Narrow band filter based on surface plasmon interference

ABSTRACT

Due to simple structure and easy-to-integration, metallic single slit array structure has attracted considerable attention and been widely investigated in recent years. A multi-channel comb filter composed of Au slit and graphene was proposed in this paper. It works at infrared wavelength range with narrow single-channel bandwidth and high pass band transmittance. After structure optimization, the single-channel bandwidth of the comb filter can reach 4.2 nm, which is nearly one time higher than the existing multi-channel comb filter based on surface plasmon polariton. Additionally, the structure of the filter is simple and more suitable for on-chip integration.

Keywords:
Comb filter; Surface plasmon polariton; Graphene; Microcavity

1. INTRODUCTION

Surface plasmons (SP) [¹] is a special form of electromagnetic field localized at the metal dielectric interface. It propagates along the metal surface and decays exponentially to both sides perpendicular to the interface. Due to its unique characteristics, functional devices based on SPPs can overcome the traditional optical diffraction limit, making optical integration in the micro- nano range possible. At present, the functional structures based on plasmon [²] are mainly concentrated on absorber [³,⁴,⁵], detector [⁶], modulator [⁷], sensor [⁸,⁹,¹⁰] and filter [¹¹,¹²,¹³,¹⁴,¹⁵,¹⁶]. Among them, the infrared filter has a wider range of applications, but most of the research focuses on single channel filtering [¹²–¹⁶]. The reports on multi-channel comb filtering are relatively few. Mainly, ZHENG et al. [¹⁷] designed a quasi-periodic sequence grating structure multi-channel filter based on MIM waveguide unit, and obtained 10 reflection channels in the frequency band of 1.2–1.8 um, but the single channel bandwidth was more than 30 nm; GONG et al. [¹⁸] inserted periodic structures composed of two different insulating media alternately between the two metal interlayer, and obtained 14 channels in the wavelength range of 1–2 um. Although the number of channels has been improved, the single channel bandwidth is still over 7 nm. To meet the practical requirement and make full use of the limited bandwidth resources, further improvement and optimization of the filter structure based on SPPs is in-dispensable.

A narrow-band comb filter based on SP interference is proposed in this paper. By introducing graphene into the surface of the metal single slit structure, the surface plasmons are excited to realize the coupling of the surface modes. It is known that photons in the infra-red can be readily coupled to surface plasmons in graphene and low losses can be expected resulting from long lifetime with hundreds of optical cycles [¹⁹]. In addition, a graphene filling in the single slit is employed to form a passband microcavity combined with the upper graphene layer. It produces interference effect and greatly narrows the single channel bandwidth in the transmission spectrum. In particular, SiO₂ dielectric layers are arranged on the upper surfaces, which strongly suppresses the reflection of the incident light wave and improve the transmittance uniformity between the channels. The interference comb filter has the advantages of simple structure, small size, easy on-chip integration, which shows a good application prospect in the fields of multi-channel data acquisition.

2. MATERIAlS AND METHOD

The structural diagram of the comb filter is shown in Figure 1. The lowest layer is gold film (Au) with a single slit of. The thickness of the gold film is 90 nm; The upper surface of the Au film is covered with a graphene layer. The uppermost layer is silicon dioxide (SiO₂) material, which is used to reduce light reflection and increase transmittance. In addition, silicon dioxide and graphene layers are arranged in the single slit from top to bottom to form a pass band microcavity, which will narrow the single channel bandwidth and improve the homogeneity.

Figure 1
Schematic diagram of the device structure (a) graphene layer on Au slit; (b) graphene in slit to form cavity and (c) comb filter structure.

FDTD (Lumerical solution, Inc) is used to simulated the transmission spectrum characteristics of the comb filter. Symmetry boundary conditon was used in the directions perpendicular to the light incident direction, and perfectly matched layer (PML) conditions was used in light incident direction. The refraction indexes n and absorption coefficients k of Au were taken from the FDTD solver database. In the near-infrared band, the refractive indexs of 1.45 was used for SiO₂ in the calculation. The dielectric constant of Au is expressed by Drude model [²⁰, ²¹]. The dielectric constant of graphene is [²²]:

(1) $${\epsilon }_{\text{c}}\text{= 1 +}i{\sigma }_g\text{/}\omega {\epsilon }_0\xi$$

Where ξ is the thickness of graphene, σ_g is the conductivity of graphene, ε₀ is the vacuum dielectric constant,

(2) $${\sigma }_g=\frac{i2e^2{k}_{B}T}{\pi {\hslash }^2(\omega +i{\tau }^{-1})}\left[\frac{{\mu }_c}{k_{B}T}+2ln\left(e{}^{\left(-\frac{{\mu }_c}{K_{{}_B}}+1\right)}\right)\right]+\frac{i{e}^2}{4\pi \hslash }ln\left[\frac{\mathrm{2|}{\mu }_c\text{|}-\hslash (\omega +i{\tau }^{-1})}{\mathrm{2|}{\mu }_c\text{|}+\hslash (\omega +i{\tau }^{-1})}\right]$$

Where e and μ_c are electron charge and Fermi level energy, K_B and ħ are Boltzmann constant and Planck constant respectively. T and τ are temperature and carrier life of the material.

3. RESULTS

The transmission spectrum of the device structure is illustrated in Figure 2(a). In this design, the thickness of Au and graphene is 90 nm and 1.7 nm, respectively. It can be seen that some interference peaks are presented in the 1–1.3 um range, which is in the near-infrared band. It comes from long-term interference of surface plasmon mode situated at upper and bottom surfaces of the graphene layer. The interference field extends to a certain area of the gold film where the single slit is located. However, the transmittance of the structure is low, and the maximum value is only 2.2%. Additionally, the transmittance peaks are linearly attenuated from short wavelength to long wavelength. The transmittance decrease is evident especially beyond 1.15 um.

Figure 2
Transmittance of device structure in Figure 1(a) and (b).

When graphene was inserted in the slit, as shown the device structure in Figure 1(b). A microcavity was formed between the graphene filled in the single slit and the upper graphene layer. It can be seen from the transmittance spectrum in Figure 2(b) that the interference peak was enhanced remarkably comparing to Figure 2(a). The peak wavelength of each transmission channel shifts slightly, and the transmittance increases significantly. Especially on the long wave side, the maximum transmittance can reach 85%. The single channel bandwidth is significantly narrowed, up to 4.2 nm. It proved that the Fabry-Perot microcavity enhanced the surface plasmon interference field significantly, and the multi-channel and ultra narrowband outputs results from two interferences under the condition of phase matching [³]. The first interference originates from the generation of SPPs on the upper surface of graphene by incident plane waves and the secondary excitation of SPPs on the lower surface of graphene by light fields localized at the left and right ends of a single slit. Finally, it is apparent that the transmittance value of each channel varies widely, covering a large range from 30% to 85%. For a comb filter, the uniformity of each channel is a critical requirement.

To improve the transmittance uniformity, as Figure 1(c) show, a SiO₂ layer was introduce on the top of graphene layer, which is expected to reduce the light reflectance. Moreover, SiO₂ is insert in the microcavity to form the same dielectric environment between the upper and bottom interface of graphene. According to the equivalent medium theory, silicon dioxide dielectric layers are set on the upper and lower surfaces of graphene where a single slit is located, it can strongly suppress the reflection of incident light waves, enhance the transmittance, and at the same time improve the channel uniformity. In this design, the thickness of graphene and silicon dioxide are 1.7 nm and 11 nm respectively. The width of the single slit is 21 nm and it was filled with graphene and dioxide with the thickness of 4.5 nm and 85.6 nm. The transmittance spectrum of the device structure is illustrated in Figure 3. It can be observed that apart from wide transmission band at about 1.22 um, the transmission channel is narrow and uniform distributed in the 1–1.2 um range. The transmittance of each channel in 1.0–1.2 um range is between 50% and 60%, which is about 8 times that of a single slot structure in Figure 1(a), and the transmittance of each channel is more uniform comparing with the cavity structure shown in Figure 1(b). The number of channels is as high as 15, and the spacing between adjacent channels is almost 11.5 nm. The single channel transmittance width (full width at half maxima, FWHM) is 4.2 nm, which is much narrower than the reported single channel bandwidth of multi-channel filters.

Figure 3
Transmittance of comb filter device structure in Figure 1(c).

Through step-by-step simulation and analysis, the structure of a multi-channel and ultra-narrow band comb filter was obtained. In order to improve the performance of the filter, the influence of different structure design parameters on the comb transmission spectrum of the filter is analyzed in detail. First, the thickness of SiO₂ layer was increased from 18 nm to 30 nm. The transmittance spectra of the filters are illustrated in Figure 4. The spectra in 1–1.2 um range are presented to remove the influence of irregular band beyond 1.2 um. As shown, with the thickness of SiO₂ increased from 18 nm to 25 nm, the change in transmittance value and peak position of each channel is slight. However, when the thickness was increased further to 30 nm, the transmittance of each band decreased obviously, especially in the wavelength range before 1.15 um, and then the transmittance increases sharply beyond 1.15 um. Not only the transmittance uniformity of each channel is deteriorated, the peak position of each channel redshifts as the thickness of SiO₂ is increased.

Figure 4
Transmittance of comb filter device structure with different thickness of SiO₂ layer.

Figure 5 shows the transmission spectra of the device with different slit width. Other device structural parameters are the same as Figure 2. It can be seen from Figure 5 that with the increase of the slit width, the number and the bandwidth of channels for the passband do not change, but the pass band central frequency of the channels at longer wavelength beyond 1.1 um redshifts. Additionally, transmittance value decrease of these channels was also observed. The maximum transmittance of 0.62 was attenuated to 0.48 at the channel near 1.19 um.

Figure 5
Transmittance of comb filter device structure with different width of slit.

The reason is that with the increase of the width of the top layer silica, the reflected light is better suppressed, resulting in the enhancement of the surface plasma light wave, resulting in the increase of the surface reflectivity of the graphene microcavity. According to formula Δλ = 2 (1 – R) n_eff L/m²πR^1/2 [²³] (where R is the cavity surface reflectivity, n_eff is the refractive index of the cavity medium, is the cavity distance), the single channel bandwidth increases with the increase of R.

4. CONCLUSIONS

A comb filter working at the near-infrared range of 1–1.25 um was proposed in this study. According to the step-by-step structure simulation and analysis, it is proved that the comb filter composed of Au slit and graphene nanocavity has a large number of narrow transmission bands due to SPPs coupling and microcavity interference. The number of the transmittance channels of the filter can approach up to 15 and the bandwidth of each channels is narrowed to about 4 nm. Additionally, the transmittance uniformity of the comb filter can be adjusted to 50%–60% by the filter structure parameter optimization.

5. ACKNOWLEDGMENTS

This work was supported by the technology project of Maoming Supply Company of State Grid Guangdong Electric Power (030900KC23040002 (GDKIXM20230474)).

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Publication Dates

• Publication in this collection
  09 Dec 2024
• Date of issue
  2024

History

• Received
  25 June 2024
• Accepted
  26 Aug 2024