We report on the design and experimental demonstration of a system based on an L3 cavity coupled to a photonic crystal waveguide for in-plane single-photon emission. A theoretical and experimental investigation for all the cavity modes within the photonic bandgap is presented for stand-alone L3 cavity structures. We provide a detailed discussion supported by finite-difference time-domain calculations of the evanescent coupling of an L3 cavity to a photonic crystal waveguide for on-chip single-photon transmission. Such a system is demonstrated experimentally by the in-plane transmission of quantum light from an InAs quantum dot coupled to the L3 cavity mode.
©2012 Optical Society of America
Single photons are considered excellent candidates for carriers of quantum information due to their immunity to decoherence . A breakthrough in 2001 showed that it is possible to realize scalable quantum computing by using only single-photon (SP) sources, beam-splitters and SP detectors, without the need of any optical nonlinearity . Remarkable experiments have been performed with single or entangled photons created by laser pumping of nonlinear crystals [3,4]. However, for future implementations of quantum information processing on a semiconductor chip, an integrated, on-demand SP source is highly desirable. Indeed, devices with high out-of-plane SP emission efficiency using semiconductor quantum dots (QDs) as quantum emitters have been demonstrated [5–8], proving the potential of these systems.
For on-chip quantum information processing using quantum light, efficient transmission and control of the photons is desired. Systems based on photonic crystal (PC) structures are very promising since one can tailor their optical properties by a careful design. PC structures consist of a periodic array of materials with different refractive indices, which gives rise to a photonic bandgap within a certain frequency range . Interestingly, by introducing defects in the crystals, it is possible to create optical cavities with extremely high Q-factors and small modal volumes [10,11] as well as waveguide structures with low-loss optical transmission . Both these systems can be exploited for on-chip quantum information purposes: two-dimensional PC slab cavities have been used to increase the spontaneous emission rate of an exciton in a coupled QD through the Purcell effect [13–15] and waveguide structures have been used to transmit single photons along the semiconductor plane . Since the Purcell enhancement of the excitonic recombination in a QD leads to higher SP emission rates and improved photon indistinguishability, it is important to incorporate two-dimensional nanocavities coupled to PC waveguides for more efficient creation and transmission of quantum light along the chip plane. The importance of such a system in future photonic quantum circuits has been highlighted in earlier works [17,18].
In this work, we demonstrate a system comprising a L3 cavity coupled to a PC waveguide through evanescent coupling. By careful design, we achieve the coupling of a single QD to the fundamental mode of the L3 cavity and the subsequent transmission of SPs through the waveguide structure. A detailed theoretical analysis of the system is presented, supported by optical characterization experiments. Two major results are presented: first, we report for the first time the experimental observation of the complete set of confined modes within the photonic bandgap of a stand-alone L3 cavity. Second, we demonstrate the in-plane transmission of quantum light emitted from a QD coupled to an L3 cavity. Our findings highlight the potential of this system as a building block in future optical quantum circuits.
2. Mode structure of the stand-alone L3 photonic crystal cavity
The L3 cavity consists of three missing holes along a line in photonic crystal slab with a hexagonal lattice. A top view SEM image of such a defect cavity surrounded by 10 periods of the photonic crystal is shown in Fig. 1(b) . Figure 1(a) shows the corresponding mode structure of this cavity as calculated with the finite-difference time-domain technique. Within the photonic band-gap of the two-dimensional photonic crystal, the L3 cavity supports five different modes labeled M0 through M4 in order of decreasing normalized wavelength. The calculated mode structure is used as a reference for the experimental investigation, described below.
Our samples were grown by molecular beam epitaxy on an undoped GaAs (100) substrate. Self-assembled InAs QDs grown in the Stranski-Krastanow regime were embedded in the middle of a 200 nm thick layer of GaAs. Below this GaAs layer, a 900 nm thick layer of Al0.75Ga0.25As was grown and served as the sacrificial layer for the slab formation. The PC structures were written into a resist layer (ZEP520A, Zeon Corp.) by 100 kV electron beam lithography. The pattern was transferred directly to the wafer by inductively coupled plasma reactive ion etching (ICP-RIE) using a gas mixture of SiCl4 and Ar. Subsequently, the Al0.75Ga0.25As layer was selectively etched by dilute hydrofluoric acid to form the suspended PC slab. Micro-photoluminescence experiments were carried out at 5 K in a continuous-flow liquid helium cryostat. The spot from a continuous-wave helium-neon laser (at 633 nm) was focused by a 50X microscope objective (numerical aperture NA = 0.4) onto the top of the L3 cavity. Emission from the top of the device was collected with the same objective, dispersed by a single-grating spectrometer and recorded by a charge-coupled device camera.
In Fig. 1(c) we present measurements of how the mode structure depends on the lattice constant of the photonic crystal for a L3 defect cavity. The experimental values of the emission wavelength of each mode were extracted using Lorentzian functions. The wetting layer and the ensemble of medium-density quantum dots were used as an internal light source, emitting in a spectral range from approximately 860 nm to 895 nm (indicated by the hatched area in Fig. 1(c), lower panel). However, since the five modes of the L3 cavity span over a spectral range of about 200 nm in the devices used here, it is not possible to observe all five modes simultaneously in one device with this technique. Therefore, the modes were spectrally tuned through the observable wavelength window by fabricating a large number of L3 cavities with lattice constants a ranging from 190 nm to 290 nm. The solid discs and open circles in the lower panel of Fig. 1(c) represent the experimental and calculated spectral positions of the different modes, respectively. The device parameters for the simulation process were extracted from an SEM image analysis (normalized hole radius of r/a = 0.312, constant nominal slab thickness d of 200 nm). The generally reasonable agreement between experiment and simulation as well as the fact that all possible modes within the photonic band gap were observed systematically allows for an unambiguous assignment of the experimentally observed to the theoretically predicted modes M0 - M4. To the best of our knowledge and despite earlier attempts [19,20], this is the first time that the complete mode structure of the L3 defect cavity was observed experimentally.
The experimentally observed emission wavelengths tend to be slightly blue-shifted with respect to the simulated ones for all modes, which has been shown to be attributable to local-field perturbations at the gallium arsenide – air interface due to fabrication imperfections . Notably, modes M2 and M4 are particularly affected, which suggests that the spectral position of these modes is more sensitive to these perturbations. The theoretically predicted inverse proportionality between the blue shift and the modal volume  cannot be responsible for this observation since the calculated mode volumes of the modes M2 and M4 are the smallest and largest, respectively, among the five modes supported by the L3 defect cavity. However, an analysis of the mode profiles shows that the electric field components of the modes M2 and M4 have their maxima close to the gallium arsenide – air interface (see Fig. 2 ), making them particularly sensitive to imperfection-induced local-field perturbations at these interfaces. The larger blue shifts for these modes are therefore attributable to their particular mode profiles rather than to their mode volumes.
The upper panel of Fig. 1(c) shows the experimental Q-factors of the observed modes. As a general trend, experimental Q-factors decrease with increasing mode number from exceeding 3000 for mode M0 to about 160 for mode M4. The comparison of the mean of the experimentally observed Q-factors with the simulated Q-factors for the ideal structures in Table 1 shows that for all modes, the experimentally achieved Q-factors are significantly lower than predicted theoretically. This is attributed to surface recombination at the GaAs-air interface, scattering due to deviations from the ideal structural characteristics such as non-vertical and rough side walls, and size-, shape- and position disorder of the holes  as well as to absorption by the active layer. The mode volumes for the five modes supported by the L3 cavity are also given in Table 1, and are around 0.8 cubic wavelengths for all modes with the notable exception of mode M4, for which it is 1.11 cubic wavelengths.
A figure of merit for the efficient coupling of an emitter with a cavity mode is the Purcell factor FP, which is proportional to the Q-factor over the modal volume ratio. From Table 1, it is clear that the most promising mode for this coupling is M0. Another important factor is the mode profile, which should exhibit the field maximum at the centre of the cavity, as far as possible from any gallium arsenide – air interfaces. This is because surface defect states can be optically absorbing (or scattering) and offer competing non-radiative pathways, which would limit experimentally attainable Q-factors. Furthermore, QDs need to be placed at the field maximum in order to obtain maximum Purcell enhancement. Since the proximity of quantum dots to gallium arsenide - air interfaces degrades their optical properties, modes with the field maximum close to such interfaces are not desirable [23,24]. As seen from Fig. 2(b), the mode profile for the Ey component (see Fig. 2(a) for axis definition) of the target mode M0 shows electric field maxima at the center of the cavity, in contrast with modes M2 and M4, for example.
We followed a procedure presented previously  in order to further optimize the Purcell factor we can obtain from an emitter coupled to the M0 mode. Critical parameters that need to be optimized are the hole radius r, and the shifts of the nearest neighboring holes A, B and C, as indicated in the sketch in Fig. 2(a). In the latter case, the corresponding increase in the mode’s Q-factor is attributed to phase-matching of the partial Bragg reflections at the photonic crystal mirrors by smoothing the envelope function of the electric field profile at the cavity edges . We performed detailed simulations and we found that the highest Q-factor and smallest modal volume for the mode M0 is obtained for an L3 cavity with hole radius of r = 0.315a and with first, second, and third hole shifts of A = 0.18a, B = 0.01a, and C = 0.16a, respectively.
3. Coupling of the L3 cavity to a PC waveguide
A fundamental requirement for the coupling of a cavity to a waveguide is the existence of a guided mode in the waveguide at the resonant frequency given by the cavity. The left panel in Fig. 3(a) shows the dispersion relation of a W1 waveguide (one line of missing air-holes) in the hexagonal lattice of a two dimensional photonic crystal slab, as simulated with the plane-wave expansion technique. Within the photonic band gap and below the light cone, a number of guided modes are present. The right panel in Fig. 3(a) shows the mode structure of an L3 defect cavity in a photonic crystal slab characterized by the same fundamental parameters. As described in the previous section, an optimization procedure was performed to allow for the highest Q/Vm-ratio for mode M0. The y-scales of the plots in both panels of Fig. 3(a) are identical, and the red dashed lines serve as a guide to the eye, indicating that a simple W1 waveguide exhibits a guided mode at the frequency of the mode M0 of the L3 defect cavity. We note that at this frequency, the corresponding guided mode in the W1 exhibits a relatively low dispersion, or equivalently a low group velocity. This improves the coupling between a cavity and a waveguide mode due to a longer interaction time , but it also increases losses in the photonic crystal waveguide due to optical scattering, which scale inversely with the group velocity . For future designs of larger photonic circuits with photonic crystal waveguides, it would therefore be advantageous to optimize the dispersion in different parts of the waveguide by tailoring its design. Since only a short portion of a waveguide was used in the devices studied here, however, such a procedure was not required.
In order to obtain efficient coupling between the cavity and the waveguide modes, a good matching between their field patterns and their parities is required . Figure 3(b) shows the modes’ field patterns at the frequency given by the mode M0 of the L3 cavity for the Ey, field component. The right panel shows the mode profile in an optimized L3 defect cavity, and the left panel the one for a W1 waveguide in a photonic crystal slab characterized by the same parameters. The corresponding field patterns exhibit not only same parity, but indeed very similar field patterns. This striking similarity can be understood if the L3 defect cavity is viewed as Fabry-Perot resonator in a short W1 waveguide terminated at both ends with matched photonic crystal mirror . In terms of field patterns and their parity, the M0 mode of the L3 cavity and the corresponding W1 waveguide mode are hence ideally suited for coupling.
For evanescent coupling, the L3 defect cavity and the W1 waveguide are brought into proximity, separated only by a few unit cells of the photonic crystal lattice. To this end, different geometries have been studied experimentally, including side-coupling the L3 cavity to the waveguide  or tilting the L3 cavity by 60° with respect to the waveguide axis . In order to obtain efficient coupling to a unidirectional waveguide, we study devices with a straight cavity configuration, in which the L3 cavity and the W1 waveguide share the same axis (see Fig. 3(b)). Figure 4(a) shows the simulated Q-factor of the mode M0 of the L3 cavity as a function of cavity–waveguide separation. As expected, the Q-factor of the cavity mode decreases as the waveguide is brought into close proximity due to the coupling to and energy transfer into the waveguide. The resulting Q-factor of the coupled cavity, Qcpl, relates to the Q-factor of the uncoupled cavity, Qcav, as Figure 4(a) (right axis) shows the corresponding coupling strength Γ as a function of the cavity – waveguide separation. For separations of four or more unit cells, or holes, the coupling strength is negligible, but it increases strongly for three, two, and one holes. For an efficient Purcell-enhanced quantum emitter, there is therefore a trade-off between high Q-factors of the coupled cavity mode and efficient coupling of single-photons into the waveguide. Since Qcpl for a separation of one unit cell is very low even for the ideal structure simulated here and Γ becomes negligible for separations exceeding three unit cells, we restrict our study only to devices with cavity – waveguide separations of two and three unit cells.
Similar to the experiments with stand-alone L3 defect cavities described above, devices with a small range of lattice constants were fabricated such that the expected spectral position of the mode M0 of the coupled L3 cavity covers the emission range of the wetting layer and medium-density QDs. For characterization, we performed micro-photoluminescence experiments, in which the samples were excited optically from the top and the in-plane emission was collected from the exit of the waveguide, at 90° with respect to the excitation . Although this technique is powerful for the determination of the cavity mode structure, it does not allow for a direct study of the coupling strength since the detected emission intensities vary strongly from device to device due to the random nucleation of QDs.
Figure 4(b) compares the experimentally observed Q-factors for devices with cavity – waveguide separations of two and three holes, but otherwise nominally identical structural parameters. Q-factors of the M0 mode of the coupled L3 cavity are extracted from the recorded spectra by Lorentzian fitting. While Q-factors generally scatter around 3000 for the sets of devices studied here, devices with lattice constants below 226 nm exhibit markedly lower Q-factors due to the spectral overlap of the mode M0 with the wetting layer for these lattice constants. That results in a degradation of Q-factors due to increased absorption in the slab material . For a > 226 nm, the mean Q-factor is found to be 2720 ± 750 for devices with a cavity – waveguide separation of two holes and 3200 ± 890 for those with a separation of three holes. The mean values therefore are consistent with the decrease in coupled cavity Q-factors with decreasing cavity –waveguide separation that is predicted by the simulated results shown in Fig. 4(a). However, the substantial deviation of the experimentally observed Q-factors from the simulated Qcpl, in particular for the devices with three holes separations, suggests that these Q-factors are not limited by radiation losses into the waveguide but rather by systematic fabrication imperfections. Moreover, experimentally observed Q-factors exhibit considerable scatter for both types of devices, which in turn is due to random fabrication imperfections. In view of this scatter and since the lower coupling strength Γ for devices with a cavity–waveguide separation of three holes is not accompanied by drastically higher Q-factors as theoretically expected, the device design with a separation of two holes is preferable for current fabrication techniques. Figure 4(c) shows the mode profile of a complete waveguide-coupled L3 defect cavity with a separation of two holes for the Ey, field components. The mode profiles closely resemble those for the individual component of the device presented in Fig. 3(b), but the relative field intensities in the cavity and waveguide areas show that light is confined much more strongly in the cavity area, and only slowly leaks into the waveguide, resulting in relatively lower field intensity in the waveguide area.
New samples with two-hole separation between the cavity and the waveguide were fabricated with lower QD density in order obtain L3 cavities containing few QDs. The fabrication process was re-calibrated by using the actual device parameters extracted from the previous run in order to achieve better agreement with the desired optimized values. Figure 5(a) shows the emission wavelength and the corresponding Q-factor of the M0 mode extracted from spectra collected from the waveguides’ exit (in-plane). We observe an increase of the Q-factors compared to the previous set of devices, with a mean of 3440 ± 920, significantly larger than mean values for sets of similar devices reported previously (in out-of-plane and indirect in-plane experiments) [30,31]. In fact, the device with a lattice constant of 231 nm (the corresponding data points are marked with a yellow circle in Fig. 5(a), spectrum shown in Fig. 5(b)) exhibits a Q-factor of 5150, which is, to the best of our knowledge, the highest reported value for a device with a straight cavity-waveguide configuration.
4. On-chip single-photon emission from an L3 cavity - waveguide system
Devices containing a small number of QDs in the active region allow for the study of the coupling of a single quantum emitter to the confined mode in an L3 cavity. For the transmission of quantum light along the chip plane, a photo-excited QD in the L3 cavity region is used as the SP source. Coupling of the QD with the target cavity mode (M0) induces Purcell-enhanced SP emission rates and photons are injected into the waveguides’ propagating mode and transmitted along the plane. An illustration of the process and an image of a fabricated device are shown in Figs. 6(a) and 6(b), respectively. The device under study here has a lattice constant of a = 226 nm and image analysis revealed an r/a of 0.329. The spectrum of the in-plane emission (recorded again from the exit of the waveguide) is shown in Fig. 6(c) and exhibits emission from the wetting layer that extends to about 875 nm. A number of transitions stemming from different QDs (or different electronic configurations in the same QD) are apparent in the low-energy part of the spectrum. The transition of interest is marked with an arrow in Fig. 6(c) at 894.2 nm. Figure 7(a) shows the evolution of this part of the spectrum with increasing temperature from T = 5 K to T = 37 K. While the transition is approximately in resonance with the mode M0 in a temperature range from 5 K to 30 K, it clearly tunes out of resonance for higher temperatures. The spectral location of the experimentally observed M0 mode at about 894.2 nm is in reasonable agreement with the corresponding simulation, which predicts the mode to be at a wavelength of 904.8 nm for these structural parameters. The deviation is comparable to those observed in the discussion of the stand-alone L3 defect cavity in the previous section and equally attributed to local-field perturbations at the gallium arsenide – air interface due to fabrication imperfections. A Lorentzian fit of the spectrum at T = 37 K reveals a Q-factor of 3100 for the mode M0. Considering the calculated volume for this mode, the estimated Purcell factor for perfect QD-cavity mode spatial matching is ~290.
The temporal evolution of the photoluminescence signal of the transition at different temperatures is shown in Fig. 7(b). In this case, the sample was excited by a pulsed diode laser emitting at 780 nm with pulse duration and repetition rate of 400 ps and 80 MHz, respectively. Again, the signal was collected from the exit of the waveguide. Off-resonance, at T = 37 K, the lifetime was found to be τ = 2.4 ns. At lower temperatures, as the transition tunes into resonance with the mode of the L3 defect cavity, the lifetime decreases to 1.7 ns and 1.4 ns for T = 34 K and T = 30 K, respectively. The lifetime measured off-resonance is relatively long compared to excitonic transitions in QDs in an unprocessed part of the sample . This suppression of the spontaneous emission rate is due to the decrease of the local density of optical states at energies far from the confined mode in PC cavities. By contrast, the enhancement of the spontaneous emission rate when the transition is spectrally matched with the mode (by decreasing temperature) reflects the higher density of available optical states. This is a direct indication of the coupling of the QD to the cavity mode and the resulting Purcell effect. The rather moderate enhancement of the emission rate is attributed to the poor spatial overlap of the emitter with the electric field maximum of the cavity mode.
Using a Hanbury-Brown and Twiss set-up , we studied the photon statistics of the transition at T = 5 K, i.e. in resonance with the M0 mode. At the autocorrelation experiment we observed clear single photon emission, with a value for the second order correlation function g(2)(t = 0) ~0.4 (see inset in Fig. 7(b)). The deviation from a perfect single photon source (g(2)(0) = 0) is mainly attributed to the far off-resonant coupling of emission into the cavity mode . Resonant excitation schemes have been shown to suppress this far off-resonant coupling and to lead to essentially background-free single photon emission .
An in-depth discussion and experimental study of the complete mode structure of the L3 defect cavity was presented. The entire mode structure was observed experimentally for the first time, with reasonable agreement between experiment and the accompanying simulations. The mode M0 was identified to be attractive for the Purcell enhancement of radiative recombination of excitonic states in quantum dots and well suited for coupling to a W1 waveguide for on-chip light extraction. This coupling was first studied theoretically and the most promising configurations were studied experimentally. The systematic design process led us to the demonstration for the first time of a cavity-enhanced on-chip single photon emission in a waveguide – coupled L3 defect cavity. Our findings indicate that such a system can be an important component in future optical quantum circuits where integrated quantum light sources with high emission rates and on-chip waveguiding are required.
This work was partly supported by the EU through the Integrated Project Q-ESSENSE (contract no. FP7/2007–2013). A.S. acknowledges financial support from EPSRC, Cambridge European Trust, Kurt Hahn Trust, Thomas-Gessmann Stiftung, and the Richard-Winter-Stiftung. We thank K. Cooper and M. Tribble for help with the device processing and A. J. Bennett for discussions.
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