Article | Open Access | Published:

Ultrahigh-Q metallic nanocavity resonances with externally-amplified intracavity feedback

Scientific Reports volume 4, Article number: 7124 (2014) | Download Citation

Abstract

We propose a mechanism of ultrahigh-Q metallic nanocavity resonances that involves an efficient loss-compensation scheme favorable for room-temperature operation. We theoretically show that surface plasmon-polaritons excited on the entrance and exit interfaces of a metallic nanocavity array efficiently transfer external optical gain to the cavity modes by inducing resonantly-amplified intracavity feedback. Surprisingly, the modal gain in the nanocavity with the externally amplified feedback is inversely proportional to the cavity length as opposed to conventional optical cavity amplifiers requiring longer cavities for higher optical gain. Utilizing this effect, we numerically demonstrate room-temperature nanocavity resonance Q-factor exceeding 104 in a 25-nm-wide silver nanoslit array. The proposed mechanism provides a highly efficient plasmonic amplification process particularly for subwavelength plasmonic cavities which are essential components in active nanoplasmonic devices.

Introduction

To develop advanced optical elements requiring small feature dimensions and innovative light-interaction schemes, plasmonic nanosystems are of immense interest because of their unique deep-subwavelength light localization properties and associated strong field enhancement. These attributes potentially enable various applications such as optical sensors1, light absorbers2, metamaterials3,4,5, and nonlinear optical devices6. Among the many challenges in converting these properties to practice in device engineering is achieving high-Q plasmonic resonances in real metallic nanosystems that generally possess large ohmic absorption.

Considerable research has been devoted to establishing high-Q resonances in various metallic structures. In the classical attenuated total reflection configurations, the surface plasmon-polariton (SPP) resonance Q-factor is normally on the order of ~10–102 in the visible spectral domain7. In more advanced geometries such as metal-coated whispering gallery microcavities8,9,10,11, the resonance Q-factor approaches ~104. Despite the modest resonance Q-factors associated with plasmonic resonators as compared to those exceeding 108 in photonic microcavities12,13, high-Q plasmonic resonators are under extensive investigation due to their deep-subwavelength localization properties. In addition to the potential for high-density optical integration, plasmonic nanocavities may enable quantum optical devices that take advantage of large Purcell enhancement and strong cavity QED coupling14,15,16. Achieving large figure-of-merit (FOM) λ3Q/D3 is important in this context; here λ is the vacuum wavelength and D is the feature dimension of the resonant mode. Recent theoretical analyses show low-temperature FOM ~ 109 and extremely large Purcell enhancement factor ~105 in various types of plasmonic nanocavities17,18,19 with D ~ λ/10. However, plasmonic modes in metallic nanocavities have inherently large ohmic damping that scales with 1/D, resulting in substantially limited FOM at room temperature. Recovering high FOM by gain-assisted loss compensation is presently believed to be difficult because of strong fluorescence quenching caused by lossy surface wave excitations20,21. Therefore, most of the previous work on loss compensation in plasmonic nanocavities has been performed at low operating temperatures since the optical gain required for room-temperature operation is unrealistically large.

In this paper, we propose a new mechanism of ultrahigh-Q metallic nanocavity resonances assisted by amplified cavity-boundary feedback. We show that SPPs at the entrance and exit interfaces of a nanocavity array can be used as carriers of external optical gain furnished to the plasmonic modes inside metallic nanocavities. Notably, the SPP-mediated optical gain transfer to the nanocavity provides a promising loss-compensation channel that is favorable for room-temperature operation of narrow nanocavity resonances with moderate optical gain. This loss-compensation channel allows the nanocavity mode to obtain dominant modal gain by the externally amplified feedback from the interfacial SPPs rather than the direct stimulated emission inside the nanocavity. In contrast to conventional optical cavity amplifiers that require a longer cavity length for larger modal gain, the nanocavity gain due to the externally amplified feedback is inversely proportional to the cavity length. We theoretically demonstrate a room-temperature resonance Q-factor exceeding 104 for a plasmonic nanocavity mode with feature size D ~ λ/30 in a metallic nanoslit array surrounded by an external gain medium with a moderate gain constant.

Metallic nanocavities under the influence of a gain-assisted interfacial Fano resonance

We consider plasmonic nanocavity resonances in a periodic array of deep-subwavelength metallic nanoslits as schematically depicted in Fig. 1. An incident transverse-magnetic planewave at the entrance interface couples to a fundamental cavity mode (CM) with the single-interface transmission coefficient τ. For deep-subwavelength slits, the excited CM generally has a fairly high internal reflection coefficient ρin because of the large impedance mismatch between the unbound external wave and CM with tight lateral confinement. Therefore, the excited CM induces characteristic Fabry-Pérot-like resonances22,23,24,25 when a constructive interference occurs at the phase-matching condition where L is the thickness of the metal film or cavity length equivalently, β′ is real part of the complex propagation constant of the CM, and the integer q is Fabry-Pérot order corresponding to the number of longitudinal nodes inside the cavity.

Figure 1: Schematic of a metallic nanoslit array with resonant SPP and CM excitations.
Figure 1

Coupling of external light with the fundamental CM is described by the single-interface transmission τ and internal reflection ρin coefficients, respectively. SPPs at the entrance and exit interfaces lead to resonant behavior of τ and ρin that drastically modify CM resonance properties inside the slits.

According to our recent analysis26, surface plasmon-polaritons (SPP) at the entrance and exit interfaces cause interfacial Fano resonances that drastically modify τ and ρin within their resonance bandwidth. The effects of the SPP-mediated interfacial Fano resonance include the antiresonant extinction of τ, i.e., τ → 0, and associated total internal reflection of the CM, i.e., |ρin| → 1. This antiresonance effect causes non-radiative CM resonances with extremely high-Q factors. For real metals at room temperature, high ohmic absorption strongly suppresses this resonance.

The purpose of this paper is to demonstrate the possibility of ultrahigh-Q plasmonic nanocavity resonances at the SPP-induced antiresonance condition with an appropriate loss compensation method. Plasmonic amplification or SPASER oscillation in metallic nanocavities is generally challenging due to the high loss of the plasmonic modes and strong fluorescence quenching of the emitters in the nanometric vicinity of metal surfaces20,21. In this aspect, loss compensation of the resonance with the total internal reflection due to the interfacial SPPs provides an amplification channel via the external gain medium that avoids the fluorescence quenching effect inside the nanoslit.

We now theoretically demonstrate a gain-assisted ultrahigh-Q CM resonance near the antiresonance condition. We consider an Ag nanoslit array imbedded in a host dielectric with optical gain. We use the finite element method27 (FEM) and rigorous coupled-wave analysis28 (RCWA) for our numerical study. We assume the realistic εM = εM′ + M″ of Ag experimentally obtained by Johnson and Christy29 and the host dielectric material is modeled by a complex refractive index 1.5 + ik, where k < 0 adjusts the amount of optical gain.

We first find the response of an isolated surface of an Ag nanoslit array in the absence of optical gain. Figure 2(a) shows the spectral profiles of the single-interface transmittance |τ|2 and surface-excitation intensity |Ez|2 averaged over a period at the Ag-dielectric interface for a semi-infinite array depicted in the inset. These single-interface responses are calculated using FEM. The single Lorentzian peak centered at wavelength λ = 715 nm in the surface excitation spectrum and the associated Fano profile in the single-interface transmittance spectrum confirm the SPP-induced Fano resonance at the Ag-dielectric interface.

Figure 2: Ultrahigh-Q nanocavity resonance by loss compensation with experimentally realistic level of optical gain in the surrounding dielectric.
Figure 2

(a) Single interface transmittance |τ|2 (blue solid curve) and average surface excitation |Ez/E0|2 (red dotted curve) spectra with no optical gain (k = 0) in the dielectric host. Film-transmittance T for Ag film thickness L = 460 nm is shown in (b) for no optical gain (k = 0) and in (c) for optical gain of k = −2.26 × 10−3. The inset color-density plot in (c) shows electric field intensity |E/E0|2 (E0: incident electric field) at the CM resonance peak for q = 3.

This interfacial Fano resonance profile in the |τ|2 spectrum has its enhanced maximum at λ = 700 nm and antiresonant extinction at λ = λAR = 745 nm. For an Ag nanoslit array with the identical slit width and period but finite thickness, a high-Q nanocavity resonance is expected near λAR where the total internal reflection occurs. Figure 2(b) shows the film-transmittance (T) spectrum for Ag-film thickness L = 460 nm with no optical gain (k = 0) in the dielectric host. This film-transmittance spectrum is calculated using RCWA. Three major CM resonance peaks appear at wavelengths 644.5 nm, 706.0 nm, and 877.5 nm for Fabry-Pérot resonance orders q = 5, 4, and 2, respectively. The CM resonance peak for q = 3 at wavelength 740.5 nm is under the effect of the antiresonance condition and is missing in the T spectrum because of the high loss-sensitivity of a high-Q CM resonance. A more detailed explanation of the CM resonance under the influence of the SPP-induced antiresonance condition in the presence of material dissipation is provided in [26].

We apply a realistic amount of optical gain in the top and bottom dielectric layers and assume no gain inside the nanoslit cavities. The optical gain is described by the negative imaginary part k = −2.26 × 10−3 of the dielectric film's refractive index. This value corresponds to an optical gain constant 192 cm−1 at λ = 740.5 nm and is experimentally obtainable in dye-doped poly(methyl methacrylate)30 (PMMA) with moderate doping concentration ~1019 cm−3 and pumping density ~10 mJ/cm2. Taking a small signal approximation that is reasonable for a low-intensity response of a gain medium under the lasing threshold31,32, we calculate the T spectrum using RCWA; the result is shown in Fig. 2(c). We confirm an extremely narrow bandwidth ~44 pm (FWHM) and a high resonance Q-factor ~1.7 × 104 of the CM resonance peak for q = 3. At the peak wavelength, the electric field intensity enhancement factor |E/E0|2 inside the 25-nm-wide nanoslit exceeds 3.6 × 104 as shown in the inset of Fig. 2(c).

The gain-assisted CM resonance in Fig. 2(c) is not simply understood by a direct stimulated emission to the CM because the optical gain region is external to the nanoslit cavities. Moreover, the assumed gain constant 192 cm−1 is far smaller than the attenuation constant β″ = 630.5 cm−1 of the CM. The β″ value is given by the dispersion equation33 at λ = 740.5 nm for the case in Fig. 2(c), where β = β′ + iβ″ is the complex propagation constant of the CM, k0 = 2π/λ is the vacuum wave number and w is the slit width.

Externally amplified intracavity feedback

To understand this seemingly counter-intuitive result, we further analyze the response of the SPP-resonant surface of the Ag nanoslit array in the presence of optical gain in the host dielectric medium. Thus, we estimate the attenuation αSPP and gain ΓSPP constants of the SPP at the Ag-dielectric interface. We calculate the surface excitation |Ez|2 spectrum of a semi-infinite Ag nanoslit array as a function of absorption factor 0 ≤ fabs ≤ 1 that controls the amount of ohmic absorption in Ag with its dielectric constant εM = εM′ + ifabsεM″. In real experiment, adjusting fabs corresponds to temperature tuning such that fabs = 1 at room temperature and fabs < 1 in the lower temperature range34. Figure 3(a) shows the result for fabs = 0.2, 0.4, 0.6, 0.8, and 1.0 with no optical gain (k = 0) in the host dielectric. The bandwidth of the surface excitation spectrum indicates the total decay constant of the SPP. Figure 3(b) shows the measured half-width at half-maximum (HWHM), i.e., total decay constant γtot of the surface excitation spectrum, as a function of fabs. The total decay constant at fabs = 0, γtot(fabs = 0), represents the radiation decay constant γrad and thereby the attenuation constant αSPP at fabs = 1 is given by αSPP = γtot(fabs = 1) − γtot(fabs = 0). This method to estimate αSPP is valid for the small modal attenuation regime34 where γtot is a linear function of fabs. Figure 3(b) shows the linear dependence of γtot on fabs and thus justifies the method to estimate αSPP in our case. We obtain αSPP = 53.7 cm−1 as indicated in Fig. 3(b). The gain constant ΓSPP is obtained by the difference between the HWHM values for k = 0 and k = −2.26 × 10−3 at fabs = 1. The surface excitation spectrum for k = −2.26 × 10−3 at fabs = 1 is indicated by black curve in Fig. 3(a), and its HWHM is indicated by the blue dotted horizontal line in Fig. 3(b). We obtain ΓSPP = 152.1 cm−1. As a result, we confirm a positive net modal gain of ΓSPPαSPP = 98.4 cm−1 of the SPP for the Ag nanoslit array considered in Fig. 2.

Figure 3: Gain-assisted properties of an SPP on an Ag slit array.
Figure 3

(a) Surface excitation |Ez/E0|2 spectra for different absorption factor fabs and gain in the top dielectric layer. The black curve represents fabs = 1 and the top dielectric layer with optical gain given by negative imaginary refractive index k = −2.26 × 10−3. No optical gain (k = 0) in the top dielectric layer is assumed in the spectra for fabs = 0.2 (blue), 0.4 (cyan), 0.6 (green), 0.8 (orange), and 1.0 (red). (b) Estimated modal attenuation and gain constants of the SPP. The square symbols represent half-width at half-maximum (HWHM) of the surface excitation spectra in (a) as a function of fabs, and the blue dotted horizontal line indicates HWHM for the top PMMA with optical gain.

The response of the SPP-resonant surface in the presence of optical gain suggests that the dominant loss-compensation channel is the externally-amplified internal reflection (ρin) provided by the SPP at the interface as no optical gain is assumed inside the nanoslits. Thus, the amplified SPP yields the amplified internal reflectance |ρin|2 > 1 at the SPP-mediated antiresonance condition. Using the FEM, we calculate the single-interface transmittance |τ|2 and internal reflectance |ρin|2 for k = 0 and −2.26 × 10−3. Figure 4 shows the results. We confirm amplified internal reflectance |ρin|2 > 1 over the wavelength range from 719 nm to 772 nm. In particular, |ρin|2 = 1.0595 at wavelength 740.5 nm corresponding to the high-Q CM resonance peak in Fig. 2(c). This internal reflectance value leads to an effective modal gain ΓSPP-to-CM = ln|ρin|/L = 628.2 cm−1 to the CM inside the nanoslit. With this optical gain from the amplified internal reflection, the high-Q CM resonance is obtained with a negligibly small net attenuation of the CM αnet = β″−ΓSPP-to-CM = 2.3 cm−1. Note that the attenuation constant β″ = 630.5 cm−1 without the SPP-induced interfacial amplification. Importantly, the optical gain ΓSPP-to-CM = ln|ρin|/L transferred from the SPP to the CM is inversely proportional to the cavity length L because the number of internal reflections per unit optical path length is inversely proportional to L. Therefore, the SPP-induced antiresonance effect provides a mechanism for generating strong optical fields particularly in short cavities.

Figure 4: Gain-assisted responses of an SPP-resonant Ag slit interface.
Figure 4

The single-interface transmittance |τ|2 and internal reflectance |ρin|2 of the SPP-resonant Ag nanoslit array with (blue solid curve) and without (red dotted curve) optical gain in the host dielectric material.

Conclusions

In conclusion, we propose a new ultrahigh-Q nanocavity resonance mechanism pertinent to metallic nanoslit arrays. The SPP-induced antiresonant extinction condition leads to non-radiative resonances providing an efficient loss compensation channel based on externally-amplified interfacial feedback. Assuming a 25-nm-wide Ag nanoslit array imbedded in a dye-doped polymer film under realistic optical pumping density, we theoretically demonstrated an ultrahigh-Q plasmonic nanocavity resonance with resonance Q-factor exceeding 104. Considering further experimental study, the proposed device architecture with high aspect ratio nanoslits can be fabricated preferably by metallization of a lamellar dielectric grating structure35,36 as this method does not demand challenging deep anisotropic etch through a metallic film to define nanoscale slits. It is of great interest to apply the proposed nanocavity feedback mechanism to various plasmonic nanosystems for ultra-small plasmonic lasers, efficient quantum-plasmonic elements, and compact nonlinear optical templates.

References

  1. 1.

    et al. Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers. Nat. Mater. 11, 69–75 (2012).

  2. 2.

    et al. Omnidirectional absorption in nanostructured metal surfaces. Nat. Photonics 2, 299–301 (2008).

  3. 3.

    et al. Three-dimensional optical metamaterial with a negative refractive index. Nature 455, 376–379 (2008).

  4. 4.

    et al. A terahertz metamaterial with unnaturally high refractive index. Nature 470, 369–373 (2011).

  5. 5.

    , , & Optical cloaking with metamaterials. Nat. Photonics 1, 224–227 (2007).

  6. 6.

    et al. Collective effects in second-harmonic generation from split-ring-resonator arrays. Phys. Rev. Lett. 109, 015502 (2012).

  7. 7.

    , & Surface plasmon resonance sensors: review. Sens. Actuator B-Chem. 54, 3–15 (1999).

  8. 8.

    et al. High-Q surface-plasmon-polariton whispering-gallery microcavity. Nature 457, 455–458 (2009).

  9. 9.

    et al. High-Q exterior whispering-gallery modes in a metal-coated microresonator. Phys. Rev. Lett. 105, 153902 (2010).

  10. 10.

    & High Q long-range surface plasmon polariton modes in sub-wavelength metallic microdisk cavity. Plasmonics 6, 183–188; 10.1007/s11468-010-9185-0 (2011).

  11. 11.

    et al. High-Q hybrid plasmon-photon modes in a bottle resonator realized with a silver-coated glass fiber with a varying diameter. Phys. Rev. Lett. 111, 253901 (2013).

  12. 12.

    , , & Ultra-high-Q toroid microcavity on a chip. Nature 421, 925–928 (2003).

  13. 13.

    et al. Chemically etched ultrahigh-Q wedge-resonator on a silicon chip. Nat. Photonics 6, 369–373 (2012).

  14. 14.

    & Design of plasmon cavities for solid-state cavity quantum electrodynamics applications. Appl. Phys. Lett. 90, 033113 (2007).

  15. 15.

    et al. Generation of single optical plasmons in metallic nanowires coupled to quantum dots. Nature 450, 402–406 (2007).

  16. 16.

    , & Quantum plasmonic circuits. IEEE J. Sel. Top. Quantum Electron. 18, 1781–1791 (2012).

  17. 17.

    , , & Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity. Nano Lett. 9, 4078–4082 (2009).

  18. 18.

    , , & Ultrasmall subwavelength nanorod plasmonic cavity. Opt. Lett. 36, 2011–2013 (2011).

  19. 19.

    Deep subwavelength plasmonic whispering-gallery-mode cavity. Opt. Express 20, 24918–24924; 10.1364/OE.20.024918 (2012).

  20. 20.

    Fluorescence near interfaces: the role of photonic mode density. J. Mod. Opt. 45, 661–699 (1998).

  21. 21.

    et al. Fluorescence quenching of dye molecules near gold nanoparticles: radiative and nonradiative effects. Phys. Rev. Lett. 89, 203002 (2002).

  22. 22.

    , & Transmission resonances on metallic gratings with very narrow slits. Phys. Rev. Lett. 83, 2845–2848 (1999).

  23. 23.

    , , , & Mapping surface-plasmon polaritons and cavity modes in extraordinary optical transmission. IEEE Photon. J. 3, 365–374; 10.1109/JPHOT.2011.2138122 (2011).

  24. 24.

    & Theory of extraordinary light transmission through arrays of subwavelength slits. Phys. Rev. B 77, 075106 (2008).

  25. 25.

    , , & Analytic theory of the resonance properties of metallic nanoslit arrays. IEEE J. Quantum Electron. 48, 852–861 (2012).

  26. 26.

    , , & Unified theory of surface-plasmonic enhancement and extinction of light transmission through metallic nanoslit arrays. Sci. Rep. 4, 5683; 10.1038/srep05683 (2014).

  27. 27.

    The finite element method in electromagnetic. 2nd Ed. New York: John Wiley and Sons (2002).

  28. 28.

    & Rigorous coupled-wave analysis of planar-grating diffraction. J. Opt. Soc. Amer. 71, 811–818 (1981).

  29. 29.

    & Optical constants of the noble metals. Phys. Rev. B 6, 4370–4379 (1972).

  30. 30.

    et al. Stimulated emission of surface plasmon polaritons. Phys. Rev. Lett. 101, 226806 (2008).

  31. 31.

    Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain. Phys. Rev. B 70, 155416 (2004).

  32. 32.

    et al. Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium. Opt. Express 16, 1385–1392; 10.1364/OE.16.001385 (2008).

  33. 33.

    , & Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization. Phys. Rev. B 73, 035407 (2006).

  34. 34.

    , & Extraction efficiency of highly confined surface plasmon-polaritons to far-field radiation: an upper limit. Opt. Express 16, 1269–1279; 10.1364/OE.16.001269 (2008).

  35. 35.

    et al. Localized surface plasmons in lamellar metallic gratings. J. Lightwave Technol. 17, 2191–2195 (1999).

  36. 36.

    et al. Nearly perfect Fano transmission resonances through nanoslits drilled in a metallic membrane. Phys. Rev. Lett. 104, 027401 (2010).

Download references

Acknowledgements

The research leading to these results was supported in part by the Texas Instruments Distinguished University Chair in Nanoelectronics endowment and also by the Global Frontier Program through the National Research Foundation of Korea grant NRF-2014M36AB3063708 under the Ministry of Science, ICT & Future Planning.

Author information

Affiliations

  1. Dept. of Electrical Engineering, University of Texas - Arlington, Box 19016, Arlington, TX 76019, USA

    • Jae Woong Yoon
    •  & Robert Magnusson
  2. Dept. of Physics, Hanyang University, Seoul 133-791, KOREA

    • Seok Ho Song

Authors

  1. Search for Jae Woong Yoon in:

  2. Search for Seok Ho Song in:

  3. Search for Robert Magnusson in:

Contributions

This research was planned by J.W.Y., S.H.S. and R.M. Numerical simulation was performed by J.W.Y. The authors J.W.Y., S.H.S. and R.M. discussed the results. J.W.Y., S.H.S. and R.M. wrote the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Jae Woong Yoon.

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/srep07124

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.