-axis on a SiO2 dielectric layer, serves the function of decoupling the SPPs into free space.
Fig. 1 Schematic diagram of the asymmetric optical transmission device. Region surrounded by dashed white line corresponds to two super-cells of the metasurface.
Intuitively, the opaque Au film in the metasurface seems to block the incident light. However, through the formation of SPPs, it can assist to couple more SPPs into the bottom grating layer and thus enhance the transmission of forward-propagating light. Conversely, without the formation of SPPs, the opaque Au film will indeed block the incident light. This is the basis of our proposed asymmetric transmission device.
The operation principle of asymmetric transmission is as follows. When a x-polarized light illuminates the device in the forward direction (i.e., along the negative z-axis), it is efficiently coupled into SPPs propagating along the metal/dielectric interface, then tunnels through the Au thin film, decoupled by the bottom grating layer, and finally enters into the free space. By contrast, under backward illumination, the lightwave first hits the bottom grating layer, where SPPs cannot be excited because wave vector matching is not satisfied there. Consequently the backward incident light is very hard to penetrate the opaque Au film, and most of the incident light is reflected.
The mechanism can also be understood by temporal coupled mode theory [27,28], which elucidates that the energy exchange between an incoming light and a local system is connected by the radiative process of the system, and the spectroscopic properties of optical systems can be well controlled by manipulating the radiative decay rate [25]. Here we define as the decay rate of the SPP mode radiating into the reflection space where the incoming light comes from, and the counterpart for transmission space. When the lightwave with power |s0|2 is incident on the system, the time variant of the SPP mode amplitude, a, can be expressed as [25,28]:
where is the angular frequency of the SPP mode, and is absorption rate. From conservation of energy, the amplitude of the outgoing wave st can be given as [25]:where the first term describes the contribution from direct transmission with t being the direct transmission coefficient, and the second term represents the contribution of radiative coupling from SPP modes. From Eq. (1) and Eq. (2), transmittance T for an incoming wave with angular frequency ω can be written as [25]:Considering a forward incident EM wave with angular frequency , SPPs can be efficiently excited by the gradient metasurface as mentioned above, its transmittance Tf1 can be readily simplified as:
Due to the opaque Au film in the metasurface, direct transmission coefficient is very small, i.e. t «1 [25]. However, the MIM gradient metasurface still can get high transmittance Tf1 as a result of the excitation of SPPs. And then the forward propagating lightwave will subsequently pass through the bottom grating layer, and the total forward transmittance Tf will be relatively higher.
Nonetheless, the situation for backward illumination is quite different. When the same optical wave with angular frequency illuminates the bottom grating layer, no SPPs can be excited at the grating because of the asymmetry of the device structure and momentum mismatch problem: the period of the bottom grating layer is not the same as that of the metasurface, and then the angular frequency of SPPs that can be excited in this case no longer equals . Then under backward illumination, even if the backward-propagating wave is able to pass through the bottom grating layer with relative transmittance Tb1, it will be largely blocked by the opaque Au film without the help of SPPs. Consequently, the total backward transmittance Tb will be relatively lower.
In brief, the key factors that contribute to asymmetric transmission lie in the asymmetric device structure and the resulting unidirectional excitation of SPPs and SPP-assisted extraordinary optical transmission. Under forward illumination, the generation of SPPs by the metasurface helps the device to obtain a higher transmittance. In comparison, no SPPs is excited under backward illumination, and then little light can penetrate the system into the transmission space.
3. Design guidelines for asymmetric transmission device
In the following, we first explain how to design the gradient metasurface to efficiently excite SPPs, and then discuss how to construct the asymmetric transmission device by combining the gradient metasurface and a 1D grating.
3.1. Design of gradient metasurface
For the sake of simplicity and without loss of generality, we consider a metasurface offering phase gradient along the x direction, anomalous reflection is achieved by the phase gradient dϕ/dx = 2π/η, where η denotes the period of a super-cell of the metasurface, dϕ and dx are the phase difference and the distance between adjacent units in a super-cell. According to the generalized Snell’s law [20], for a normally incident light, reflection angle θr follows:
where λ0 and 2π/λ0 are the wavelength and wave vector of the incident EM wave in vacuum, respectively. It is clear that, if phase gradient dϕ/dx is bigger than the wave vector of the incident wave, namely, λ0 ≥ η, then a normally incident light will be coupled into SPP that propagates along the interface.Figure 2(a) shows the elementary unit for constructing the super-cell of the metasurface, in which the upper layer is an Au cross-shaped antenna with thickness t1, the middle layer is a SiO2 spacer layer with thickness t2, and the bottom layer is an Au thin film with thickness t3. When the unit is illuminated with a normally incident x-polarized EM wave along the negative z-axis, electric currents will be induced in both the top Au antenna and the underneath Au film. Because the two layers are in close proximity and only separated by a thin dielectric spacer, strong near-field coupling would lead to anti-parallel currents circulating between the top Au antenna and the underneath Au thin film, generating a magnetic resonance at a particular wavelength inside the SiO2 spacer [26,29]. Obviously, such a magnetic resonance is related to the size of the top Au antenna, so the reflection phase delay of each unit can be readily tuned by varying the arm length L of the Au antenna. Fixing the period of the unit p = 300 nm, t1 = 30 nm, t2 = 50 nm, t3 = 25 nm, w = 120 nm, we vary the arm’s length L of the cross-shaped Au antenna to realize different reflection phases. Figure 2(b) shows that reflectance and phase of the reflected light vary as the arm’s length L. According to Eq. (5), the period of the super-cell should be smaller than the wavelength of incident waves to realize the vertical coupling of SPPs. Specifically, we consider a normally forward incident wave with wavelength λ0 = 1305 nm and choose four units to construct a super-cell with periodicity η = 1200 nm, as shown in Fig. 2(c). The four units, with arm lengths L1 = 90 nm, L2 = 199 nm, L3 = 218 nm and L4 = 254 nm, respectively, provide similar reflectivity and incremental reflection phase with 90° steps, as can be seen from the marked squares in Fig. 2(b).
Fig. 2 Super-cell design of the gradient metasurface. (a) Structure of a unit. (b) Reflectance and phase of the reflected light as a function of arm’s length L, the incident wavelength is 1305 nm. The squares indicate the simulated reflection and phase of the four units shown in Fig. 2(c). (c) Front view of a super-cell.
To confirm the SPP excited by the designed gradient metasurface, an infinite gradient metasurface is simulated using full three-dimensional finite-difference time-domain (FDTD) simulations, in which periodic boundary conditions are used along the x- and y-directions, and perfectly matched layer boundary condition is applied to the z-direction. The x-polarized plane waves normally illuminate from the negative z direction. Figure 3 gives the simulated reflectance spectrum. Compared with other reflection dips, the sharp dip at λ0 = 1305 nm has higher Q factor, implying that stronger SPPs might be generated in the metasurface. To confirm this, we present in Fig. 4(a) the z-components of electric field Ez in the x-z plane at wavelength 1305 nm, which clearly shows that strong surface-confined SPP wave is generated in the gradient metasurface. And the Ez field distribution in the x-y plane depicted in Fig. 4(b) also indicates that a well-defined SPP with wavelength λSPP = 1230 nm.
Fig. 4 Electric field distributions at incident wavelength 1305 nm. Simulated Ez field distributions on the (a) x-z and (b) x-y planes. The dashed white rectangles denote the location of the gradient metasurface. And λSPP = 1230 nm is the wavelength of the SPPs.
3.2. Design of asymmetric EM wave transmission device
Now let us consider how to realize asymmetric transmission. As we know, when the thickness of the metal film is smaller than SPP’s penetration depth, SPP field is able to penetrate the metal film [30]. The penetration depths of SPPs in the metal (δm) and dielectric (δd) layers are expressed as [31]:
where ε'm and εd are the real permittivity of the metal and dielectric, respectively.The thickness of the Au film in the metasurface is smaller than the SPP’s penetration depth, then under forward incidence, the SPP wave excited by the metasurface is able to penetrate the Au film into the bottom grating, then decoupled by it, and finally enters the transmission space.
As for the bottom grating, in order to ensure it to decouple light around 1.3 µm optical communication band and avoid the excitation of SPPs, its grating constant d is specifically chosen to be 300 nm, which is different from the period of a super-cell (η = 1200 nm) in the metasurface. Our simulation results, which will be discussed later in the next section, also confirm that SPPs are not excited in the grating layer around this wavelength range because momentum conservation condition for SPP excitation, i.e, k'SPPs = k0 ± 2nπ/d, is not satisfied, where k'SPPs is the wave vector of the SPPs in the grating, k0 = 2π/λ0 is the wave vector of the incident wave in the vacuum, θi is the incident angle and n is an integer. Consequently, without the aid of SPPs, the back-incident light can hardly penetrate the opaque Au film, and the total backward transmission will be very low.
Following these design guidelines for asymmetric optical transmission device, we choose parameters as follows: for the gradient metasurface, the corresponding parameters are given in Section 3.1. As for the 1D subwavelength Au grating, the grating constant, the width and thickness of the Au wire are d = 300 nm, w1 = 230 nm, t4 = 30 nm, respectively, and the thickness of SiO2 in the grating layer is 50 nm.
4. Results and Discussion
To verify the operation principle of asymmetric optical transmission, we performed full three-dimensional FDTD simulations. Figure 5(a) shows the simulated transmittance spectra for forward and backward propagating waves. As can be clearly seen, forward transmittance is much higher than the backward one over a broad range of wavelengths. However, it should be mentioned that the backward transmittance spectrum exhibits a maximum at wavelength 750 nm, which is a result of the generation of SPPs by the grating layer. And one also can see that around this wavelength 750 nm, the difference between forward and backward transmittances is small, which will cause a small contrast ratio and then deteriorate the performance of the asymmetric transmission device. Therefore we don’t discuss this wavelength range in the following because of the lower transmission and the lower contrast ratio. Instead, we focus on our targeted wavelengths, i.e., the 1.3 µm optical communication band in which a relatively higher forward transmittance and a larger contrast ratio can be obtained simultaneously.
Fig. 5 (a) Transmittance spectra for the forward and backward directions. (b) The contrast ratio versus wavelength.
The contrast ratio (CR) of asymmetric optical transmission is expressed as:
where Tf and Tb are the transmittance for the forward and backward propagating waves, respectively. Figure 5(b) presents contrast ratio versus wavelength. One can see that there is a contrast ratio peak of 11.6 dB at wavelength 1354 nm with forward transmittance of 0.57. It is noteworthy that this wavelength deviates from the designed wavelength (λ0 = 1305 nm) of the individually designed gradient metasurface, the reason lies in the near-field coupling between the gradient metasurface and the 1D grating. Moreover, one can see that among wavelength range of 1291 nm ~1436 nm (denoted by the two vertical dashed lines in Fig. 5(b)), contrast ratio is more than 5.8 dB, meaning the 3-dB working bandwidth of the asymmetric transmission device is as wide as 145 nm.To further comprehend the mechanism of the asymmetric transmission, Fig. 6 depicts the x- and z-components of electric field distributions at wavelength 1354 nm for the two opposite incidence directions. When the forward incident light illuminates the device, it is coupled into the SPPs by the gradient metasurface. Then the SPPs penetrate the Au thin film, finally it is decoupled into the free space as higher order transmission mode, as shown in Figs. 6(a) and 6(b), the inset is the zoomed map of Fig. 6(b). Namely, this transmission process contains three steps, i.e., coupling into the gradient metasurface, tunneling through the Au thin film, and coupling out of the 1D grating. In contrast, when the backward incident light illuminates the device (see Figs. 6(c) and 6(d)), the SPPs can’t be excited by the subwavelength grating so that the incident light is very hard to penetrate the opaque Au thin film and therefore it is mostly reflected. Even though a little of the energy is able to pass through the Au thin film, it is converted into SPPs by the upper gradient metasurface, thereby confined in the metasurface with little transmitted into the free space, as shown in Figs. 6(c) and 6(d).
Fig. 6 Electric field distributions at wavelength 1354 nm for the two opposite directions of incidence: (a) Ex and (b) Ez field distributions under forward illumination, transmission is in the higher order mode; the inset is the zoomed map of Fig. 6(b). (c) Ex and (d) Ez field patterns under backward illumination, transmission is suppressed. The white dashed rectangles denote the location of the asymmetric transmission device.
The Au film is a key part of the MIM metasurface, and its thickness t3 is crucial to asymmetrical transmission. In what follows, we change thickness t3 while fixing other parameters and depict the transmittance spectra and contrast ratio against wavelength for t3 = 15, 25, 35 nm in Fig. 7.
Fig. 7 (a) Transmittance spectra of the asymmetric transmission device for the forward and backward directions and (b) contrast ratio against wavelength for t3 = 15, 25, 35 nm. “F” and “B” in the legend represent “Forward” and “Backward”, respectively.
It can be observed when t3 is 25 nm, the asymmetric transmission device has better performance with higher forward transmittance and contrast ratio over a wider spectral range. However, when t3 = 15 nm or t3 = 35 nm, the corresponding forward transmittance is relatively lower despite of higher contrast ratio.
In order to understand the underlying mechanism, we map in Fig. 8 the z-component of the electric field pattern at wavelength 1354 nm for different thicknesses t3. When Au film is too thin, the coupling between the cross-shaped antennas in the metasurface and the grating is so strong that it ruins the initially designed gradient phase distribution in the metasurface and thereby SPPs can’t be excited by the metasurface (see Fig. 8(a) for t3 = 15 nm), resulting in a lower forward transmittance. Likewise, a too thick Au film also brings a lower forward transmittance, because when the thickness of the Au film is bigger than the penetration depth of the SPPs in the metal layer, the generated SPPs can’t efficiently tunnel through the metal and thus be trapped in the upper metasurface layer, as seen in Fig. 8(c) for t3 = 35 nm. Generally speaking, the Au film plays triple roles in the asymmetric optical transmission device, it not only can block direction transmission [25] and guide SPP wave, but also can tune the coupling strength between the upper antennas and the lower grating. And an optimized thickness of Au film (t3 = 25 nm in our case, see Fig. 8(b)) is beneficial for guiding SPP wave under forward illumination and blocking transmission under backward illumination, hence the device can realize both high forward transmission and large contrast ratio.
Fig. 8 Under forward illustration, z-component of electric field distributions at wavelength 1354 nm for different Au film thickness t3. (a) t3 = 15 nm, (b) t3 = 25 nm and (c) t3 = 35 nm. The white dashed rectangles denote the location of the asymmetric transmission device.
In addition to the Au film, the bottom 1D grating layer is also necessary to be optimized for higher contrast ratio while maintaining larger forward transmission. By varying the width w1 of the Au wire in the grating while keeping grating constant d = 300 nm and other parameters unchanged, we investigate the effect of filling fraction f (f = w1/d) of the grating, as shown in Fig. 9. As can be clearly seen, both transmittance spectra and contrast ratio strongly depend on filling fraction f. When f is smaller, the grating allows more lightwave to pass through it, hence both backward and forward transmittances are higher, consequently resulting in a smaller contrast ratio. On the contrary, when filling fraction f is larger, either the forward or the backward wave is largely blocked by the metal grating, hence their transmittances are lower even though contrast ratio is bigger. By adopting an appropriate filling fraction f (f = 0.7 in our case), the asymmetric transmission device can obtain a higher forward transmittance and bigger contrast ratio.
Fig. 9 Transmittance spectra of the asymmetric transmission device for f = 0.3, 0.7, 0.9. (a) Forward and (b) backward directions, (c) contrast ratio versus wavelength.
5. Conclusion
To summarize, we have proposed a new mechanism to achieve asymmetric optical transmission by combining a gradient metasurface and a 1D subwavelength grating. Quite different from previously reported works, we employ the unidirectional excitation of SPPs together with the SPP-assisted extraordinary optical transmission to realize asymmetric transmission device with high-contrast, large forward transmittance. Apart from the major contribution of gradient metasurface generating SPPs, the Au thin film and the bottom 1D grating also play important roles in blocking transmission under backward illumination, and guiding the SPP wave under forward illumination. Though the proposed device works around the 1.3 µm optical communication band, by scaling down the unit size, operation wavelength could also be extended to other wavelength bands, such as millimeter wave, terahertz, or even visible range.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (No. 61675074).
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