1. Introduction

Recently, color elements based on Fabry-Perot (FP) resonators [1–6] have attracted a great deal of interest as a promising platform for a next generation of coloration technology. Compared to other approaches such as plasmonic resonators [7–13], photonic crystals [14–17], and dielectric scatterers [18–20], the FP coloration technology offers several advantages, including large-area scalability, high optical efficiency, and high image resolution. For many potential applications of the FP coloration technology such as color filters, camouflage, optical data storage, and color barcoding, a prerequisite is a versatile and scalable fabrication method of constructing different color elements on a single substrate with high spatial resolution. Since the thickness of a resonant cavity (RC) primarily determines the phase retardation of electromagnetic waves and in turn, the resonance condition of a FP resonator, a number of previous works have mainly focused on varying the thickness of the RC by means of focused ion-beam milling [21], grayscale photolithography [5,22], a series of vacuum depositions [23–25], and sequential transfer-printings [2]. However, these approaches inevitably result in geometrical steps across the boundaries between different pixels [2,5] and accordingly, can limit the image resolution and the color saturation of final color devices due to unwanted scatterings at the steps. Moreover, inhomogeneous electrical performances may be accompanied when FP resonators are incorporated in electro-optic devices such as liquid crystal displays [26].

One of the solutions to overcome such problem inherent to the FP resonance for given RC thickness is the use of the phase-shifting elements of deep-subwavelength-scale thick, capable of modulating the phase of an incoming electromagnetic wave. In the field of metasurfaces, for example, ultrathin metallic or dielectric nanostructures have been utilized as phase-shifting elements, in which the phase retardation is determined by the lateral dimensions of the nanostructures to tailor the wave front of propagating light [10,27–31]. The FP resonators with nanostructures embedded inside the RC have been studied as model systems to investigate the coupling of the FP resonances with other types of optical modes such as surface plasmon resonances in the visible and near-infrared regime [32,33]. For color applications, however, such strategy has been rarely exploited except for a few cases [34] since the nanostructure implementation into the FP resonators inevitably limits the scalability and the design flexibility for practical applications.

In this work, we demonstrate a new approach to realize the full coloration based on the FP resonators without changing the thickness of the RC. This approach becomes possible by embedding silver nanostructures in the middle of the RC as phase discontinuities. In contrast to previous works using serial nanopatterning techniques such as electron-beam and focused ion-beam lithography, the silver nanostructures are formed spontaneously during the deposition of thermally evaporated silver in vacuum, allowing to form subwavelength phase-shifting elements in a scalable and controllable manner. Depending on the target thickness for the deposition, two types of silver nanostructures having continuous (nanofilm) and discontinuous (nanoislands) features were produced in the middle of RC. The FP resonances for two different nanostructures were shifted toward the opposite directions to each other and the magnitude of the shift was dependent on the geometrical dimensions of the nanostructures that are determined by the conditions of thermal evaporation. From the numerical results based on the rigorous coupled wave analysis, the resonance shifts in the opposite directions were found to originate from the opposite signs of the phase retardations by a nanofilm and nanoislands. Based on the above concept, we demonstrated a flexible full-color plate produced from the pixel patterns of a nanofilm and nanoislands on a single substrate.

2. Basic concept and phase modulation property of free-standing nanostructures

We first present the basic concept of tuning the color from the FP resonator with nanoscale phase-shifting elements inside the RC. The geometrical structure of such FP resonator is schematically illustrated in Fig. 1. Basically, the FP resonator consists of two transreflective layers (TRLs) and RC between them. In contrast to conventional FP resonators, however, two elementary types of phase-shifting elements composed of a nanofilm and a layer of nanoislands are placed in the middle of RC. Here, the thicknesses of all the TRLs are identical and denoted by t_T and that of RC is d. The geometrical structure of the nanofilm is characterized only by the thickness (t₁) while that of the nanoislands is by three parameters of the periodicity (p), the width (w), and the thickness (t₂). The refractive indices of the RC and the substrate are represented by n and n_s, respectively.

 

Fig. 1. Geometrical configuration of the FP resonator having a nanofilm and a layer of nanoislands inside a resonant cavity (RC). Here, the thicknesses of RC and two transreflective layers (TRLs) are denoted by d and t_T, respectively. The nanofilm and nanoislands are placed in the middle plane (represented by a black dashed line) of RC. For a nanofilm, the thickness is t₁. For nanoislands, the thickness, the width, and the periodicity are denoted by t₂, w, and p, respectively. Here, n and n_s denote the refractive indices of RC and a substrate, respectively.

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The effect of the phase-shifting elements can be explored using a simple analytic equation which is modified from the original condition of the FP resonance [32] as follows.

To understand the effect of the phase-shifting elements embedded in the FP resonator, the phase modulation property of such elements should be first investigated. Figure 2(a) shows the conceptual geometry for numerical simulations where the transverse magnetic (TM)-polarized plane wave is incident on either a freestanding nanofilm or an array of nanoislands in vacuum. We used silver for phase-shifting elements due to its low optical loss. Here, the optical constants for silver were taken from the literature [35]. Following Eq. (1) for the FP resonance condition [32], the phase retardation, Δϕ, is positive when the plane wave that passes through a phase-shifting element lags behind the one that propagates in the same direction without encountering any phase-shifting element.

 

Fig. 2. (a) Conceptual geometry for numerical simulations of the phase retardation on passing through a freestanding nanofilm and an array of nanoislands. (b) Simulated phase retardation as a function of the wavelength for a nanofilm (t₁ = 8 nm) and an array of nanoislands (t₂ = 8 nm, w = 30 nm, and p = 60 nm).

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In the geometry illustrated in Fig. 2(a), for both a typical nanofilm (t₁ = 8 nm) and an array of nanoislands (t₂ = 8 nm and p = 60 nm), the calculated values of the phase retardation are shown as a function of a wavelength in Fig. 2(b). In the case of the nanofilm, the sign of Δϕ is mostly negative at the concerned wavelengths. In contrast, the sign of Δϕ for the case of nanoislands is mostly positive except for the wavelengths around 400 nm. The rapid changes at certain wavelengths (around 400 nm) in the phase retardation curves are mainly attributed to the presence of localized surface plasmon resonances (LSPRs). Such swings in the phase retardation become large and can result in the negative phase retardation when the aspect ratio of a nanoisland, t₂/w, is small and accordingly, optical absorption dominates the LSPR response [36–38]. Our numerical results show that by increasing t₂ and the resultant scattering component of the LSPR [37], the phase retardation can be positive at most of the wavelengths (see Fig. 8)

3. Effect of silver nanostructures on cavity mode and coloration principle

Let us now describe how the nanostructures present inside RC modulate the FP resonance using numerical simulations. In all cases, the refractive indices of the RC and the substrate were taken to be 1.6 and 1.5, respectively. Figure 3(a) shows the transmittance for a Fabry-Perot resonator with a nanofilm as a phase shifting element whose thickness t₁ varies from 0 nm to 15 nm. Here, d is 110 nm to produce the FP resonance at λ_FP = 550 nm when no nanofilm exists (the gray dotted line). As clearly seen from Fig. 3(a), the coupled mode represented by the dashed black line is shifted to shorter wavelengths with increasing t₁. The increase in the magnitude of the blue shift is attributed to the increase in the magnitude of the phase retardation by a nanofilm.

 

Fig. 3. (a) Optical transmittance through the FP resonator with a nanofilm in RC upon the incidence of the plane wave with a transverse magnetic (TM) polarization for t₁ ranging from 0 to 15 nm. Here, the gray dotted and black long dashed lines represent the resonant wavelength in the reference and nanofilm cases, respectively. The electric field distribution for the x component in RC (b) at λ_FP = 550 nm (reference) and (c) at λ_FP = 456 nm with a 8 nm-thick nanofilm (corresponding to the red star in (a)). In (b) and (c), the black short dashed lines denote the intensity profiles along the z direction.

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The effect of a phase shifting element can be observed in the electric field distribution inside RC. For the reference case with no nanofilm, at the resonance (λ_FP = 550 nm), the normalized x-component of the electric field was first calculated together with the intensity profile along the z axis (represented by the black dashed line) as shown in Fig. 3(b). At the resonance condition, the intensity is maximum in the middle of RC and symmetric with respect to the mid-plane. The intensity profile also suggests that a phase-shifting element should be placed in the middle of RC to enhance the coupling with the FP resonance. Figure 3(c) shows the numerical results for the normalized x-component of the electric field at the resonance (λ_FP = 456 nm) for the case of a nanofilm of 8 nm thick. Again, the symmetric field distribution indicates that the resonance condition is met at this wavelength. The negative phase retardation effectively increases the propagation distance of light in RC and fulfills the resonance condition that is otherwise impossible to satisfy without a nanofilm. The presence of the phase shift is also represented as the dip observed in the middle of the intensity profile.

In contrast to the nanofilm case, the rapid change of Δϕ around the LSPR wavelength leads to a mode splitting and accordingly, two coupled modes are present at the wavelengths of interest (cavity mode 1 and 2). For the cavity mode 1, the resonance is shifted to longer wavelengths with respect to the reference case without nanoislands and the magnitude of the shift increases with increasing w. The increase in the magnitude of the shift with increasing w is consistent with the increase in the magnitude of Δϕ at above the LSPR wavelength as shown in Fig. 2(b). On the other hand, the transmittance for the cavity mode 1 becomes small with increasing w, which is attributed to the increase in the optical absorption in a nanoisland as its aspect ratio decreases. Our numerical results show that the transmittance can be improved by increasing t₂ for a given w (see Fig. 9) but at the expense of the tuning range for the cavity mode 1. In contrast to the cavity mode 1 whose shift significantly increases with increasing w, the shift of the cavity mode 2 is quite limited by the high optical absorption of silver in the ultraviolet regime. With increasing w, the cavity mode 2 becomes distinct as the resonance shifts away from the high absorption regime of silver.

The electric field distributions for the cavity mode 1 and 2 are shown in Figs. 4(b) and 4(c). Here, the cavity mode 1 at λ_FP = 618 nm (Fig. 4(b)) and the cavity mode 2 at λ_FP = 441 nm (Fig. 4(c)) correspond to the green star and the blue circle denoted in Fig. 4(a), respectively. In the case of the cavity mode 2, the electric fields inside RC mostly propagate through nanoislands, thereby being similar to the case of an array of isolated nanofilms. This electric field distributions account for the small (or even negative) value of the phase retardation around this wavelength. On the other hand, the cavity mode 1 accompanies the strong scattering by nanoislands which leads to the positive phase retardation.

 

Fig. 4. (a) Optical transmittance through the FP resonator with nanoislands inside RC upon the incidence of TM-polarized plane wave for t₂ = 8 nm and p = 60 nm. Here, the gray dotted line represents the reference while the blue and green dashed lines represent the cavity mode 1 and 2, respectively, when the nanoislands are present inside RC. The white dot-dashed line represents the wavelength of the localized surface plasmon resonance (LSPR) for free-standing nanoislands in the same dielectric material as RC. The electric field distribution for the x component in RC at (b) λ_FP = 441 nm and (c) λ_FP = 618 nm corresponding to the blue circle and green star in (a) (t₂ = 8 nm and w = 18 nm), respectively.

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From numerically calculated transmission spectra, we generate a color palette in a wide range of colors achieved in our device configuration as shown in Fig. 5. Here, the thickness of RC is 110 nm for all cases and the identical optical parameters for the numerical results in Figs. 3 and 4 are used. The color coordinates are obtained from the transmission spectra using the color matching function for a standard observer [39]. The column enclosed by the white dashed line corresponds to the reference case where no phase-shifting element exists. When a nanofilm is embedded, the color generated from the FP resonator changes from green to blue and becomes more bluish according to the shift of the cavity mode toward shorter wavelengths with increasing t₁. In the case of nanoislands, a wider range of colors can be obtained by the combinations of two geometrical parameters, t₂ and w. For smaller values of t₂ (3 and 5 nm) where optical absorption becomes significant for the cavity mode 1, the color changes from green to blue with increasing w since the cavity mode 2 plays a dominant role in shaping the transmission spectra (see Fig. 9). For larger t₂, the color mainly comes from the cavity mode 1 and accordingly, the color becomes reddish with increasing w.

 

Fig. 5. Numerically calculated color palette from the FP resonator with a nanofilm and nanoislands. The column enclosed by the white dashed line corresponds to the reference case (d = 110 nm) with no phase-shifting element. With respect to the reference, the column in the left side corresponds to the nanofilm case while the columns in the right side correspond to the case of nanoislands.

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4. Spontaneous formation of nanoislands through vacuum deposition

For the demonstration of our concept, it is important to construct a nanofilm and nanoislands in a controllable manner. Unlike a rather uniform nanofilm, it is difficult to produce nanoislands with small lateral dimensions at a deep-subwavelength level. Vacuum deposition of silver was carried out to spontaneously form metallic nanoislands [40–43]. Compared to other methods such as electron-beam lithography, thermal deposition in vacuum is much simple and compatible with a variety of substrates such as curved or flexible substrates. In our work, a layer of nanoislands was produced when the deposited thickness is smaller than a percolation threshold that is related with the surface energy of the substrate and the deposition conditions including the deposition rate and the chamber pressure. As the deposited thickness increases, the size and the surface coverage of nanoislands increase. Above the percolation threshold, the deposited silver tends to form a continuous nanofilm rather than nanoislands. Therefore, two different nanostructures can be selectively produced by simply controlling the deposition rate and/or time.

The silver nanostructures fabricated according to the strategy outlined above were characterized using scanning electron microscopy (SEM) and atomic force microscopy (AFM) as shown in Fig. 6. For convenience, we define d_unif as the thickness when deposited silver forms a uniform film instead of nanostructures. As clearly seen in the SEM images of Figs. 6(a) and 6(b), silver nanoislands were well produced in the cases of d_unif = 1.5 nm and 2.5 nm. The surface coverage, r_s, being the ratio of the area occupied by nanoislands in unit area, was 24.2% and 31.7%, respectively.

 

Fig. 6. Scanning electron microscopic images of thermally deposited silver nanostructures with different values of the thickness assuming a uniform layer (d_unif) of (a) 1.5 nm, (b) 2.5 nm, (c) 8 nm, and (d) 15 nm thick. (e), (f), (g), and (h) show the atomic force microscopic images corresponding to (a), (b), (c), and (d), respectively. (i) and (j) represent the average profiles of an individual nanoisland for d_unif = 1.5 nm and 2.5 nm, respectively. (k) and (l) represent the line profiles along the red solid lines in (g) and (h), respectively.

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From the AFM images of Figs. 6(e) and 6(f), twenty individual nanoislands were randomly selected and the average profile of them was estimated. For d_unif = 1.5 nm, the average profile in Fig. 6(i) shows that the thickness and the width were 6.2 nm and 13.7 nm, respectively. For d_unif = 2.5 nm, as shown in in Fig. 6(j), the thickness and the width were increased to 7.9 nm and 20.4 nm, respectively. Note that the surface coverage and the width of the nanoislands generated by vacuum deposition are coupled in the sense that they increase with increasing the deposition thickness for given surface energy and deposition conditions. The surface modification through a plasma treatment or a self-assembled monolayer will provide another scheme of controlling the two geometrical parameters. In contrast, the SEM images in Figs. 6(c) and 6(d) shows that for d_unit= 8 nm and 15 nm, rather continuous nanofilms were produced although incidental cracks were appeared. As shown in the AFM images in Figs. 6(g) and 6(h), the grain size becomes larger for a larger value of d_unif = 15 nm. Figures 6(k) and 6(l) represent the line profiles along the red solid lines in the AFM images, showing that the surface roughness is significantly low in both cases.

5. Color characteristics of nanostructure-embedded FP resonator

Based on the coloration strategy given in the previous section, we fabricated the FP resonators composed of either a nanofilm or nanoislands as the phase-shifting elements inside the RC. The details for the fabrication process can be found in Appendix 1. Figure 7(a) shows the experimental spectra together with numerical results for transmission through the FP resonators with two different nanofilms of d_unif = 8 nm and 15 nm in the RC. The reference case with no nanofilm was also included for comparison. Compared to the reference resonance at λ = 570 nm, the cavity mode for d_unif = 8 nm was blue-shifted to 442 nm and that for d_unif = 15 nm to 422 nm. These resonance wavelengths agree well with 453 nm and 421 nm in the numerical results. Figure 7(b) shows the experimental and simulated results for two cases of the nanoislands with d_unif = 1.5 nm and 2.5 nm. Numerical simulations were carried out in a simplified model where real nanoislands were dispersed in two-dimension. For small values of r_s, the optical characteristics can be described well in the framework of an effective medium theory [44]. Thus, it is reasonable to obtain numerical results in three-dimensional case from two-dimensional approximation [45]. The average profile of a single nanoisland was approximated to be rectangular and the geometrical parameters were taken from Fig. 6. The periodicity was determined from the condition that the surface coverage for the two-dimensional case is the same as that for the three-dimensional case. Under this circumstance, the periodicity is 56.7 nm for d_unif = 1.5 nm and 64.4 nm for 2.5 nm.

 

Fig. 7. Transmittance through the FP resonator (a) with a nanofilm of d_unif = 8 nm and 15 nm thick (b) with nanoislands of d_unit = 1.5 nm and 2.5 nm thick together with that of the reference where no nanostructures are present inside RC. Microscopic images of a color plate using the nanostructure-embedded FP resonators fabricated on a flexible substrate (c) before and (d) after bending. Here, the green color in background comes from the FP resonator without nanostructures (reference) whereas the red color for ‘SNU’ and the blue color for ‘MIPD’ are from the FP resonators with nanoislands of d_unif = 2.5 nm and with a nanofilm of d_unif = 8 nm, respectively.

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As seen in Fig. 7(b), for the case of nanoislands, the cavity mode 1 for d_unif = 1.5 nm was red-shifted to 610 nm and that for d_unif = 2.5 nm to 656 nm. The increase in the magnitude of the red-shift with d_unif comes from the increase of the nanoisland size (t₂ and w) and the surface coverage as well. The resonance wavelengths of the cavity mode 1 agree well with 609 nm and 645 nm as estimated from the numerical results although the transmittance at the resonance is relatively low owing to the polydispersity of real nanoislands. In addition to the polydispersity, the deviation of the optical property of silver from its bulk counterpart is associated with the absence of the cavity mode 2. The surface treatment before the formation of silver nanostructures is expected to enhance the transmittance at the resonance by the increase in the aspect ratio of a nanoisland.

In accordance with the color palette shown in Fig. 5, we demonstrate the versatility of our coloration approach in a color plate of the FP resonators with nanostructures fabricated on a flexible PEN substrate as shown in Fig. 7(c). The green color in the background arises from the FP resonator with no nanostructure. For the red color of ‘SNU’, the nanoislands of d_unif = 2.5 nm (the average height of 7.9 nm) were employed whereas for the blue color of ‘MIPD’, the nanofilm of d_unif = 8 nm was placed in the RC. Since the thickness variation across different color elements is minimal, no scattering at the boundaries between color elements is observed and accordingly, a sharp color contrast is achieved. Since the minimal optical scattering is expected at the boundaries between different color elements, the spatial resolution of about 1 µm, reported for the color filter based on FP resonator [5], can be achieved. Figure 7(d) shows the microscopic image of the flexible color plate under bending deformation. A very small change in ‘SNU’ is attributed to the angle-independent nature of LSPR-mediated scatterings. In the nanofilm case, the angle-independence comes mainly from the decrease in the effective thickness of the RC.

6. Conclusions

We presented the full-coloration platform based on the FP resonators having metallic nanostructures in the middle of the RC as phase discontinuities. The nanostructures of either a nanofilm or nanoislands enable to tune the resonance without changing the thickness of the RC. The subwavelength-scale phase discontinuities were spontaneously produced by vacuum deposition. The deposition conditions, such as the deposition rate and the chamber pressure, and the surface energy of the substrate determine the types and the geometrical parameters of the nanostructures. Compared to the previous works requiring expensive and complicated fabrication tools including electron-beam lithography, our coloration platform is simple, versatile, and compatible with a variety of substrates. The virtue of our approach was well demonstrated in a flexible color plate in accordance with a full-color palette obtained from the numerical simulations. Due to the minimal geometrical steps across different color elements, a sharp color contrast is achieved. In addition, the optical properties of the color plate composed of the nanostructures show less angular dependence than conventional devices with no phase-shifting element. The coloration strategy based on the phase discontinuities in the FP resonator opens a route toward developing scalable and flexible color elements for use in displays, anti-counterfeitings, barcodes, and image storage devices.

Appendix 1. Materials and methods

For the fabrication of the FP resonators having phase-shifting elements, a 20 nm-thick silver was first deposited as the TRL on a precleaned glass or flexible polyethylene naphthalate (PEN) substrate. For the bottom half of the RC, a solution of photopolymer (SU-8 2005; MicroChem), diluted in 5 wt.% with propylene glycol monomethyl ether acetate (PGMEA; Sigma Aldrich), was then spin-coated on the substrate at the rate of 3000 rpm for 30 s. Note that SU-8 is highly transparent (over 90% in transmittance) at visible wavelengths and inert (or orthogonal) to most of solvents after being cured by ultraviolet (UV) light, allowing for spin-coating of another layer on the previously formed SU-8 layer. The phase shifting elements of silver were fabricated on the photopolymer layer. A thermal evaporator (MHS-1800; Muhan Vacuum) was used for a vacuum deposition at the rate of 0.1 nm/s and 1 nm/s for producing nanoislands and a nanofilm, respectively, with the chamber pressure of 1${\times} $10⁻⁵ torr. In the nanofilm case, the photopolymer layer was treated with UV/ozone (AHS-1700; Ahtech LTS) to achieve the high surface energy for promoting the film growth of silver during deposition. The deposited silver nanostructures were characterized using SEM (S-4800; Hitachi) and AFM (XE-150; PSIA). In fabricating a full-color plate, photolithography was employed to pre-define color patterns on the SU-8 layer before a deposition of silver for the phase-shifting elements. After patterning, photoresist (AZ 1512; AZ electronic materials) was removed in acetone (Sigma Aldrich). These processes were repeated several times to pattern different phase-shifting elements. After that, the top half of the RC was then produced on the silver nanostructures by spin-coating under the same condition, meaning that the nanstructures were positioned in the middle of RC. The fabrication of color elements was completed by thermal deposition of the other TRL on the top of RC.

Appendix 2. Phase modulation property of a nanofilm and nanoislands

In this section, we investigate the phase modulation property of a nanofilm and nanoislands in more details. The geometry for numerical simulations is illustrated in Fig. 8(a). Figures 8(b)–8(d) show the calculated Δϕ as a function of the wavelength for a nanofilm and nanoislands with t₁ = t₂ = 3, 8, and 15 nm, respectively. In the case of nanoislands, w varies from 12 nm to 30 nm at the interval of 6 nm for each t₁. In the nanofilm case, Δϕ monotonically increases with the wavelength along the negative direction. Since no optical resonance is involved in this case, the wavelength dependence of Δϕ traces that of the dielectric constant of silver. At a given wavelength, the increase of t₁ results in the increase of Δϕ. In the nanoisland case, a localized surface plasmon resonance (LSPR) occurs and the sign of Δϕ flips over at near the LSPR wavelength. The LSPR wavelength is red-shifted as the aspect ratio of t₂/wincreases, which is well described in the picture of electrical dipole-dipole bonding. The magnitude of Δϕ becomes generally large with increasing w and t₂, both of which result in the increase of the effective dipole moment in an individual nanoisland at the resonant wavelength [37]. As t₂ increases, the scattering effects dominate and accordingly, the phase retardation curve is shifted toward the positive direction. Thus, for t₂ = 8 nm and 15 nm, in most of all cases, it is positive in the whole spectrum.

 

Fig. 8. (a) Geometry for the numerical simulations of the phase retardations of waves on passing through a freestanding nanofilm and nanoislands. The phase retardations through both nanofilm and nanoislands for different values of w (12, 18, 24, and 30 nm) as a function of the wavelength in the case of (b) t₁ = t₂ = 3 nm, (c) t₁ = t₂ = 8 nm, and (d) t₁ = t₂ = 15 nm, respectively.

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Appendix 3. Effect of geometrical parameters of nanoislands on FP resonance

Figures 9(a)–9(c) show how the geometrical dimensions of nanoislands defined by w and t₂ influence the optical characteristics of the FP resonators. For t₂ = 3 nm, the opposite sign of Δϕ in the visible spectrum leads to two optical modes, i.e., cavity mode 1 and 2. A small value of t₂ results in the strong confinement of the LSPR mode, which in turn, increases the magnitude of the resonance shift with w when compared to the case of a large value of t₂. The strong confinement also leads to the increase in the optical loss. Accordingly, the cavity mode 2 plays a dominant role in generating a color from the coupled structure. As t₂ becomes large, the LSPR mode becomes less confined and thus the magnitude of the shift decreases with w. Instead, the optical loss by the LSPR mode decreases and the transmittance for the cavity mode 1 significantly increases. At the same time, the increase in the magnitudes of electrical dipoles for the LSPR mode also leads to the increase in the coupling strength between the FP resonance and the LSPR mode. The increase in the coupling strength further blue-shifts the cavity mode 2 to the ultraviolet regime where the mode is significantly damped by the increased optical absorption of silver. Therefore, the cavity mode 1 is mostly accountable for generating a color for large values of t₂.

 

Fig. 9. Transmittance through the FP resonator with nanoislands inside RC upon the incidence of TM-polarized plane wave for different values of w at (a) t₂ = 3 nm, (b) t₂ = 8 nm, and (c) t₂ = 15 nm. In all cases, p is 60 nm. Here, the gray dotted line represents the reference while the blue and green dashed lines represent the cavity mode 1 and 2, respectively when the nanoislands are present inside RC. The white dot-dashed line represents the localized surface plasmon resonance (LSPR) for freestanding nanoislands in the same dielectric material.

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Funding

Samsung; Ministry of Education.

Disclosures

The authors declare no conflicts of interest.

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