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Abstract
We study a polymer-based hyperbolic metamaterial (HMM) structure composed of three Au-polymer bilayers with a hyperbolic dispersion relation. Using an effective refractive index retrieval algorithm, we obtain the effective permittivity of the experimentally fabricated polymer-based structure. In particular, the unique polymer-based HMM shows the existence of high-k modes that propagate in the metal-dielectric multilayered structure due to the excitation of bulk plasmon-polaritonic modes. Moreover, we compare the experimental luminescence and fluorescence lifetime results of the multilayered Au and a dye-doped polymer (PMMA) to investigate the dynamics of three different emitters, each incorporated within the unique polymer-based HMM structure. With emitters closer to the epsilon-near-zero region of the HMM, we observed a relatively high shortening of the average lifetime as compared to other emitters either close or far from the epsilon-near-zero region. This served as evidence of coupling between the emitters and the HMM as well as confirmed the increase in the non-radiative recombination rate of the different emitters. We also show that the metallic losses of a passive polymer-based HMM can be greatly compensated by a gain material with an emission wavelength close to the epsilon-near-zero region of the HMM. These results demonstrate the unique potential of an active polymer-based hyperbolic metamaterial in loss compensation, quantum applications, and sub-wavelength imaging techniques.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years, there has been a surge in scientific interest in metal-dielectric multilayered structures, owing in part to the new and related concepts of transformation optics [1,2], optical imaging [3], and metamaterials [4–8]. These multilayered structures composed of alternating subwavelength metal and dielectric layers provide unique optical properties useful for a wide range of advanced applications and devices. Typically, one can obtain a hyperbolic dispersion relationship in multilayered systems where the permittivity along different axes of the medium are different [9]. This anisotropic tensor behavior of the multilayered systems exhibits unique structural properties that do not exist naturally [9–11].
Note, the term hyperbolic metamaterial (HMM) was coined to describe a hyperbolic dispersion relation of a medium [10]. The unique property of HMMs has increased their applicability in numerous fields, such as negative refraction [12,13], superlenses [14,15], hyper-lenses [16], sub-diffraction imaging [17], remarkable waveguiding [18–20], and thermal emission engineering [11]. In addition, the effective permittivity of such media extends to zero within a certain spectral range known as epsilon-near-zero (ENZ) region. Within this spectral range, the HMM structure exhibits different physical phenomena such as an excitation of electromagnetic waves which propagates at long distances with negligible phase variations [21].
However, the fundamental constraint in the application of HMMs is the intrinsic loss of the metal layers. Nonetheless, the intrinsic loss can be overcome by the presence of a gain medium in the polymer-based HMM composite. Gain media have been experimentally incorporated into a variety of plasmonic and metamaterial systems, a technique relevant in quantum nanophotonics and radiative decay engineering. The incorporation of gain within a multilayer HMM system compensates for metallic loss and could potentially enhance the robustness of HMM applications as compared to the passive HMM applications [22]. Moreover, HMMs have been shown by many authors to exhibit bulk plasmon modes which enhance its photonic density of state (PDOS) [23–25]. An increase in the PDOS property of HMMs has been identified to support subwavelength Bloch modes which could be quenched by the intrinsic metallic loss of the structure. Thereby embedding emitters in HMMs could compensate for these losses. Also, the existence of the high-k resonant modes in HMMs generates enormous enhancement of PDOS [10,26,27]. As a result of the continuum high-k modes of HMMs, a broadening of the Purcell factor full width at half maximum (FWHM) is exhibited in HMM and emitter complex structure. This could potentially be applicable in broadband single-photon generation [28–31]. Note that the emission rate of a spontaneous emitter embedded in a hyperbolic structure relative to the free-space decay rate is referred to as the Purcell factor [26,32,33].
HMM also possess additional states (i.e., propagating modes, plasmon modes) that are also prominent in HMM applications such as subwavelength imaging and sensing [34]. Although these exotic properties of HMM are prominent in various applications, the dissipation of coupled energy of emitters due to loss in the metal-dielectric complex has been a constraint in radiative decay engineering [22,27,35]. As such, various design and engineering techniques including adiabatic tuning of filling fraction to tunnel trapped high-k modes, incorporating a high-index grating configuration on the HMM, and nanopatterning of HMM slab known as hyper-crystals have been proposed by many authors to overcome these constraints [10,14,27]. In particular, loss-compensation and enhancement of spontaneous emission in active multilayered structures have been theoretically studied based on the dispersion relations of the multilayered structure as well as the geometry of the near fields [22,36,37]. Thus far, the practical realization of emitters coupled to a multilayered structure consisting of metal and a polymeric material have been studied with a focus on transient technology whereby a water-soluble and biocompatible polymer is utilized in forming a transient and flexible HMM structure [38].
Here, we propose a polymer-based active HMM structure composed of alternating layers of a metal and polymethyl methacrylate (PMMA) medium to study the decay rate mechanism of emitters not only dispersed on the top layer but also in-between the PMMA layers. We engineered relatively thin PMMA films to serve as a dielectric medium to incorporate quantum emitters in the proposed structure. This active dye-doped HMM structure is envisaged to compensate for the losses in a metal-dielectric structure due to the enhanced coupling of emitters dispersed on top and within the polymer-based HMM. This provides insight into the radiative decay mechanisms of emitters coupled to the HMM structure and its relation to the ENZ region of the polymer-based HMM structure, which is prominent in efficient dipole engineering model design.
2. Methods
2.1 Structure Design and modelling
Numerical optimization for thicknesses of the metal and dielectric layers (i.e. filling fraction) was implemented to attain the required epsilon-near-zero (ENZ) region with high PDOS and high phase velocity electromagnetic waves and match it with the emission and absorption wavelengths of the selected emitters. A desired thickness of 9 $nm$ of gold (Au) and 29 $nm$ of PMMA was attained using the aforementioned optimization codes. PMMA is a versatile polymeric material that is well suited for many applications such as high-resolution positive resist, protective coating, and as a sacrificial layer [39]. Based on the thickness values, we obtained an ENZ region comparable to the emission wavelength of Rhodamine 590 (Rh590) dye molecule. The spectral response, PDOS, Electric (E) field distribution, transmission dispersion relation, and Purcell factor calculations were numerically implemented using a commercial Ansys Lumerical FDTD solutions software package and an in-house developed transfer matrix method (TMM) code. Experimental wavelength-dependent complex dielectric functions for Au [40] and PMMA [41] were used for the numerical calculations. Figure 1(a) [Inside HMM] illustrates the schematic of the proposed type-2 [7] HMM structure with emitters embedded within the polymeric PMMA layer. Fig. 1(b) [on top of HMM], (c) [MIM], and (d) [on 9nm Au ] illustrate the schematic of the corresponding reference samples used to comprehend the decay rate mechanism and luminescence response of the proposed dye-doped HMM structure.
Fig. 1. (a) Schematic of the Au-PMMA structure consisting of 9 $nm$ thick Au and 29 $nm$ thick PMMA layers. Three polymeric PMMA samples were incorporated with three different dyes each [HMM + 3L dye]. I-M represents the insulator-metal interface. M-I-M represents the metal-insulator-metal interface. (b) similar HMM structure with dye-doped PMMA on the top layer [HMM + 1L dye]. (c) schematic of the MIM structure. (d) similar representation of dye-doped PMMA on top of the 9 $nm$ Au layer [IL Au + 1L dye].
2.2 Sample fabrication and characterization
The proposed polymer-based HMM structure was fabricated using a metallic electron-beam (e-beam) evaporator and spin-coating techniques. The samples were fabricated on a fused silica (SiO2) substrate with a refractive index of 1.45. Three active HMM samples were fabricated with each embedded with one of the different emitters. Reference samples of each dye embedded in PMMA-A1 (1%wt PMMA and 99%wt anisole) spin-coated on a homogeneous glass substrate were also prepared. Each dye was also spin-coated on a 9 $nm$ Au film to serve as a reference to study the coupling effects of dye on a metal substrate. Rh590, Styryl-11 (LDS 798), and Pyromethene 650 (PYR650) dye-doped PMMA samples were fabricated for characterization. The PMMA with dyes complex were spin-coated on the Au layers at a speed of 2000 rpm for 30secs. The thickness of the polymeric material was measured using a profilometer.
A Confocal Raman microscope from WiTec (alpha300R) was used for the characterization of the fabricated samples. The reflectance and transmittance measurements were carried out using a broadband optical source (Energetiq EQ-99XFC LDLS, spectral range 190-2100 nm) to excite the samples. The optical spot is focused on the samples using a Zeiss "Epiplan-Neofluar" 20X objective (Numerical aperture (NA=0.4)) for both reflectance and transmittance measurements. To acquire the photoluminescence (PL) of the samples, a 532 $nm$ laser was used to excite the samples to attain signal counts of the emission peak intensity for the different dyes. A polarization-dependent 375 $nm$ pulsed laser source (with a diffraction-limited spot size of $\approx$ 1.14 $\mu m$) was utilized to attain the fluorescence lifetimes of the samples with the help of a Picoquant HydraHarp device and a single-photon avalanche diode (SPAD) detector. All measurements were performed under optimal laboratory conditions. The response of the samples was coupled to an optical fiber connected to Ocean Optics Flame UV-VIS spectrometer for spectral response and PL measurement and a SPAD detector for the fluorescence lifetime measurement.
3. Results and discussion
Before the experimental characterization, we numerically calculated the dispersion relation of the proposed structure using both local and non-local effective medium theory (EMT) and the TMM approach to determine the wavevectors that are supported by the polymer-based hyperbolic metamaterial. The dispersion relation illustrated in Fig. 2(a), (b) and (c) shows the transmission of evanescent waves through the proposed structure. The local EMT approach represents the multilayered structure as an effective bulk medium with hyperbolic dispersion. As shown in Fig. 2(a), infinitely large wavevectors can be transmitted through the entire bandwidth of this ideal structure. However, in a realistic structure with a finite number of layers and considering the inherent losses in the metal layers, there is a cutoff to the largest wavevector that can propagate through the HMM structure. This is evident in the TMM dispersion relation illustrated in Fig. 2(c), which shows two bright bands at $k_{x}/k_{0} < 5$ and is comparable to the non-local EMT approach [42] illustrated in Fig. 2(b). Non-local EMT approaches have been quite realistic in describing metal-dielectric hyperbolic metamaterials due to their spatial dispersion effects corrections as compared to the local EMT approach [42–44]. The existence of the bright bands in the dispersion relation of the polymer-based HMM structure shows that the medium supports bulk plasmon-polaritonic modes. The bright bands coined as the bulk plasmon modes are due to the coupling of surface-plasmon-polaritons at each metal-dielectric interface. These modes also exhibit high electric field intensity that overlaps with emitters placed close to the metamaterial, resulting in an increased photonic density of states (PDOS) which is presented in Fig. 2(d). It is also interesting to note that the proposed material is a type 2 HMM structure which shows several high-k modes as compared to type 1 HMM which can support a lesser number of these modes [45].
Fig. 2. Dispersion relation of the polymer-based structure exhibiting high-k modes and the associated photonic density of states (PDOS). (a) Transmission of evanescent waves in logarithmic scale through the three bilayers of Au (9 $nm$)-PMMA (29 $nm$) multilayered structure using the local EMT approach. In the local effective medium limit, there are infinite high-k waves in a type 2 HMM due to the existence of strong spatial dispersion effects which can be corrected using the non-local EMT approach presented in (b). (c) Similar dispersion relation using the TMM approach. In this realistic case, the size of the unit cell imposes a cut-off to the tunneling of the high-k modes in the structure. (d) The corresponding PDOS of the polymer-based HMM composite using the TMM approach.
3.1 Spectral response of the polymer-based hyperbolic metamaterial
In addition to the dispersion relation, we calculated the field distribution through the polymer-based HMM structure using the TMM approach. Figure 3(a) illustrates propagation mode along the multilayered metal-dielectric interface composed of three subdivisions with labels: IM [ 0 $nm$ $\leq$ Z $\leq$ 38 $nm$], MIM1 [ 29 $nm$ $\leq$ Z $\leq$ 76 $nm$], and MIM2 [ 67 $nm$ $\leq$ Z $\leq$ 114 $nm$] layers. We obtained appreciably high electric field intensity at the ENZ wavelength of the proposed structure. However, the field intensity decays due to propagation losses and inherent metallic losses of the multilayer HMM structure. Note that at the HMM structure thickness $Z > 60$ $nm$, enhanced electric field intensity decays along the metal-dielectric layer thickness. Thus, emission of the embedded emitters results mainly from the first PMMA layer, while emitters in the other two layers contribute minimally. The enhanced spectral region of the electric field distribution shown in Fig. 3(a) correlates to the figure of merit (FOM) bandwidth as shown in Fig. 3(b). The FOM is defined as the ratio of the effective parallel $\varepsilon _{||}$ and perpendicular $\varepsilon _{\perp }$ permittivities of the HMM structure acquired via local EMT. The FOM shows higher values at the ENZ wavelength ($\lambda = 570$ $nm$). Figure 3(b) also shows the parallel $\varepsilon _{||}$ and perpendicular $\varepsilon _{\perp }$ dielectric tensor as a function of wavelength. The dispersion relation above the ENZ wavelength shows type 2 HMM behavior (i.e., $Re (\varepsilon _{||})< 0, Re(\varepsilon _{\perp })> 0$) with inherent optical losses and high impedance mismatch with respect to vacuum. In addition, we obtained the extracted effective permittivity $Ext(\varepsilon _{||})$ [dashed lines] of the fabricated polymer-based HMM structure by implementing an inverse TMM code and applying it on the attained spectral response of the HMM-dye complex structure. It is evident that the extracted effective permittivity $Ext(\varepsilon _{||})$ [dashed lines] matches well with the calculated effective parallel $\varepsilon _{||}$ permittivity [solid lines] possessing a similar ENZ wavelength as predicted numerically by EMT. Figure 3(c) illustrates the reflectance $R$ and transmittance $T$ of the polymer-based HMM structure obtained both numerically [solid lines] and experimentally (i.e. $R_{Exp}$, $T_{Exp}$) [dashed lines]. It can be seen that the spectral reflectance range above the ENZ wavelength is high as compared to the spectral range below ENZ. This role of a medium exhibiting dielectric (i.e., $\lambda < 570$ $nm$ with $Re(\varepsilon _{||}) > 0$ ) and metallic behaviour (i.e., $\lambda > 570$ $nm$ with $Re(\varepsilon _{||}) < 0$ ) shows the hyperbolic nature of the HMM composite. As stated initially, this nature brings about the inherent losses which can be compensated by using a gain medium, shown as an inset in Fig. 3(c). The inset shows the enhancement of the optical transmission $T$ response of the active polymer-based HMM structure in the presence of a pump source $T_{pump}$ which complements the emitter’s ability to help in the inherent metallic loss compensation.
Fig. 3. (a) P-polarized field ($E_{p}$) distribution through the HMM composite as a function of spectral wavelength. I-M corresponds to the insulator (PMMA) and metal (Au) interface. (b) Real [$Re(\varepsilon _{||})$, $Re(\varepsilon _{\perp }$] and imaginary [$Im(\varepsilon _{||})$] permittivitities from local EMT, experimentally retrieved effective permittivity $Ext(\varepsilon _{||})$ [dashed lines] and the figure of merit (FOM) of the polymer-based HMM composite. ENZ wavelength is defined as the spectral wavelength where the structure permittivity crosses zero. (c) Spectral response of the polymer-based HMM material. Reflectance $R$ and transmittance $T$ acquired both numerically (using TMM) and experimentally ($R_{Exp}$, $T_{Exp}$). The inset depicts the experimentally measured transmission in the presence of a pump source $T_{pump}$ and without a pump source $T$.
3.2 Purcell enhancement calculations
In addition to the spectral response implementations, we numerically calculated the Purcell factor and experimentally measured the photoluminescence of the polymer-based HMM structure to determine the decay rate mechanism of emitters coupled to the polymer-based HMM structure. We considered three scenarios in the numerical implementation. First, we numerically calculated the spectral-dependent far-field power density $\mathrm {W} /\left (\mathrm {m}^{2} \times \mathrm {sr}\right )$ at polar angle $\theta = 0$ of emitters embedded within the polymer-based HMM structure at different dipole positions $Z$. Note that $Z$ = 0 $nm$ corresponds to an unpolarized dipole placed at the topmost insulator part of the IM layer as shown in Fig. 3. $Z$ = 105 $nm$ also corresponds to the bottom insulator layer of the polymer-based HMM structure. The far-field power density calculations helped to determine the directional extraction effectiveness of emitters embedded within the polymer-based HMM as well as to numerically optimize the position of the dipoles embedded within the polymer-based HMM structure. Figure 4(a) delineates the far-field distribution of emitters embedded within the polymer-based HMM structure. We obtained high Purcell power density values at near-field which depicts that emitters close to the edge of the HMM medium exhibit high Purcell enhancement factor due to the high PDOS of the exotic HMM structure at the ENZ region. Also, to comprehend the emitter decay dynamics of the active HMM structure, we numerically placed three unpolarized dipoles (averaged x and y orientations) each at the central part of the three dielectric layers of the HMM structure to calculate their corresponding Purcell factors $F_{rad}/F_{0}$. Figure 4(b) presents the emitter decay rate mechanism at the three corresponding layers (i.e., IM, MIM1, MIM2). Note that MIM1 and MIM2 are similar as shown in Fig. 3(a), labeled as MIM layers. Evidently, due to the inherent lossy nature of metals, we see a weak Purcell factor in the IM layer as compared to the resonant metal-insulator-metal (MIM) case of the multilayered HMM structure. We assumed a collective emitter decay mechanism by taking the average of the Purcell factor [Mean Purcell Factor] at the corresponding layers. We obtained a high Purcell factor as compared to the IM case which we compared with the experimental PL measurement as we shall see in Fig. 5. Figure 4(c) also shows the collective logarithmic scale Purcell enhancement heatmap of multiple emitters embedded within the MIM layer of the polymer-based HMM structure. It is evident that the large thickness of the dielectric and lossy nature of the structure inhibits the coupling of the spontaneous decay of emitters embedded within the layers. This predicts that the unique property of high wavevectors and photonic density of states potentially also play a role in compensating for the lossy nature of the type 2 HMM structure.
Fig. 4. Purcell factor calculation of the polymer-based HMM structure. (a) Spectral dependent far-field power density $\mathrm {W} /\left (\mathrm {m}^{2} \times \mathrm {sr}\right )$ distribution of emitters embedded within the polymer-based HMM composite. (b) Purcell enhancement factor $F_{rad}/F_{0}$ for three different positions of emitters coupled to the polymer-based HMM structure. IM represents the insulator-metal interface. (c) Collective logarithmic scale Purcell factor enhancement for multiple dipoles placed in the MIM layer of the multilayered HMM structure.
3.3 Luminescence and lifetime measurement
To realize these exotic effects of the active polymer-based HMM structure, we experimentally measured the luminescence and the fluorescence lifetimes for three different dyes (i.e., Rh590, LDS798, and PYR650) within the polymer-based HMM structure. These dyes were selected due to their emission spectra having different amounts of overlap with the ENZ wavelength ($\lambda = 570 nm$) of the structure. Figure 5(a) presents the luminescence measurement of Rh590 dye with a maximum emission wavelength of 569 $nm$ which is close to the ENZ wavelength (570 $nm$) of the HMM structure. We compared the emission of each dye on a 9 $nm$ gold layer (IL Au + 1L dye), on top of the HMM layers (HMM + 1L dye), and within the HMM layers (HMM + 3L dye), respectively. We obtained high luminescence counts on and within the HMM layers as compared to the metallic cases. Evidently, we identified non-radiative quenching of the emitters when placed on the metallic layers due to the inherent lossy nature of Au. However, in the polymer-based HMM, we obtained improved luminescence counts as compared with the metallic case. This is due to the gold film absorbing the emitted waves with large k-vectors in the near field. On the other hand, in the HMM, these waves are mainly converted into propagating waves which help in compensating the loss of the metal (Au). Furthermore, the field confinement between the metal layers gives rise to emission rate enhancement of the emitters via Purcell effect. The improved luminescence within the polymer-based HMM structure is also compared to the luminescence counts of each dye on top of the HMM structure to compare their luminescence trends. It is noteworthy that the unique nature of the active polymer-based HMM structure compensates for the inherent losses as compared with the metal (Au) layer, yet possesses relatively similar luminescence counts either within or on top of the HMM layers. Figure 5(b) and (c) illustrate similar trend for PYR560 and LDS798 dye molecules. It must be pointed out that the emission wavelength of PYR650 is around 621 $nm$ which is far from the ENZ wavelength of the polymer-based HMM. As a result of the hyperbolic nature of the HMM structure in such a spectral region, we obtained a relatively higher luminescence trend for the PYR650 dye molecules as compared to the Rh590 dye molecules. Figure 5(c) also shows similar results for LDS798 dye molecule depicting weaker luminescence counts with emission wavelength of LDS798 dye far from the ENZ wavelength of the polymer-based HMM structure.
Fig. 5. Spectral luminescence measurement of emitters embedded within the polymer-based HMM composite. (a) Luminescence measurement of Rh590 dye molecule active polymer-based HMM structure. L represents the layers of emitters and metal-dielectric used, respectively. IL Au + 1L dye represents one layer of dye (0.01% concentration)-doped PMMA spin-coated on one layer of metal (Au) on top of a substrate. HMM + 1L dye depicts one layer of dye-doped PMMA spin-coated on top of the HMM structure. HMM + 3L dyes represent a polymer-based HMM structure with dyes doped at each PMMA layer of the HMM structure (3L). Similar measurement for (b) PYR650 dye-doped and (c) LDS798 dye-doped polymer-based HMM structure.
In addition, we compared the experimentally attained fluorescence lifetime values for each of the three different dye-doped HMM structures. Table 1 contains the lifetime components and the corresponding amplitudes fitted to the measured time-correlated single-photon counting (TCSPC) data as well as the calculated average lifetimes based on the amplitudes. For all dyes ($\approx$ 40 molecules/(10$\times$10$\times$29 nm$^{3}$) in the presence of one gold layer, we observed shortening of the average lifetime by more than a half, which is attributed to increased non-radiative decay due to near field absorption of the gold film. This is important to keep in mind when inspecting the lifetimes of dyes on top or embedded inside the polymer-based HMM, as the effect of dyes interacting with the thin gold film is also present in the HMM. Nonetheless, in the polymer-based HMM we observe even shorter lifetimes. Fermi’s golden rule states that the number of radiative decay channels depends on the number of PDOS available to the emitter [23]. Therefore, an increased PDOS can be experimentally verified by observing a shortened lifetime. Thus, these lifetime results act as evidence of coupling between the emitters (Rh590 and PYR650) and the high-k modes of the polymer-based HMM complex as well as coupling to the surface plasmon polariton modes at each metal-dielectric interface. This results in an additional increment to the non-radiative recombination rate of the emitters. However, for LDS798 no additional shortening of lifetime is observed in the HMM when compared with the metal case. As seen from Fig. 2(d), the increase in PDOS is highest near the ENZ wavelength. As the emission of LDS798 has the least overlap with that region, the coupling between the emitters and the high-k modes is weakest, thus not resulting in further shortening of the lifetime. Additionally, as seen in Fig. 3(a), the structure exhibits field confinement in the polymeric region between the gold layers spectrally overlapping with the ENZ wavelengths. The resulting enhancement of the radiative decay rate due to the Purcell effect can also be observed through lifetime shortening. However, lifetime shortening can differ from the calculated Purcell factor, since fluorescence lifetime is dependent mainly on the radiative and non-radiative rates. On the other hand, Purcell factor enhancements can be attributed to distinct factors such as local field intensity of the HMM structure, varied dye molecules orientations, as well as positions [46]. This accounts for the difference between the calculated Purcell factor and the experimental decay rates of the polymer-based HMM structure. Furthermore, the emission lifetimes of the polymer-based HMM structure may vary at different characterization spots due to different emitter orientations and their various separation distances from the metallic layers. As such, we measured the fluorescence lifetimes of each sample at several spots to attain their collective mean values and standard deviations. Average lifetime values of [$\approx$ 0.66 $\pm$ 0.0064, $\approx$ 0.78 $\pm$ 0.0044, and $\approx$ 0.41 $\pm$ 0.0043] ns were attained for (Rh590, PYR650, and LDS798) dyes inside HMM structures, respectively.
Table 1. Lifetime measurements of the three dyes on fused silica substrate, on 9 $nm$ gold (Au) layer and, on top of the HMM structure and embedded within the polymer-based HMM structure.
3.4 Polymer-based HMM for subwavelength imaging application
To emphasize the relevance of the proposed active polymer-based HMM structure, we further calculated the subwavelength resolution of two-dipoles with a separation distance of 50 $nm$ ($\approx \lambda /12$) placed at 10 $nm$ away from the polymer-based HMM medium as shown in Fig. 6. We compared the passive (a), (b), and (c) and the active (d), (e), and (f) polymer-based HMM structures at three different wavelengths ($\lambda =$ 570 $nm$, 621 $nm$, and 700 $nm$) which are comparable to the emission wavelength of the dye molecules embedded within. It is evident that the active polymer-based HMM medium (d), (e), and (f) depicts enhanced field amplitude as compared to the passive (a), (b), and (c) HMM. Figure 6(a) shows the dipole resolved field distribution along the propagation axis (Z) for the passive HMM structure at resonance wavelength $\lambda =$ 570 $nm$. Similar results are shown in Fig. 6(b) and (c) at different spectral regions which correlate to the emission wavelength of PYR650 and LDS798 dyes, respectively. Evidently, incorporating dye molecules in the passive polymer-based HMM structure compensates for the metallic losses in the HMM and enhances the field distribution illustrated in Fig. 6(d), (e), and (f). The polymer-based HMM structure’s ability to transmit high order evanescent waves from the near-field to the far-field and the existence of a gain medium embedded within enhances its applications in subwavelength resolution imaging. Thus utilizing the proposed polymer-based HMM structure breaks the diffraction limit and enhances dipole subwavelength resolution as well as projecting an image with subwavelength details into the far-field. This unique nature of the polymer-based HMM structure could be utilized in relevant photonic applications such as hyperlens.
Fig. 6. (a), (b), and (c) Sub-wavelength resolved two dipole sources using a passive polymer-based HMM structure and their corresponding active case (d), (e), and (f) at different wavelengths (i.e., 570 $nm$, 621 $nm$, 700 $nm$) comparable to the emission wavelength of the dye molecules. In between the two white lines represents the metal layers and the blue line depicts the topmost layer of the polymer-based HMM layers. The insulator layer is also represented as I.
4. Conclusion
In summary, we have shown the dynamics of emission and decay rate of different dyes incorporated with a polymer-based HMM structure and numerically predicted the existence of its corresponding non-radiative high-k modes. We illustrated the shortening of the average lifetime and increment in the luminescence intensity of emitters embedded within and on top of the polymer-based HMM structure which are due to the increase in the non-radiative decay channels of the proposed structure. With emitters spectrally closer (Rh590) to the ENZ region of the polymer-based HMM structure, we observed a relatively high shortening of the average lifetime as compared to other emitters spectrally close (PYR650) or far (LDS798) from the ENZ region. This observation confirms the increase in non-radiative decay channels of the polymer-based HMM structure with a gain medium at the ENZ region. We also showed that our proposed dye-doped polymer-based HMM structure compensates for the losses in a metal-dielectric HMM structure by observing an enhanced transmittance in the presence of a pump source and numerically implemented the sub-wavelength two dipoles resolution to emphasize the relevance of incorporating emitters into a passive polymer-based HMM structure. The unique properties of our proposed polymer-based HMM structure could be a paradigm shift to enhance the robustness of HMM structures in nano-imaging and quantum optics applications.
Funding
H2020 European Research Council (802986); Academy of Finland (320165).
Acknowledgments
We acknowledge the financial support of the European Research Council (Starting Grant project aQUARiUM, Agreement No. 802986) and Academy of Finland Flagship Programme (PREIN) (320165).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results are presented in the paper.
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