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Abstract
A narrow-band and high-contrast asymmetric transmission (AT) device based on metal-metal-metal (M-M-M) asymmetric grating structure is proposed and investigated. Significantly distinct from previous reports, the upper and lower metallic silver (Ag) gratings are connected by a very thin metallic Ag film, without any dielectric spacer layer or subwavelength slit. Under forward incidence, the M-M-M structure supports efficient surface plasmon polaritons (SPPs) excitation and tunneling, more importantly, it promotes direct and thus high-efficiency SPPs decoupling, enabling high forward transmittance. While under backward incidence, the M-M-M structure offers not only high reflection by the Ag film but also a strong near-field coupling effect between the upper and lower gratings, which further suppresses backward transmittance, leading to near-zero backward transmittance. In addition, the M-M-M structure is optimized for narrow-band operation by employing grating groove depth effect and multiple interference effect. Numerical simulation results demonstrate that high-performance AT with high-quality factor (Q≈91), narrow-bandwidth (6.7 nm) and high contrast ratio is achieved, with forward transmittance of 0.72 and backward transmittance of 0.0015 at visible light (610 nm). Our work provides an alternative and simple way to high-performance AT devices.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Photonic devices with asymmetric transmission (AT) characteristic have attracted much attention due to their important applications in noise control or cancelation [1,2], source protection [3–5], systems for one-side detection / sensing [6–8], etc. For an ideal AT device, nearly 100% transmission is expected for light propagating from one side to the other in the forward direction but the light propagating should be restricted in the backward direction. A number of AT devices, including optical isolators, have been widely demonstrated by breaking time-reversal symmetry with magnetic-optical materials [9–11], but they have bulky size and need external magnetic field, making on-chip integration difficult. Alternatively, AT devices can also be realized by breaking spatial inversion symmetry with the use of the artificial structures, such as chiral metamaterials [12], asymmetric photonic crystals [13] and asymmetric gratings [14,15], and so on. Although they are significantly smaller in size, the main drawback is that it is difficult to realize narrow-band and high-quality factor (high-Q) AT characteristics due to the intrinsic loss of metallic materials [16–19] and the structures themselves having high radiative damping rates, which relatively limit their practical applications.
In recent years, AT devices based on the unidirectional excitation of surface plasmon polaritons (SPPs) have also been extensively studied by using metal-insulator-metal (M-I-M) asymmetric gratings [20], multi-layer gradient metasurfaces [21], and asymmetric metallic gratings coupled with extraordinary optical transmission through subwavelength slits (holes or apertures) [22]. However, these structures usually exhibit AT in a relatively wide range of wavelengths, not suitable for applications requiring narrow-band or single-wavelength operation. Although a high-Q AT device based on micro-ring nonlinear effect has been proposed [23], it requires large size and high input optical power due to a small nonlinear susceptibility coefficient, bringing challenges for its application.
In this paper, we present a narrow-band and high-contrast AT device by using metal-metal-metal (M-M-M) asymmetric grating structure, which consists of an upper silver (Ag) grating, a middle Ag thin film, and a lower Ag grating. Significantly distinct from other metamaterial-based AT devices using metal-insulator-metal (M-I-M) structure or with subwavelength slits (holes or apertures), the upper and lower Ag gratings here are directly connected by the very thin Ag film, without any dielectric spacer layers or any subwavelength slits in the AT device. When forward incident light illuminates the device, the SPPs, excited by the upper grating and tunneling through the Ag film, are directly and thus highly-efficiently decoupled by the lower grating, thereby achieving high forward transmittance. For backward incidence, the device can achieve near-zero backward transmission thanks to the strong reflection of the Ag film and the near-field coupling effect between the upper and lower gratings. In addition, by employing grating groove depth effect and multiple interference effect, the device exhibits narrow-band and high-Q AT characteristics.
The paper is organized as follows. In section 2, the device structure and operation principle are illustrated. Then the results and discussions are given in section 3, and finally conclusions are presented in section 4.
2. Device structure and operation principle
Figure 1(a) shows the schematic of the designed AT device, and Fig. 1(b) shows its structural unit, the period of which is p = 1200 nm. Unlike the usually used metal-insulator-metal (M-I-M) structure for AT devices in which the upper and lower metallic gratings (or metasurfaces) are separated by one or more dielectric layers [14,15,20,21], our proposed AT device is of metal-metal-metal (M-M-M) structure, which consists of an upper Ag grating, a middle Ag film layer and a lower Ag grating patterned on a SiO2 substrate. Therefore, the upper and lower Ag gratings here are directly connected by the Ag film layer, which is beneficial to enhance forward transmittance as we will demonstrated later. For the upper grating, its grating constant and Ag wire width are Δ1 = 600 nm, w1 = 220 nm, respectively; and its grating groove depth h1 is small, only 15 nm, meaning this grating has a shallow groove depth. For the lower grating, its grating constant, Ag wire width and grating groove depth are Δ2 = 400 nm, w2 = 200 nm, h2 = 110 nm, respectively. The middle Ag film layer is very thin with a thickness d of only 20 nm.
Fig. 1. (a) Schematic diagram of the AT device. The blue dotted line denotes one structural unit. (b) The unit cell includes two upper grating units (p = 2Δ1) and three lower grating units (p = 3Δ2). The upper and lower Ag gratings are separated by Ag film, and the lower grating is embedded in the SiO2 substrate.
The designed AT device is based on the unidirectional excitation of SPPs. The upper grating is optimally designed so that it can provide an appropriate wave vector increment to the forward incident light to excite SPPs on the air/upper grating interface. Meanwhile, in order to facilitate the excited SPPs to tunnel through the Ag film, the thickness of the Ag film needs to be smaller than the penetration depth of the SPPs in the metallic film [24,25]. While for the lower grating, it is designed to not satisfy the wave vector matching condition for SPPs excitation such that the backward incident light cannot excite SPPs at the same frequency.
The working principle for asymmetric transmission (AT) is as follows. When x- polarized incident light illuminates the device in the forward direction (i.e., along the positive z-axis), the SPPs excited by the upper Ag grating tunnel through the Ag film, and then are directly and thus efficiently decoupled into the SiO2 substrate by the lower grating layer. Therefore, the device can achieve high forward transmission. By contrast, in the case of backward illumination (along the negative z-axis), since the designed lower grating cannot excite SPPs in the same frequency vicinity, the backward incident light is very hard to penetrate the Ag film and is strongly reflected by it. In addition, we will reveal in the following section that the near-field coupling effect between the upper and lower Ag gratings also helps to suppress backward transmission. As a result, near-zero transmission can be achieved for backward propagating light.
In addition to high contrast between forward and backward transmissions, the designed device can also achieve AT operation with narrow bandwidth and high quality factor (Q-factor). According to groove depth effect in gratings [26], the smaller the grating groove depth is, the higher and narrower the transmission peak is. Hence, the groove depth of the upper grating is chosen very small (h1=15 nm) to achieve narrow-band transmission under forward incidence. In addition, multiple interference effect inside the device will further promote narrow-band operation.
At first glance, the structure and principle of this proposed device seems similar to some previous reports, especially the one we published in [21]. However, several notable differences exist. Firstly, the AT device in [21] consists of five structural layers (an upper gold (Au) metasurface and a lower Au grating, a layer of Au film, and two dielectric spacer layers); while the proposed device here has only three structural layers (the upper and lower Ag gratings, and the middle Ag film), which is more compact in structure and thinner in thickness (less than 1/4 of the operating wavelength). Secondly, stronger near-field coupling effect exists between the two grating layers in the proposed device here, while that in [21] exhibits no such effect because of the two thicker dielectric spacer layers inserted between the metallic layers. Thirdly, the working bandwidth in [21] is wide and the contrast ratio is not high, while the deigned device here exhibits narrow-band and high-Q performance by employing grating groove depth effect and multiple interference effect.
3. Results and discussions
In order to prove that the designed device can achieve AT with narrow-band and high-contrast performance, we adopt full three-dimensional finite-difference time-domain (FDTD) for numerical simulations, in which periodic boundary conditions are applied to the x- and y-directions, and perfectly matched layer condition is used along the z-direction. Here, the refractive index of SiO2 is set as 1.45, and the dependence of silver (Ag) permittivity on optical wavelength λ is taken from the experimental data by Johnson and Christy [27]. When 0.3µm < λ < 1.94µm, the permittivity of Ag can be expressed as [27]:
Figure 2(a) shows the simulated forward and backward transmittance spectra of the designed device. Here, the backward (or the forward) transmittance is the total transmittance, including the contributions from both the fundamental and all higher-order transmission modes [12,20,21,28,29]. It can be clearly seen from Fig. 2(a) that forward transmittance reaches 0.72 at wavelength 610 nm, while the backward transmittance is extremely low, only 0.0015. The full width at half maximum (FWHM = Δλ) of the AT device is as low as 6.7 nm.
Fig. 2. (a) Forward and backward transmittance spectra of the AT device. (b) Contrast ratio versus wavelength.
The contrast ratio of asymmetric optical transmission can be written as [20]:
where Tf and Tb are the transmittances of the forward and backward propagating light, respectively. Figure 2(b) shows the contrast ratio as a function of wavelength, it reaches 0.996 at 610 nm. It is worth pointing out that a good asymmetric transmission device requires not only larger contrast ratio but also higher forward transmittance.The above results show that the designed device can realize high-performance AT with higher forward transmittance (0.72), narrow bandwidth (6.7 nm), high quality factor (Q = λ/Δλ ≈91) and high contrast ratio, which can be used as a unidirectional bandpass filter [30]. Next, we will further explore how the device can achieve high forward transmission, near-zero backward transmission and narrow operation bandwidth.
3.1 Realization of high forward transmission
For forward incident light at wavelength 610 nm, Fig. 3 shows the corresponding Ex and Ez electric-field distributions, where the dotted rectangle represents the location of the device. As can be clearly seen in Figs. 3(a)–3(c), SPPs are excited in the air/upper grating interface, tunnel through the Ag film, and then are decoupled by the lower grating, and finally enter into the SiO2 substrate.
Fig. 3. Electric-field distribution for forward incidence at 610 nm: (a) Ez distribution along the x-z plane; (b) The zoomed map of (a); (c) Ex distribution along the x-z plane; (d) Ez distribution along the x-y plane, and the wavelength of the SPPs is found to be 590 nm. The dotted rectangle represents the location of the AT device.
Figure 3(d) depicts Ez distribution along the x-y plane, from which the wavelength of the stimulated SPPs is found to be 590 nm. Below we estimate SPPs wavelength (λSPPs) by theoretical calculations. Since the upper grating has a shallow groove depth (h1=15 nm), and shallow grooves are small perturbations to the flat interface, the wave vector of SPPs (kSPPs) in the air/grating is approximately equal to that in a flat interface between metal and air [31,32]:
It is clear that the excitation and tunneling of SPPs are prerequisite and main mechanisms for high forward transmission. Equally importantly, the direct decoupling of SPPs by the lower grating also contributes to high forward transmission. In our proposed M-M-M structure device, the upper grating and the Ag film has a very small total thickness (35 nm), and they are directly connected to the lower grating, which is beneficial to high-efficiency decoupling of SPPs.
In order to verify the contribution of the abovementioned three factors (i.e., the SPPs excitation by the upper grating, tunneling through the Ag thin film, and direct decoupling by the lower grating), we analyze them one by one.
3.1.1 Excitation of SPPs by the upper grating
We employ diffraction compensation method to excite SPPs (i.e., use a grating to compensate the incident light for wave vector matching). The wave vector β for the light incident onto a grating is [31]:
where λ0 is the incident wavelength in vacuum, n is the refractive index of the dielectric, θ is the incidence angle, N is an integer representing diffraction order, and Δ represents grating constant. To excite SPPs, β should be equal to the wave vector of SPPs (i.e., kSPPs).It is noted that, the grating constants of the upper and lower metallic gratings are different, and their dielectric environments are also different from each other, hence the two gratings provide different wave vector increments to the incident light. In forward incidence case, the upper grating can excite SPPs; while for the backward incident light at the same wavelength, the lower grating cannot excite SPPs.
In order to further confirm that the designed upper grating can excite SPPs, Fig. 4(a) shows the schematic diagram of a structure consisting of the upper grating and a thicker Ag film. Here, we change the thickness of Ag film to d = 130 nm while fixing the upper grating parameters (i.e., the upper grating parameters of this structure are the same as the corresponding parameters in the proposed AT device shown in Fig. 1). Under forward incidence, the reflectance (R), transmittance (T) and absorbance (A) spectra are shown in Fig. 4(b).
Fig. 4. (a) Schematic diagram of the upper grating unit on a 130 nm-thick Ag film. (b) Corresponding reflectance (R), transmittance (T) and absorption (A) spectra. The inset is the Ez distribution in the x-z plane at peak wavelength 609.8 nm. The dotted rectangle represents the location of the AT device.
As can be seen, the transmittance is almost zero because the thickness of the Au film is bigger than the penetration depth of the SPPs. Moreover, a sharp reflection dip and absorption peak appear at 609.8 nm, with a high absorption of 0.71. It is reasonable to believe that this strong absorption peak is caused by the SPPs excited by the upper grating layer. This can be further proved by the distribution of the electric-field component Ez in the x-z plane as shown in the inset of Fig. 4(b). It proves that the upper grating is indeed able to excite SPPs at the incidence wavelength of 609.8 nm, which is also consistent with the peak transmittance wavelength of 610 nm as shown in Fig. 2(a) and Fig. 3.
3.1.2 Tunneling of SPPs through the Ag thin film
After ensuring that the upper grating can excite SPPs at the operating wavelength, we must carefully consider the thickness of the middle layer of Ag film to allow efficient tunneling of the SPPs. The penetration depth of SPPs in metal (δm) can be expressed as [32]:
In our design, the thickness of the Ag film is 20 nm, smaller than the above calculated penetration depth. Therefore, under forward illumination, the SPPs excited by the upper grating can tunnel through the Ag film, and then directly enter the lower grating to be decoupled.
3.1.3 Direct and high-efficiency decoupling of SPPs by the lower grating
As we mentioned earlier, previously reported AT devices based on unidirectional excitation and tunneling of SPPs usually have one or more dielectric spacer layers inserted between the upper and lower metallic grating (or metasurface) layers [14,20,21], that is to say, the stimulated SPPs have to pass through one or more dielectric layers before they reach the lower grating to be decoupled. In distinct contrast to this kind of indirect SPPs decoupling, the lower metallic grating in our proposed AT device naturally support direct decoupling of SPPs because no dielectric spacer layer is inserted in the metal-metal-metal (M-M-M) structure.
Here, we investigate the impacts of indirect and direct decoupling by inserting a SiO2 spacer layer between the Ag film and the lower grating, and comparing the corresponding forward transmittance spectra for different thicknesses S in Fig. 5, the inset of which schematically depicts the indirectly decoupled AT device with a SiO2 spacer layer of thickness S . It is worth mentioning that when S = 0 nm, direct decoupling of SPPs takes place in the lower grating, and in this case, the AT device shown in Fig. 5 becomes identical to our proposed AT device shown in Fig. 1. While when S≠0 nm, indirect decoupling takes places.
Fig. 5. Forward transmission spectra of direct decoupling and indirect decoupling of SPPs. The inset shows the indirectly decoupled AT device with a SiO2 spacer layer of thickness S.
As shown in Fig. 5, the AT device with S = 0 nm obtains the biggest forward transmittance, meaning that direct SPPs decoupling is helpful for bigger decoupling efficiency and consequently higher forward transmission.
To explore the mechanism behind this, we plot the electric distributions at transmittance peak-wavelengths for S = 0, 10, 40 and 60 nm in Fig. 6, where the dotted rectangle represents the location of the AT device.
Fig. 6. Ez electric-field distributions under forward incidence at transmittance peak-wavelengths: (a) at 610 nm for S = 0 nm; (b) at 610.6 nm for S = 10 nm; (c) at 612.3 nm for S = 40 nm; (d) at 611.5 nm for S = 60 nm. The dotted rectangle represents the location of the AT device.
As can be clearly observed in Fig. 6, for the indirectly decoupled AT device (S = 10, 40 and 60 nm), with the insertion of the SiO2 spacer layer, a restricted cavity forms between the middle Ag film and the lower Ag grating, and a portion of photons are confined within this cavity, taking part in cavity resonance (see Figs. 6(b)–6(d)), thus unable to propagate into the lower Ag grating to be decoupled. As a result, the decoupling efficiency of SPPs is attenuated, leading to a decrease in forward transmittance. While for S = 0 nm, after the SPPs tunnel through the Ag film, they are directly and promptly decoupled by the lower grating. Consequently, the decoupling efficiency of the SPPs is bigger and thereby a higher forward transmittance is achieved.
Therefore, we conclude that the direct and prompt decoupling of SPPs in the lower grating play an important role in the realization of high forward transmittance.
3.2 Realization of near-zero backward transmission
In the following analyses, we will elucidate that the near-zero backward transmittance originates from the following three factors: (i) The lower grating does not satisfy the wave vector matching condition for exciting SPPs at operation wavelength 610 nm; (ii) the Ag film reflects the backward propagating light; (iii) the near-field coupling effect of the upper and lower gratings further suppresses backward transmission.
It can be seen from the Ez and Ex electric-field distributions in Figs. 7(a)–7(b), the backward incident light at wavelength 610 nm does not excite SPPs. The light passing through the lower grating is strongly reflected by the Ag film layer, resulting in a low backward transmittance.
Fig. 7. (a) Ez and (b) Ex distributions in the x-z plane for backward incident light at 610 nm. The dotted rectangle represents the location of the AT device.
In the designed M-M-M structural AT device, strong near-field coupling effect exists between the upper and lower gratings since there is only a thin layer of Ag film separating them. To investigate this effect on backward transmission, we compare the backward transmittance spectra of three structures in Fig. 8.
Fig. 8. Backward transmittance spectra for the single-layer, two-layer, and our three-layer structures.
As can be seen from Fig. 8, Structure A, i.e., the single layer structure (blue solid line) which has only a lower Ag grating on the SiO2 substrate, has the biggest backward transmittance around working wavelength 610 nm. Then, by adding a middle Ag film to Structure A, one gets Structure B, i.e., the two-layer structure (black dotted curve) which comprises a lower Ag grating followed by a middle Ag film on the SiO2 substrate. In comparison with Structure A, Structure B exhibits significantly reduced backward transmittance because of the strong reflection of the Ag film. By further adding an upper grating to Structure B, one gets Structure C, i.e., our M-M-M three-layer structure (red dashed line) which is composed of a lower Ag grating followed by a middle Ag film layer and an upper grating on the SiO2 substrate. Compared with Structure B, Structure C displays a further suppressed backward transmission around working wavelength because of the near-field coupling effect between the upper and lower gratings, thereby achieving a near-zero backward transmittance of 0.0015 at 610 nm.
3.3 Realization of narrow operation bandwidth
According to groove depth effect in a grating, as the depth of grating groove decreases, the interaction of incident light with the grating is attenuated, causing absorption damping to decrease, therefor leading to an increase in the amplitude of the resonant peak and a decrease in bandwidth [26]. Figure 9 shows the forward transmittance spectra when the upper Ag grating has different groove depths while other parameters are kept unchanged. One can clearly see that as the grating groove depth h1 decreases from 40 nm to 15 nm, the transmittance at the resonant peak is increased while the bandwidth is decreased. In our AT device of M-M-M structure, the upper grating has a very shallow grating groove (h1=15 nm), this contributes to the narrow band characteristic. In addition, multiple interference effect between the light coupled from the SPPs excited by the upper grating and the light directly reflected by the Ag film will further narrower operation bandwidth [31].
Fig. 9. Forward transmittance spectra for the AT device when the upper grating has different grating groove depths. The inset shows the corresponding structure.
It is worth mentioning that, though the upper Ag grating has a very small groove depth, it can be fabricated by using focused-ion-beam milling [33–35].
3.4 Effect of Ag film thickness
As discussed above, the middle Ag film layer plays different roles in forward and backward illuminations. Under forward incidence, it promotes the efficient tunneling of SPPs, thus helps to increase forward transmission. While under backward incidence, it enhances reflection and thus reduces transmission. Therefore, it is critical to choose suitable thickness for the Ag film. We here study the effect of Ag film thickness d by changing d while fixing other parameters, and depict in Fig. 10 the forward and backward transmittance spectra for d = 15, 20, 35 nm.
Fig. 10. Forward and backward transmittance spectra of the AT device for d = 15, 20, 35 nm. ‘F’ and ‘B’ indicate that the incident directions of light are forward and backward, respectively.
Under forward illumination, one can find that when the Ag film is thicker (d = 35 nm), it is difficult for the SPPs to tunnel through the Ag film, resulting in a significant decrease in forward transmission. On the other hand, when the Ag film is thinner (d = 15 nm), the strong near-field coupling between the upper and lower gratings will change the excitation condition of SPPs, and then accordingly change the corresponding SPPs wavelength, resulting in a decrease in the forward transmittance at the operating wavelength.
But for the backward incident light, because the lower grating is designed such that it cannot excite the SPPs around the operating wavelength, and the Ag film enhances reflection, consequently, changing the thickness of the Ag film has no significant effect on the backward transmittance spectra.
4. Conclusion
In summary, we propose a high-performance asymmetric transmission (AT) device based on metal-metal-metal (M-M-M) three-layer structure, which consists of an upper Ag grating, a middle layer of Ag film and a lower Ag grating on a SiO2 substrate. Under forward incidence, the M-M-M structure enables efficient SPPs excitation and tunneling, more importantly, it promotes direct and thus high-efficiency SPPs decoupling in the lower grating, thereby achieving high transmittance of 0.72 at operation wavelength 610 nm. While under backward incidence, the M-M-M structure offers strong reflection by the Ag film, besides, the strong near-field coupling effect between the upper and lower gratings further suppresses backward transmittance, obtaining a near-zero backward transmittance of 0.0015 at operation wavelength 610 nm. Meanwhile, this high-contrast AT device also has narrow-band (full width at half maximum = 6.7 nm) and high-Q factor (Q≈91) characteristics by employing a shallow groove in the upper grating and multiple interference effect. Our proposed AT device may find applications in asymmetric narrow-band transmission, optical sensing, filtering, modulating and photonic integrated circuits. In addition, by changing the size of the structure unit, the operating wavelength can also be extended into other waveband.
Funding
National Natural Science Foundation of China (61675074, 61705127).
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