Coupling in a Dual Metallo-Dielectric Nanolaser System

4760 Vol. 42, No. 22 / November 15 2017 / Optics Letters Letter

Coupling in a dual metallo-dielectric nanolaser system

1 1 2 1 1, SURUJ S. DEKA, SI HUI PAN, QING GU, YESHAIAHU FAINMAN, AND ABDELKRIM EL AMILI * 1Department of Electrical and Computer Engineering, University of California at San Diego, La Jolla, California 92093-0407, USA 2Department of Electrical and Computer Engineering, University of Texas at Dallas, Richardson, Texas 75080-3021, USA *Corresponding author: [email protected]

Received 14 September 2017; revised 23 October 2017; accepted 24 October 2017; posted 25 October 2017 (Doc. ID 306989); published 15 November 2017

To achieve high packing density in on-chip photonic overlap and, hence, the Joule loss. Additionally, the metal integrated circuits, subwavelength scale nanolasers that should also aid in isolating the electromagnetic field inside each can operate without crosstalk are essential components. resonator from the surrounding environment. Whether the Metallo-dielectric nanolasers are especially suited for this isolation provided can prevent crosstalk between optical com- type of dense integration due to their lower Joule loss ponents for purposes of dense integration on chip, however, is and nanoscale dimensions. Although coupling between op- yet to be explored to the best of our knowledge. tical cavities when placed in proximity to one another has The observation of coupling between non-metal based been widely reported, whether the phenomenon is induced optical cavities when placed in proximity of each other has been for metal-clad cavities has not been investigated thus far. widely reported in a host of systems such as photonic crystal We demonstrate coupling between two metallo-dielectric nanocavities [12,13], photonic molecule microdisk lasers nanolasers by reducing the separation between the two [14–18], microring lasers [19,20], ridge lasers [21], and porous cavities. A split in the resonant wavelength and quality fac- silicon based microcavities [22]. Though coupling can rely on tor is observed, caused by the creation of bonding and anti- varying types of physics to occur, the most commonly reported bonding supermodes. To preserve the independence of the form is based on evanescent interaction between the electro- two closely spaced cavities, the resonance of one of the magnetic fields of the individual resonators which results in cavities is detuned relative to the other, thereby preventing a characteristic splitting of the observed optical modes in both coupling. © 2017 Optical Society of America frequency and loss [12,14,17,18,23]. This bifurcation arises OCIS codes: (130.3120) Integrated optics devices; (250.5300) due to the presence of bonding and anti-bonding states in Photonic integrated circuits; (140.3325) Laser coupling; (140.0140) the coupled system, the latter of which generally exhibits lower Lasers and laser optics. losses and, hence, becomes the lasing mode. These supermodes can then give rise to new functionalities, for instance such as https://doi.org/10.1364/OL.42.004760 possible use in memory due to bistable behavior exhibited by the anti-bonding mode [12,18]. However, for nanoscale devices, if the primary goal is to achieve high packing density Future integrated photonic chips would necessitate coherent for on-chip design, it is essential that the individual cavities light sources with ultra-compact footprints and low power con- composing the coupled system can operate independently from one another. This would allow one laser to be operated or sumptions. Many efforts have already been made to realize such ’ subwavelength scale nanolasers, albeit the emitters have been modulated without interfering in its neighbor s emission behav- implemented based on a myriad of cavity designs, including ior. Since metal-clad nanolasers are ideally suited for this type of those based on photonic crystal [1–3], metallo-dielectric [4–7], dense integration due to their subwavelength and nanoscale coaxial metal [8], and plasmonic cavities or spasers [9–11]. dimensions, whether coupling is induced when two such de- Usually, shrinking the size of the resonator in all three vices are designed near one another needs to be investigated. dimensions leads to a spatial spreading of the optical mode In this Letter, we report the effect of gradually reducing the beyond the resonator’s physical boundaries which induces an separation between two metallo-dielectric nanolasers using increase in optical loss and threshold. In metallo-dielectric three-dimensional finite-element method simulations. In con- nanolasers, this limitation is overcome by cladding the active trast to expectations that the metal should inhibit coupling, a medium with a combination of a dielectric shield and metal splitting of the optical modes in both the resonance wave- layer [5]. The metal cladding helps confine the optical mode length, λ, and quality factor, Q, is observed for the coupled to the high index active core, thereby increasing the mode-gain metallo-dielectric nanolaser system akin to what is reported overlap while the dielectric shield pushes the electromagnetic in coupled microcavities [14,20]. The split is caused by the mode away from the metal walls, thus reducing the mode-metal creation of bonding and anti-bonding states, as the distance

Fig. 2. Electric field intensity profile across the side (top row) and top (bottom row) cross sections of the dual-cavity nanolaser system. (a) Distance between the dielectric shields is 90 nm and the system supports two identical modes. (b) Shields are now in contact, and Fig. 1. Schematic of the dual-cavity system with the constituent an anti-bonding supermode is created with strong confinement of materials labeled. The heights of the gain, SiO2 cladding, airgap, the electromagnetic mode to the gain medium of each resonator. and radius of the gain are represented by hInGaAsP, hSiO2, hAir and (c) New bonding mode is created for the same separation as in (b), rInGaAsP respectively. The distance, d, between the dielectric shields but the mode is poorly confined to the gain regions for this state. is the parameter changed during a parametric sweep to probe the char- acteristics of the modes. The bonding state, shown in Fig. 2(c), demonstrates poor con- between the dielectric shields of the nanolasers is decreased. finement of the mode to the gain media of the two resonators Since the two nanoresonators share the same metal cladding, with a significant portion of the field interaction seen to be it is not possible to engineer any changes in the metal coating occurring in the dielectric shields. In contrast, the anti-bonding for one without affecting the other. Therefore, a method is pre- state in Fig. 2(b) still shows the mode to be strongly confined to sented whereby slight detuning of one of the cavity resonances the gain medium of each resonator. In fact, the mode profile of can prevent the phenomenon of coupling from occurring and, the anti-bonding state is nearly identical in appearance to thereby, preserve the independence of the two nanolasers. when the cavities support independent modes of their own Figure 1 shows a representative schematic of the dual-cavity when designed far apart, as seen in Figs. 2(b) and 2(a), system to be simulated. The gain medium is composed of bulk respectively. InGaAsP modeled with a height of hInGaAsP 300 nm, radius To further elucidate the impact of coupling between the two ε rInGaAsP 225 nm, and permittivity of gain 11.56 [5]. cavities, d was varied in an eigenfrequency solver module of λ Each gain was conformally cladded with SiO2 of height COMSOL Multiphysics. The eigenmode wavelength, , and hSiO2 100 nm, selected to minimize the gain threshold of quality factor, Q, for the modes supported by the system the nanolaser. Additionally, an airgap of hAir 400 nm height, are calculated for each d. As seen in Fig. 3(a), the wavelengths below the gain layer, was designed to provide optimal mode for the two modes supported by the system are nearly identical confinement. Finally, the cavities were covered with a 1 μm to each other when the two cavities are placed far enough apart; layer of Ag. The permittivities for the SiO2, air, and Ag material the same can be said for the quality factor shown in Fig. 3(b). ε ε ε layers were taken to be dielectric 2.16, air 1, and silver Therefore, only intercavity spacings up to 60 nm are plotted for −130 − 3i [24], respectively, with the values chosen considering better contrast. In fact, this behavior is expected, since the the eigenmode wavelength supported by the nanocavity design modes supported in these high-separation designs are a pair (around 1.55 μm) and assuming room temperature operation. To study the effect of reducing the separation, d, between the dielectric shields of the two cavities composing the dual system, we first consider two cases—when the cavities are far apart at 90 nm and when they are in contact at 0 nm. For each separation distance, the electric field intensity across a two-dimensional side and top cross section of the gain was recorded. Figure 2 illustrates the side and top profiles of the magnitude of the electric field of the TE011 mode supported by each nanocavity for the two separations mentioned. For the case of d 90 nm, the metal between the two cavities pre- vents the electromagnetic fields inside each resonator from in- teracting with one another. In other words, the evanescent field from each cavity is allowed adequate space to decay exponentially due to damping by the metal, thereby producing little to no interaction of fields in the metallic region. This isolation can be clearly seen in Fig. 2(a), where the two identically sized Fig. 3. Resonance wavelengths, Q-factors, and gain thresholds for cavities support the same resonant modes, but there is no in- each of the two modes of the system at different intercavity separa- teraction between the two TE011 modes. However, for smaller tions. The red represents the bonding state, and the blue represents d, and taking the extreme case of when d 0nm as in the anti-bonding state at lower separations. (a) Eigenmode wavelength, λ Figs. 2(b) and 2(c), two new optical modes are observed , (b) the Q-factor, and (c) the gain threshold, gth. Inset: electric field due to increased evanescent coupling between the two cavities. distribution of the anti-bonding (left) and bonding (right) supermode. 4762 Vol. 42, No. 22 / November 15 2017 / Optics Letters Letter of isolated cavity modes with the mode profile of each identical the bonding mode demonstrating a lower Q and, hence, a to the illustration shown in Fig. 2(a). At larger d, the two higher λ (due to lower energy) than its anti-bonded counter- cavities are essentially independent of one another, despite sup- part, as seen in Figs. 3(a) and 3(b), is in line with the expected porting almost the same resonant frequencies. As the nanocav- behavior from a coupled system [25]. The slight asymmetry in ities are brought closer together, two new states emerge—an the two modes supported by the metallo-dielectric cavities is anti-bonding and bonding state, as depicted in Figs. 2(b) caused by the bonding mode having a significant overlap with and 2(c), respectively. The cavity resonant wavelength and the dissipative metal, while the anti-bonding mode has a min- quality factor for the bonding state are higher and lower, respec- imal overlap with the metal as d decreases to 0. Consequently, tively, than those for the individually isolated cavity mode. the dissimilarity in the dissipative losses experienced by the two Conversely, for the anti-bonding mode, the λ and Q are lower supermodes results in an asymmetric split. and higher than the same parameters of an isolated cavity Though coupling is generally sought after, in the case that a mode. Consequently, a split, which can be visibly discerned bifurcation of states is not desirable, methods must be intro- at around d 50 nm in Fig. 3, arises in these two parameters duced to control or at least mitigate the coupling between of the new supermodes as d is decreased. To better delineate the cavities. For non-metal based cavities, coupling can be reduced coupling and non-coupling regions, the ratio between Δλ, through various means. The region between the resonators which represents the difference between the two eigenmode itself, which can act as a barrier for coupling, can be altered wavelengths, and the resonance width of an isolated cavity by increasing its size, for instance, as in photonic crystal micro- mode can be calculated. Doing so reveals that the ratio sharply cavities, thereby reducing the mode interaction needed for cou- increases from 0.82 at 50 nm to 1.38 at 40 nm, indicating onset pling [23,26]. One cavity can also be detuned dynamically of coupling as d decreases below 50 nm since the ratio starts from its neighbor via thermal or carrier effects [13]. In contrast, exceeding one. This signifies that the split in resonant wave- for the nanocavities simulated in this Letter, the common metal lengths now starts becoming much greater than the resonant shield covering both the resonators makes the above techniques width for an isolated cavity mode. Coupling is most pro- less feasible to implement. Any attempt to independently nounced when the SiO2 shields of the cavities contact each control one cavity or engineer changes in its cladding is ren- other at d 0nm. Hence, the difference in λ and Q between dered futile, since the changes will affect the other cavity as well the bonding and anti-bonding eigenmodes is maximum at this via the shared metal coating. point with values of Δλ 14.6 nm and ΔQ 1347. In this scenario, one possible way to curb the evanescent Since the simulated nanocavities are purposed for lasing, field interaction outside the gain media is to detune the reso- observing the change in parameters such as the λ and Q does nances of the cavities relative to each other. By incorporating not provide any helpful insight on how coupling can affect the slight changes in the physical dimensions of one of the cavities likelihood for lasing. Therefore, the gain threshold, gth,is in the dual-cavity system, eigenmodes for the altered cavity can calculated with the equation 2πn g g ; (1) th λQΓ Γ where ng is the group refractive index, and is the electromagnetic mode confinement factor [6]. The material gain spectrum is not considered, assuming that the high carrier density re- quired to pump the devices would produce negligible difference between the gain experienced by the bonding and anti-bonding supermodes. Instead, just the gth is used which encompasses all three parameters, λ, Q, and Γ, that undergo significant change as d nears 0 nm. Figure 3(c) shows that for the bonding mode, the threshold increases exponentially as the resonators are placed closer together. The stark contrast between the lasing tendencies of the bonding and anti-bonding modes is evident when, for d 0nm, the difference in the respective gain Δ −1 thresholds of the supermodes is found to be gth 217 cm . The split in the resonant wavelength of emission as the cavities are designed closer together is a signature of coupling as reported for both micro- [14–18,22] and nanoscale struc- tures [12,13]. In fact, an exponential rise in Δλ for the coupled system is observed as the separation between resonators is reduced [14,20]. This exponential behavior can be seen in Fig. 3(a) for d close to 0 nm. When placed far enough apart, however, there is no coupling between the metal-clad cavities, and the modes supported in the individually isolated resonators Fig. 4. Resonance wavelengths, Q-factors, and gain thresholds for are independent of one another as has also been observed for each of the two modes of the system at different intercavity separations coupled photonic molecules [14–18,22,23]. Additionally, the such as in Fig. 3. The radius of one of the cavities (shown in red) is new bonding supermodes created during coupling between designed to be five percent larger than that of the other cavity (in blue). λ cavities generally incur higher losses [14,17,18,23]. Thus, (a) Eigenmode wavelength, (b) the Q-factor and (c) gain threshold, gth. Letter Vol. 42, No. 22 / November 15 2017 / Optics Letters 4763 be shifted far enough away to prevent any significant coupling Acknowledgment. The authors acknowledge the staff λ ’ from occurring. Figure 4 depicts the , Q, and gth for the two of NSF-NNCI s San Diego Nanotechnology Infrastructure modes supported in a dual-cavity system where the radius of (SDNI) for their continued support in sample fabrication one cavity has been designed to be 236.25 nm, exactly five and characterization. percent more than that of its neighbor. Unlike in Fig. 3,no pronounced split in any of the three quantities is observed, as d between the two size-mismatched cavities is decreased REFERENCES Δλ Δ Δ to zero. The values for , Q, and gth when the shields of the respective resonators are in contact with each other 1. H. Altug, D. Englund, and J. Vučković, Nat. Phys. 2, 484 (2006). are 52.5 nm, and 157 and 25.15 cm−1, respectively, the latter 2. K. Nozaki, S. Kita, and T. Baba, Opt. Express 15, 7506 (2007). 3. B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, two of which are much smaller in comparison to the previously and J. Vučković, Nat. Photonics 5, 297 (2011). mentioned values for these quantities for the case of two 4. M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. equal-sized cavities. The greater difference in Δλ in the size- Veldhoven, F. W. M. Van Otten, T. J. Eijkemans, J. P. Turkiewicz, mismatched case is due to the size detuning of one of the H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, and cavities and not to coupling. This becomes evident when by M. K. Smit, Nat. Photonics 1, 589 (2007). comparing d 0nm with d 60 nm in Fig. 4(a), the 5. M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. change in Δλ is only ∼3.3%, whereas for the case of equal-sized Feng, V. Lomakin, and Y. Fainman, Nat. Photonics 4, 395 (2010). cavities shown in Fig. 3(a), the change is many times more pro- 6. Q. Gu, J. Shane, F. Vallini, B. Wingad, J. S. T. Smalley, N. C. nounced at 2650%. Thus, implementing a slight design change Frateschi, and Y. Fainman, IEEE J. Quantum Electron. 50, 499 (2014). results in the dual system exhibiting only independent lasing 7. S. H. Pan, Q. Gu, A. El Amili, F. Vallini, and Y. Fainman, Optica 3, modes, instead of any coupled supermodes, regardless of the 1260 (2016). distance separating the nanocavities. 8. M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. To conclude, we analyzed a system of two spatially close Lomakin, and Y. Fainman, Nature 482, 204 (2012). metallo-dielectric nanolasers and demonstrated coupling upon 9. D. J. Bergman and M. I. Stockman, Phys. Rev. Lett. 90, 027402 reducing the separation between them. A split observed in both (2003). resonant wavelengths, λs, and the Q-factors of the two modes 10. M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. for intercavity separations below 50 nm is akin to bifurcations Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, Nature observed in coupled cavities on the micron scale. The fact that 460, 1110 (2009). 11. Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C. Y. inter-cavity separations needed to observe coupling for metallo- μ Wang, M. Y. Lu, B. H. Li, X. Qiu, W. H. Chang, L. J. Chen, G. Shvets, dielectric nanolasers (<50 nm) is much smaller than the m C. K. Shih, and S. Gwo, Science 337, 450 (2012). scale distances needed in non-metal based cavities further 12. P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. strengthens their viability for dense on-chip integration. The Sagnes, A. Levenson, and A. M. Yacomotti, Nat. Photonics 9, 311 increasing difference between the wavelengths and quality fac- (2015). tors of the two modes is caused by the creation of anti-bonding 13. D. O’Brien, M. D. Settle, T. Karle, A. Michaeli, M. Salib, and T. F. and bonding states due to evanescent electromagnetic field Krauss, Opt. Express 15, 1228 (2007). interaction outside the gain media of the resonators. If the 14. A. Nakagawa, S. Ishii, and T. Baba, Appl. Phys. Lett. 86, 041112 primary purpose for such nanoscale light sources is dense (2005). 15. S. V. Boriskina, J. Opt. Soc. Am. 23, 1565 (2006). integration on chip, then preserving the independence of each ’ 16. S. V. Boriskina, Opt. Lett. 32, 1557 (2007). emitter is of paramount importance to allow control over one s 17. E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. emission behavior without interfering in that of its neighbors. Top. Quantum Electron 12, 78 (2006). To eliminate the two supermodes, a method of shifting the 18. S. Ishii, A. Nakagawa, and T. Baba, IEEE J. Sel. Top. Quantum resonance of one of the cavities by altering its radius by five Electron 12, 71 (2006). percent of that of the other cavity is presented. By doing so, 19. M. T. Hill, H. J. S. Dorren, T. D. Vries, X. J. M. Leijtens, J. H. D. Besten, albeit the resonances of the cavities were made to be dissimilar, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, a coupled supermode that essentially treats the system as one Nature 432, 206 (2004). cavity was avoided. Such size-mismatched metal-clad nanolas- 20. H. Hodaei, M. A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, Opt. Lett. 40, 4955 ers can be modulated independently without concern for (2015). crosstalk between components. Given that even with current 21. M. Liertzer, L. Ge, A. Cerjan, A. D. Stone, H. E. Tureci, and S. Rotter, state-of-the-art fabrication procedures slight fluctuations from Phys. Rev. Lett. 108, 173901 (2012). the intended size are unavoidable, even two identical cavities 22. M. Ghulinyan, C. J. Oton, G. Bonetti, Z. Gaburro, and L. Pavesi, may produce a size mismatch and, hence, not couple. Instead, J. Appl. Phys. 93, 9724 (2003). the now disparate lasing wavelengths may prove to be useful 23. K. A. Atlasov, K. F. Karlsson, A. Rudra, B. Dwir, and E. Kapon, Opt. for applications such as on-chip dense wavelength division Express 16, 16255 (2008). multiplexing. 24. P. B. Christy and R. W. Christy, Phys. Rev. B. 6, 4370 (1972). 25. Q. Wang, H. Zhao, X. Du, W. Zhang, M. Qiu, and Q. Li, Opt. Express 21, 11037 (2013). Funding. Army Research Office (ARO); National Science 26. S. Haddadi, P. Hamel, G. Beaudoin, I. Sagnes, C. Sauvan, P. Foundation (NSF); Office of Naval Research (ONR); Lalanne, J. A. Levenson, and A. M. Yacomotti, Opt. Express 22, Semiconductor Research Corporation (SRC). 12359 (2014).