Letter pubs.acs.org/NanoLett
Confined Tamm Plasmon Lasers C. Symonds,*,† G. Lheureux,† J. P. Hugonin,‡ J. J. Greffet,‡ J. Laverdant,† G. Brucoli,† A. Lemaitre,§ P. Senellart,§ and J. Bellessa† †
Institut Lumière Matière, Université de Lyon, UMR5306 Université Lyon 1-CNRS, 69622 Villeurbanne, France, Laboratoire Charles Fabry, Institut d Optique, CNRS, Univ Paris-Sud, 2 avenue Fresnel, 91127 Palaiseau cedex, France § Laboratoire de Photonique et de Nanostructures, CNRS UPR20, Route de Nozay, F-91460 Marcoussis, France ‡
ABSTRACT: We demonstrate that confined Tamm plasmon modes can be advantageously exploited for the realization of new kind of metal/semiconductor lasers. Laser emission is demonstrated for Tamm structures with various diameters of the metallic disks which provide the confinement. A reduction of the threshold with the size is observed. The competition between the acceleration of the spontaneous emission and the increase of the losses leads to an optimal size, which is in good agreement with calculations.
KEYWORDS: Plasmon, Tamm plasmon, laser, semiconductor devices, hybrid metal/dielectric structures
T
semiconductor quantum dot. A coupling to the mode (β factor) close to 1 was demonstrated.24 This efficient coupling of the spontaneous emission into the Tamm mode is promising to reduce the laser threshold.25 The confinement of Tamm mode also makes it possible to control and modify the radiation pattern of the laser. In this Letter, we demonstrate that lasing can be obtained in confined Tamm structures and that the confinement induces a reduction of the laser threshold. Depending on the material chosen for the fabrication of the active DBR, this new type of laser could be developed in a large range of wavelength (from UV to near IR).26,27 They should also be compatible with electrical excitation using existing technologies.20,21 Moreover, the technological simplicity of the confinement mechanism makes this approach very flexible for the possible geometries of lasing structures. Tamm lasers thus open a viable route toward electrically driven complex laser structures. The confined Tamm plasmon (CTP) structures consist in metallic microdisks deposited on a bidimensional distributed Bragg reflector (DBR), as presented in Figure 1. The active DBR is formed by a stack of 30 AlAs/AlGaAs pairs grown by molecular beam epitaxy on a GaAs substrate. The layers present a thickness gradient along the wafer, which enables a precise spectral tuning of the DBR and thus of the Tamm mode with the position on the sample. Each of the five upper AlGaAs quarter-wavelength layers contains two 9.5 nm thick InGaAs quantum wells (QWs) as active medium, whose emission lies
he realization of efficient laser sources, still more compact and integrated in optoelectronic devices, is a key issue at the heart of a considerable number of applications. In order to produce the optical feedback necessary to the lasing effect, different geometries have been developed such as distributed feedback structures,1 vertical cavity surface-emitting lasers,2 or photonic crystals.3 More recently, hybrid metal/dielectric structures have attracted large attention for the high confinement enabled by the metal4−9 as well as for the plasmon they support. A “spaser” effect similar to the laser effect but involving plasmons was recently demonstrated10,11 and different types of spasers have been proposed.12−15 Beside the reduction of the size of the laser, the parallelization of the emitting structure compatible with an electrical excitation remains a key issue for numerous applications.16,17 Tamm plasmon modes, recently demonstrated in the optical domain,18,19 are good candidates for the fabrication of complex laser arrays and integrated devices for a wide number of applications ranging from the development of inorganic exciton-polaritons integrated circuit20 to the coherent control of the emission of metal−organic microcavities.21 The Tamm plasmon modes appear at the interface between a metallic film and a Bragg mirror and exhibit properties of both cavity modes and plasmons.19 They present relatively low losses, as cavity modes, and lasing in bidimensional Tamm structures has recently been evidenced.22 But the most promising property of Tamm plasmons lies in the tailoring of the mode by structuring only the metallic part of the structure. The confinement of Tamm modes depositing micrometer scale gold disk on a Bragg mirror has been recently demonstrated.23 It has allowed controlling the spontaneous emission of a single © 2013 American Chemical Society
Received: April 4, 2013 Revised: May 24, 2013 Published: June 18, 2013 3179
dx.doi.org/10.1021/nl401210b | Nano Lett. 2013, 13, 3179−3184
Nano Letters
Letter
Figure 1. Schematic representation of the sample. The active region of the 30 pairs DBR is obtained by including 2 InGaAs quantum wells in its 5 upper AlGaAs layers. A resist (PMMA, 90 nm) is deposited on the top of the DBR, and circular patterns with diameter ranging from 1 to 40 μm are defined by e-beam lithography. Silver (40 nm) is deposited on the top of the structure by thermal evaporation. No liftoff is performed; the Tamm modes only exist in the circular areas where the metal is in direct contact with the semiconductor.
around 855 nm at 77 K. A 90 nm thick layer of poly(methyl methacrylate) PMMA (refractive index 1.49) was spin-coated on the top of the sample, and annealed at 170° for 10 min. Circular patterns with diameters ranging from 1 to 40 μm have been defined by e-beam lithography on the resist, and a 40 nm silver layer has been evaporated to form the microdisk. The Tamm modes only exist under the metallic microdisks, where the metal is in direct contact with the last high refractive index layer of the DBR. In order to mask the emission from the QWs located outside the disks, no lift-off has been performed, leaving the 90 nm resist layer beneath the silver layer in the areas surrounding the Tamm structure. Considering the small thickness of the resist, cavity effects can be excluded in the remaining resist layer at the wavelength of interest (∼850 nm). The sample is placed in a cryostat and cooled at 77 K. The CTP structures are optically pumped through the silver layer by a mode locked Ti:Sapphire laser (repetition rate 80 MHz, pulse width 370 fs) tuned at 785 nm and focused on a 8 μm diameter spot. Transfer matrix simulations at the pump wavelength indicate that about 99.4% of the incident light is reflected by the structure, and that the losses through the silver layer amount to about 0.5%; only 0.1% is absorbed by the QWs. The light emitted by the sample is collected by a long working distance microscope objective (numerical aperture 0.75) and detected either by a charge-coupled device (CCD) detector associated to a spectrometer or by a CCD camera. The Fourier plane of the objective can also be imaged on the CCD camera, enabling a direct visualization of the angular pattern of the emission, or on the entrance slit of the spectrometer, thus giving access to the emission dispersion relation. Contrary to unconfined Tamm that presents polarization splitting for inplane wavevector different from 0,19 no particular polarization direction is expected in our system due to the cylindrical symmetry. The properties of the CTP structures are first studied in a low excitation regime in order to extract the main parameters of the confined modes. For a disk diameter of 20 μm, the recorded emission dispersion is displayed in Figure 2a, and presents a parabolic shape as is the case for conventional bidimensional Tamm modes.22 For small disk diameters, the emission dispersion shows discrete resonant wavelengths associated to the three-dimensional confinement of the electric field, as
Figure 2. (a,b) Emission dispersion for disk diameters of 20 and 5 μm, respectively. (c) Variation of the spectral detuning between the fundamental and first CTP mode as a function of the disk diameter (left axis). The open circles correspond to experimental data, the solid red line to calculations. Calculated variation of the spectral position of the fundamental CTP mode with the disk diameter (right axis). (d) Calculated electric field for a 4 μm CTP structure.
presented in Figure 2b for a 5 μm disk. The vertical confinement is provided by the metal/dielectric multilayer while the lateral confinement is ensured by the finite lateral dimension of the disk. Indeed, the electric field associated with the Tamm mode remains confined beneath the metal disk23 as shown in Figure 2d. As the disk diameter decreases, the localized Tamm resonances blue shift and the wavelength separation between the different sublevels increases. The Tamm modes have been numerically described using a coupled wave analysis.28−30 The field is expanded over a basis of modes eiKzf(kr)eiLθ characterized by the wavevector along the disk normal K, the integer L, and the complex eigenvalue k of the radial transverse wavevector; f(kr) is an incoming or outgoing cylindrical mode. The method is generalized to the study of nonperiodic objects by introducing perfectly matched layers (PML). The complex refractive index of the silver layer was modeled using a Drude function adjusting the values given by Johnson and Christy31 around 850 nm. We did not take into account the possible reduction of the losses at low temperature,32 as previous study showed that the values given by Johnson and Christy gave a good agreement with experimental results in our systems.33 A good agreement with the experimental results is obtained as shown in Figure 2c. The disk size reduction is also associated to a broadening of the modes, that is, a decrease of their quality factor Q (Figure 4c). This loss increase can be attributed to diffraction at the disk 3180
dx.doi.org/10.1021/nl401210b | Nano Lett. 2013, 13, 3179−3184
Nano Letters
Letter
Figure 3. Emission of a 4 μm diameter CTP structure with increasing pump power. (a−d) Emission dispersion for pump powers of 28, 38, 55, and 81 μW. (e) Angular intensity profile of the emission for 81 μW of pump power. (f) Emission spectra recorded over the whole numerical aperture and normalized by the pump power.
edge.24 It has to be noticed that experimental determination of the Q factor is difficult due to the hybridization of the QW excitons with the Tamm modes at low excitation power. In order to demonstrate lasing operation with CTP modes, we studied the evolution of the emission of a CTP structure as the pump power is increased. As previously evidenced for bidimensional Tamm structures,33 under very low pump power (below 3 μW, data not shown) the system is in strong coupling regime, where QW excitons and Tamm plasmons hybridize to form Tamm/excitons polaritons. When the number of injected carriers in the structure increases, several phenomena are present (electron hole pair screening of the quantum well exciton,34,35 saturation of the oscillator strength36) leading to a progressive transition from weak to strong coupling regime as previously demonstrated in bidimensional Tamm lasers.22 In the following, we will only present emission dispersions and spectra for pump power higher than 20 μW for which the strong coupling starts to be screened. Figure 3 shows the emission dispersion relations for absorbed pump powers ranging from 28 to 81 μW for a 4 μm diameter structure that presents the typical behavior of CTP modes. Under low pump power (28 μW, Figure 3a) the first two confined modes appear in the emission diagram, lying at 856.9 and 855.7 nm, respectively. When the pump power is increased, a spectral narrowing as well as an increase of the emission intensity in the fundamental mode occurs, as shown in Figure 3b,c. Finally, at high pump power most of the emission is concentrated in the fundamental mode with an angular aperture of 14° (Figure 3d,e). The strong emission increase in the fundamental mode can also be observed in Figure 3f presenting the emission spectra integrated over the whole numerical aperture and normalized by the pump power (spectrometer resolution ∼0.5 nm). The total emission intensity as a function of the absorbed pump power presented as squares in Figure 4a shows a clear nonlinear increase above 35 μW. The spectral narrowing of the emission, the concentration of the emission in the lower mode,
and the nonlinear increase of the intensity indicate unambiguously a lasing effect in the confined Tamm structure. The lateral confinement of the Tamm mode can considerably increase the ratio of spontaneous emission directed in the Tamm mode with respect to the total emission (β factor).23 The increase of this β factor induces a reduction of the lasing threshold.25 On the contrary, a decrease of the lateral disk size induces additional losses associated to diffraction on the disk edges24 and reduces the quality factor, increasing the threshold. In order to determine the contribution of these contradictory effects, the lasing threshold has been measured for CTP lasers with disk diameters ranging from 8 to 3 μm. To measure the threshold a nonresonant pump spot with a diameter of 8 μm has been used. As the absorption coefficient (∼0.1%) at the pump wavelength is the same on the CTP structure and on the surrounding area where the same silver thickness remains (with a resist spacer beneath the metal), the injected carriers in the structure is proportional to the excitation power and thus independent of the disk diameter. Furthermore, in order to compare the results obtained with the different structures it is also necessary to maintain a fixed spectral detuning between the QWs’ emission and the fundamental CTP mode. The spectral shift of the fundamental mode as the confinement is increased was thus compensated by taking advantage of the thickness gradient allowing changing the detuning between the CTP and the QW across the wafer. As presented in Figure 4a for disk diameters of 8, 6, 5, and 4 μm, the emission as a function of the pump power presents a nonlinear behavior with a pump power at threshold decreasing with the disk diameter. The evolution of the pump power at threshold as a function of the disk size is summarized in Figure 4b (open circles). This evolution has been recorded with a constant 8 μm pump spot size, and it has been experimentally checked that a smaller pump diameter does not affect the threshold behavior. For disk diameters above 6 μm, the threshold values are constant and amount to approximately 65 3181
dx.doi.org/10.1021/nl401210b | Nano Lett. 2013, 13, 3179−3184
Nano Letters
Letter
threshold observed experimentally results from the competition between the increase of the β factor and the degradation of Q when decreasing the disk diameter. It has to be noticed that due to nonradiative effects and to the smooth transition from strong to weak coupling regime, the β factor cannot be directly deduced from the step height of the input-output curves of Figure 4a.38,39 The β factor has thus been calculated using the ratio
β=
Fp Fp + γ
where Fp is the Purcell factor (function of the ratio between Q and the mode volume) and γ is the inhibition factor of the spontaneous emission in all modes except the Tamm mode. The colored solid lines in Figure 4b present the calculated thresholds taking into account a varying β for different values of γ: 1, 0.5, 0.1 (γ = 1 corresponds to no inhibition). Indeed, for a point quantum emitter deterministically positioned at the center of a CTP structure, a strong inhibition was observed experimentally,23 corresponding to a very low value of γ. Here, with a QW coupled to the CTP mode, we find that the best agreement with the experimental data is obtained for a weak inhibition (0.5 < γ < 1). The calculated β factor corresponding to the case γ =1 is plotted in Figure 4c as an example. The calculated threshold curves reproduce quite well the minimum threshold obtained for disk diameters around 3−4 μm. For disks smaller than the optimal size, the threshold increases with a very steep slope explaining that no lasing has been experimentally observed for disks smaller than 3 μm. The plateau reached for disks diameter larger than 7 μm however is not reproduced by the calculations. This could be explained by considering that for large diameters the lateral extension of the mode does not follow the geometrical dimension of the disk (used in the calculations) but reaches a maximum that is the extension of the 2D Tamm mode, around 7 μm in our case. The confinement can also be exploited to tailor the emission pattern. In Figures 3 and 4, the spectral detuning between the CTP mode and the QWs emission has been kept constant (∼+1.3 nm), and for each disk diameter the lasing effect occurred on the fundamental mode of the structure. An example of the emission relation dispersion above laser threshold for a 6 μm diameter disk is presented in Figure 5a. For this sample, lasing operation occurs in the fundamental mode and the direct observation of the emission with a CCD camera gives a quasi-Gaussian spatial repartition of the intensity as shown in Figure 5b. The angular emission pattern can also be recorded in Fourier space (Figure 5c) and also shows a Gaussian repartition. The numerical aperture of this emission is 0.17, compatible with optical fiber coupling. By increasing the spectral detuning (∼+3.2 nm) it is possible to obtain laser operation of higher order modes. The measured threshold for the first higher order mode for this disk is of the same order of magnitude as the one obtained for the fundamental mode (Pth ∼ 65 μW). This similar threshold can be qualitatively understood considering the close value of the volume and Q factor for large metallic disks for the fundamental and first higher order modes. In this case the angular and spatial repartition of the emission are concentrated in the two lobes associated with the second confined mode (Figure 5d,e,f) showing that the emission pattern of such CTP structures can be modified by the detuning. For a more versatile and efficient
Figure 4. Impact of the diameter reduction on lasing thresholds. (a) Emitted signal as a function of the pump power for disk diameters of 4, 5, 6, and 8 μm. (b) The open circles correspond to the experimental lasing thresholds obtained for disk diameters ranging from 4 to 9 μm. The three upper solid lines represent the calculated threshold as a function of the disk diameter for inhibition factors γ of 1 (red), 0.5 (blue), and 0.1 (green). The black solid line corresponds to calculated thresholds with γ = 1 and a β factor kept constant (β = 0.1). The calculated thresholds are scaled at the same value for a 4 μm diameter disk. (c) Calculated β (red curve, left) and Q (black curve, right) factors as a function of the disk diameter. The β factor was calculated considering an inhibition factor γ of 1.
μW (horizontal dotted line). For 5 and 4 μm however the threshold pump power drops, and a minimal value is obtained for the 4 μm CTP structures with a reduction of almost a factor 2 compared to large CTP structures (diameters larger than 6 μm). For CTP structures with diameters smaller than 4 μm, no lasing operation has been achieved in the pump power range investigated. To model the behavior of the threshold variation as a function of the diameter of the CTP structure, we used the model proposed by Björk et al.37 where the threshold is related to β and Q with 1 Pth ∝ βQ This threshold corresponds to equal average rates of spontaneous and stimulated emission in the laser mode. The quality factor Q is deduced from the calculations presented previously (Figure 4c). To stress the influence of the Purcell effect and hence the β factor on the reduction of the lasing threshold, we first plot the threshold variation with a constant β (β = 0.1, γ = 1, black line in Figure 4b). This β value corresponds to the one calculated for a disk with a diameter of 9 μm (see below). In this case, the calculated pump power at threshold presents a constant increase when decreasing the disk diameter. This indicates that the optimum disk size in term of 3182
dx.doi.org/10.1021/nl401210b | Nano Lett. 2013, 13, 3179−3184
Nano Letters
Letter
(2) Li, H.; Iga, K. Vertical-Cavity Surface-Emitting Laser Devices, 1st ed.; Springer: New York, 2002. (3) Painter, O.; Lee, R. K.; Scherer, A.; Yariv, A.; O’Brien, J. D.; Dapkus, P. D.; Kim, I. Science 1999, 284, 1819−1821. (4) Hill, M. T.; Oei, Y. S.; Smalbrugge, B.; Zhu, Y.; De Vries, T.; Van Veldhoven, P. J.; Van Otten, F. W. M.; Eijkemans, T. J.; Turkiewicz, J. P.; De Waardt, H.; Geluk, E. J.; Kwon, S. H.; Lee, Y. H.; Notzel, R.; Smit, M. K. Lasing in metallic-coated nanocavities. Nat. Photonics 2007, 1, 589−594. (5) Perahia, R.; Alegre, T.; Safavi-Naeini, A.; Painter, O. Surfaceplasmon mode hybridization in subwavelength microdisk lasers. Appl. Phys. Lett. 2009, 95, 201114. (6) Hill, M. T. Status and prospects for metallic and plasmonic nanolasers. J. Opt. Soc. Am. B 2010, 27, B36−B44. (7) Lu, C. Y.; Chuang, S. L.; Mutig, A.; Bimberg, D. Metal-cavity surface-emitting microlaser with hybrid metal-DBR reflectors. Opt. Lett. 2011, 36, 2447−2449. (8) Matsudaira, A.; Lu, C. Y.; O’Brien, T.; Chuang, S. L. Metal-cavity quantum-dot lasers with enhanced thermal performance. Opt. Lett. 2012, 37, 3297−3299. (9) Khajavikhan, M.; Simic, A.; Katz, M.; Lee, J.; Slutsky, B.; Mizrahi, A.; Lomakin, V.; Fainman, Y. Thresholdless nanoscale coaxial lasers. Nature 2012, 482, 204−7. (10) Bergman, D. J.; Stockman, M. I. Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems. Phys. Rev. Lett. 2003, 90, 027402. (11) Stockman, M. I. Spasers explained. Nat. Photonics. 2008, 2, 327− 329. (12) Noginov, M. A.; Zhu, G.; Belgrave, A. M.; Bakker, R.; Shalaev, V. M.; Narimanov, E. E.; Stout, S.; Herz, E.; Suteewong, T.; Wiesner, U. Demonstration of a spaser-based nanolaser. Nature 2009, 460, 1110−1112. (13) Oulton, R. F.; Sorger, V. J.; Zentgraf, T.; Ma, R. M.; Gladden, C.; Dai, L.; Bartal, G.; Zhang, X. Plasmon lasers at deep subwavelength scale. Nature 2009, 461, 629−632. (14) Berini, P.; De Leon, I. Surface plasmon-polariton amplifiers and lasers. Nat. Photonics 2012, 6, 16−24. (15) Oulton, R. F. Surface plasmon lasers: sources of nanoscopic light. Mater. Today 2012, 15, 26−34. (16) Ding, K.; Hill, M.; Liu, Z.; Yin, L.; van Veldhoven, P.; Ning, C. Record performance of electrical injection sub-wavelength metalliccavity semiconductor lasers at room temperature. Opt. Express 2013, 21, 4728−33. (17) Costantini, D.; Greusard, L.; Bousseksou, A.; Wilde, Y. D.; Habert, B.; Marquier, F.; Greffet, J.-J.; Lelarge, F.; Decobert, J.; Duan, G.-H.; Colombelli, R. A hybrid plasmonic semiconductor laser. Appl. Phys. Lett. 2013, 102, 101106. (18) Kavokin, A. V.; Shelykh, I. A.; Malpuech, G. Lossless interface modes at the boundary between two periodic dielectric structures. Phys. Rev. B 2005, 72, 233102. (19) Kaliteevski, M.; Iorsh, I.; Brand, S.; Abram, R. A.; Chamberlain, J. M.; Kavokin, A. V.; Shelykh, I. A. Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror. Phys. Rev. B 2007, 76, 165415. (20) Liew, T.; Kavokin, A.; Ostatnicky, T.; Kaliteevski, M.; Shelykh, I.; Abram, R. Exciton-polariton integrated circuits. Phys. Rev. B 2010, 82, 033302. (21) Bruckner, R.; Zakhidov, A. A.; Scholz, R.; Sudzius, M.; Hintschich, S. I.; Frob, H.; Lyssenko, V. G.; Leo, K. Phase-locked coherent modes in a patterned metal-organic microcavity. Nat. Photonics 2012, 6, 322−326. (22) Symonds, C.; Lemaitre, A.; Senellart, P.; Jomaa, M. H.; Guebrou, S. A.; Homeyer, E.; Brucoli, G.; Bellessa, J. Lasing in a hybrid GaAs/silver Tamm structure. Appl. Phys. Lett. 2012, 100, 121122. (23) Gazzano, O.; de Vasconcellos, S. M.; Gauthron, K.; Symonds, C.; Bloch, J.; Voisin, P.; Bellessa, J.; Lemaitre, A.; Senellart, P. Evidence for confined Tamm plasmon modes under metallic microdisks and application to the control of spontaneous optical emission. Phys. Rev. Lett. 2011, 107, 247402.
Figure 5. Effect of the spectral detuning on the lasing properties. (a− c) Emission dispersion, direct emission, and emission recorded in Fourier space for a 6 μm diameter disk lasing in the CTP fundamental mode. (d−f) Emission dispersion, direct emission, and emission recorded in Fourier space for a 6 μm diameter disk lasing in first CTP mode.
control of the directivity, refined geometries of the metallic structure could be advantageously exploited. In conclusion, we demonstrated that lasing can be achieved with confined Tamm plasmon structures containing semiconductor quantum wells. A threshold reduction of a factor 2 when decreasing the CTP lateral size is evidenced. We also showed that the confinement can be used to modify the radiation pattern of the laser. The versatility of the Tamm laser properties as well as the simplicity of their fabrication make this type of confined lasers very promising for applications requiring a large number of paralleled sources or an easy control of the directivity and polarization.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS We thank Paul Voisin for fruitful discussions. We acknowledge support by the French ANR P3N DELIGHT. This work was partly supported by the french RENATECH network.
■
REFERENCES
(1) Numai, T. Fundamentals of Semiconductor Lasers, 1st ed.; Springer: New York, 2004. 3183
dx.doi.org/10.1021/nl401210b | Nano Lett. 2013, 13, 3179−3184
Nano Letters
Letter
(24) Gazzano, O.; de Vasconcellos, S. M.; Gauthron, K.; Symonds, C.; Voisin, P.; Bellessa, J.; Lemaitre, A.; Senellart, P. Single photon source using confined Tamm plasmon modes. Appl. Phys. Lett. 2012, 100, 232111. (25) Yamamoto, Y.; Machida, S.; Björk, G. Microcavity semiconductor laser with enhanced spontaneous emission. Phys. Rev. A 1991, 44, 657−668. (26) Tsang, S. H.; Yu, S. F.; Li, X. F.; Yang, H. Y.; Liang, H. K. Observation of Tamm plasmon polaritons in visible regime from ZnO/Al2O3 distributed Bragg reflector − Ag interface. Opt. Commun. 2011, 284, 1890−1892. (27) Sasin, M. E.; Seisyan, R. P.; Kalitteevski, M. A.; Brand, S.; Abram, R. A.; Chamberlain, J. M.; Egorov, A. Y.; Vasil’ev, A. P.; Mikhrin, V. S.; Kavokin, A. V. Tamm plasmon polaritons: Slow and spatially compact light. Appl. Phys. Lett. 2008, 92, 251112. (28) Bonod, N.; Popov, E.; Nevière, N. Differential theory of diffraction by finite cylindrical objects. J. Opt. Soc. Am. A 2005, 22, 481−490. (29) Armaroli, A.; Morand, A.; Benech, P.; Bellanca, G.; Trillo, S. Three dimensional analysis of cylindrical microresonators based on the aperiodic Fourier modal method. J. Opt. Soc. Am. A 2008, 25, 667− 675. (30) Belacel, C.; Habert, B.; Bigourdan, F.; Marquier, F.; Hugonin, J.P.; Michaelis de Vasconcellos, S.; Lafosse, X.; Coolen, L.; Schwob, C.; Javaux, C.; Dubertret, B.; Greffet, J.-J.; Senellart, P.; Maitre, A. Controlling spontaneous emission with plasmonic optical patch antennas. Nano Lett. 2013, 13 (4), 1516−1521. (31) Johnson, P. B.; Christy, R. Optical constants of the noble metals. Phys. Rev. B 1972, 6, 4370. (32) Bouillard, J.-S. G.; Dickson, W.; O’Connor, D.; Wurtz, G.; Zayats, A. Low-temperature plasmonics of metallic nanostructures. Nano Lett. 2012, 12, 1561−5. (33) Symonds, C.; Lemaitre, A.; Homeyer, E.; Plenet, J. C.; Bellessa, J. Emission of Tamm plasmon/exciton polaritons. Appl. Phys. Lett. 2009, 95, 151114. (34) Houdre, R.; Gibernon, J. L.; Pellandini, P.; Stanley, R. P.; Oesterle, U.; Weisbuch, C.; Ogorman, J.; Roycroft, B.; Ilegems, M. Saturation of the strong coupling regime in a semiconductor microcavity - Free-carrier bleaching of cavity polaritons. Phys. Rev. B 1995, 52, 7810−7813. (35) Bajoni, D.; Senellart, P.; Wertz, E.; Sagnes, I.; Miard, A.; Lemaitre, A.; Bloch, J. Polariton laser using single micropillar GaAsGaAlAs semiconductor cavities. Phys. Rev. Lett. 2008, 100, 047401. (36) Vasa, P.; Pomraenke, R.; Cirmi, G.; De, Re E.; Wang, W.; Schwieger, S.; Leipold, D.; Runge, E.; Cerullo, G.; Lienau, C. Ultrafast manipulation of strong coupling in metal-molecular aggregate hybrid nanostructures. ACS Nano 2010, 4, 7559−65. (37) Björk, G.; Heitmann, H.; Yamamoto, Y. Spontaneous-emission coupling factor and mode characteristics of planar dielectric microcavity lasers. Phys. Rev. A 1993, 47, 4451−4463. (38) Shin, J. H.; Ju, Y. G.; Shin, H. E.; Lee, Y. H. Spontaneous emission factor of oxidized vertical-cavity surface-emitting lasers from the measured below-threshold cavity loss. Appl. Phys. Lett. 1997, 70, 2344−2346. (39) Fujita, M.; Ushigome, R.; Baba, T. Large spontaneous emission factor of 0.1 in a microdisk injection laser. IEEE Photon. Technol. Lett. 2001, 13, 403−405.
3184
dx.doi.org/10.1021/nl401210b | Nano Lett. 2013, 13, 3179−3184
