1. Introduction

In the last years new ways to manipulate the light-matter interaction were realized by modifying photonic components which confine light on its own wavelength scale by means of semiconductor microcavities (MCs) [1]. This research is motivated by the request to exploit cavity quantum electrodynamic phenomena, such as a strong enhancement of the spontaneous emission rate of quantum dots (QDs) coupled to a discrete mode of the MC (Purcell effect) [2] for efficient single-photon sources (e.g. Ref. [3, 4]) with controlled quantum states. Due to their importance in quantum optics they are attracting considerable interest.

However, for quantum information processing it is also crucial to control the polarization state of the emitted photons. This can be achieved by altering the shape of the micropillars, leading to a control of the photonic mode structure to some extent [5]. With this technique a polarized QD emission could be shown for elliptically shaped MCs in the III–V material system [3,6,7] as well as an increase of the quality factor for these structures due to the polarization dependence of the losses through the microcavity mirrors [8]. Furthermore, the coupling of microcavities that allows for photon transfer, which are referred to as photonic molecules (PMs), can form a basis for the interaction of spatially separated QDs. This is of high interest for the realization of entangled photons [9] generated by two QDs coupled via the delocalized optical field in such a PM. In addition, the mediating field can be used to exchange excitations between spatially separated QDs. This could be used as a read out technique for one QD by an other QD, while this process can be switched on and off by different spectral tuning methods. Furthermore, the efficiency of a single-photon source can be enhanced by the use of a PM [10]. Coupled microcavities were investigated in different arrangements such as microdisks [11], photonic crystal MCs [12, 13], and coupled pillar MCs structures [9, 10, 14, 15]. First investigations of the spatial modes distribution in PMs [10, 14] giving indications for their analogy to diatomic molecules [9] were reported.

These results have been achieved almost exclusively with the technologically well-developed (Al,Ga,In)As system. However, due to the comparatively shallow electron confinement in this system, the applicability of these structures is limited to low temperatures. In this contribution the properties of elliptically shaped pillars and PMs fabricated of ZnSe-based microcavities are presented. The utilization of this material system has the advantage of a high temperature stability of the emission for devices emitting in the blue to green spectral region. QDs being formed on base of the II–VI-compounds, for example, are characterized by large oscillator strength and pronounced temperature stability resulting in the realization of single-photon emission of CdSe QDs up to 200 K [16] and a high quantum efficiency for CdSe QDs with MgS barriers up to room temperature [17]. Furthermore, a green MC laser [18] has been demonstrated. Other reports treat MCs with dielectric Bragg mirrors [19] and ZnSe-based microdisk resonators with CdSe QDs embedded [20].

Here, we will report on the influence of the geometry of elliptical and coupled circular microcavity structures on their emission spectrum. Furthermore, detailed measurements on the spatial mode distribution will be compared to calculations showing the analogy to diatomic molecules.

2. Experimental details

The investigated structures are based on all-epitaxial planar MC samples grown by molecular beam epitaxy on a GaAs substrate. The ZnSSe λ-cavity layer contains either three ZnCdSSe quantum wells (QWs) or a single sheet of CdSe/ZnSSe QDs with an additional MgS barrier [21], grown by migration-enhanced epitaxy. This cavity is positioned between an 18.5-period bottom and a 15-period top distributed-Bragg-reflector stack, made of alternating layers of ZnS_0.06Se_0.94 (52.5 nm) and superlattices (32.5 periods) of MgS (1.5 nm) and ZnCdSe (0.5 nm). For details, see Refs. [22–24]. Single elliptically shaped pillar (QW-based sample) or coupled circular MCs (QD-based sample) were prepared from the planar cavity by focused-ion-beam (FIB) etching using a FEI Nova NanoLab system [24]. A micro-photoluminescence (μPL) setup has been used for the optical characterization of individual pillar structures with a continuous wave laser excitation at a minimum of the DBR reflectivity at variable temperatures. The PL emission was detected by a charged-coupled device camera after dispersion in a monochromator.

Information about the farfield emission pattern of the pillar structures can be achieved by μPL measurements. With this setup the sample surface is imaged on the entrance slit of the spectrometer yielding a spectrally resolved quasi one-dimensional cut of the farfield at the position of the CCD array detector. A two-dimensional cross sectional map is constructed for each emission energy by combining the 1D profiles corresponding to the cut through the farfield, each one of them obtained at a different imaging position along the direction perpendicular to the one for which the 1D profile is measured.

In the inset of Fig. 1 a) the SEM image of an elliptically shaped MC with axis lengths of 3.9 μm (a) and 2 μm (b) is exemplarily shown together with its emission spectra. The measurement was performed at T=4 K for orthogonal polarizations defined as 0° and 90° by polarizer settings in the detection beam path parallel to the long or short axis of the ellipse, respectively. For this structure a Q-factor of 7900 is determined. A clear energy separation of the fundamental mode (FM) (amounting to 0.3 meV for an ellipticity factor of ε = ((a – b)/b + 1)^0.5 – 1 = 0.4 [25]) for both polarizer orientations is observed with a nearly 95% polarized light emission (polarization degree P = (I_max – I_min)/(I_max + I_min)). Respective energy separations occur for the higher-order modes. This is caused by the spatial asymmetry of the elliptical pillar which lifts the polarization degeneracy. For the FM, this results in a splitting into two modes with an energy separation of up to 4.5 meV (ε = 0.8) and with orthogonally oriented polarization. For the optical active layer of the MC emitting in such a resonator mode the detected PL intensity is selected by the polarizer orientation due to the polarization of the mode. This yields, e.g., a polarization degree of 83% for the emission a CdSe QD being in resonance with the cavity mode [26]. In Fig. 1 b) the polarization splitting of the fundamental mode is shown in dependence on the ellipticity of the investigated structures. With increasing ellipticity a rising split can be measured, as expected because of the increased assymetry of the geometry. The polarization splitting of the fundamental mode energy ΔE can be calculated following Ref. [25]:

 

Fig. 1 (a) Spectra of an elliptical pillar for orthogonal polarizer orientations at T=4 K (ε = 0.4) showing the mode splitting. Inset: SEM picture of an elliptical pillar. (b) Measured and calculated fundamental mode splitting for structures with different ellipticity factors. (c) Influence of the ellipticity on the quality factors (Q) for both polarization directions (data points) in comparison to the fitted variation (solid line).

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In Fig. 1 c) the Q-factor of the fundamental mode for both polarizer orientations is plotted versus the ellipticity, whose increase results in a decrease of Q. Although the quality factors should, in principle, reach higher values compared to circularly shaped MCs [8], this was not seen in the experiment. A different FIB-structuring routine was needed for milling such asymmetrically-shaped pillars which causes higher sidewall roughnesses resulting in the observed reduction of Q. This influence on the Q-factor is approximated as outlined in Ref. [27] for a circular geometry, implementing the increased surface roughness with rising ellipticity in the scattering losses:

In Fig. 2c) the PL spectrum of the elliptically shaped pillar for a polarizer orientation of 90° is shown together with the two-dimensional (2D) spatially and spectrally resolved cross section maps of the modes emission (Fig. 2 b)). The emission is detected from the top of the pillar at the energy position corresponding to the seven lowest-energy optical modes, enabling direct visualization of the mode structure (only one polarization component is shown). The top row (Fig. 2 a)) displays the calculated transverse electric-field patterns of the modes. Simulations were performed by ab initio calculations of the mode distribution for periodic dielectric structures by using the MPB (MIT) package [28]. An overall good agreement between the calculated and measured mode distributions is obtained, comparable to the findings in Ref. [29] for the III–V material system. While for the FM the field maximum is positioned in the center of the structure, the higher order modes, with their larger number of field maxima, are orientated along the elongated axis of the structure.

 

Fig. 2 (c) and (d) show the PL spectrum of the elliptical MC (polarizer orientation of 90°) and the PM (CC=1.9 μm, unpolarized). In rows (b) and (f) the corresponding measured 2D spatial distribution of the resonator modes is displayed. The emission is detected from the top of the structures and the mode order increases from left to right. The lines (a) and (e) show the calculated transverse electric-field patterns of the modes.

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The unpolarized spectrum of a photonic molecule built up of two connected circular pillars which possess a diameter of 2.8 μm each and have a center-to-center (CC) distance of CC=1.9 μm is shown in Fig. 2 d) together with the measured f) and calculated e) 2D maps of their optical field distribution. The FM consists of two components with an energy separation of 1.8 meV. Each mode component has a slightly broader spectral width in comparison to the ellipse. Beside the sample quality at that positions, this might be due to a detected small polarization splitting (≈ 200μeV) of the modes I and II. This was already observed for circular shaped QD-based MCs [30] caused by a local strain induced refractive index difference within the sample. Comparing the maps of the PM and the elliptical pillar, one observes a high correlation between the modes with respect to their shape and their progression. Taking now a closer look at the recorded spectra for the PM and the elliptical structure one can see comparable signatures for the labeled PL bands, except for the energy splitting between the modes being reduced for the PM.

To elucidate the energy splitting between the resonator modes several photonic molecules were produced with different center-to-center distances (CC) between the two circular pillars which possess a diameter of 2.8 μm each. For CC=3.5 μm the pillars are connected by a small bar. In Fig. 3 a) an SEM image of such a photonic molecule is shown. All measurements were performed under excitation into the center of the PM. The resulting PL spectra exhibiting several modes are presented in Fig. 3 b) for different CC distances in comparison to a circular pillar MC with a diameter of 2.7 μm. For the structure with a CC=1.9 μm distance the FM possesses the already mentioned energy splitting of 1.8 meV as well as a larger splitting for the higher order modes. This spectral splitting decreases with increasing distance of the individual pillars. Thus, at a CC distance of 2.6 μm the value is reduced to 0.7 meV. Going onwards to a CC=3.5 μm the modes I and II are superpositioned to each other and the detected spectrum is strongly approaching the purely circular pillar MC as presented at the top of the graph. This trend for the FM and the higher order modes is indicated by the dotted lines as guides to the eye in the figure. The higher-order modes were assigned by their spatial mode profile. As a consequence of the overall observations, the reduction of the CC distance results in a distinct coupling of the optical field of the individual pillars [9,10]. Polarization resolved measurements on these PM structures revealed a polarization splitting of the modes in the order of 200 μeV. This value is much smaller in comparison to our findings for the elliptical structures, indicating that no pronounced lifting of the polarization degeneracy occurs for the PM structures.

 

Fig. 3 (a) SEM picture of a photonic molecule. The circular pillars have a diameter of d=2.8 μm and are connected by a bar (0.64 μm length and 0.53 μm width). (b) PL spectra of PMs with different center-to-center (CC) distances in comparison to a circular pillar all recorded at T=4 K. The dotted lines are guides to the eye. (c) Calculated coupling strength between distinct resonator modes.

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In Ref. [9] this splitting of the resonator modes was discussed in analogy to a diatomic molecule, in which the interaction of the two atoms results in a splitting of the degenerate atomic levels into bonding and antibonding orbitals. By comparing the measured and calculated 2D maps of the resonator modes with the well known molecular orbitals one can assign the binding (one maximum, I) and antibinding (two close lying maxima, II) s-state, the symmetric and antisymmetric orbitals of the p-state in σ (III, V) and π (IV, VI) configuration as well as indications for the d-state.

Comparable to diatomic molecules, the energy splitting of the degenerate states depends on the overlap of the electron wavefunctions, respectively the optical field. This explains the decrease of the energy splitting with increasing CC distance for the photonic molecules, because the overlap depends on the channel length and width, as discussed in Ref. [9] for MCs and in Ref. [12] for photonic crystals.

On the other hand the optical field of the modes of the two PM pillars can be treated like two coupled oscillators. Hence, the photonic splitting of the coupled-cavity modes can be expressed by $\Delta E=\sqrt{{\delta }^2+4g^2}$ where δ is the energy detuning between the uncoupled pillar MCs and g is the coupling strength of the modes [12,31]. By deducing the coupling constant from the energy splitting (the detuning is neglected), as expected a clear decrease of the coupling constant from 0.75 meV for CC=1.9 μm down to 0.25 meV for CC=2.6 μm is observed for the fundamental mode (see Fig.3 c)). The higher-order modes show a coupling constant being about a factor of three larger, probably due to their larger optical field overlap. When calculating the coupling constant for an elliptical structure with comparable dimensions the value of the energy splitting observed for the FM is about a factor of two larger in comparison to the PMs. This can be explained by the reported decrease of the coupling strength with decreasing channel width between the two resonators [9]. Because this channel is much wider for an elliptical pillar in comparison to the PMs the coupling of the resonator modes within the elliptical structure is stronger. Thus, for both type of structures the desired delocalized modes can be realized. Moreover, the elliptical structure shows a larger energy separation between the localized binding FM and the delocalized antibinding state of 3 meV. In addition, the elliptically-shaped MCs exhibit a pronounced polarization splitting of the resonator modes in contrast to the PMs, giving the possibility to control the polarization of the emitted photons.

3. Conclusion

In conclusion, three-dimensionally confined optical modes were investigated in ZnSe-based monolithic microcavities with elliptical shape or build of two coupled circular pillars forming a photonic molecule. Their two dimensional spatial mode maps were comparably discussed with the calculated distribution. For both geometries delocalized modes were observed showing comparable signatures to the orbitals of a diatomic molecule. This analogy was up to now only reported for photonic molecules. The realization of such delocalized modes in elliptically shaped structures is of considerable importance, as they are favorable for controllable interaction of QDs at different positions within the microcavity. In addition, the elliptically-shaped MCs would give the possibility to control the polarization of the emitted photons.