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Nanoscale Metallo-Dielectric Coherent Light Sources

Maziar P. Nezhad, Aleksandar Simic, Amit Mizrahi, Jin-Hyoung Lee, Michael Kats, Olesya Bondarenko, Qing Gu, Vitaliy Lomakin, Boris Slutsky and Yeshaiahu Fainman

1.1 Introduction

Compact photonic components are important for the design and fabrication of integrated optical devices and circuits. In the case of light sources, reducing the size can result in improved metrics such as higher packing density and reduced power consumption and also may enhance cavity–emitter interactions such as the Purcell effect. Until recently it was commonly known that the minimum size for a laser is ultimately determined by the free-space wavelength, λ0. For example, as the size of a conventional Fabry–Perot semiconductor laser is scaled down in all three dimensions toward λ0, three effects adversely influence the lasing process. Firstly, the roundtrip path of the optical wave in the gain medium is shortened. Secondly, radiative losses from the end mirrors have an increased effect. Thirdly, the lateral field confinement in the resonator waveguide is reduced, resulting in a smaller overlap of the optical mode with the gain medium. All these effects lead to a significant increase in the lasing threshold. As a result lasing cannot be achieved below a certain size limit. By allowing the laser size to increase in one or two dimensions, it is possible to reduce the physical size of the laser in the remaining dimension(s) to values below this limit. For example, the disk thickness in whispering-gallery-mode (WGM) lasers [1] can be reduced to a fraction of the free-space wavelength [2] but, to compensate for the small thickness, the disk diameter must be increased. It should be noted that, in addition to the optical mechanisms noted above, nonradiative surface recombination can have a non-negligible negative effect on the emitter efficiency and thus needs to be accounted for in the design and analysis of such sources. The ultimate challenge in this respect is concurrent reduction of the resonator size in all three dimensions, and, at the same time, satisfying the requirements for lasing action.

The size of an optical cavity can be defined using different metrics, for example, the physical dimensions of the cavity or the size of the optical mode. However, if the goal of size reduction is to increase the integration density (for example, in a laser array), the effective cavity size should account for both the overall physical dimensions of the resonator and the spread of the optical mode beyond the physical boundary of the resonator. By this token, most conventional dielectric laser cavities are not amenable to dense integration because they have either a large physical footprint or a large effective mode. For example, distributed Bragg resonators [3] and photonic-crystal cavities [4] (both of which can be designed to have very small mode volumes) have physical footprints that are many wavelengths in size, due to the several Bragg layers or lattice periods that are required for maintaining high finesse. On the other hand, it has been demonstrated that the diameter of thick (λ0/n) micro-disk lasers can be reduced below their free-space emission wavelength [5]; however, the spatial spread of the resultant modes (which have low azimuthal numbers owing to the small disk diameters) into the surrounding space beyond the physical boundaries of the disks may lead to mode coupling and formation of “photonic molecules” in closely spaced disks [6]. For illustration purposes, an M = 4 WGM for a semiconductor disk with radius rc = 460 nm and height hc = 480 nm (Figure 1.1a) is shown in Figure 1.1b, clearly indicating the radiative nature of the mode and its spatial spread, which, as mentioned, can lead to mode coupling with nearby structures. (M is the azimuthal order of the resonance, corresponding to half the number of lobes in the modal plot of |E|.)

Figure 1.1 The M = 4 whispering gallery resonance for a thick semiconductor disk (a) is shown in (b) (rc = 460 nm, hc = 480 nm, and nsemi = 3.4). Note the spatial spread of the mode compared to the actual disk size. (c) The same disk encased in an optically thick (dm = 100 nm) gold shield will have well-confined reflective (d) and plasmonic (e) modes but with much higher mode losses. |E| is shown in all cases and the section plane is horizontal and through the middle of the cylinder. (From [7].). (Please find a color version of this figure on the color plates.)

One approach to alleviate these issues is to incorporate metals into the structure of dielectric cavities, because metals can suppress leaky optical modes and effectively isolate them from their neighboring devices. The modes in these metallo-dielectric cavities can be grouped into two main categories: (i) surface bound (that is, surface plasmon polariton (SPP)) resonant modes and (ii) conventional resonant modes (called photonic modes), resulting purely from reflections within the metal cavity. Although they are highly confined, the disadvantage of plasmonic modes is their high loss, which is caused by the relatively large mode overlap of the optical field with the metal (compared to the reflective case). Owing to the high Joule loss at telecommunication and visible wavelengths, the lasing gain threshold for such cavities can be very large. On the other hand, the negative permittivity of metals not only allows them to support SPP modes, but also enables them to act as efficient mirrors. This leads to the second class of metallo-dielectric cavity modes, which can be viewed as lossy versions of the modes in a perfectly conducting metal cavity. Because the mode volume overlap with the metal is usually smaller than in the plasmonic case, in a cavity supporting this type of mode it is possible to achieve higher resonance quality-factors (Q-factors) and lower lasing gain thresholds, albeit at the expense of reduced mode confinement (compared to plasmonic modes). In general, both types of modes can exist in a metal cavity. Embedding the gain disk mentioned earlier in a gold shield (Figure 1.1c) effectively confines the resonant modes while increasing Joule losses. As discussed, the surface bound plasmonic mode (Figure 1.1e) has both a higher M number and higher losses (M = 6, Q = 36) compared to the non-plasmonic mode (Figure 1.1d, M = 3, Q = 183). It should be noted that even though the metal shield is the source of Joule loss, the large refractive index of the semiconductor core (nsemi ≈ 3.4) aggravates the problem and increases both the plasmonic and Fresnel reflection losses. For SPP propagation on a (planar) semiconductor–metal interface, the threshold gain for lossless propagation is proportional to nsemi3 [8]. This means that, even though plasmonic modes with relatively high Q can exist inside metal cavities with low-index cores (for example, silica, for which n = 1.48), using this approach to create a purely plasmonic, room-temperature semiconductor laser at telecommunication wavelengths becomes challenging, due to the order of magnitude increase in gain threshold. However, plasmonic modes also have an advantage in co-localizing the emitters with the resonant mode volume, thereby leading to a more efficient emission into the lasing mode. This mode of operation is discussed further below, but at this point we focus on novel composite metal-dielectric resonators and the resonant modes that they support.

One possible solution for overcoming the obstacle of metal loss is to reduce the temperature of operation, which will have two coinciding benefits: a reduction of the Joule losses in the metal and an increase in the amount of achievable semiconductor gain. Hill and colleagues [9] have demonstrated cryogenic lasing from gold-coated semiconductor cores with diameters as small as 210 nm. However, in this case the metal is directly deposited on the semiconductor core (with a 10-nm SiN electrical insulation layer between). As a result, owing to the large overlap of the mode with the metal, the estimated room-temperature cavity Q is quite low. The best case is ∼180 for a silver coating (assuming the best reported value for the permittivity of silver [10]) which corresponds to an overall gain threshold of ∼1700 cm−1 and is quite challenging to achieve at room temperature. Even though this device lases when cooled to cryogenic temperatures, it would be challenging to achieve room-temperature lasing with the same approach and a similar sized cavity, owing to the constraints imposed by the amount of available semiconductor gain and the metal losses. The gain coefficient for optically pumped bulk InGaAsP emitting at 1.55 μm is reported to be ∼200 cm−1 [11]. Electrically pumped multiple quantum wells (MQWs), on the other hand, have been reported to have higher material gain coefficients of over 1000 cm−1 [12]. Furthermore, recent results obtained from Fabry–Perot type metallic nanolasers at room temperature indicate that this level of gain is also achievable in bulk InGaAs [13]. However, even if the required gain is achievable at room temperature, efficient operation of the device would still be a challenge because of thermal heating and nonradiative recombination processes (for example, Auger...