1. Introduction

Strong coupling exhibits ubiquitous characteristics in light-matter interaction and has a wide range of applications in quantum dot emitters [1], polariton lasers [2] biosensors [3], and frequency-tunable devices [4]. It is initially implemented in cavity quantum emitter systems and forms new hybrid states [5], exhibiting unique properties and energy spectra different from those of the individual systems [6,7]. Subsequently, similar physical phenomena are extended to varied material systems, such as organic molecules [8], two dimensional gases [9], ions [10], excitons [11], and phonons [12]. Owing to the extreme confinement of electromagnetic fields to subwavelength scales and flexible tunability [13,14], plasmonic resonators are integrated into microcavities in recent studies to provide an efficient and controllable way to achieve energy redistribution and local enhancement [15,16]. However, most research has focused on the tunability of emitters or plasmon resonators under strong coupling states, while the modulation effect on microcavities is still to be researched and developed [17], especially in the terahertz (THz) regime [18,19]. Since THz microcavities have great application prospects in the THz lasers [20], time-domain spectrometers [21], biochemical sensors [22], and communication devices [23], efficient modulation of THz microcavities urgently needs to be explored to facilitate advanced functionalities and unlock more application scenarios. As a novel method, strong coupling modulation exploits the strong light-matter interaction mechanism to manipulate microcavities through plasmonic resonators [24,25]. Furthermore, plasmonic resonators are usually designed at subwavelength scales, which is conducive to the miniaturization of THz microcavity modulation systems and the integrated development of compact THz on-chip functional devices [26,27].

In this paper, we demonstrate a novel strategy to effectively modulate the THz microcavity by strongly coupling it to plasmonic resonators. Finite-difference time-domain (FDTD) method and time-resolved phase-contrast imaging technique are used to study the resonance characteristics of the microcavity-plasmon hybrid system in simulations and experiments, respectively. When the resonant frequency of the plasmonic resonators is close to that of the THz microcavity, the resonances of the hybrid system behave as two polaritons, which is caused by the strong coupling between THz microcavity mode and the plasmonic resonance. Two polaritons redistribute the THz electric field in the microcavity and present distinct profiles. We perform a detailed analysis of the polaritons whose energy is mainly distributed in the THz microcavity. The resonant frequency of the hybrid microcavity has a blue shift of 6.2% compared to that of the bare one, resulting from the frequency splitting of the polaritons in the strong coupling regime. The frequency shift rate reaches maximum at zero detuning point and decreases as detuning increases. We believe that our strategy can provide a new degree of freedom for the modulation of on-chip THz microcavities, contributing to the future development of THz integrated devices.

2. Design and simulation

The basic building block under study is illustrated in Fig. 1(a). It consists of a Fabry-Perot microcavity on the lithium niobate (LN) wafer and a periodic line array of subwavelength plasmonic resonators placed on its surface. The Fabry-Perot microcavity is formed by a central microcavity and two distributed Bragg reflectors (DBRs) on both sides [18]. The DBRs are composed of alternating materials (LN and air) with varying dielectric constants along the $x$-axis, while the air gaps are fabricated on a 50 $\mathrm{\mu}$m-thick LN wafer using femtosecond laser direct writing technique [28]. The designed DBRs have a period of $a$ = 200 $\mathrm{\mu}$m and air gaps of width $d$ = 100 $\mathrm{\mu}$m, ensuring effective confinement of the researched THz waves. A column of plasmonic resonators is fabricated on the surface of the LN wafer and at the center of the microcavity along the $z$-axis using ultraviolet lithography and magnetron sputtering (see Appendix). The patterns consist of an 85 nm-thick Au layer with a 5 nm Ti layer acting as adhesion [29]. The inset of Fig. 1(a) shows the specific parameters of the unit plasmonic resonator. Considering that the resonant frequency of the localized surface plasmon is strongly dependent on the geometry of the plasmon and the refractive index of the surrounding medium, we can scale the inner radius $r$ of the resonator to cover spectral regions of interest, while the other structural parameters remain fixed in the following research. Here, the period $p$ = 100 $\mathrm{\mu}$m, width $w$ = 12 $\mathrm{\mu}$m, and gap $g$ = 3 $\mathrm{\mu}$m. Figure 1(c) shows an optical microscopy image of the manufactured sample in the experiment, where the scale bar corresponds to 50 $\mathrm{\mu}$m.

 

Fig. 1. Hybrid system overview. (a) Illustration of the microcavity-plasmon hybrid system: an array of plasmonic resonators positioned at the surface of the Fabry-Perot microcavity. The Fabry-Perot microcavity is fabricated on a 50 $\mathrm{\mu}$m-thick LN wafer. The DBRs has a period of $a$ = 200 $\mathrm{\mu}$m with 100 $\mathrm{\mu}$m-wide LN rod and 100 $\mathrm{\mu}$m-wide air gap in each cell. The microcavity length $l$ = 300 $\mathrm{\mu}$m. The inset shows the specific parameters of the unit plasmon resonator: period $p$ = 100 $\mathrm{\mu}$m, width $w$ = 12 $\mathrm{\mu}$m, inner radius $r$ = 10 $\mathrm{\mu}$m, and gap $g$ = 3 $\mathrm{\mu}$m. (b) THz sources in the microcavity-plasmon hybrid system. (c) Optical microscope image of the hybrid system. The scale bar corresponds to 50 $\mathrm{\mu}$m.

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To better illustrate the modulation effects of the plasmonic resonators on the THz microcavity, we perform FDTD numerical simulations (see Appendix). Figure 2(a) shows the magnitude of the THz electric field spatially averaged inside the THz microcavity, as a function of inner radius $r$ of the plasmonic resonator and the frequency $f$, while the microcavity length $l$ is fixed at 300 $\mathrm{\mu}$m. For a visual comparison between the spectra of hybrid systems with the THz microcavity and plasmonic resonators, we plot them with blue dashed lines in Fig. 2(a), where $f_{\text {pr}}$ denotes the plasmonic resonant frequency and $f_{\text {cav}}$ denotes the resonant frequency of the third order mode in the THz microcavity. When the resonant frequency $f_{\text {pr}}$ of the plasmonic resonators overlaps with the third order mode resonant frequency $f_{\text {cav}}$ of the bare THz microcavity, the hybrid system achieves a coupling state, and energy exchange occurs between the THz microcavity and plasmonic resonators. Different from traditional cavity quantum electrodynamic experiments with atomic systems, neither the bare THz microcavity mode nor the plasmonic resonance is ’sharp’ in our study, where the full widths at half maximum of both resonances exceed 3.5% of their center frequencies. However, the coupling rate is still larger than the loss mechanisms present in the hybrid system in this case. Mathematically, it meets the criterion for strong coupling $g>\sqrt {\kappa \gamma }$, where $g$ represents half the coupling rate, while $\kappa$ and $\gamma$ are the loss rates of the THz microcavity and plasmonic resonators, respectively. Two polariton branches with clear anti-crossing behavior can be observed in the frequency domain, and a larger anti-crossing denotes a stronger coupling strength. In a zero-detuning state, the normalized coupling strength of the hybrid system is defined as ${\Omega }/{f_{\text {cav}}}$, where $\Omega$ denotes the frequency difference between the two polaritons. In Fig. 2(a), $\Omega$ is about 0.046 THz at ${f_{\text {pr}}} = f_{\text {cav}}$ = 0.342 THz, corresponding to the normalized coupling strength of about 13.5%, clearly indicating the strong coupling regime in the hybrid systems. The black curves in Fig. 2(a) show the theoretical curves calculated using the rotating wave approximation in the standard Jaynes-Cummings model (see Appendix), consistent with the simulation results [30]. Moreover, we plot the electric field oscillation in the time domain of the hybrid system and a 300 $\mathrm{\mu}$m long bare THz microcavity for comparison, as shown in Fig. 2(b). The time domain signal of the hybrid system exhibits a period beating behavior, which corresponds the ultrafast energy exchange between the THz microcavity and the plasmonic resonators. This also provides evidence that the hybrid system has reached the strong coupling regime. These phenomena can be explained by the spatial distribution of the electric field of multimode in the THz microcavity, as shown in Fig. 2(d). There is an antinode of the third order mode at the center of the THz microcavity, and the electric field intensity reaches its maximum, which promotes the occurrence of strong coupling and polaritons splitting. Hence, to achieving a pronounced strong coupling phenomenon, we expect to place the plasmonic resonators at the center of the THz microcavity and have them interact with the third order mode of the THz microcavity.

 

Fig. 2. (a) The averaged electric field mapping of the hybrid system as a function of inner radius and the frequency. Blue dashed lines indicate the resonant frequencies of the plasmonic resonators and the bare THz microcavity. Black curves represent the theoretical results. (b) Time-domain signal of the hybrid system (red line) and the bare THz microcavity (blue line). (c) Time-domain signal of the plasmonic resonator. (d) The electric field distribution of third order mode within a 300 $\mathrm{\mu}$m long bare THz microcavity. The shadow rectangles indicate the positions of the etched air slots.

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At zero detuning point, the microcavity modulation can reach the best efficiency. Thus, we calculated the intensity of the THz field $|E_z|^2$ in the $x$-$y$ cross-section of both the polariton branches at zero detuning point. Figures 3(a) and (b) show the opposite intensity profiles of the two polariton branches in the 300 $\mathrm{\mu}$m long THz microcavity. In Fig. 3(c), the intensity profile of the bare THz microcavity is used as a reference. The strong coupling with plasmonic resonators changes the electric field intensity distribution inside the THz microcavity. For the lower polariton branch, the electric field is confined to the interface between the THz microcavity and plasmonic resonators. On the contrary, the electric field of the upper frequency branch is mainly distributed in the area where $y$ < 0 inside the THz microcavity, making it convenient to observe using time-resolved phase-contrast imaging system in experiments.

 

Fig. 3. (a) and (b) The intensity profile in the $x$-$y$ cross section of lower and upper polaritons, respectively. (c) The intensity profile in the $x$-$y$ cross section of the bare THz microcavity for reference. Two black dashed lines indicate boundaries of the cross section of the LN wafer.

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3. Results and analysis

Figure 4(a) shows the diagram of the time-resolved phase-contrast imaging system. Femtosecond laser pulses from a Ti:sapphire regenerative amplifier (800 nm central wavelength, 1 kHz repetition rate, 120 fs duration, 500 $\mathrm{\mu}$J/pulse) are split into two pulses at a power ratio of 9:1. The higher power pump pulse (BS reflected) is directed to a mechanical time-delay line, and then line-focused in the THz microcavity region of the LN wafer by a 10-cm focal-length cylindrical lens. The pump pulse generates THz pulses in the microcavity and act as a line source. The generated THz waves propagate in the LN wafer along $\pm x$ axis, as shown in Fig. 1(b). In this process, the polarization of the pump pulse is optimized parallel to the optical axis of LN ($z$-axis) for the most efficient excitation. The lower power probe pulse (BS transmitted) is frequency doubled to 400 nm, spatial filtered, and then irradiates the entire sample. The existence of THz waves will result in a change of the refractive index of LN via the electro-optic effects, introducing a phase shift during the propagation of the probe light [31]:

 

Fig. 4. (a) Schematic diagram of the time-resolved phase-contrast imaging system. Red and blue beams represent 800 nm pump and 400 nm probe pulses, respectively. Black dashed box represents the mechanical time-delay line. (b) Spatiotemporal evolution of THz waves in the hybrid system. The center of the microcavity is set as the $x$ = 0. The shaded rectangles represent the etched air gap. (c) Dispersion relations by taking a 2D Fourier transform of (b). (d) Spectrum of the hybrid system, bare THz microcavity, and plasmonic resonators.

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Since the pump laser is focused along the $z$-axis by a cylindrical lens and the hybrid system is periodic along the same direction. We integrate the signals along the $z$-axis into a row vector relating to the $x$-axis position at each time delay and repeat the process in chronological order to obtain the full spatiotemporal evolution $E (t,x)$, as shown in Fig. 4(b). The bright line at $x$ = 0.09 mm indicates the position of the pump pulse caused by nonlinear effects, and the dark line at $x$ = 0 mm denotes the position of the plasmonic resonators. The shaded rectangles represent the etched air gap. Due to limitations of the band structure of the Bragg grating, only THz waves with frequencies in the band gap range can be confined in the microcavity, while other frequency components would propagate outward through the Bragg grating. Figure 4(c) shows the dispersion relations of THz waves in the hybrid system $|E (f,k)|$, which is obtained by performing two-dimensional Fourier transforms of the spatiotemporal evolution $E (t,x)$. The dispersion relation remains constant at certain frequency, indicating the modulated microcavity resonates at 0.361 THz. This is consistent with the simulation results in Fig. 3. In addition, the THz intensity distribution of the lower polariton branch is located near the plasmonic resonators, which is less possible to be collected in the experiments since the Au layer blocks and energy out of the LN crystal. Figure 4(d) shows the spectrum of the hybrid system and bare THz microcavity to better quantify the effect of frequency modulation through strong coupling. The grey line denotes the transmission spectra of the plasmonic resonators on the LN wafer. When the resonances of individual THz microcavity and plasmonic resonators overlap spectrally, the strong coupling occurs. A significant frequency shift is observed in the hybrid system. Compared to the bare microcavity, the resonant frequency of the upper branch polariton is blue shifted from 0.340 THz to 0.361 THz with a shift rate of about 6.2%, showing consistency with simulation in Fig. 2(a). In addition, the resonant mode in the hybrid system is slightly broadened, due to the extra loss induced by the plasmonic resonators.

Furthermore, we also investigated the modulation of this method to the different THz microcavities. By choosing inner radius as $r$ = 10 $\mathrm{\mu}$m, we changed the lengths of the THz microcavity from 220 to 380 $\mathrm{\mu}$m, the calculated results are shown in Fig. 5. When the resonant frequency of THz microcavity approaches to that of plasmonic resonators, the resonance mode of the microcavity shows an obvious modulation. As the microcavity length increases, the lower polariton transitions to the THz microcavity dominated mode from a plasmon-dominated mode, while the upper polariton is pushed to the blue shift because of the strong coupling with the plasmonic resonators and acquires a plasmon-like property. In the case of detuning of short and long microcavities, the energy of the polaritons is concentrated in the upper and lower branches, respectively. That is to say, the energy is always concentrated in the microcavity-dominated branch at detuning. This is because THz waves are initially generated in the microcavity, the coupling between the THz microcavity and the plasmonic resonators is weak at the detuning state, resulting in most of the energy is still distributed in the microcavity. Similar phenomena can also be found in Fig. 2(a), these results indicate that the strong coupling modulation induces the variation of the resonant frequency of the THz microcavity. Thus, the resonant frequency of the THz microcavity can be effectively modulated by changing the degree of detuning with the plasmonic resonators.

 

Fig. 5. The averaged electric field mapping of the hybrid system as a function of inner radius and the frequency. Blue dashed lines indicate the resonant frequencies of the plasmonic resonators and the bare THz microcavity. Black curves represent the theoretical results.

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Notably, the resonance properties of plasmonic resonators will show great variations under external stimuli, such as changes in voltage, temperature, or surrounding refractive index. Therefore, the strong coupling modulation can be combined with electro-optical modulation, thermo-optic modulation and other techniques to achieve the versatility of THz microcavity modulation and improve overall performance in the future. The same modulation effect can also be achieved in 2D photonic crystals, whispering gallery cavities, and semiconductor heterostructures, providing an excellent extensions.

4. Conclusion

In conclusion, we propose an approach to effectively modulate the resonant frequencies of THz microcavities. The resonant frequency of the microcavity can be actively tuned by coupling with the plasmonic resonators deposited in the center of the THz microcavity. At the zero-detuning point, the microcavity-plasmon hybrid system exhibits two anti-crossing polariton branches in the frequency domain, and they have opposite electric field distributions. Through microcavity-resonator strong coupling, we obtain a 6.2% blue-shift of the resonant frequency relative to the bare THz microcavity. These results provide a feasible method for developing efficient modulation on-chip THz microcavities, which provides possibilities to achieve compact THz on-chip devices.

Appendix

Sample fabrication

Firstly, the LN wafer is cleaned in acetone and isopropanol in ultrasonicator, and dried with N₂ blow. Secondly, a 1.5 $\mathrm{\mu}$m thick layer of photoresist (AR-N-4340) was spin coated onto the LN wafer. Thirdly, the LN wafer under the mask plate with the designed pattern was exposed to ultraviolet light via photolithography. Fourthly, the unexposed photoresist was removed away with developer. Fifthly, an 85 nm layer of Au with a 5 nm adhesion layer of Ti were sputtered on the LN wafer by magnetron sputtering. Finally, the designed patterns were formed on the LN wafer by removing the residual photoresist with acetone.

Simulation setting

The numerical calculations are performed using the commercial software ANSYS FDTD Solution. Parameters of materials, excitation sources, and simulation settings are shown as follows. The dielectric constant of LN is diagonal, and the ordinary and extraordinary components are:

(3)$$\varepsilon =\varepsilon_{\infty} + \frac{\omega^{2}_{\text{TO}}(\varepsilon_{0}-\varepsilon_{\infty})}{\omega^2_{\text{TO}} - i\omega\varGamma-\omega^2}.$$

where $\varepsilon _{0}$ and $\varepsilon _{\infty }$ are the dielectric constants in low and high frequency limits, $\omega _{\text {TO}}$ and $\varGamma$ are the resonant frequency and damping rate of the lowest transverse optical phonon mode. $\varepsilon _{0}$ = 26.0, $\varepsilon _{\infty }$ = 10, $\omega _{\text {TO}} = 2\pi \times 7.6$ THz, and $\varGamma = 2\pi \times 0.63$ THz, respectively. Because Au has conductivity on the order of 10$^7$ S/m at THz frequencies, the plasmonic resonators are assumed to be perfect electrical conductor (PEC).

The THz waves sources consist of a column of $z$-polarized dipoles with an interval of 5 $\mathrm{\mu}$m, and each dipole radiates THz waves with a frequency range of 0.2$\sim$0.6 THz as shown in Fig. 6(a), which corresponds to a broadband pulse in the time domain as shown in Fig. 6(b). Both the center frequency and bandwidth of the broadband pulse are 0.4 THz.

 

Fig. 6. The incident THz signal in simulations in (a) frequency domain and (b) time domain.

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The dimensions of the simulation region along the $x$, $y$ and $z$ axes are set to 4 mm, 0.3 mm and 0.1 mm, respectively. Convergence results can be obtained by employing perfectly matched layer absorbing boundaries along the $x$- and $y$-axes and periodic boundary conditions along the $z$-axis.

Theoretical curves

The frequency shift of the THz microcavity can be described by the Jaynes-Cummings model using the rotating wave approximation. The Hamiltonian of the microcavity-plasmon hybrid system can be expressed as a 2$\times$2 matrix:

(4)$$H = h\begin{bmatrix} f_{\text{cav}} & g \\ g & f_{\text{pr}} \end{bmatrix}.$$

To facilitate the description of the frequency shift, we use frequency instead of angular frequency to characterize the Hamiltonian. Here, $f_{\text {cav}}$ denotes the resonant frequency of the third-order mode in the THz microcavity, and $f_{\text {pr}}$ denotes the plasmonic resonant frequency. $g$ is the half the coupling rate between the THz microcavity and the plasmonic resonators. The frequencies of the two polaritons can be determined by solving the eigenvalues of the Hamiltonian matrix. The resonant frequencies of the upper and lower branches are:

(5)$$f_{\text{upper, lower}}=\frac{f_{\text{cav}}+f_{\text{pr}}\pm \sqrt{(f_{\text{cav}}+f_{\text{pr}})^2+4g^2}}{2},$$

where $+$ and $-$ correspond to the resonant frequencies of the upper and lower branches, respectively.

Funding

National Natural Science Foundation of China (11974192, 62205158); China Postdoctoral Science Foundation (2022M711709); Foundation of State Key Laboratory of Laser Interaction with Matter (SKLLIM2101); 111 Project (B23045); Program for Changjiang Scholars and Innovative Research Team in University (IRT_13R29).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. N. Tomm, A. Javadi, N. O. Antoniadis, et al., “A bright and fast source of coherent single photons,” Nat. Nanotechnol. 16(4), 399–403 (2021). [CrossRef]  

2. A. Kavokin, T. C. Liew, C. Schneider, et al., “Polariton condensates for classical and quantum computing,” Nat. Rev. Phys. 4(7), 435–451 (2022). [CrossRef]  

3. M. Hertzog, B. Munkhbat, D. Baranov, et al., “Enhancing vibrational light-matter coupling strength beyond the molecular concentration limit using plasmonic arrays,” Nano Lett. 21(3), 1320–1326 (2021). [CrossRef]  

4. D. Najer, I. Söllner, P. Sekatski, et al., “A gated quantum dot strongly coupled to an optical microcavity,” Nature 575(7784), 622–627 (2019). [CrossRef]  

5. Y. Kaluzny, P. Goy, M. Gross, et al., “Observation of self-induced rabi oscillations in two-level atoms excited inside a resonant cavity: The ringing regime of superradiance,” Phys. Rev. Lett. 51(13), 1175–1178 (1983). [CrossRef]  

6. D. S. Dovzhenko, S. V. Ryabchuk, Y. P. Rakovich, et al., “Light-matter interaction in the strong coupling regime: configurations, conditions, and applications,” Nanoscale 10(8), 3589–3605 (2018). [CrossRef]  

7. X. Yu, Y. Yuan, J. Xu, et al., “Strong coupling in microcavity structures: Principle, design, and practical application,” Laser Photonics Rev. 13(1), 1800219 (2019). [CrossRef]  

8. R. Damari, O. Weinberg, D. Krotkov, et al., “Strong coupling of collective intermolecular vibrations in organic materials at terahertz frequencies,” Nat. Commun. 10(1), 3248 (2019). [CrossRef]  

9. D. G. Suárez-Forero, D. W. Session, M. J. Mehrabad, et al., “Spin-selective strong light-matter coupling in a 2D hole gas-microcavity system,” Nat. Photonics 17(10), 912–916 (2023). [CrossRef]  

10. H. Takahashi, E. Kassa, C. Christoforou, et al., “Strong coupling of a single ion to an optical cavity,” Phys. Rev. Lett. 124(1), 013602 (2020). [CrossRef]  

11. X. Liu, T. Galfsky, Z. Sun, et al., “Strong light–matter coupling in two-dimensional atomic crystals,” Nat. Photonics 9(1), 30–34 (2015). [CrossRef]  

12. M. Barra-Burillo, U. Muniain, S. Catalano, et al., “Microcavity phonon polaritons from the weak to the ultrastrong phonon–photon coupling regime,” Nat. Commun. 12(1), 6206 (2021). [CrossRef]  

13. R. Ameling and H. Giessen, “Cavity plasmonics: Large normal mode splitting of electric and magnetic particle plasmons induced by a photonic microcavity,” Nano Lett. 10(11), 4394–4398 (2010). [CrossRef]  

14. F. J. Garcia-Vidal, A. I. Fernández-Domínguez, L. Martin-Moreno, et al., “Spoof surface plasmon photonics,” Rev. Mod. Phys. 94(2), 025004 (2022). [CrossRef]  

15. P. Peng, Y. Liu, D. Xu, et al., “Enhancing coherent light-matter interactions through microcavity-engineered plasmonic resonances,” Phys. Rev. Lett. 119(23), 233901 (2017). [CrossRef]  

16. J. Chen, Q. Zhang, C. Peng, et al., “Optical cavity-enhanced localized surface plasmon resonance for high-quality sensing,” IEEE Photonics Technol. Lett. 30(8), 728–731 (2018). [CrossRef]  

17. M. Ossiander, M. L. Meretska, S. Rourke, et al., “Metasurface-stabilized optical microcavities,” Nat. Commun. 14(1), 1114 (2023). [CrossRef]  

18. C. Pan, Q. Wu, Q. Zhang, et al., “Direct visualization of light confinement and standing wave in THz Fabry-Perot resonator with Bragg mirrors,” Opt. Express 25(9), 9768–9777 (2017). [CrossRef]  

19. Q. Zhang, J. Qi, Y. Lu, et al., “Cavity-cavity coupling based on a terahertz rectangular subwavelength waveguide,” J. Appl. Phys. 126(6), 063103 (2019). [CrossRef]  

20. C. A. Curwen, J. L. Reno, and B. S. Williams, “Broadband continuous single-mode tuning of a short-cavity quantum-cascade vecsel,” Nat. Photonics 13(12), 855–859 (2019). [CrossRef]  

21. L. Chen, D. Liao, X. Guo, et al., “Terahertz time-domain spectroscopy and micro-cavity components for probing samples: a review,” Front. Inf. Technol. Electron. Eng. 20(5), 591–607 (2019). [CrossRef]  

22. K. Okamoto, K. Tsuruda, S. Diebold, et al., “Terahertz sensor using photonic crystal cavity and resonant tunneling diodes,” J. Infrared, Millimeter, Terahertz Waves 38(9), 1085–1097 (2017). [CrossRef]  

23. A. Kumar, M. Gupta, P. Pitchappa, et al., “Active ultrahigh-Q (0.2 ×10⁶) THz topological cavities on a chip,” Adv. Mater. 34(27), 2202370 (2022). [CrossRef]  

24. N. Rivera and I. Kaminer, “Light–matter interactions with photonic quasiparticles,” Nat. Rev. Phys. 2(10), 538–561 (2020). [CrossRef]  

25. X. Xu, Y. Lu, Q. Wu, et al., “Terahertz microcavity modulation mediated by strongly coupled to LSPR mode,” in Conference on Lasers and Electro-Optics (Optica Publishing Group, 2022), paper JW3B.3.

26. X. Zhang, Q. Xu, L. Xia, et al., “Terahertz surface plasmonic waves: a review,” Adv. Photonics 2(01), 1 (2020). [CrossRef]  

27. X. Zhang, W. Y. Cui, Y. Lei, et al., “Spoof localized surface plasmons for sensing applications,” Adv. Mater. Technol. 6(4), 2000863 (2021). [CrossRef]  

28. P. Sivarajah, C. A. Werley, B. K. Ofori-Okai, et al., “Chemically assisted femtosecond laser machining for applications in LiNbO₃ and LiTaO₃,” Appl. Phys. A 112(3), 615–622 (2013). [CrossRef]  

29. W. Zhao, J. Qi, Y. Lu, et al., “On-chip plasmon-induced transparency in THz metamaterial on a LiNbO₃ subwavelength planar waveguide,” Opt. Express 27(5), 7373–7383 (2019). [CrossRef]  

30. E. Jaynes and F. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51(1), 89–109 (1963). [CrossRef]  

31. Q. Wu, C. A. Werley, K.-H. Lin, et al., “Quantitative phase contrast imaging of THz electric fields in a dielectric waveguide,” Opt. Express 17(11), 9219–9225 (2009). [CrossRef]