1. Introduction

Visible wavelength filters have been regarded as an indispensable component in a variety of applications, such as complementary metal-oxide-semiconductor (CMOS) image sensors, fluorescence imaging, display devices, multi-spectral sensors, colored lighting, light modulators, and light-emitting diodes [1–7]. In particular, they play the pivotal role of boosting energy harvesting efficiency for organic solar cells [8]. So far, they are mostly embodied by spin-casting multiple dye films in accordance with target spectral bands, and are disadvantageous from the aspect of cost effectiveness. Recently, the guided mode resonance (GMR) effect has been extensively exploited, to create reflection type spectral filters, engaging a sub-wavelength grating in dielectric materials, on account of their advantages, like low loss and small thickness [9–12]. Since in other applications a transmission type device is often preferred to a reflection type, numerous approaches have been undertaken to make transmissive filters by use of complex multilayer films in combination with mirror structures, as well as metal grating structures [13–18]. It is to be noted that unfortunately they were susceptible to significant level of polarization dependence, resulting in a degraded transmission for unpolarized light.

In this work, an ultra-thin nanophotonic visible wavelength filter that takes advantage of a symmetric metal-dielectric resonant structure, where a dielectric waveguide is loaded with a sub-wavelength grating based on a two dimensional (2D) array of square metal patterns, was demonstrated. A polarization independent bandpass filtering was attained, via the GMR between orthogonally diffracted waves and both transverse electric (TE) and transverse magnetic (TM) guided modes. So the proposed structure has identical transfer characteristic for arbitrary polarization without polarization dependent loss. Furthermore, the transmission band can be adjusted by controlling structural parameters. In this paper, three different filters for red, green and blue were rigorously designed and optimized with the help of finite-difference time-domain (FDTD) based simulations; they were then produced via e-beam lithography and dry etching, exhibiting negligible polarization dependence and a high transmission efficiency of over 85%.

2. Proposed visible wavelength filter

The proposed visible wavelength filter consists of a symmetric 2D metal grating integrated with a dielectric slab waveguide, as illustrated in Fig. 1 . The planar waveguide involves a core in Si₃N₄ (n = ~2.0), which is sandwiched with an upper cladding in SiO₂ (n = ~1.47), and a lower cladding made of quartz. On top of the waveguide, a 2D symmetric grating is formed, comprising an array of square Al patterns. As regards the structural parameters of concern, the pitch, width and thickness of the metal grating are denoted Λ, w and H_m, respectively. H_d2 and n_d2 stand for the thickness and refractive index of the core, respectively, while H_d1 and n_d1 denote the thickness and refractive index of the cladding. The fill factor ( = w/Λ) of the grating is defined as the ratio of the metal width to the pitch.

 

Fig. 1 Polarization-insensitive visible filter utilizing a symmetric metal grating integrated with a waveguide structure.

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The operation of the proposed device is first addressed. Normal incoming light is mostly reflected by the metallic grating, bringing about a broad cutoff band. In accordance with the GMR effect, however, a strong transmission can be introduced at certain wavelengths, where a resonant coupling is made possible between the incident light diffracted by the metal grating, and the guided mode of the planar waveguide [18]. The resonantly coupled light is presumed to preferentially undergo a constructive interference with non-diffracted light, which has been transmitted uninterrupted via the grating. The resonance position is determined by virtue of a phase matching condition, requiring that the propagation constant β for the TM/TE guided modes to be excited should equal the magnitude of the grating vector k_Λ = 2π/Λ.

Since the proposed device includes a 2D symmetric grating, the GMR initiated coupling may engage both TM and TE guided modes associated with the waveguide, for normal incident light assuming arbitrary polarization [19,20]. The polarization is identified depending on the E-field, which is aligned either in the x- or y-direction. As shown in Fig. 2 , in the case of one polarization denoted L_x, with the E-field parallel to the x-direction, a TM guided mode is excited to travel in the x-direction, while a TE guided mode is simultaneously induced, propagating in the y-direction. In the case of the other polarization denoted L_y, with the E-field parallel to the y-direction, in view of the symmetric configuration of the grating, the coupling of the diffracted waves to the TE and TM guided modes should still be the same as the former case. Therefore, the proposed device is supposed to exhibit an identical optical response, regardless of the polarization, giving rise to double transmission peaks located at wavelengths of λ_TM and λ_TE, which are attributed to the TM and TE guided mode, respectively.

 

Fig. 2 Excitation of the TE and TM guided modes of the waveguide, through the GMR that is driven by the 2D sub-wavelength metal grating, for the L_x-polarization.

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In order to verify the operation of the proposed device, the dispersion and propagation properties of the waveguide were investigated, with the assistance of a commercially available FDTD solution, Lumerical, Canada. Here, only the resonant coupling between the first-order diffracted wave of normal incident light and the fundamental guided mode was considered. Figure 3(a) plots the calculated dispersion of the waveguide for the TE and TM guided modes for H_d2 = 100 nm, while n_d2 was varied to take values of 1.65, 2 and 2.5, with n_d1 fixed at 1.47. For a symmetric waveguide, the dispersion relation is given by:

 

Fig. 3 Transfer characteristics induced by the GMR effect. (a) Calculated dispersion relation for a dielectric planar waveguide. (b) Calculated transfer characteristics of the proposed filter with structural parameters: H_d1 = 110 nm, H_d2 = 100 nm, n_d1 = 1.47 and Λ = 314 nm, for n_d2 = 1.65, 2 and 2.5. (c) Distribution of the magnetic H-field intensity |H_y|² observed at a resonant wavelength λ = 550 nm for n_d2 = 2.5.

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In relation to the phase matching condition, a filter device was initially studied to have a pitch of Λ = 314 nm, contributing a grating vector k_Λ = 0.02 nm⁻¹. As observed in Fig. 3(b), which depicts the transfer curves with H_d1 = 110 nm and H_m = 40 nm for the L_x-polarization, not merely a primary main peak but also a secondary sub-peak were obtained in pairs, for each case of n_d2. The resonant peaks were found to shift towards longer wavelengths with increasing refractive index of the core, with the phase matching condition (β = k_Λ) satisfied. Owing to the symmetric configuration of 2D gratings, both TE and TM guided modes are anticipated to be excited together for an arbitrary polarization, including the L_x- and L_y-polarizations. The transmission is certainly much larger for the TM guided mode than the TE guided mode, since the incoming light is dominantly reflected rather than transmitted when the incident beam is linearly polarized such that the E-field is parallel to the grating groove, which is reportedly typical of a sub-wavelength patterned grating in metals [21]. In this respect, the resonance stemming from the TM guided mode is regarded as the desired primary resonant peak, instead of the secondary peak led by the TE guided mode. Noting that the difference between the TE and TM guided modes is accounted for by the term (n_d2/n_d1)^2ρ in the aforementioned dispersion relation in Eq. (1), the deviation of the primary peak from the secondary peak can be preferably alleviated by diminishing the core-cladding index contrast associated with the waveguide, thus mitigating the discrepancy in the dispersion between the two guided modes. As implied in Fig. 3(a), the distinction in the dispersion properties between the two modes dwindles with decreasing core-cladding index contrast. For the particular case of the blue line, as shown in Fig. 3(b), the individual resonant peaks in relation to the two modes ultimately coincided with each other, thanks to sufficiently small index contrast involved. That is, the secondary peak at λ_TE is too close to λ_TM to be concretely discernible. Finally, in an effort to validate the role played by the GMR effect, the profile of the magnetic H-field intensity corresponding to a resonant wavelength was numerically probed into. As monitored in Fig. 3(c), a strong standing wave was generated inside the core, attesting to the substantial GMR mediated by the metal grating.

3. Device design and experimental results

The proposed visible filters were efficiently designed and assessed, relying on FDTD simulations. The thickness of the waveguide core and metal grating was determined to be H_d2 = 100 nm and H_m = 40 nm, respectively. The fill factor of the grating pattern was 0.75. Taking into account their potential compatibility with the prevalent CMOS process, the devices were constructed by employing Al, Si₃N₄ (n_d2 = ~2.0) and oxide (n_d1 = ~1.47) for the metal grating, the core and cladding of the waveguide, respectively. The refractive index of the quartz substrate was assumed to be the same as the oxide. The dispersion information for the Al metal, derived from the Drude model, was fully reflected.

First, the relationship between the resonant wavelength and the grating pitch was numerically explored, as plotted in Fig. 4(a) . For comparison, theoretical results were also derived from the dispersion relation for the waveguide. The center wavelength can be located in the visible band, for the pitch ranging from 200 to 500 nm. The dependence of the spectral response upon the thickness of the upper cladding in between the grating and the core was investigated. As shown in Fig. 4(b), the spectral bandwidth Δλ decreased approximately from 20 to 3 nm, when the cladding increased from 50 to 200 nm in thickness. This is believed to be because the optical loss, incurred by the Al film, increases with shrinking cladding; as a result, the quality factor of the resonant structure declines to broaden the Δλ [17]. This discovery hints at the fact that the bandwidth Δλ can be tailored by controlling the cladding thickness, entailing a minimal shift in the resonant wavelength.

 

Fig. 4 (a) Resonant wavelength with the grating pitch for the TE and TM guided modes of the dielectric waveguide. (b) Effect of the thickness of the oxide cladding upon the optical transmission for the proposed device with Λ = 350 nm, H_m = 40 nm, and H_d2 = 100 nm.

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Finally, Fig. 5(a) presents the calculated spectral response of three device candidates, DEV I, II and III, with grating pitches of 285, 355 and 395 nm, respectively. The upper cladding was set at H_d1 = 110 nm to gain a bandwidth Δλ of less than 20 nm. DEV I, II and III were tested to have center wavelengths at ~460, 560 and 610 nm in the blue, green and red bands, respectively. It is noteworthy that a high peak transmission beyond 85%, which has been enhanced by virtue of the dielectric layer mediated GMR effect, was attained over the entire visible band. The proposed nanophotonic wavelength filters were manufactured exploiting conventional e-beam lithography in association with dry etching technique. Initially a Si₃N₄ and SiO₂ film were successively deposited on quartz substrate via radio-frequency (RF) sputtering, and an Al film was subsequently formed via thermal evaporation. With an e-beam resist pattern serving as a soft mask, the Al film was selectively dry etched so as to produce the symmetric 2D grating. The insets in Figs. 5(b), 5(c) and 5(d) display the SEM (scanning electron microscope) images of the three devices. DEV I, II and III were all monitored to have clearly defined metal patterns, which are adequate for the gratings, with pitches of 285, 355 and 395 nm, respectively. Their measured fill factors were nearly the same, at about 0.75, as intended.

 

Fig. 5 (a) Calculated spectral responses of the designed three devices. Demonstrated and calculated transfer characteristics for unpolarized light for (b) DEV I. (c) DEV II. (d) DEV III.

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A halogen lamp (Avantes AvaLight-HA) in combination with a spectrometer (Avantes Avaspec-3648) was used for evaluating the prepared devices. When the source light was shining the filter via a focusing objective lens, the optical output was detected by the spectrometer. Figures 5(b) through 5(d) present the observed transfer characteristics for the case of unpolarized incident light. A high correlation was witnessed between the observed and calculated results. As shown in Figs. 5(b), 5(c), and 5(d), the three devices acted as a good bandpass filter, in the blue, green, and red bands, respectively, exhibiting a center wavelength λ_TM of ~460, 560, and 610 nm and a bandwidth Δλ of ~13, 14, and 17 nm, respectively. For all of them, a peak transmission exceeding 85% was attained. Besides the targeted primary peaks, DEV I, II and III were unavoidably accompanied by corresponding secondary peaks located at 488, 588 and 639 nm, causing unwanted transmissions of about 15, 20 and 22%, respectively. As discussed earlier, these sub-peaks are ascribed to the excitation of the TE guided mode in the dielectric waveguide, which may be engineered to either converge on the primary peaks, by minimizing the index contrast, or they may be sufficiently set apart from the main peaks of interest, by raising the index contrast.

Lastly, the influence of the light polarization on the transfer characteristics of the filter devices was inspected. As depicted in Fig. 6(a) , three linear polarizations, denoted L_x, L_xy, and L_y, were considered, assuming the E-field aligned parallel to the x-, xy- and y-direction, respectively. In light of the spectral response for each of the devices, which are shown in Figs. 6(a), 6(b) and 6(c), it was consequently proven that the polarization dependence is negligibly small, as expected. Here, some irregular mismatches of the undesirable structural asymmetry manifested in the grating patterns are deemed to be the result of the fabrication error. In this work the case of normal incidence with an angle of incidence of 0° was primarily considered. For an oblique incidence with a nonzero angle, the primary resonant peak may be either shifted or split into double peaks, depending on the direction of the E-field in relation to the plane of incidence, since the phase matching condition, underlying the GMR effect, is basically susceptible to the angle of incidence, azimuth angle, and polarization of incident light.

 

Fig. 6 Transfer characteristics in terms of the light polarization. Three linear polarizations are considered, including L_x-, L_xy- and L_y-polarizations, as indicated in (a). Transfer curves are obtained for (b) DEV I. (c) DEV II. (d) DEV III.

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4. Conclusion

In summary, a highly efficient visible wavelength filter, tapping into a symmetric 2D metal-dielectric resonant structure, was successfully designed and demonstrated. The resonant coupling between the incoming light and the guided modes of a dielectric planar waveguide, which was mediated through the metallic grating, was taken advantage of to produce a transmission type filter, the center wavelength and bandwidth of which could be readily tailored by altering the grating pitch and the thickness of the oxide cladding. The polarization independent operation could be accomplished as a result of simultaneously inducing the TM and TE guided modes for unpolarized light. The achieved transmission exceeded 85% across the visible bands. The proposed device could be appropriately applied to build miniaturized spectral sensors by spatially modifying the pitch of the metal grating.