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We demonstrate negative refraction at telecommunication wavelengths through plasmon-photon hybridization on a simple microcavity with metallic mirrors. Instead of using conventional metals, the plasmonic excitations are provided by a heavily doped semiconductor which enables us to tune them into resonance with the infrared photon modes of the cavity. In this way, the dispersion of the resultant hybrid cavity modes can be widely adjusted. In particular, negative dispersion and negative refraction at telecommunication wavelengths on an all-ZnO monolithical cavity are demonstrated.
© 2015 Optical Society of America
1. Introduction
The refraction of light at the interface between two materials is described by Snell’s law. Naturally occurring materials have a positive index of refraction. As a consequence, incident and refracted beam propagate on opposite sides of the surface normal or, in other words, the direction of the beam’s propagation component parallel to surface is not altered. In what follows, we focus on the opposite case where forward traveling light is refracted into backward direction, i.e., negative refraction. Many fascinating phenomena beyond traditional optics occur under such conditions [1–3]. In the past years, the demonstration of this phenomenon succeeded on metamaterials [4–12] where a complex inner structure provides negative values of both electric permittivity and magnetic permeability [3]. The concept that we pursue in this work is based on a compact multi-layer planar film structure, as commonly used in guided-wave optics. The negative refraction originates from coupling of surface plasmon polaritons (SPPs) propagating at a metal/isolator interface [13] and photon modes built-up in a cavity formed by two of such interfaces. The key for reaching the coupling regime is use of the semiconductor ZnO, instead of a conventional metal. ZnO can be doped n-type without significant crystal degradation up to free-electron concentrations of almost 1021 cm−3 [14,15]. These electrons create a Drude-type infrared permittivity with a negative-to-positive crossover frequency tunable by the doping level [16–19]. In this way, SPP and infrared photon mode can be brought into resonance as schematized in Fig. 1. Similar geometries have been studied in relation with metal-isolator-metal (MIM) waveguide structures [20–28]. However, previous theoretical analyses of MIMs are oriented towards traditional metals and widely disregarded resonant coupling [21, 23, 24] or treated only ultra-thin isolator layers (width « plasma wavelength) [20]. In line with this, experimental MIMs realized so far [21, 24, 26–28] exhibit a photon mode typically in the visible spectral range while the surface plasmon frequency of the Au or Ag claddings is in the UV. The SPPs at the frequency of the cavity mode are hence themselves largely photon-like and the SPP-photon coupling is strongly off-resonant and weak. Negative refraction on an Au/Si2N4/Ag MIM structure has been demonstrated at visible wavelength by utilizing the standard back bending of the SPP dispersion beyond the surface plasma frequency [29]. Unlike to what is presented below, negative refraction is restricted to the frequency-wave vector range right of the photon line and cannot be addressed by light incident from free space.
Fig. 1 Schematics of the dispersion relations (frequency ω versus in-plane wave vector k) of the isolated excitations under study: SPP of an air/metal interface and photon mode of an air-filled microcavity. The surface plasmon frequency is given by ωsp = ωp/(1 + εB)1/2 where ωp is the plasma frequencies of the Drude metal with a background permittivity εB. The frequency of the photon mode at k = 0 for a cavity with length L (and constant reflectivity) is ωph = πc/L. Dashed line: ω = ck (c: light velocity in air).
2. Experimental
The Ga-doped ZnO samples used in this study are grown in a DCA 450 molecular beam epitaxy system equipped with standard solid-source effusion cells (Zn and Ga) and an Addon rf plasma source providing O [14,15]. Secondary ion mass spectroscopy and Hall measurements are performed on reference samples to control doping level and free-electron concentration within a few percent. The individual layer thickness is defined by growth time. Structural quality is monitored by in situ reflection high-energy electron diffraction. Optical spectra are recorded by a BRUKER IFS66v/S vacuum Fourier transform spectrometer using a motorized A-513 reflection unit to control the angle of incidence with an accuracy of better than 2°. Attenuated-total reflection (ATR) measurements are performed in Otto configuration using a polished Si hemisphere as coupling medium [30]. The spectral resolution in all measurements is better than 4 cm−1 and the diameter of the excitation spot is 300 µm.
Two types of cavities were fabricated. For investigating systematically the change of the mode spectrum as a function of the cavity length L, an air configuration with two identical mirrors is used [Fig. 2(a)]. The individual mirrors consist of a sapphire substrate, fully transparent in the relevant wavelength range, on which a layer of ZnOGa is grown. The Ga-induced free-electron concentration of n = 4.6·1020 cm−3 results in a negative real part of the permittivity below photon energies ħωcr = 0.77 eV. Figure 2(b) depicts the dispersion curves of the SPPs supported by the air/ZnOGa interface of the individual mirror structures. The experimental data are deduced from ATR measurements in transverse magnetic (TM) polarization. The ZnOGa layer thickness of d = 280 nm ensures separation from the sapphire/ZnOGa interface so that these SPPs are of no relevance (see Appendix A). The two mirrors are clamped together leaving an air gap that is adjusted between L = 0.4 − 2.5 μm enabling tuning of the cavity mode relative to the SPP dispersion. For the second all-ZnO cavity, an undoped ZnO layer with an infrared refraction index of nC = 1.92 was grown on the sapphire/ZnOGa bottom mirror, followed by a ZnOGa cap with the same Ga-doping and thickness (d = 200 nm) as in the bottom mirror. Free-electron concentration (n = 8.0·1020 cm−3) and ZnO cavity length (L = 170 nm) are optimized for achieving negative refraction at telecommunications wavelengths.
Fig. 2 Free-space reflection spectra of the air-filled microcavity. a) Design of the cavity. b) Air/ZnOGa SPP dispersion of the individual mirrors. Dots: Experimental ATR minima in TM polarization. Full line: Calculated dispersion relation (ħωp = 1.48 eV, εB = 3.7, Drude damping: γ = 0.11 eV). c) Experimental spectra. d) Transfer matrix calculations. Upper panels: TM polarization. Lower panels: TE polarization. The angle of incidence changes for all curves from θ = 14 – 54° (bottom to top). The cavity length is denoted above the figures. Dotted lines are to guide the eye. The spectra are vertically shifted for better visibility.
3. Results
We are interested in the eigenstates of the cavity left of the light line (ω > ck/nC) characterized by a finite frequency at k = 0 and a real normal wave vector in the absence of losses. These eigenstates representing cavity fields with no intrinsic evanescent decay component are hence called ”cavity modes”. For the air configuration (nC = 1), their dispersion relation is provided by the minima in the cavity’s free-space reflection (FSR) spectrum when changing the angle of incidence θ defining the in-plane wave vector k = ω/c sinθ. In transverse electric (TE) polarization, SPPs do not exist and inspection of that spectrum provides hence the reference modes of a conventional metal cavity with no coupling to SPPs. Figures 2(c) and (d) collect FSR data of the air cavity for a set of incident angles at three representative values of L. For a relatively wide cavity (L = 2.55 μm), a group of cavity modes is identified in the spectral range of the SPP. The spectra in TE and TM polarization differ only slightly signifying weak SPP-photon coupling. Striking changes in the TM reflectivity occur at smaller cavity lengths where the lowest-order cavity mode moves into resonance with the surface plasmon frequency. Coupling to the SPP is manifested by an increasingly weaker angle-dependence of the minimum position indicative of a flattening of the dispersion. At L = 0.67 μm, the mode becomes practically angle-independent and, for even shorter cavities, a backward shift occurs. All experimental FSR spectra can be very well reproduced by transfer matrix calculations where the exact cavity length is the only adjustable parameter.
4. Theoretical analysis
To complement these findings with a theoretical analysis of the coupled SPP-photon dispersion, we consider the roundtrip condition
which is solved for complex ω at given real k. As the sapphire substrate can be safely ignored, the amplitude reflectivity rM (M = TE, TM) of the mirrors is given by the standard Fresnel reflection coefficients of the air/ZnOGa interface. As seen in Fig. 3, the calculated dispersion relations (Re ω) are fully consistent with those derived from the experimental FSR minima. At the smallest cavity length, the FSR minima appear naturally at somewhat higher frequency as they are superimposed to a background of decreasing reflectivity when approaching the transparency edge of the mirrors (ω → ωcr). In order to make the dispersion evolution plausible, also the region right of the light line is presented. There are specific points which can be analyzed analytically. At k = 0, the squared reflectivity is identical in TE and TM polarization providing ωTE(0) = ωTM(0) = ωph, i.e., TE and TM frequencies are degenerate. In the limit k → ∞, the interfaces decouple at any L ≠ 0 and the roundtrip condition demands rM−1(ω,∞) = 0 for obtaining a finite frequency. Since excluded in TE polarization, these modes approach the light line. Contrary, the singularities of the TM reflectivity define just the SPP dispersion of the isolated interfaces. Therefore, the lowest TM cavity mode with an antisymmetric field profile develops into a respective superposition of the decoupled SPPs and meets with the symmetric superposition at ωTM(∞) = ωsp. Higher-order modes have more than one node in their field distribution and cannot evolve into a SPP [23]. The pinning of the lowest TM cavity mode to the TE frequency at k = 0 and, for k → ∞, to the surface plasmon frequency results hence ultimately in a downward-bending of its dispersion when ωph exceeds ωsp. Here, due to the negative group velocity, a light beam incident from free space is converted into a cavity field propagating in the opposite in-plane direction, as if the cavity is consisting of a material with negative refractive index. The hybridization of cavity modes and SPP states left of the photon-line underlying the anomalous dispersion is also manifested by the coupled-mode damping (Im ω). As shown in Fig. 3(d), the damping at k = 0 is solely determined by the photon lifetime in the cavity and identical for TE and TM polarization. With increasing in-plane wave vector, the damping of the TE mode slightly decreases because of an increasing reflectivity of the ZnOGa mirror. In TM polarization, however, the admixture of a plasmonic component into the coupled eigenstate results in an increase of the damping which eventually approaches the pure SPP damping of the ZnOGa mirror.Fig. 3 Coupled modes of the air cavity. a)-c) Dispersion relations for the cavity lengths of Fig. 2 (L = 2550, 670, 410 nm). Blue rectangles: Experimental minima in TE. Red circles: Experimental minima in TM. Full curves: Calculated from Eq. (1). Red: TM polarization. Blue: TE polarization. Dashed black curve: SPP dispersion of the solitary mirrors. Dotted: photon line. Note that the modes in c) appear at frequencies above ħωsp = 0.68 eV but only slightly below ħωcr = 0.77 eV of the ZnGaO mirrors. d) Damping of the modes for L = 410 nm shown in c). Circles denote positions where the dispersion is experimentally verified.
5. Negative refraction at telecommunication wavelength
Based on the above insight into the hybridization scenario, monolithic ZnO devices with negative refraction in the wavelength range around 1.5 μm can be designed [Fig. 4(a)]. Here, the region left of the ZnO photon line has to be addressed. Thus, in addition to the FSR measurements, ATR spectra were recorded on the all-ZnO cavity. The dispersion curves constructed from these spectra are shown in Fig. 4(b). The group velocity vg = dω/dk in TM polarization (inset) reaches negative values of about −0.05c. The negative refraction supplied by the layered film can be estimated from the components of the total Poynting vector parallel (Sx) and perpendicular (Sz) to the cavity plane defining an effective angle of refraction θB by
Sx and Sz are functions of k and, thus, θ and evaluation for the present cavity parameters yields the θB versus θ plot in Fig. 4(c). As illustrated in the inset of Fig. 4(c), this negative refraction can be addressed from free space distinguishing it from demonstrations on Au/Si2N4/Ag MIMs [29] or predictions for ultrathin metal layers [31] where the observability is restricted to light propagating within the waveguide.Fig. 4 Coupled modes of the all-ZnO cavity. a) Cavity design b) Dispersion relations. Rectangles: Experimental FSR minima in TE. Circles: Experimental FSR and ATR minima in TM. Note that the modes appear at frequencies above ħωsp = ħωp/(2εB)1/2 = 0.72 eV but significantly below ħωcr = 1 eV of the ZnGaO mirrors. Full lines: Calculated from Eq. (1) with Drude-parameters ħωp = 1.95 eV and γ = 0.11 eV. Red line: TM polarization. Blue line: TE polarization. Dotted: Photon line. Inset: Group velocity deduced from the dispersion relation in TM polarization. c) Refraction law derived from Eq. (2). Inset: The negative refraction refocuses beams behind the sample. d) Verification of negative refraction at an angle of 55°. Top: Schematics of the experiment in which the unpolarized transmitted beam is partly blocked by a razor blade. In the case of negative refraction, the beam is displaced away from the blade resulting in an increased signal whereas the beam is shifted behind the blade in the case of positive refraction. Main graph: Relative transmittance (ratio of partly blocked to full transmitted beam). Red line: The experimental configuration is as schematically shown. Black line: Control experiment in which the beam is blocked from the opposite direction. Red, dashed line: Transmission recorded in TM. Blue, dashed line: Transmission recorded in TE.
In the experiment, the direction of refraction of the TE and TM mode is identified by exploiting their different displacement of a transmitted beam [32]. First, the spectrum of the unpolarized transmitted beam, partially blocked by a razor blade, is recorded. Subsequently the blade is removed and the spectrum of the full beam is measured. If the blade is positioned as sketched in Fig. 4(d), positively refracted light shifts behind the blade and the transmission is slightly reduced. Negatively refracted light shifts to the opposite direction resulting in an increased signal. Hence, the ratio of partially blocked beam to full beam reveals the direction of refraction. This signal is reduced for higher photon energies, i.e. in the spectral region of the TE mode. For smaller photon energies, in the spectral region where the TM mode is predominantly located, the signal goes up directly demonstrating negative refraction of this mode [Fig. 4(d)]. In the control experiment, the beam is blocked from the opposite direction and the reversed signal is obtained.
6. Conclusion
In conclusion, by using a heavily doped semiconductor with tunable free-carrier concentration, we have studied the coupling of SPPs and cavity photons under resonance conditions. By adjusting the plasmon-photon detuning through the cavity length, the group velocity of the hybrid mode can be systematically lowered and adjusted to zero as required in slow-light applications, e.g., for stopped light lasing [33]. Eventually, when the on-axis frequency of the photon mode exceeds the surface plasmon frequency, negative group velocities and negative refraction are achieved. The dispersion parameter β = d2ω/dk2 is also negative so that standard pulse up-chirp can be compensated. The three-layer structure presented here is the first step towards many-layer stacks constituting for appropriate design, e.g., hyperbolic metamaterial with even more catching features [32,34]. ZnO so far only considered in the context of short-wavelength optoelectronics is also a potential candidate for developing novel functional elements at telecommunication wavelengths.
Appendix A Transfer matrix calculations
The transfer matrix calculations [35] of the FSR spectra reported in Fig. 2 for the air cavity account for the sapphire substrates of lower and upper mirror as semi-infinite media (εsap = 2.89), the ZnOGa layers with Drude permittivity
as well as the air gap. Plasma frequency (ωp) and Drude damping (γ) where deduced from free-space reflection and transmission measurements on ZnOGa reference films. The background permittivity (εB) is that of non-doped ZnO. The only parameter not precisely known is the width L of the air gap which is fine adjusted such that experimental and calculated FSR minima best match. Increasing in the calculations the separation between sapphire and air beyond the experimental value of d provides no essential changes, demonstrating electromagnetic decoupling of these interfaces.Appendix B Dispersion relation and refraction law
The reflection coefficients of the air/ZnOGa interfaces read as
withUsing these expressions, the roundtrip condition can be recast intoor, after some algebra, into the more frequently used equations for the dispersion relations of planar MIMs [23]where plus and minus sign correspond to symmetric and antisymmetric field distributions, respectively, with respect to the cavity median. In TM polarization, the lowest symmetric solution provides the coupled SPP state with a dispersion extending always right of the light line, while the antisymmetric solution represent the lowest cavity mode, starting left of the light line and merging the symmetric solution at k → ∞. For decoupled interfaces (L → ∞), it follows which is used to calculate the SPP dispersion of the individual mirrors.For deriving the refraction law presented in the main text, the averaged components of the Poynting vector parallel (x) and normal (z) to the cavity plane
are calculated for the TM magnetic-field profileandprovidingandwith . Replacing the in-plane vector k = ω/c sinθ by the angle of incidence θ, the frequency by the complex mode dispersion ω(k), and inserting the parameters for the all-ZnO cavity yields the θB - θ plot of Fig. 4(c).Acknowledgments
The authors acknowledge financial support by the Deutsche Forschungsgemeinschaft in the frame of SFB 951 (HIOS). We thank O. Benson for helpful discussion.
References and links
1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]
2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
3. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968). [CrossRef]
4. S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68(2), 449–521 (2005). [CrossRef]
5. C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007). [CrossRef] [PubMed]
6. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]
7. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]
8. A. A. Houck, J. B. Brock, and I. L. Chuang, “Experimental observations of a left-handed material that obeys Snell’s law,” Phys. Rev. Lett. 90(13), 137401 (2003). [CrossRef] [PubMed]
9. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005). [CrossRef] [PubMed]
10. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006). [CrossRef] [PubMed]
11. G. Dolling, M. Wegener, and S. Linden, “Realization of a three-functional-layer negative-index photonic metamaterial,” Opt. Lett. 32(5), 551–553 (2007). [CrossRef] [PubMed]
12. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Technol. 47(11), 2075–2084 (1999). [CrossRef]
13. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
14. S. Sadofev, S. Kalusniak, P. Schäfer, and F. Henneberger, “Molecular beam epitaxy of n-Zn(Mg)O as a low-damping plasmonic material at telecommunication wavelengths,” Appl. Phys. Lett. 102(18), 181905 (2013). [CrossRef]
15. S. Sadofev, S. Kalusniak, P. Schäfer, H. Kirmse, and F. Henneberger, “Free-electron concentration and polarity inversion domains in plasmonic (Zn,Ga)O,” Phys. Status Solidi B 252(3), 607–611 (2015). [CrossRef]
16. A. Boltasseva and H. A. Atwater, “Low-loss plasmonic metamaterials,” Science 331(6015), 290–291 (2011). [CrossRef] [PubMed]
17. G. Naik, J. Kim, and A. Boltasseva, “Oxides and nitrides as alternative plasmonic materials in the optical range,” Opt. Mater. Express 1(6), 1090–1099 (2011). [CrossRef]
18. H. Kim, M. Osofsky, S. M. Prokes, O. J. Glembocki, and A. Piqué, “Optimization of Al-doped ZnO films for low loss plasmonic materials at telecommunication wavelengths,” Appl. Phys. Lett. 102(17), 171103 (2013). [CrossRef]
19. D. C. Look and K. D. Leedy, “ZnO plasmonics for telecommunications,” Appl. Phys. Lett. 102(18), 182107 (2013). [CrossRef]
20. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969). [CrossRef]
21. B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B Condens. Matter 44(24), 13556–13572 (1991). [CrossRef] [PubMed]
22. P. Tournois and V. Laude, “Negative group velocities in metal-film optical waveguides,” Opt. Commun. 137(1-3), 41–45 (1997). [CrossRef]
23. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]
24. Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocavities: Analysis of optical properties,” Phys. Rev. B 75(3), 035411 (2007). [CrossRef]
25. M. Litinskaya and V. M. Agranovich, “Polariton trap in microcavities with metallic mirrors,” J. Phys. Condens. Matter 24(1), 015302 (2012). [CrossRef] [PubMed]
26. S. Hayashi, Y. Ishigaki, and M. Fujii, “Plasmonic effects on strong exciton-photon coupling in metal-insulator-metal microcavities,” Phys. Rev. B 86(4), 045408 (2012). [CrossRef]
27. J. R. Tischler, M. S. Bradley, V. Bulović, J. H. Song, and A. Nurmikko, “Strong coupling in a microcavity LED,” Phys. Rev. Lett. 95(3), 036401 (2005). [CrossRef] [PubMed]
28. M. Oda, K. Hirata, T. Inoue, Y. Obara, T. Fujimura, and T. Tani, “Strong exciton-photon coupling and its polarization dependence in a metal-mirror microcavity with oriented PIC J-aggregates,” Phys. Status Solidi, C Conf. Crit. Rev. 6(1), 288–291 (2009). [CrossRef]
29. H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007). [CrossRef] [PubMed]
30. S. Kalusniak, S. Sadofev, and F. Henneberger, “ZnO as a tunable metal: new types of surface plasmon polaritons,” Phys. Rev. Lett. 112(13), 137401 (2014). [CrossRef] [PubMed]
31. Y. Liu, D. F. P. Pile, Z. Liu, D. Wu, C. Sun, and X. Zhang, “Negative group velocity of surface plasmons on thin metallic films,” Proc. SPIE 6323, 63231M (2006). [CrossRef]
32. A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007). [CrossRef] [PubMed]
33. T. Pickering, J. M. Hamm, A. F. Page, S. Wuestner, and O. Hess, “Cavity-free plasmonic nanolasing enabled by dispersionless stopped light,” Nat. Commun. 5, 4972 (2014). [CrossRef] [PubMed]
34. A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013). [CrossRef]
35. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).
