Hyperbolic polariton-coupled emission optical microscopy

1.1 Experimental setup

The HPCE microscope is designed to leverage the unique dispersion of HMMs to tailor the fluorescence properties of a fluorophore. The HMMs used in the HPCE microscope are composed of a multilayer structure consisting of three pairs of alternating 10-nm silver (Ag) and 4-nm silicon dioxide (SiO₂) layers (similar to the configuration described in previous research [9]), which facilitates high spatial frequency wave propagation with enhanced light–matter interaction.

As shown in Figure 1a, the HPCE microscope is in an inverted microscope configuration with an HMM substrate positioned under the sample. The sample is illuminated off-centered at the back focal plane (BFP) to control the incidence angle θ _ex, which allows for precise control of the excitation conditions – crucial for achieving time-dependent modulation of fluorescence intensity. The results for the fluorescence intensity as a function of θ _ex are depicted in Figure 1b. It shows that, by modulating θ _ex through a galvo scanner, one can dynamically adjust the excitation conditions, achieving a maximum enhancement in fluorescence intensity at the HPCE angle θ _HPCE. Such tunability offers significant advantages in applications requiring time-resolved intensity modulation. Moreover, this tunability is wavelength-dependent due to the dispersive nature of the HMM substrate, which enables selective excitation of fluorescence at different angles, providing additional degrees of freedom for modulating the fluorescence intensity. In Figure 1c, back focal plane (BFP) images captured at different incidence angles, i.e., c1 (3π/8 radian), c2 (7π/32 radian), and c3 (0 radian), demonstrate the optimal angle c2 with the highest fluorescence intensity. The corresponding fluorescence images (Figure 1d) at the image plane (IP) show enhanced fluorescence intensity under the optimal excitation condition (i.e., c2), illustrating the effectiveness of HPCE in improving signal sensitivity and contrast.

Figure 1:

Experimental setup and imaging results of hyperbolic polariton-coupled emission (HPCE). (a) Schematic of the setup. The fluorophores, i.e., green emission fluorescent beads and red emission quantum dots, positioned on an HMM substrate (at the image plane, IP), are illuminated by a blue excitation laser (λ _ex = 488 nm) off-centered at the back focal plane (BFP) to control the incidence angle (θ _ex). The emission intensity is maximized at the specific incidence angle θ _ex = θ _HPCE for the HPCE wavelength λ _HPCE. (b) Wavelength-dependent angular emission profiles. The θ _HPCE values at the green and red wavelengths differ, as shown by the peaks in their respective intensity distributions, highlighting the role of hyperbolic dispersion of the HMM substrate in controlling the θ _HPCE. (c) BFP images captured at different incidence angles c1, c2, and c3, demonstrating the optimal angle c2 with the highest fluorescence intensity. (d) Corresponding fluorescence images at the IP. These images also show enhanced fluorescence intensity under the optimal excitation condition (i.e., c2), illustrating the effectiveness of HPCE in improving signal sensitivity and contrast.

2.1 Comparison of TIRF and HPCE

The time-dependent modulation of the incidence angle used in the experiment is shown in Figure 2a. The angle sweeps between 0 and 3π/8 radians and is adjusted to enhance fluorescence emission. Figure 2b shows the resultant emission intensity variation under TIRF using glass. Even though TIRF gives rise to enhanced emission intensity at the total internal reflection angle of the air/glass interface, the emission intensity remains relatively low and lacks distinct peaks due to the limited enhancement capability of TIRF when using glass. On the other hand, the fluorescence emission for HPCE on an HMM substrate (Figure 2c) exhibits strong and clear intensity peaks for both green and red wavelengths at specific incidence angles, demonstrating the emission engineering ability of the HPCE.

Figure 2:

Comparison of fluorescence emission for red quantum dots (605 nm) and green fluorescent beads (515 nm) under TIRF using glass and HPCE using HMM. (a–c) Incidence angle modulation over time (a) and the resultant emission intensity variations for TIRF on glass (b) and HPCE on HMM (c), respectively. (d, e) Corresponding BFP and IP images for TIRF on glass (d) and HPCE on HMM, respectively.

The BFP and IP images of both green fluorescent beads and red quantum dots under TIRF using glass (Figure 2d) and HPCE using HMM (Figure 2e) are shown. For TIRF on glass, the fluorescence emission is weak and lacks clear angular control, resulting in lower signal intensity and contrast in the IP images. In contrast, for HPCE on HMM, BFP images of both green fluorescent beads and red quantum dots display distinct ring patterns, indicating strong, angle-selective enhancement of these fluorophores. Moreover, the corresponding IP images exhibit significantly increased fluorescence intensity for both the green and red fluorophores, confirming that HPCE on HMM provides superior signal enhancement and contrast compared with TIRF on glass.

2.2 Analysis of HPCE physical origin

The physical origin of HPCE is the excitation of hyperbolic polaritons supported by the HMMs used, which has been confirmed through precise measurement of the angle-dependent emission and the attenuated total internal reflection (ATR) as shown in Figure 3. In the angle-dependent emission experiments, peaks in emission intensity are expected to be observed at the optimal angles for hyperbolic polariton excitation within the HMMs when strong coupling between the incident light and the hyperbolic polaritons takes place. To find out such conditions, the incidence angle was systematically varied from 30° to 55° in 1° steps, while the corresponding emission intensity was monitored. The results for both the green (515 nm) and red (605 nm) wavelengths under the two conditions, i.e., HPCE using an HMM substrate and TIRF using a glass substrate, are summarized in Figure 3a. The HPCE on HMM shows a significant increase in emission intensity for both wavelengths, with a distinct time-dependent modulation. This modulation is attributed to angle sweeps across optimal incidence angles, which align with the hyperbolic polariton excitation in the HMM, resulting in enhanced fluorescence emission. In contrast, TIRF on glass displays lower and more stable intensity modulation, indicating limited enhancement due to the lack of hyperbolic polariton excitation.

Figure 3:

Analysis of the physical origin behind the HPCE microscope. (a) Angle-dependent emission results. Emission intensity modulation is achieved by varying the incidence angle over time for both the green (515 nm) and red (605 nm) wavelengths under two conditions, i.e., HPCE using an HMM substrate and TIRF using a glass substrate. (b) Corresponding attenuated total internal reflection (ATR) results. Reflection dips reach their minimum at the resonance angles where hyperbolic polariton excitation occurs, aligning with the peaks observed in HPCE emission intensity.

The attenuated total internal reflection (ATR) experiments [19], [20] were conducted to analyze how light interacts with the HMM substrate across this range of incidence angles (Figure 3b). The ATR results reveal the angle-dependent excitation characteristics of the hyperbolic polaritons, providing insight into the resonance conditions that enhance HPCE. As the incidence angle is swept from 30° to 55°, the HMM substrate exhibits pronounced dips in reflected intensity around specific angles for each wavelength. The reflection dips observed in the ATR experiment align with the emission intensity peaks, confirming the role of hyperbolic polariton excitation in achieving enhanced fluorescence in HPCE. In contrast, the ATR experiment with the glass substrate shows no significant changes in reflected intensity, underscoring the lack of angle-dependent coupling effects.

2.3 Simulations of optical field enhancement in HPCE

To have a better understanding of the enhanced fluorescence in the HPCE microscope, numerical simulations were carried out based on the finite difference time domain (FDTD) method. Figure 4 summarizes the simulation results of the excitation field enhancement using both the glass and HMM substrates at wavelengths of 488 nm, 515 nm, and 605 nm for each substrate, respectively. In these simulations, the excitation field is modeled as an obliquely incident plane wave from the glass side. The HMM substrate used in the HPCE microscope is a multilayer structure consisting of three pairs of alternating 10-nm silver (Ag) and 4-nm silicon dioxide (SiO₂) layers. The intrinsic dielectric permittivity values of Ag and SiO₂, as reported in the Palik database [21], were used for each material. As shown in Figure 4a–c, the field intensity, ∣E∣², is localized near the glass–air interface with a limited intensity peak around the critical angle, exhibiting the typical optical response of TIRF. The excitation field decays rapidly beyond the penetration depth, limiting the enhancement effect achievable on the glass substrate. Figure 4d–f shows the excitation field intensity using the HMM substrate. The incident plane wave excites surface plasmon polaritons at the interfaces of individual metal layers, which subsequently couple to form bulk hyperbolic polaritons. A significantly large field enhancement across a broad range of incidence angles is observed, owing to the hyperbolic dispersion of the HMM. This extended angular range, combined with the higher field intensity near the HMM surface, enables a more robust excitation field that is not limited to the critical angle region, as observed in TIRF. Although the radiative decay rate enhancement is not included in these simulations, the excitation field enhancement alone suggests that HPCE using an HMM substrate can achieve over six times the fluorescence emission enhancement compared to conventional TIRF using the glass substrate. This result indicates that the HMM structure, by enhancing the excitation field, also significantly improves the emission efficiency, which is consistent with experimental measurements (Figure 3a). These FDTD simulations confirm that the excitation field enhancement on HMMs is significantly greater than that on glass, even without accounting for radiative decay rate enhancements, such that HMM-based substrates inherently boost fluorescence signal through excitation field amplification. It is worth noting that the contribution of radiative decay rate enhancement is minimal in nonpatterned HMM substrates compared to nonradiative effects [22]; additionally, radiative decay rate enhancement does not depend on the incidence angle, which is crucial for HPCE-induced emission enhancement.

Figure 4:

Analysis of the optical field enhancement in the HPCE microscope. (a–f) FDTD simulation results showing field enhancement using both the glass (a–c) and HMM (d–f) substrates at wavelengths of 488 nm, 515 nm, and 605 nm, respectively, for each substrate.

2.4 Optimization of HPCE enhancement

Hyperbolic polariton excitation in HMMs leads to significant field enhancement at the HMM surface, which in turn results in HPCE enhancement. Figure 5 shows the calculated hyperbolic polariton dispersion of HMMs composed of three pairs of alternating metal (Ag) and dielectric layers. The hyperbolic polariton modes are calculated through the transfer matrix method. The wavelength-dependent nature of hyperbolic dispersion is influenced by the material properties of the HMM, including the thickness of the metal and dielectric layers, the fill fraction ρ = t m / t m + t d of the metal, where t _m and t _d are the thicknesses of the metal and dielectric films, and the refractive index n of the dielectric material. HPCE occurs when the momentum of the excitation beam matches the momentum of the hyperbolic polariton dispersion. This matching condition depends on the hyperbolic dispersion, which varies with wavelength and is directly affected by the optical properties of the metal and dielectric layers. As a result, the optimal incidence angle for HPCE varies depending on the fluorescence wavelengths of the sample. By tuning the material parameters – such as layer thicknesses and refractive indices – and adjusting the incidence angle of the excitation beam, HPCE can be optimized for specific fluorescence wavelengths to achieve maximum fluorescence enhancement. The choice of materials and their structural parameters plays a critical role in determining the hyperbolic dispersion and the conditions for optimal HPCE. This enables the customization of fluorescence enhancement for imaging applications by aligning the HPCE conditions with the spectral properties of the fluorescent sample.

Figure 5:

Calculated hyperbolic polariton dispersion for HMMs with varying material parameters. (a) Hyperbolic polariton dispersion with a fill fraction ρ = 0.25 and refractive index of the dielectric layer n = 1.54. (b) Dispersion for ρ = 0.29 and n = 1.54, which are the parameters used in our experiment. (c) Dispersion for ρ = 0.33 and n = 1.54. (d) Effect of increasing the dielectric refractive index to n = 2.0 for ρ = 0.29, demonstrating how material parameters influence the hyperbolic polariton excitation conditions across wavelength and incidence angle.