1. Introduction

Plasmonic gratings can flexibly tailor the behavior of light by modifying the propagation direction [1], intensity [2], polarization [3], and frequency [4]. These have extensive applications in sensors [5,6], polarizers [7,8], switches [9,10], splitters [11], and filters [12]. The spectroscopic response of plasmonic diffraction grating is strongly modulated by the Rayleigh anomaly and the particle plasmon resonance of metallic nanowires [13]. Thus, the diffraction of a plasmonic grating is within a selected spectral band with a fixed bandwidth determined by the Rayleigh anomaly, where the efficiency of the TM diffraction (polarized perpendicular to the nanowires) is significantly enhanced with respect to the TE diffraction (parallel to the nanowires) through interaction with the metallic nanowires due to particle plasmon resonance. Two juxtaposed parallel gratings with different periods form a compact device, which is defined as “heterograting”, that shows intriguing physical properties. The diffraction bandwidth of the heterograting, determined by both gratings, is tunable by changing the incidence angle and can be freely narrowed; that is, a tunable narrowband filter can be achieved. Furthermore, this kind of secondary diffraction beam propagates in a different direction and a separate path with respect to the reflected beam in the same device, hence can be picked out conveniently in practical applications.

It should be noted that the polarization device based on plasmonic gratings can be used directly in optical engineering for their high efficiency (>80%) [7] and high extinction ratio (>145) [8]. In this paper, we report a type of plasmonic heterograting that can be used directly as a bandwidth-tunable polarization filter. This compact device is composed of two gold nanogratings sitting on a transparent glass substrate and is fabricated using a simple solution-processible method [14] combined with interference lithography [15]. The TM polarization can be picked out in a tunable narrowband efficiently and conveniently using this heterograting device. These polarization features can be used to develop new polarization devices.

2. Fabrication of plasmonic heterogratings

The plasmonic heterograting is fabricated using a solution-processible method [14]. The photoresist (PR) mask grating is first produced by interference lithography as shown in Figs. 1(a) and 1(b). The S1805 photoresist (Rohm and Haas Electronic Materials Ltd.) is spin-coated (2000 rpm) onto a 180-nm (d₁)-thick indium-tin-oxide (ITO)-coated glass substrate of area 20 mm × 20 mm and thickness 1 mm (d₂), forming a high-quality thin film about 200-nm (h) thick. One-half of the film is exposed to a two-beam interference pattern with included angle α₁ between the two incident beams (Fig. 1(a)), and the other half is exposed with a different angle α₂ (Fig. 1(b)). The two-step exposure produces two adjacent gratings with different periods (Λ₁ and Λ₂), forming a PR mask of heterograting. A baffle, consisting of two flaps (A and B) which can move freely up and down, is employed to shield the underlying half of the PR film from unnecessary exposure. The trick here is that the exposure dose of the secondary exposure is larger than that of the first. Thus, the second grating will erase the first one in the overlapping region, enabling excellent connection between the two gratings. A continuous wave laser at 325 nm (Klmmon Kohn Co. Ltd.; Model: IK3301R-G) is used as the UV light source. Next, a colloid of gold nanoparticles [16] in p-xylene solvent with a concentration of 100 mg/ml is spin-coated (1800 rpm) onto the PR mask (Fig. 1(c)). Figure 1(d) illustrates the annealing process to form the plasmonic heterograting; in brief, the sample is heated to 400°C for 20 min in a muffle furnace and then cooled to room temperature.

 

Fig. 1 Schematic of the fabrication procedure of the plasmonic heterograting device. (a) One half of the PR film is exposed to a two-beam interference pattern with an included angle α₁, forming a grating with period Λ₁, and (b) the other half is exposed with a different angle α₂, forming a grating (Λ₂). A baffle is used to shield the appropriate half of the film from unnecessary exposure as shown in the inset. (c) The solution of the colloidal gold nanoparticles (100 mg/ml) is spin-coated onto the PR heterograting. (d) The plasmonic heterograting is formed by annealing. The grating ridge width is w; thicknesses of grating, ITO, and glass substrate are h, d₁, and d₂, respectively.

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The ITO layer, used as a waveguide in our previous work [6], plays no role in the performance of the plasmonic diffraction grating and is employed to fabricate high quality gold nanowires enabled by its different surface energy from normal glass [14]. We also emphasize that the gold grating is introduced to improve the performance of the plasmonic device using the strong polarization dependence of the particle plasmonic resonance for gold nanowires [7].

Figure 2 shows a photograph (left) and scanning electronic microscopy (SEM) image (right) of the plasmonic heterograting device. The blue and aurantium areas in the photograph identify the two period-differing halves of the heterograting. The SEM image of the interface between the two halves shows excellent connection.

 

Fig. 2 (a) Photograph identifying the two period-differing halves of the plasmonic heterograting device. Scale bar, 20 mm. (b) SEM image of the interface of the plasmonic heterograting marked by a square in (a). Scale bar, 1 μm. Λ₁ = 420 nm; Λ₂ = 480 nm.

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3. Spectroscopic and tuning properties of the compact polarization filters

The basic principles of the band-selective polarizers have been interpreted in our previous work [7, 8]. The incident light is diffracted by the grating and excites the propagation mode in the waveguide formed by the substrate, and then the diffracted beam is diffracted secondarily by the top grating, as shown in Fig. 3(a). The Raleigh anomaly at the grating-air and grating-silica interfaces set the lower and upper limits of the spectral band of the diffraction processes, which determines the bandwidth of the device. The first-order diffraction (the first- and second diffraction) of the device is considered in the structure, and the other diffraction orders do not exist due to the small periods.

 

Fig. 3 (a) Schematic of the principles of the plasmonic heterograting as a polarization filter. ③ and ④ identify reflected (R) and secondarily diffracted beams, respectively. θ₁ and θ₂ are the respective angles of incidence and diffraction. T identifies the transmitted beam. (b) Light-propagation tailoring by a plasmonic heterograting. ⑤ and ⑥ identify the secondarily diffracted beam of the heterograting around the interface. θ₃ and θ₄ are the respective diffraction angles for the first and second time. (c) Spots from the incident (①) and secondary-diffracted (②) beams from the device, and the reflected (③) and secondary-diffracted (④) beams impinging on a sheet of white paper. (d) Similar spots from two secondary-diffracted beams (⑤, ⑥) of the plasmonic heterograting. Λ₁ = 420 nm; Λ₂ = 480 nm. The blue dots and arrows in (a) and (b) indicate the direction of polarization of the light. The green arrows indicate the light propagation direction.

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Figure 3 demonstrates the difference between a plasmonic grating and the plasmonic heterograting as an optical filter; note the ITO layer is not included because of its extreme thinness with respect to the glass substrate. The bandwidth of the diffraction of a grating is determined by the Rayleigh anomaly, described by the formula:

For the grating with a period of Λ₁ shown in Fig. 3(a), the Raleigh anomaly at the grating-air interface satisfies condition: ${\Lambda }_1\sin {\theta }_1+{\Lambda }_1={\lambda }_1$. λ₁ sets the lower limit of the bandwidth of the diffraction. The Raleigh anomaly at the grating-silica interface satisfies condition: ${\Lambda }_1\sin {\theta }_1+n_s{\Lambda }_1={\lambda }_2$, where n_s = 1.5 at 600 nm is the refractive index of the silica substrate. If λ₂ denotes the upper limit of the bandwidth, the spectral band for the first-order diffraction is then defined by ${\lambda }_1<\lambda <{\lambda }_2$. The diffracted beam couples into the substrate and is diffracted secondarily by the same grating. Thus, the diffraction spectra for the first and the second time have the same fixed bandwidth

For the heterograting shown in Fig. 3(b), the diffraction bandwidths of the two gratings become different. The diffraction bandwidth for the grating with period Λ₁ is defined by ${\lambda }_1<\lambda <{\lambda }_2$ as discussed above. For the diffraction bandwidth of the grating with period Λ₂, the Raleigh anomaly at the grating-air interface satisfies condition: ${\Lambda }_2\sin {\theta }_4+{\Lambda }_2={\lambda }_3$, with λ₃ denoting the lower limit of the bandwidth. The Raleigh anomaly at the grating-silica interface satisfies condition: ${\Lambda }_2\sin {\theta }_4+n_s{\Lambda }_2={\lambda }_4$, with λ₄ denoting the upper limit of the bandwidth. Therefore, the spectral band is defined by ${\lambda }_3<\lambda <{\lambda }_4$, i.e., the bandwidth of the heterograting can be defined as

For practical applications, the diffracted beam (beam ⑥ in Figs. 3(b) and 3(d)) with TM polarization should be distinguished from the reflected beam (beam ③ in Figs. 3(b) and 3(d)), guaranteeing that it can conveniently be picked out. The displacement of the diffracted beam in the substrate (red line in Fig. 3(b)) is calculated by d₂tgθ₃, which is larger than the thickness of the substrate d₂, since θ₃ is larger than 45° due to the total reflection process, indicating that the separation between the two gratings of the heterograting is comparable to d₂ without deteriorating the performance of the device. The secondary diffraction angle (θ₄) also can be controlled by varying the grating period Λ₂. Thus, the separation between beams ③ and ⑥ can be adjusted by changing the thickness of the transparent substrate and the periods of the heterograting. Moreover, the separation between the reflected and the diffracted beams is bigger in the heterograting (beams ③ and ⑥ in Fig. 3(d)) than that in the conventional grating (beams ③ and ④ in Fig. 3(c)).

In the experiment, a nonpolarized white light from a tungsten halogen lamp (HL-2000) impinges on the surface of the plasmonic device at incidence angle θ₁. The sample is mounted on a rotating stage enabling the measurement of the angle-resolved tuning property of the device as shown in the inset in Fig. 4(d). The axis of rotation is parallel to the grating orientation. Almost all energy of the secondary diffraction beam is collected by the detection fiber of the spectrometer, where a lens with diameter 10 mm and a focal length of about 50 mm has focused the studied light beam into the fiber (F) with an diameter of 600 μm as shown in the inset in Fig. 4. Light-propagation tailoring by the plasmonic device is demonstrated in Figs. 3(c) and 3(d); there, the color of the secondary diffraction of the plasmonic heterograting (⑥) is purer than that of the plasmonic grating (④). Furthermore, the secondary diffraction angle (θ₄) and the reflection angle (θ₁) are different in the plasmonic heterograting, meaning that the secondarily diffracted beam can be observed more conveniently than from the single-period grating.

 

Fig. 4 The tunable spectral response of the plasmonic heterograting at different incidence angles from (a) theory and (c) experiment. (Here, Λ₁ = 420 nm, Λ₂ = 540 nm, and Λ₂/Λ₁≈1.29.) The spectral response at different period ratios from (b) theory and (d) experiment. The incidence angle θ₁ is 10°. The grey zones indicate the bandwidth of the device; the blue/red hashed zone denotes the diffraction bandwidth of the grating with a period of Λ₁/Λ₂. The colors and spectral positions of the double-arrows in (a)/(b) correspond directly to the spectra in (c)/(d). The panels above (a) and (b) show the rotation axis and the measuring setup, respectively. F denotes the fiber optic spectrometer, L denotes the lens, B is the baffle, S is the sample, and R is the rotating stage.

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The secondary-diffraction bandwidth of the heterograting device, defined as in Eq. (3), can be tuned by changing the incidence angle and the period ratio as marked by the grey zones in Figs. 4(a) and 4(b), respectively. From Fig. 4(a), λ₁ and λ₂ set the lower and upper limits of the bandwidth ($\Delta \lambda ={\lambda }_2-{\lambda }_1=\left(n_s-1\right){\Lambda }_1=210nm$) for the grating with period Λ₁, whereas λ₃ and λ₄ set the lower and the upper limits of the bandwidth ($\Delta \lambda ={\lambda }_4-{\lambda }_3=\left(n_s-1\right){\Lambda }_2=270nm$) for the grating with period Λ₂. The bandwidth for the heterograting is determined from the overlap of these two grey zones, which can be tuned from $\left(n_s-1\right){\Lambda }_1$ to zero. The spectroscopic characterization of the plasmonic device is measured using a spectrometer (Maya 2000 Pro, Ocean Optics). Figure 4(c) gives the incidence-angle dependence of the tuning of the output spectrum of the heterograting device, for setting shown in Fig. 4(a). For a fixed incidence angle, the bandwidth of the device can be tuned by changing the period ratio of the heterograting as indicated in Fig. 4(b).

The secondary diffraction beams of the plasmonic grating take more than 80% the total energy of the incident light, which have been reported in our previous work [7]. Similarly, the secondary diffraction (TM polarized beam) efficiency of the plasmonic hetero grating is around 80% when the period ratio is around 1 and decreases when it deviates from 1. For our experimental curves shown in Figs. 4(c) and 4(d), the lowest efficiency of the polarizer device is about 10%.

For a thorough understanding of the spectroscopic characteristics of the heterograting, we demonstrate the tuning of the secondary diffraction bandwidth (beam ⑥ in Figs. 3(b) and 3(d)) as a function of the incidence angle and the period ratio of the heterograting based on Eqs. (1) and (3). Figure 5 shows the standard bandwidth (defined by Δλ/Λ₁) of the heterograting as a function of the incidence angle and the period ratio, calculated based on Eqs. (1) and (3). The color bar codes the standard bandwidth. The horizontal and vertical white lines mark the respective cases shown in Figs. 4(a) and 4(b). Thus, a greater difference between the two periods yields a smaller maximum for the bandwidth. Also, the bandwidth of the heterograting device can be adjusted continuously by changing the incidence angle. These features enable the development of new polarization elements.

 

Fig. 5 (a) The standard bandwidth of the heterograting as a function of the incidence angle and the period ratio calculated by Eqs. (1) and (3). The color bar represents the value of the standard bandwidth (Δλ/Λ₁). The horizontal/vertical white line indicates the case shown in Fig. 4(a)/(b).

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5. Conclusions

We introduced a type of plasmonic heterograting that can be directly used as a compact bandwidth-tunable polarization filter. The bandwidth of the filter depends on the overlap of the first- and second diffraction and on the incidence angle of light. The bandwidth can be adjusted flexibly and continuously. Moreover, because of the difference in the reflection and diffraction angles, and the interaction with the gold nanowires through particle plasmon resonance, the TM-polarized output coupling of the heterograting can be picked out conveniently and efficiently. These features, which are quite different from the single-period device, can be exploited in developing new optical devices.