We demonstrate highly efficient evanescent coupling via a silica loop-nanowire, to ultra-small (0.5 (λ/n)3), InAs/InP quantum dot photonic crystal cavities, specifically designed for single photon source applications. This coupling technique enables the tuning of both the Q-factor and the wavelength of the cavity mode independently, which is highly relevant for single photon source applications. First, this allows for the optimization of the extraction efficiency while maintaining a high Purcell factor. Second, the cavity mode can be matched with a spectrally misaligned quantum dot without changing the structure or degrading the Q-factor: a 3 nm resonance shift is reported.
©2007 Optical Society of America
Single semiconductor quantum dots (QDs) have attracted much attention this last decade because of their atom-like emission at telecom wavelengths. Not only do they have the potential to emit triggered single photons one at a time [1–4], but they can be embedded into solid-state, three-dimensional microcavities  that are capable of channelling the single photon emission. The resulting QD-microcavity combination promises to provide efficient single photon sources (SPS) at telecom wavelengths; a key enabler for optical fiber-based quantum key distribution (quantum cryptography) and quantum information processing [6–8]. The practicality of such sources depends crucially on the degree to which the photons can be efficiently extracted, a process which, as pointed out by Gerard et al , can be addressed by (a) redirection of the QD emission into a single cavity mode and (b) efficient extraction of the photons that are in the cavity mode to the outside world.
In addressing point (a), one notes that microcavities can funnel a large fraction (β) of the spontaneous emission (SE) of an emitter into the available cavity mode, potentially enhanced [10–12] by the well-known Purcell factor Fp, which is proportional to the ratio Q/V for the mode, where Q and V are the quality factor and the effective mode volume respectively. The Purcell factor actually represents the maximum possible enhancement of the QD SE rate into the cavity mode. Achieving this maximum requires precise matching of the QD emission characteristics and its spatial location relative to the cavity mode. Many efforts are currently devoted to the realization of QD-microcavity systems that fill those conditions through sophisticated fabrication process [10, 13–15]. For coupling the cavity mode to the outside world, point (b) above, there are two main strategies: one can either collect part of the intrinsic optical losses of the mode using collection optics with limited numerical aperture, or alternatively introduce an additional channel of escape to the photons. The appropriate coupling strategy to maximize the collection efficiency is highly dependent on the characteristics of the cavity mode that the emitter is coupled to . SPS based on micropillar or VCSEL-type cavities [17, 18, 3] offer a natural direct “end-fire” coupling along the cavity axis because of their highly directive emission radiation. On the other hand, two dimensional (2D) photonic crystal (PhC) membrane based cavities can provide modes with far more attractive Purcell factors by introducing a carefully designed defect into the PhC [19–22]. However, achieving a higher Q/V is generally accomplished to the detriment of the directionality of the emission, making the intrinsic optical losses of these modes much more difficult to collect.
By introducing an additional output channel close to the cavity, evanescent coupling via silica nanowires provides an alternative fiber-based technique to end-fire coupling. Because this approach usually requires precise matching of the nanowire mode to the probed optical modes, it has initially been used to probe “whispering-gallery-mode”-type cavities [23, 24]. PhC cavities that have been interrogated so far with this method have been largely restricted. The first realization of tapered fiber nanowire coupling to a wavelength-scale PhC microcavity was recently reported . However, the graded square lattice design involved in those experiments would not allow efficient coupling with a single quantum emitter. More recently , evanescent coupling via a nanowire taper to simultaneously pump a PhC microlaser and to collect its light emission has been reported. This demonstration used an “elongated” cavity, specifically tailored to optimize the phase matching between the nanowire taper and the microcavity.
In this work, we demonstrate efficient evanescent coupling to ultra-small (0.5 (λ/n)3) high Q PhC cavities, via a tapered silica fiber nanowire. The cavity has been specifically designed and realized for SPS applications and exhibits modes with a high Purcell factor. We show that the cavity-nanowire system displays unique properties that are especially relevant to SPS applications. This system provides a flexible and non-invasive approach to tune both the Q and the resonance wavelength of the cavity mode. Firstly, this approach allows one to adjust the coupling strength in order to achieve an optimized extraction efficiency while maintaining a high Purcell factor. Secondly, the coupling technique can also tune the cavity wavelength in order to match it to the QD emitter wavelength, enabling an actual SE rate enhancement via the Purcell effect. In section 2, we first present the design, fabrication and characteristics of the ultra-small, 0.5 (λ/n)3, single-defect, InAs/InP QD photonic crystal cavities emitting around 1.55 μm. In section 3, we describe the realization of tapered silica nanowires specifically fabricated into a tight loop and the principle of the evanescent coupling technique. Section 4 highlights the experimental transmission results that have been obtained with the cavity-nanowire coupled system and includes a demonstration of the tuning of the cavity wavelength (>3 nm) with this method. Finally, in section 5, we discuss the potential of this technique for SPS applications, focusing mainly on the analysis of the extraction efficiency.
2. Cavity design and device fabrication
The set of cavities investigated is a modified missing-hole defect in a hexagonal lattice . A typical scanning electron microscope (SEM) image of the defect microcavity studied is shown in Fig. 1(a): it consists of one hole removed that is successively surrounded by one ring of modified holes, followed by 19 rings of holes.
The basic heterostructure used in this study was grown by chemical beam epitaxy (CBE) on a semi insulating InP(001) substrate. It is comprised of one self-assembled InAs QD layer in the middle of a 293 nm thick InP cladding layer that is grown on top of an InGaAs sacrificial layer. The QD growth conditions have been optimized to ensure that the generated photoluminescence (PL) displays an emission peak around 1.55 μm at room temperature. The PhC structure is then realized by a combination of electron beam lithography and inductively coupled plasma (ICP) etching. The final wet-etching of the InGaAs layer releases the InP membrane around the PhC structure, to create a PhC suspended microcavity. Full details of the fabrication process and cavity design can be found in .
For this 293 nm thick InP membrane, with a refractive index n of 3.17, a period a of 440 nm and a hole radius r of 130 nm have been chosen as the PhC parameters in order to open up a photonic band gap around 1550 nm. Such cavities give rise to donor-type defect modes with optical field antinodes in the high index material, as displayed on Fig. 1(b), suitable for coupling to the embedded QD active medium.
Room-temperature PL measurements were made with HeNe excitation at 632.8 nm in order to extract the intrinsic Q-factor of the cavities. Excitation and collection were performed through the same large numerical aperture objective (NA=0.55) with a spot size of 2 μm. In-plane optical modes generated in the PhC microcavity undergo out of plane losses at the cavity boundaries: those losses are collected in the direction normal to the surface and spectrally analyzed. We focused on a particular set of cavities for which the fundamental mode appears within the range of interest for fiber-based SPS applications (around 1550 nm). Figure 2 shows PL spectra for a set of 3 cavity structures with nominally identical parameters. The curves are offset for clarity. Each spectrum displays several peaks corresponding to resonant modes in the cavity. The Q-factors of the primary cavity mode [see Fig. 2(b)], as determined from the linewidth of the PL peaks, range from 2000 to 2900. Theoretically, Q-factors above 40000 are possible in these cavities , together with modal volumes V of ~ 0.5 (λ/n)3, where
The corresponding Q/V-ratios of the probed cavities range between 4000 and 5800 [(λ/n)3]-1, which is around twice  and four times [28, 29] lower than the best Q/V ratios demonstrated with photonic crystal structures including QDs. Actually, the variation in Q-factor and resonant frequency, together with the overall, relatively low size of the Q-factors, demonstrate the extreme sensitivity of these modes to fabrication inaccuracies . We have recently fabricated cavities of this type displaying Q-factors as high as 28000  and associated Q/V ratios twice higher than [28, 29].
3. Tapered nanowire coupling experiment
Figure 3 illustrates the principle of operation of evanescent coupling between a tapered fiber and a PhC microcavity. The silica fiber diameter must be reduced to the micrometer-scale in order to obtain an evanescently extended mode field  that can efficiently interact with the nanocavity. The fiber taper is manufactured using a flame brushing tapering process that heats and stretches conventional SMF fiber. Taper waist lengths are typically a few millimetres, with outside diameters down to 800 nm being achieved. In order to spatially localize the interaction to the PhC cavity itself, we introduce a curvature in the taper waist by inducing a loop shape in the taper [Fig. 3(b)].
By doing so, we not only limit the interaction region to the area of interest (namely the PhC cavity defect), minimizing scattering losses, but we also reinforce the mechanical stability of the taper. Obtaining the looped nanowires involves a process of moving the tapered fiber ends closer together by 3 mm and subsequently twisting one end to induce a loop. The loop nominally forms at the taper waist where the fiber diameter is the smallest. Once the loop is formed, the ends are then moved back, tightening the loop to achieve a circumference of approximately 0.4 mm.
In this experiment, the looped taper is brought into direct contact with the PhC cavity. Light is launched into the SMF fiber using a broadband erbium source at 1550nm (Fig. 4). Before reaching the taper region the light passes through a polariser to select TE-like polarisation (E mainly lying in the plane of the PhC structure). In the taper region, light is adiabatically converted into the fundamental evanescent taper mode. The output of the fiber is connected to an optical spectrum analyser where the transmission through the nanotaper is measured (Fig. 4). The procedure has been repeated on three distinct but nominally identical cavities. All the measurements are performed at room temperature.
4. Results and discussion
Figure 5 shows the transmission spectra in dB for the three cavities, normalized with respect to the transmission through the taper in the absence of the PhC. The vertical lines indicate the wavelengths of the optical modes from the PL measurements. As can be seen, the transmittance drops dramatically at the resonant wavelengths of the cavities. The relatively good agreement of the resonance wavelengths between the PL measurements and the evanescent coupling measurements confirm our ability to excite the ultra-small cavity modes using this technique. The slight red shift observed for each resonance is expected and is a direct consequence of bringing the taper into close proximity to the cavity, inducing an increase in the effective index of the mode. Off-resonance losses are related to scattering at the taper-PhC interface and direct coupling to TM PhC Bloch modes due to the broken symmetry .
The net quality factor of the coupled system measured experimentally, QT, encompasses the different decay channels available to the photons.
where Q0 is the intrinsic Q-factor of the cavity, Qfiber the Q-factor associated with the coupling between the cavity and the taper and Qparasitic is related to the parasitic losses induced by any significant perturbation of the mode field inside the cavity (for instance TE to TM mode conversion occurring because of the broken symmetry induced by the presence of the taper). In an ideal system, the taper-cavity coupling should not induce losses other than the desirable funnelling of photons into the nanowire, meaning that Qparasitic should be infinity. From coupled mode theory in time , and under the condition that the junction behaves ideally (i.e. Qparasitic tends to infinity), the transmittance is given in terms of the intrinsic Q0 and loaded QT-factors of the cavity as
From Fig. 5, a transmittance T of 0.5 and an experimental value of QT ~ 2000 can be determined for cavity A. Note that according to Eq. (2) this value of QT yields a lower bound for the intrinsic Q0-factor due to the taper’s loading effect on the cavity. From Eq. (3), we infer an intrinsic Q0-factor of ~ 2830, in good agreement with the intrinsic Q0-factor determined from the PL line width of the resonance peak, which yields 2900.
Surprisingly, considering the taper is in contact with the cavity, this result suggests that the system is actually behaving almost as an ideal junction, with Qparasitic ~ 80000 -far greater than any other contributing Q-factors. For cavities B and C, respectively, we obtain a transmittance T of 0.75, 0.57 and experimental QT-factors of 1650 and 1850. Using the same approach, we infer intrinsic Q0-factors of 1900 and 2380, in line with the intrinsic Q0-factors evaluated from PL measurements, which confirms the degree of ideality of these junctions.
Figure 6 displays the normalized experimental transmission spectra in linear scale, showing a resonance shift with coupling conditions for cavity A. Note that the looped taper is in direct contact with the PhC cavity for each of the four spectra. As stated above, the highly localised mode is very sensitive to perturbations. In our configuration, the silica nanowire perturbs the field of the microcavity in a controlled way. Curve 1) corresponds to the case where the nanowire is positioned slightly out of the cavity field maximum [see Fig. 1(b)]. This is sufficient to induce an increase in the effective index of the cavity mode causing a slight red shift of the resonance compared to the wavelength (1571 nm) determined from the PL measurement.
By subsequently displacing the nanowire slightly, we observe a shift of the resonance towards longer wavelengths (curves 2 to 4). This can be attributed to a stronger perturbation of the cavity field by the presence of the taper, resulting in a significant tuning of the resonance of >3 nm (curve 4) without degrading the Q-factor of the resonance. This mechanism can be compared to an AFM tip probing the cavity mode .
5. Prospects of a coupled taper 2D PhC single photon source system
The results reported above quantify the loading of light from the nanowire to the optical mode of PhC microcavities. Similar out-coupling efficiencies from the cavity to the nanowire can be inferred, since the two (in- and out-) coupling processes are fundamentally equivalent. As compared to other approaches, evanescent coupling through the use of nanowires presents some unique advantages. It offers an efficient scheme for pumping/loading a PhC nanocavity  and collecting light through the same fiber-based communication channel . In addition, as discussed below, it provides an adjustable extraction channel as well as a flexible means to tune the cavity (Q, λ) properties.
As stated in the introduction, SPS out-coupling methods involve either the collection of a fraction of the photons that are “naturally” lost outside the cavity, or the introduction of a dedicated optical decay channel for photon extraction. For both approaches, efficient extraction of single photons implies maximizing the decay rate associated with the collected photons of the QD-cavity system, relative to any other photon loss contributions. However, this must be achieved without degrading too strongly the total QT-factor of the mode that the emitter is coupled to. Those ideas are more quantitatively described in the following analysis.
The extraction efficiency (ε) is equal to the product of the SE coupling factor β and the collection efficiency (η) of the photons that have been emitted into the cavity mode.
where the Purcell Factor is
In the expression (7), the total QT-factor has been explicitly divided into two terms that correspond to the optical losses either collected (Qc) or not collected (Q0). Depending on the coupling strategy, these two terms must be interpreted slightly differently. If using an additional coupling channel, Q0 is the intrinsic Q-factor of the cavity (as defined in Section 4) and Qc is associated with the optical losses induced by the coupling process (denoted as Qfiber for the nanowire coupling). Note that (6) is then valid under the assumption that no other parasitic losses are added by the additional channel (Qparasitic → ∞). On the other hand, in the case where no additional optical decay channels are offered to the cavity, Qc (Q0) must be interpreted as the intrinsic cavity optical losses that do (do not) fall into the numerical aperture of the collection optics. Whilst the discussion below does not rely on this, for simplicity, we assume that the coupling strategy involves an additional coupling channel, as is the case for the evanescent coupled nanowire.
The relations (5) and (7) highlight two counter trends as the coupling strength (∝ 1/Qc) is increased. Whereas Fp and β both increase (Fp ≫1 and β → 1) as the coupling strength is decreased (Qc → 0 or QT → Q0), the efficiency η of coupling to the outside world decreases (η→ 0). These two competing trends yield a maximum in the extraction efficiency ε as a function of the net QT -factor, as displayed in Fig. 7(a). The corresponding Purcell factor, Fp, (obtained from Eq. (6) with V=0.5×(λ/n)3) is superimposed on the same plot; indeed, the Purcell factor is important in itself, independently of the extraction efficiency, from the viewpoint of enhancing the possible repetition rate of the SPS by speeding up the the QD SE process. In addition, the Purcell effect also contributes to make the photons indistinguishable by reducing the QD radiative lifetime below the dephasing time [35, 8]. Indistinguishability proves to be important for quantum information schemes that rely on multiphoton interference. Therefore, for some applications, an overall figure of merit should be defined by the product of ε and Fp [see Fig. 7(b)]. It is clear that the optimum coupling occurs for a relatively narrow range of net QT -factors (or Qc), the width of this range being highly dependent on the volume V and intrinsic Q0 of the cavity mode.
Two points can be highlighted from this analysis. The optimal net QT -factor, that maximises ε, as well as the maximum attainable efficiency εmax, both increase with the intrinsic Q0/V factor of the cavity. Higher Q0/V factors also enlarge the range of net QT -values that enable extraction efficiencies above a benchmark value of 90%. This behavior reinforces the strong interest in high Q0/V PhC microcavities to achieve both high Purcell factors and SPS extraction efficiencies and highlights the interest in having a coupling channel whose strength is a posteriori tunable. Tuning enables one to achieve the “well balanced” coupling efficiency Qc: it allows one to take full advantage of the Q0/V cavity produced by the fabrication process regarding ε and it can be adapted to the targeted application, which in practice may require optimizing either ε for Fp.
Traditional PhC cavity out-coupling methods include vertical coupling into an objective or lateral coupling to a PhC waveguide that is integrated onto the same structure as the cavity . For the former approach, the cavity design must be optimized so that the mode displays both a high QT/V and a highly directive radiation pattern that overlaps well with the numerical aperture of the collection optics . For the second approach, a balanced and well controlled PhC cavity to waveguide coupling structure must be realized to get a net QT -value close to the optimum value [see Fig. 7(b)]. Both approaches rely on the accurate fabrication of precise designs. However, nanocavities with ultra low volumes are particularly sensitive to fabrication inaccuracies that tend to compromise the Q-factor or mode directivity designed theoretically.
In contrast, evanescent coupling to nanowires allows tuning of the coupling strength Qc by modifying the overlap of the cavity-nanowire system [20, 25]. This, in turn, enables the tuning of QT which determines both the Purcell factor and the extraction efficiency, ε. Coupling can thus be adjusted to compensate for inevitable deviations from the ideal design of the fabricated cavity characteristics (such as Q0), and according to the requirements of the particular application. Additional “parasitic” losses induced by the evanescent coupling are limited, as demonstrated above, making this approach viable. The preliminary measurements of section 4 for cavity A (QT=2000 and Q0=2830) yield a collection efficiency η of ~ 30% according to Eq. (7), while the associated cavity Purcell factor Fp is close to 300. This indicates that the extraction efficiency ε for such a system, if used as a SPS, could be as high as 30%, while maintaining a high Purcell factor. Note that even though this value of 30 % is smaller than the theoretical maximum for ε of > 90%, [from Fig. 7(a)], it is nonetheless higher than what has been achieved for PhC SPSs to date [8, 10].
Finally, our observation of a shift of cavity resonant wavelength with coupling conditions (Fig. 6) offers a way to address the extremely important issue of aligning the cavity resonant wavelength with the QD emission wavelength. Enhancing the QD SE rate via the Purcell factor offered by the cavity mode requires critical spectral matching between the single QD and the cavity mode. Whilst PhC cavities enable the achievement of both high Q0-modes and potentially high Purcell factors, they also reduce the probability of obtaining accurate spectral matching of the spectrally narrow cavity mode and the QD emission. Whilst optical tuning of PhC modes has been achieved through thermo-optic approaches , liquid infiltration of PhC  or post-process chemical treatments [27,29], evanescent coupling offers a simple and flexible method to couple a spectrally misaligned QD with the cavity mode without changing the device structure. This reversible, post-fabrication tuning approach can correct spectral mismatches as wide as 3 nm with a high degree of control.
In conclusion we have demonstrated efficient coupling to the smallest volume microcavity to date, via a tapered silica nanowire micro-loop. These PhC based nanocavities, containing QDs, are specifically designed for SPS applications. We have demonstrated that this probing technique enables us to gain accurate knowledge of the intrinsic Q-factor of the cavity mode. In addition, it offers numerous advantages for coupling to SPS, such as the ability to couple without inducing significant parasitic losses, the ability to adjust the cavity coupling strength to optimize the extraction efficiency while maintaining high Purcell factors, the ability to tune the cavity resonant wavelength in order to match it to the QD emission and finally, the ability to both deliver pump light and extract photon emission through the same fiber-based channel. These advantages demonstrate that this coupling approach is highly relevant to SPS applications.
This work was produced with the assistance of the Australian Research Council under the ARC Centres of Excellence program. CUDOS (the Centre for Ultrahigh bandwidth Devices for Optical Systems) is an ARC Centre of Excellence. The authors would like to acknowledge the financial support of the Canadian Institute for Photonic Innovation.
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