Abstract

Using a quasinormal mode (QNM) theory for open cavity systems, we present detailed calculations and designs of a photonic crystal nanocavity (PCN) side-coupled to a photonic crystal waveguide (PCW) for on-chip single photon source applications. We investigate various cavity-waveguide geometries using an L3 PCN coupled to a W1 PCW, obtaining the quality factors, effective mode volumes, and single photon Purcell factors of the complete loaded cavity-waveguide system as a function of spatial separation between the two. We also show that the quality factor does not monotonically increase with increasing separation between the PCN and PCW, and we identify a particular hole/defect which acts as the key structural parameter in the cavity-waveguide coupling.

© 2016 Optical Society of America

1. Introduction

A quantum single photon source (SPS) is highly desirable for applications in quantum information processing and secure communication. An ideal SPS should emit single photons deterministically or on-demand, and each photon should be indistinguishable with a high repetition rate and a high β factor, which is the the collection efficiency of the output photon into a desired mode. Photonic crystals (PCs) offer a platform for an all-integrated solid state SPS, and prototype QDs embedded in PC nanocavities (PCNs) [1–3] have been demonstrated. In the weak-to-intermediate coupling regime, the spontaneous emission (SE) rate of the QD is enhanced into a specific PCN mode, and large Purcell factors (FP) have been realized due to the high quality factor (Q factor) and small effective mode volume, Veff of the cavity. The bandwidth in these devices is limited by the Q factor and the far-field emission profile of the PCN dictates the maximum achievable β-factor. Single photon source from QDs embedded in a PC waveguide (PCW) have also been proposed [4–6] and realized [7–12]. The PCWs support slow light modes near the mode edge, and the large group index results in large local density of optical states (LDOS) [4, 13]; when a QD exciton is tuned in resonance with a slow light Bloch mode, enhanced SE can be observed. Besides SE enhancement, the photon can be emitted into a propagating mode, offering possibility for further on-chip manipulation. Even though these PCWs offer large β factors, they suffer from fabrication imperfections limiting the maximum achievable group index and FP [14].

A possible hybrid approach using a coupled PCN-PCW has been proposed [15, 16], where a SPS is realized by having a QD inside a PCN evanescently coupled to an output PCW. The QD emits in the modified LDOS of the PCN and the emitted photons are then coupled into the propagating Bloch mode of PCW. The PCN can be designed to have a high Q factor (large FP) and the coupling between the cavity and PCW can be optimized to give a large β factor as well. One of the advantages of working with high Q cavities is the ability to implement quantum optical manipulations, such as photon Blockade and strong coupling effect in a waveguide configuration. However, operating in the regime of large Q is not a requirement for single photon emission [17], and may actually be problematic for the various figures-of-merit such as the single photon indistinguishability. For this work we will mainly focus on the Purcell factor in in the weak coupling regime, though one can easily extend the work to explore regimes of anharmonic cavity-QED and strong coupling.

The choice of optimum geometry for the PCN-PCW coupling is, however, a complex problem, and the theoretical complexity of cavity-waveguide systems requires extra care in obtaining the normalized mode profiles and effective mode volume of the hybrid device. These open cavity systems can be rigorously described in the language of quasinormal modes (QNMs) [18–22], which are the solution to the Helmholz equation with open boundary conditions. However, as shown recently, the periodic PCW presents an extra challenge because of the nonlocal boundary conditions of the output waveguide [23]. In this work, we study an L3 PCN coupled to a W1 PCW in a membrane-based PC with a triangular lattice of air holes. The L3 PCN is formed by removing 3 holes along the nearest neighbor direction and the W1 PCW is formed by removing a row of holes along the nearest neighbor direction; such architectures have been experimentally realized [24] using an L3 PCN coupled to a W1 PCW located on the cavity axis. Here, we explore a set of coupling geometries between an L3 PCN and W1 PCW. Using a QNM approach for coupled waveguide-cavity systems [23], we calculate the Q factors and FP factors of the loaded cavity as the spatial separation between the PCN and PCW is changed and find them to be sensitive to the structural modifications of the coupling region. We present calculations of the effective mode volume for the complete structure, without recourse to approximate coupled mode theories. Our calculations also show that the loaded Q factor, which is inversely proportional to the coupling rate, does not increase monotonically with increasing separation between the PCN and PCW. In particular, we identify and show the effect of changing the radius of an h-hole [25], explained later, on the Q factors of the coupled cavity-waveguide devices.

2. Isolated cavity and isolated waveguide properties

Figure 1(a) shows the schematic of an L3 PCN. The edge-holes of the PCN are marked in bold black outline with a radius reduction of 0.04a (a is the lattice constant of the PC) and a shift of 0.19a away from the center of the cavity. This modification increases the Q factor of the fundamental cavity mode [3] by redistributing the spatial Fourier components of the mode outside the light cone (leaky mode region). The real parts of the the electric field components, Ex(r) and Ey(r), of the fundamental L3 cavity mode are shown in Figs. 1(b) and 1(c), respectively; Ey(r) is evenly symmetric about the y-axis. A schematic of the semi-infinite W1 PCW terminated at the end closest to the L3 PCN is shown in Fig. 1(d). The hole shown in bold black outline, next to which the first missing hole of the W1 PCW is located, is identified as the h-hole with radius rh. Figure 1(e) plots the band structure of an infinite W1 PCW. The blue dashed circled line is the dispersion of the fundamental Bloch mode of the W1 PCW, which is confined in a TE like band gap of PC; this mode has even symmetry about the y-axis. The dispersion goes flat near the waveguide mode edge allowing slow light propagation in the W1 PCW. The resonant frequency for our L3 cavity is shown as a dashed horizontal line in the same figure and it intersects the waveguide band at kx0 (a/2π)=0.375. This coupling region is encircled in the Fig. 1(e). The intensity of the x-component and the y-component of the Bloch mode profile of the W1 PCW at kx0 are shown in Figs. 1(f) and 1(g), respectively. Note that we focus on coupling the L3 PCN to the W1 PCW away from the slow light region, to minimize the problem of disorder-induced losses [14].

 

Fig. 1 (a) & (d) Schematic of an L3 PCN with modified edge holes shown in bold black outline and of a W1 PCW with the h-hole marked in bold black, respectively; mode profiles for the fundamental mode of L3 PCN (b) Real Ex, (c) Real Ey along with 4 different h-holes and their location in the (a1,a2) basis (see text); (e) Band structure of W1 PCW calculated for the even parity mode; intensity of electric field mode profiles for W1 PCW at the spectral location of L3 PCN (kx0 (a/2π)=0.375) (f) x-component and (g) y-component.

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A single QD can be confined inside the PCN by first locating an isolated QD on a wafer and fabricating the PCN structure around it [26]. The coupling between a QD dipole and the PCN mode depends on nd · Ec(rd), where nd is the QD dipole vector and Ec(r) is the PCN mode electric field. Thus, for maximum coupling, the QD must be near a field antinode point with its dipole moment oriented along Ec(rd). From Figs. 1(b) and 1(c), the amplitude of Ex(r) is zero and the amplitude of Ey(r) is maximum at the center of the L3 PCN. Therefore, a QD in a L3 PCN must be positioned either near the center of the cavity where Ey(r) has an antinode or near the holes where Ex(r) has an antinode. Hereafter we will study an ideal coupling between the QD (simulated as a polarization dipole) and the Ey(r) of the PCN fundamental mode by keeping the dipole moment of the QD parallel to y-axis and positioning it at the center of the PCN. Figure 1(c) also shows that the Ey(r) cavity mode spatially extends in greater magnitude along 60 degrees to cavity axis as compared to its value along the cavity axis. Thus in order to characterize the coupling between the L3 PCN and W1 PCW as a function of spatial separation between the two, the position of the h-hole was moved along this direction (diagonally away from the L3 PCN). We study the separation between the L3 PCN and the W1 PCW along three diagonals. For example, Fig. 1(c) also shows four different locations of the h-hole marked in white outline, along one diagonal, depicting four possible devices. Each of the designs is referred to by a name describing the position of the h-hole in the basis of (a1 and a2) vectors. Both a1 and a2 are measured from the edge hole of the L3 PCN and represent the number of holes along the cavity axis and the number of rows respectively to the position of the h-hole. For example, a2= 0 refers to all the devices with the PCW located on the cavity axis. Figure 2(a) shows a schematic of the device with the h-hole located two holes horizontally right and one row up from the PCN, which is referred to by its coordinates as a1=2, a2=1 or (2,1); Figs. 2(b) and 2(c) represent (2,0) and (2,2) devices, respectively, and we vary a1 from 0 to 2 (3 diagonals in total) and a2 from 0 to 6.

 

Fig. 2 Schematic of the different coupled geometries studied. The basis vectors (a1 and a2) used to identify each of the geometries are also shown. Note the origin for these vectors is the edge-hole of the cavity. The devices are identified by the position of the h-hole. (a) (a1=2, a2=1); (b) (2, 0), (c) (2, 2).

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3. Modified spontaneous emission, Green function and QNM theory of coupled cavity-waveguides

When a PCW is brought in the vicinity of the PCN, the cavity fields find an additional decay channel by evanescently coupling to the PCW Bloch modes. This modifies its Q factor, which is inversely related to the rate of decay of stored energy inside the cavity, to QL, where QL is the loaded or complete Q factor of the coupled device.

The modified SE rate relative to a homogeneous medium can be obtained from the generalized Purcell factor,

FP=Im[nG(r,r,ω)n]Im[nG0(r,r,ω)n],
where G(r, r′, ω) is the electric-field Green function and Im[G0(r,r,ω)]=ω3nb6πc3I is the homogeneous Green function [16], with I the unit dyadic.

The transverse part of the Green function can be expanded in the basis of the QNMs [22], and with one cavity mode contribution, takes the form

G(r,r,ω)ω22ω˜c(ω˜cω)f˜c(r)f˜c(r)f˜c|f˜c,
where ω̃c = ωcc/2Q is the complex eigenfrequency, and c is the normalized QNM, which is obtained from a source free solution to Maxwell’s equations with outgoing boundary conditions, namely from
××f˜(ω˜cc)2ε(r)f˜=0,
where c is the speed of light and ε is the dielectric constant.

For high Q cavities, and assuming a lossless dielectric, it is common in cavity optics to adopt “normal mode” theory, whose modes are normalized through

f˜c|f˜cNM=12V(ε(r)|f˜c(r)|2+c2μ02|h˜c(r)|2)dr,
where c =ω̃c/ic × c (obtained for the actual dissipative cavity structure) and V → ∞. However, this normal mode expression is incorrect in general as it fails to account for dissipation, and the norm diverges exponentially as a function of space [20]. Instead, in the absence of dispersion, the QNMs can be normalized from [21, 23]
f˜c|f˜cunreg=12V[ε(r)f˜c(r)f˜c(r)c2μ02h˜c(r)h˜c(r)]dr,
and once again V → ∞ and 〈〈···〉〉 now denotes the true QNM norm. This (“unregularized”) expression still requires regularization of the integral in general, which for an open cavity surrounded by a homogeneous medium can be implemented in a number of ways [27], including use of PMLs (perfectly matched layers). For PCWs, however, special care is required in obtaining a semi-infinite periodic waveguide properties since the boundary condition is nonlocal. It was recently shown [23] that regularizing this integral is elegantly achieved by separating this integral into cavity and waveguide parts, through
f˜c|f˜creg=Icav+Iwg,
where Icav=12Vcav(ε(r)f˜c(r)f˜c(r)c2μ02h˜d(r)h˜d(r))dr, and Iwg=Ia(x0)1exp(2ik˜ca), where c = ω̃c/c, and Ia(x0)=12x0x0+aε(r)f˜c(r)f˜c(r)c2μ02h˜c(r)h˜c(r)drdx.

Here Icav is evaluated over the volume,Vcav, bounded by yspan, zspan (see below) and between PML and x0 along the x-axis, chosen at a position far enough away from the cavity so that the waveguide Bloch mode is well defined [23]. The PCW waveguide integration is carried out through use of a convergent series [23]. This normalized QNM, is used to evaluate the effective mode volume (Veff) of this coupled system, evaluated at field maximum point, r0, which is obtained from

1Veff=Re(1vQ),vQ=f˜c|f˜cε(r0)f˜c(r0)f˜c(r0),
whereas the (incorrect) normal mode volume would be obtained from VeffNM=f˜c|f˜cε(r0)|f˜c(r0)|2.

4. Numerical calculations of the QNM effective mode volume and Purcell factor for a coupled cavity-waveguide geometry

To compute the QNMs and complex eigenfrequencies, we use 3D finite-difference time-domain (FDTD) techniques from Lumerical [28]. The cavity mode is excited using a dipole source which emits a Gaussian pulse in time. The fields build up while the source is emitting and start to decay after the source dies. Specifically for the structures studied here, a dipole source emitting at 952 nm with a bandwidth of 33 nm (pulse width of 40 fs) was placed at the center of the L3 PCN coupled to W1 PCW. For maximum coupling, this dipole was oriented along the y-axis and the electric fields at different spatial locations inside the cavity were recorded using time monitors. The simulation was run for tsim= 3000–4000 fs. The rate of decay of the recorded fields gave the Q factor and resonant frequency of the mode, ωc, was computed from the Fourier transform of the fields. The complex eigenfrequency of the structure was then computed using ω̃c = ωcc/2Q. The FDTD fields for the coupled system were obtained using 3D field monitors and temporal window was applied to compute the run-time Fourier transform.The fields were normalized using the above regularization technique to yield the QNM of the coupled device. Simulations were done for GaAs membranes designed to incorporate QDs emitting at 950 nm (refractive index nb=3.5 at 950 nm) with the following structural parameters: membrane thickness of t=164 nm, lattice constant a=240 nm and radius of bulk hole rb=0.28a; rh= 0.2a was used unless otherwise stated. Spatial mesh steps of a/20=12 nm, a(3/2)/20=10.39nm and h/10=16.4 nm was used along x, y and z direction, respectively; PML boundary conditions were employed along in-plane directions with 100 PML layers. The location of the PML is shown in Fig. 3(a) for the (2,0) device: xc and yc refer to the location of PML boundary from the center of the cavity and xwg and ywg measures the location from the h-hole, whose values are given in the caption; this set the xspan and yspan for the simulations, and zspan was set at 10t. It was found that increasing the value of xwg beyond 15.5a had no effect on the loaded QL factor so QL has saturated to its maximum value; we also define QV as the Q factor for an isolated cavity. The mode profile, real(Ẽy(r)), of the coupled (1,0) device is computed and shown in Fig. 3(b). Also shown is the surface x0 = 10a in white vertical line which was used for regularizing the integral. We stress that this mode is the true QNM for the entire coupled device. In order to better highlight the need for regularization with the normalized QNM, the computed mode volume was compared using both the regularized (Vreg) and unregularized (Vunreg) normalizations as a function of the number of the unit cells along the x-axis. The results are plotted in Fig. 3(d) which show Vreg in solid blue line and Vunreg in blue circles. The Vunreg oscillates and gradually increases as can be seen in Fig. 3(d). Also plotted is the normal mode volume (VNM) which clearly diverges as more number of unit cells are added to the computation domain demonstrating the need to use the regularized norm for accurate evaluation of μ(r) and Veff. To verify the accuracy of this approach, we also compared the computed FP value as a function of frequency for a nominally coupled device (1,0) (QL factor ≈ 6400) using Eq. (2) and and a full 3D dipole computation of the Green function [16]. Figure 3(c) shows the excellent match between the two computation techniques validating the use of QNM theory for FP value calculations. We thus use this approach below to compute and analyze our coupled cavity-waveguide designs. We emphasize that QNM computation makes the calculations much faster than a direct dipole simulation (since the Q factor can be obtained without a full dipole simulation), and allows one to adopt an intuitive modal approach to obtain important parameters such as a rigorous definition of the effective mode volume for the entire structure, and the Purcell factor as a function of space and frequency, without doing any more calculations (which would be required, e.g., if doing by direct FDTD for different dipole positions). The time benefit depends on the QL of the structure under investigation; for the (1,0) device shown in Fig. 3(c), regardless of the memory requirements, the full dipole calculation for obtaining the accurate FP needs a 20-fold longer run time. This becomes even worse for higher Qs. In addition, full dipole calculations allow less use of symmetry and therefore add up to the memory requirements for a typical simulation which in turn can increase the time difference mentioned earlier, at the very least, by a factor of 2. We assume the Purcell coupling regime, but the theory can easily account for strong coupling effects if desired [15]. Figure 3(e) shows the effective mode volumes for the (2,0) device, which exhibits the same trend as (1,0) with a slower divergence of the VNM.

 

Fig. 3 (a) Schematic showing the location of the PML (red) from the h-hole and edge hole for (1,0) device. xc=15a; yc=15ay; xwg=15.5a; ywg ≥ 12.5ay were used for this work. (b) The regularized QNM, real(Ẽy(r)), is also shown for the same device. The vertical white line shows the regularization boundary x0 = 10a. (c) Purcell factor computed for (1,0) device using both QNM and full dipole calculations (see text). The inset shows the zoom in of the curves around the maximum Purcell factor values. 3D Dipole method gave a maximum value of FP as 395.378 at a frequency of 312.12217 THz whereas the QNM method gave the maximum FP value of 394.038 at a frequency shifted by 950MHz (312.12122 THz). (d) Mode volume of the (1,0) device computed using three definitions as a function of x-span. Blue horizontal line shows Vreg [using Eq. (6)], the blue circles show the Vunreg[using Eq. (5)] oscillating around Vreg and gradually increasing and green squares show the rapidly diverging VNM[using Eq. (4)]. (e) As in (d), but for a (2,0) cavity-waveguide system which has a higher Q factor (note the different y scale range).

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5. Investigation and design of various off-axis cavity-waveguide coupling geometries

Physically, the complex coupling between the PCN and PCW mode depends on the polarization of the fields, the field profiles, spatial overlap between the fields and the spectral location of the modes of the two structures involved [29]. As the PCW is moved away from the PCN, the spatial overlap between the fields changes. Figures 4(a)–4(c) shows the computed QL factors and FP values for all the studied devices as a function of separation between the PCN and PCW. The QL factors are plotted on the left vertical axis in Figs. 4(a)–4(c) as a2 on the horizontal axis increased from 0 to 6 (the PCW is moved from the 0th to 6th row). For the devices along the closest diagonal (Fig. 4(a)), the QL factors increased monotonically with a2, i.e. as the separation between the PCN and PCW was increased. Note that there is no h-hole in the (0,0) or the first device in the 0th row along this diagonal. Interestingly from Fig. 4(c), the QL factors for the farthest diagonal (a1 = 2) do not increase monotonically with a2 and show an abrupt decrease for the devices in the 1st (2,1) and 4th row (2,4) indicating an increase in coupling between the PCN and PCW with (2,4) having a higher QL than the (2,1) device. For further separation of 5 and 6 rows [(2,5) and (2,6)], the QL factors increase. Calculations for the second diagonal along a1 = 1 are shown in Fig. 4(b); the QL decrease as the PCW is moved from the first to third row (a2 =1 & 2 respectively) and begin to increase for devices which are farther than the third row (a2 > 3). The right vertical axis on Figs. 4(a)–4(c) show the computed FP values. Note that as the separation between the cavity and PCW is changed along all three diagonals, the FP values and the Q factors change in a similar fashion. This is expected because changing the location of the PCW around the cavity is mainly affecting the decay rate of the cavity into the PCW with the mode volume of the cavity being unaffected. None of the devices explored here have PCW close enough to the cavity so as perturb its mode volume drastically.

 

Fig. 4 Results: (a–c) Simulated QL factors (left vertical axis) and FP (right vertical axis) values as a function of a2 for the devices along three different diagonals, a1 = 0, 1 and 2, respectively. (d) QL factors for the devices with a1 = 2 for three different rh values. Also shown are schematics for three different coupled structures with a1= 0,1,2 and a2 = 3.

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In order to understand the peak-like feature in the QL for a2 = 1, we further investigated the effect of changing the radius of h-hole, rh, for the devices along this third diagonal. These simulations were done with lower spatial resolution to make them less computationally intensive. Figure 4(d) shows QL factors for the devices with a1 = 2 for three different rh values of 0.125a, 0.2a and 0.28a. For rh = 0.28a = bulk radius, the QL factors for devices with a2 > 2 are largest indicating overall less coupling. Devices with rh = 0.2a exhibited smaller QL for a2 > 2 showing an increased coupling with smaller rh but still maintaining a similar trend in QL as a2 increased. However, as rh was further decreased to 0.125a, the peak feature shifted to a lower a2 value of 2. Besides, at this smaller value of rh, the QL factors for all the devices with a2 > 2 are lower indicative of an overall increase in coupling. The h-hole is a structural parameter shared by the PCN fields and the PCW fields probably facilitating scattering of the fields and affecting the coupling. Its position and radius therefore also affect the coupling mechanism.

Next, the waveguide β factors were computed using the decay rates of the cavity into the various channels as described below. If, QL1 is the total new decay rate of the loaded cavity, QV1 is the decay rate along the vertical channel and QWG1 is the coupling rate of the cavity into the WG then, QL1=QWG1+QV1. The β factor is then evaluated as

β=QWG1QL1+Qdis1,
where Qdis includes processes such as disorder, background dots, material losses through a complex n, etc. Figure 5 shows the computed β factors along the three different diagonals for three Qdis values of ∞, 105, 104. As can be seen, the β factors qualitatively maintain their functional dependence on the separation for different Qdis values. Also note that β factors for the all devices get smaller for Qdis=104, with the devices located along the farthest diagonal (a1=2) being influenced the most. Detailed calculations have shown that the intrinsic Q from intrinsic structural disorder is likely around 105–106 [30, 31], so the values of 104 are likely somewhat pessimistic.

 

Fig. 5 Waveguide β factors computed from Eq. (8) are plotted as a function of separation (a2) for the devices along three different diagonals, a1 = 0, 1 and 2. Each subfigure was computed using a different loss rate (a) Qdis=∞, (b) Qdis=105 and (c) Qdis=104.

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6. Summary

We have employed a QNM theory to calculate and design efficient PC coupled cavity-waveguides systems for SPS applications, and introduced important modal properties of the coupled system, including the effective mode volumes and quality factors for the complex 3D coupled cavity infinite waveguide system. We also demonstrated the critical role that the h-hole plays in coupling a PCN and PCW, and found, somewhat counter intuitively, that for intermediate PCN-PCW separations the loaded Q factor exhibits a local minimum. The precise size of the h-hole determines for which PCN-PCW separation this local minimum is achieved. In PC based SPS devices that aim to optimize Purcell factors and the collection of single photons emitted into a waveguide, the crucial role played by the h-hole must therefore be carefully taken into account. We anticipate a complete optimization of the h-hole for maximum coupling for the devices studied can possibly be accomplished using topological optimization algorithms [32].

Acknowledgments

We thank the National Science Foundation (NSF) and the Natural Sciences and Engineering Research Council of Canada. A.B. acknowledges support from NSF under CAREER Grant No. ECCS- 1454021 and Grant No. DMR- 1309734.

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20. P. T. Kristensen, C. V. Vlack, and S. Hughes, “Generalized effective mode volume for leaky optical cavities,” Opt. Lett. 37, 1649–1651 (2012). [CrossRef]   [PubMed]  

21. C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nano-size photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013). [CrossRef]  

22. R.-C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J Phys. 16, 113048 (2014). [CrossRef]  

23. P. T. Kristensen, J. R. de Lasson, and N. Gregersen, “Calculation, normalization, and perturbation of quasinormal modes in coupled cavity-waveguide systems,” Opt. Lett. 39, 6359–6362 (2014). [CrossRef]   [PubMed]  

24. A. Schwagmann, S. Kalliakos, D. J. P. Ellis, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “In-plane single-photon emission from a L3 cavity coupled to a photonic crystal waveguide,” Opt. Express 20, 28614–28624 (2012). [CrossRef]   [PubMed]  

25. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005). [CrossRef]   [PubMed]  

26. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007). [CrossRef]   [PubMed]  

27. P. T. Kristensen, R. Ge, and S. Hughes, “Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators,” Phys. Rev. A 92, 053810 (2015). [CrossRef]  

28. We used FDTD solutions from Lumerical: www.lumerical.com.

29. E. Waks and J. Vuckovic, “Coupled mode theory for photonic crystal cavity-waveguide interaction,” Opt. Express 13, 5064–5073 (2005). [CrossRef]   [PubMed]  

30. M. Minkov, U. P. Dharanipathy, R. Houdré, and V. Savona, “Statistics of the disorder-induced losses of high-Q photonic crystal cavities,” Opt. Express 21, 28233–28245 (2013). [CrossRef]  

31. D. Gerace and L. C. Andreani, “Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs,” Photonics and Nanostructures-fundamentals and applications 3, 120–128 (2005).

32. J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser & Photonics Rev. 5, 308–321 (2011). [CrossRef]  

References

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  1. W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96, 117401 (2006).
    [Crossref] [PubMed]
  2. M. D. Birowosuto, H. Sumikura, S. Matsuo, H. Taniyama, P. J. van Veldhoven, R. Nótzel, and M. Notomi, “Fast purcell-enhanced single photon source in 1,550-nm telecom band from a resonant quantum dot-cavity coupling,” Sci. Rep. 2, 321 (2012).
    [Crossref] [PubMed]
  3. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
    [Crossref] [PubMed]
  4. V. S. C. Manga Rao and S. Hughes, “Single quantum-dot purcell factor and β factor in a photonic crystal waveguide,” Phys. Rev. B 75, 205437 (2007).
    [Crossref]
  5. V. S. C. Manga Rao and S. Hughes, “Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient on chip single photon gun,” Phys. Rev. Lett. 99, 193901 (2007).
    [Crossref]
  6. G. Lecamp, P. Lalanne, and J. P. Hugonin, “Very large spontaneous-emission β factors in photonic-crystal waveguides,” Phys. Rev. Lett. 99, 023902 (2007).
    [Crossref]
  7. A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett. 99, 261108 (2011).
    [Crossref]
  8. E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
    [Crossref] [PubMed]
  9. T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
    [Crossref] [PubMed]
  10. S. J. Dewhurst, D. Granados, D. J. P. Ellis, A. J. Bennett, R. B. Patel, I. Farrer, D. Anderson, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “Slow-light-enhanced single quantum dot emission in a unidirectional photonic crystal waveguide,” Appl. Phys. Lett. 96, 031109(2010).
    [Crossref]
  11. A. Laucht, S. Pütz, T. Günthner, N. Hauke, R. Saive, S. Frédérick, M. Bichler, M. C. Amann, A. W. Holleitner, M. Kaniber, and J. J. Finley, “A waveguide-coupled on-chip single-photon source,” Phys. Rev. X 2, 011014 (2012).
  12. M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
    [Crossref] [PubMed]
  13. P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87, 347 (2015).
    [Crossref]
  14. S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
    [Crossref] [PubMed]
  15. P. Yao and S. Hughes, “Controlled cavity QED and single-photon emission using a photonic-crystal waveguide cavity system,” Phys. Rev. B 80, 165128 (2009).
    [Crossref]
  16. P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser & Photonics Rev. 4, 499–516 (2010).
    [Crossref]
  17. A. Kiraz, M. Atatüre, and A. Imamoğlu, “Quantum-dot single-photon sources: prospects for applications in linear optics quantum-information processing,” Phys. Rev. A 69, 032305 (2004).
    [Crossref]
  18. H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
    [Crossref] [PubMed]
  19. P. T. Kristensen and S. Hughes, “Modes and mode volumes of leaky optical cavities and plasmonic nanoresonators,” ACS Photonics 1, 2–10 (2014).
    [Crossref]
  20. P. T. Kristensen, C. V. Vlack, and S. Hughes, “Generalized effective mode volume for leaky optical cavities,” Opt. Lett. 37, 1649–1651 (2012).
    [Crossref] [PubMed]
  21. C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nano-size photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
    [Crossref]
  22. R.-C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J Phys. 16, 113048 (2014).
    [Crossref]
  23. P. T. Kristensen, J. R. de Lasson, and N. Gregersen, “Calculation, normalization, and perturbation of quasinormal modes in coupled cavity-waveguide systems,” Opt. Lett. 39, 6359–6362 (2014).
    [Crossref] [PubMed]
  24. A. Schwagmann, S. Kalliakos, D. J. P. Ellis, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “In-plane single-photon emission from a L3 cavity coupled to a photonic crystal waveguide,” Opt. Express 20, 28614–28624 (2012).
    [Crossref] [PubMed]
  25. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
    [Crossref] [PubMed]
  26. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
    [Crossref] [PubMed]
  27. P. T. Kristensen, R. Ge, and S. Hughes, “Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators,” Phys. Rev. A 92, 053810 (2015).
    [Crossref]
  28. We used FDTD solutions from Lumerical: www.lumerical.com .
  29. E. Waks and J. Vuckovic, “Coupled mode theory for photonic crystal cavity-waveguide interaction,” Opt. Express 13, 5064–5073 (2005).
    [Crossref] [PubMed]
  30. M. Minkov, U. P. Dharanipathy, R. Houdré, and V. Savona, “Statistics of the disorder-induced losses of high-Q photonic crystal cavities,” Opt. Express 21, 28233–28245 (2013).
    [Crossref]
  31. D. Gerace and L. C. Andreani, “Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs,” Photonics and Nanostructures-fundamentals and applications 3, 120–128 (2005).
  32. J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser & Photonics Rev. 5, 308–321 (2011).
    [Crossref]

2015 (2)

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87, 347 (2015).
[Crossref]

P. T. Kristensen, R. Ge, and S. Hughes, “Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators,” Phys. Rev. A 92, 053810 (2015).
[Crossref]

2014 (4)

R.-C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J Phys. 16, 113048 (2014).
[Crossref]

P. T. Kristensen, J. R. de Lasson, and N. Gregersen, “Calculation, normalization, and perturbation of quasinormal modes in coupled cavity-waveguide systems,” Opt. Lett. 39, 6359–6362 (2014).
[Crossref] [PubMed]

P. T. Kristensen and S. Hughes, “Modes and mode volumes of leaky optical cavities and plasmonic nanoresonators,” ACS Photonics 1, 2–10 (2014).
[Crossref]

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

2013 (2)

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nano-size photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

M. Minkov, U. P. Dharanipathy, R. Houdré, and V. Savona, “Statistics of the disorder-induced losses of high-Q photonic crystal cavities,” Opt. Express 21, 28233–28245 (2013).
[Crossref]

2012 (4)

P. T. Kristensen, C. V. Vlack, and S. Hughes, “Generalized effective mode volume for leaky optical cavities,” Opt. Lett. 37, 1649–1651 (2012).
[Crossref] [PubMed]

A. Schwagmann, S. Kalliakos, D. J. P. Ellis, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “In-plane single-photon emission from a L3 cavity coupled to a photonic crystal waveguide,” Opt. Express 20, 28614–28624 (2012).
[Crossref] [PubMed]

A. Laucht, S. Pütz, T. Günthner, N. Hauke, R. Saive, S. Frédérick, M. Bichler, M. C. Amann, A. W. Holleitner, M. Kaniber, and J. J. Finley, “A waveguide-coupled on-chip single-photon source,” Phys. Rev. X 2, 011014 (2012).

M. D. Birowosuto, H. Sumikura, S. Matsuo, H. Taniyama, P. J. van Veldhoven, R. Nótzel, and M. Notomi, “Fast purcell-enhanced single photon source in 1,550-nm telecom band from a resonant quantum dot-cavity coupling,” Sci. Rep. 2, 321 (2012).
[Crossref] [PubMed]

2011 (2)

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett. 99, 261108 (2011).
[Crossref]

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser & Photonics Rev. 5, 308–321 (2011).
[Crossref]

2010 (2)

S. J. Dewhurst, D. Granados, D. J. P. Ellis, A. J. Bennett, R. B. Patel, I. Farrer, D. Anderson, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “Slow-light-enhanced single quantum dot emission in a unidirectional photonic crystal waveguide,” Appl. Phys. Lett. 96, 031109(2010).
[Crossref]

P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser & Photonics Rev. 4, 499–516 (2010).
[Crossref]

2009 (1)

P. Yao and S. Hughes, “Controlled cavity QED and single-photon emission using a photonic-crystal waveguide cavity system,” Phys. Rev. B 80, 165128 (2009).
[Crossref]

2008 (1)

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
[Crossref] [PubMed]

2007 (4)

V. S. C. Manga Rao and S. Hughes, “Single quantum-dot purcell factor and β factor in a photonic crystal waveguide,” Phys. Rev. B 75, 205437 (2007).
[Crossref]

V. S. C. Manga Rao and S. Hughes, “Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient on chip single photon gun,” Phys. Rev. Lett. 99, 193901 (2007).
[Crossref]

G. Lecamp, P. Lalanne, and J. P. Hugonin, “Very large spontaneous-emission β factors in photonic-crystal waveguides,” Phys. Rev. Lett. 99, 023902 (2007).
[Crossref]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

2006 (1)

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96, 117401 (2006).
[Crossref] [PubMed]

2005 (5)

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[Crossref] [PubMed]

D. Gerace and L. C. Andreani, “Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs,” Photonics and Nanostructures-fundamentals and applications 3, 120–128 (2005).

E. Waks and J. Vuckovic, “Coupled mode theory for photonic crystal cavity-waveguide interaction,” Opt. Express 13, 5064–5073 (2005).
[Crossref] [PubMed]

2004 (1)

A. Kiraz, M. Atatüre, and A. Imamoğlu, “Quantum-dot single-photon sources: prospects for applications in linear optics quantum-information processing,” Phys. Rev. A 69, 032305 (2004).
[Crossref]

2003 (1)

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

1990 (1)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Akahane, Y.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Amann, M. C.

A. Laucht, S. Pütz, T. Günthner, N. Hauke, R. Saive, S. Frédérick, M. Bichler, M. C. Amann, A. W. Holleitner, M. Kaniber, and J. J. Finley, “A waveguide-coupled on-chip single-photon source,” Phys. Rev. X 2, 011014 (2012).

Anderson, D.

S. J. Dewhurst, D. Granados, D. J. P. Ellis, A. J. Bennett, R. B. Patel, I. Farrer, D. Anderson, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “Slow-light-enhanced single quantum dot emission in a unidirectional photonic crystal waveguide,” Appl. Phys. Lett. 96, 031109(2010).
[Crossref]

Andreani, L. C.

D. Gerace and L. C. Andreani, “Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs,” Photonics and Nanostructures-fundamentals and applications 3, 120–128 (2005).

Arcari, M.

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

Asano, T.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Atature, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Atatüre, M.

A. Kiraz, M. Atatüre, and A. Imamoğlu, “Quantum-dot single-photon sources: prospects for applications in linear optics quantum-information processing,” Phys. Rev. A 69, 032305 (2004).
[Crossref]

Badolato, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Barber, P. W.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Benisty, H.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

Bennett, A. J.

S. J. Dewhurst, D. Granados, D. J. P. Ellis, A. J. Bennett, R. B. Patel, I. Farrer, D. Anderson, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “Slow-light-enhanced single quantum dot emission in a unidirectional photonic crystal waveguide,” Appl. Phys. Lett. 96, 031109(2010).
[Crossref]

Bichler, M.

A. Laucht, S. Pütz, T. Günthner, N. Hauke, R. Saive, S. Frédérick, M. Bichler, M. C. Amann, A. W. Holleitner, M. Kaniber, and J. J. Finley, “A waveguide-coupled on-chip single-photon source,” Phys. Rev. X 2, 011014 (2012).

Birowosuto, M. D.

M. D. Birowosuto, H. Sumikura, S. Matsuo, H. Taniyama, P. J. van Veldhoven, R. Nótzel, and M. Notomi, “Fast purcell-enhanced single photon source in 1,550-nm telecom band from a resonant quantum dot-cavity coupling,” Sci. Rep. 2, 321 (2012).
[Crossref] [PubMed]

Chang, H.-S.

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96, 117401 (2006).
[Crossref] [PubMed]

Chang, W.-H.

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96, 117401 (2006).
[Crossref] [PubMed]

Chen, W.-Y.

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96, 117401 (2006).
[Crossref] [PubMed]

Chyi, J.-I.

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96, 117401 (2006).
[Crossref] [PubMed]

de Lasson, J. R.

Dewhurst, S. J.

S. J. Dewhurst, D. Granados, D. J. P. Ellis, A. J. Bennett, R. B. Patel, I. Farrer, D. Anderson, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “Slow-light-enhanced single quantum dot emission in a unidirectional photonic crystal waveguide,” Appl. Phys. Lett. 96, 031109(2010).
[Crossref]

Dharanipathy, U. P.

Ellis, D. J. P.

A. Schwagmann, S. Kalliakos, D. J. P. Ellis, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “In-plane single-photon emission from a L3 cavity coupled to a photonic crystal waveguide,” Opt. Express 20, 28614–28624 (2012).
[Crossref] [PubMed]

S. J. Dewhurst, D. Granados, D. J. P. Ellis, A. J. Bennett, R. B. Patel, I. Farrer, D. Anderson, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “Slow-light-enhanced single quantum dot emission in a unidirectional photonic crystal waveguide,” Appl. Phys. Lett. 96, 031109(2010).
[Crossref]

Falt, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Farrer, I.

A. Schwagmann, S. Kalliakos, D. J. P. Ellis, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “In-plane single-photon emission from a L3 cavity coupled to a photonic crystal waveguide,” Opt. Express 20, 28614–28624 (2012).
[Crossref] [PubMed]

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett. 99, 261108 (2011).
[Crossref]

S. J. Dewhurst, D. Granados, D. J. P. Ellis, A. J. Bennett, R. B. Patel, I. Farrer, D. Anderson, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “Slow-light-enhanced single quantum dot emission in a unidirectional photonic crystal waveguide,” Appl. Phys. Lett. 96, 031109(2010).
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Finley, J. J.

A. Laucht, S. Pütz, T. Günthner, N. Hauke, R. Saive, S. Frédérick, M. Bichler, M. C. Amann, A. W. Holleitner, M. Kaniber, and J. J. Finley, “A waveguide-coupled on-chip single-photon source,” Phys. Rev. X 2, 011014 (2012).

Forchel, A.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
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Frédérick, S.

A. Laucht, S. Pütz, T. Günthner, N. Hauke, R. Saive, S. Frédérick, M. Bichler, M. C. Amann, A. W. Holleitner, M. Kaniber, and J. J. Finley, “A waveguide-coupled on-chip single-photon source,” Phys. Rev. X 2, 011014 (2012).

Ge, R.

P. T. Kristensen, R. Ge, and S. Hughes, “Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators,” Phys. Rev. A 92, 053810 (2015).
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Ge, R.-C.

R.-C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J Phys. 16, 113048 (2014).
[Crossref]

Gerace, D.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
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S. J. Dewhurst, D. Granados, D. J. P. Ellis, A. J. Bennett, R. B. Patel, I. Farrer, D. Anderson, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “Slow-light-enhanced single quantum dot emission in a unidirectional photonic crystal waveguide,” Appl. Phys. Lett. 96, 031109(2010).
[Crossref]

Gregersen, N.

Griffiths, J. P.

A. Schwagmann, S. Kalliakos, D. J. P. Ellis, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “In-plane single-photon emission from a L3 cavity coupled to a photonic crystal waveguide,” Opt. Express 20, 28614–28624 (2012).
[Crossref] [PubMed]

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett. 99, 261108 (2011).
[Crossref]

Gulde, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

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A. Laucht, S. Pütz, T. Günthner, N. Hauke, R. Saive, S. Frédérick, M. Bichler, M. C. Amann, A. W. Holleitner, M. Kaniber, and J. J. Finley, “A waveguide-coupled on-chip single-photon source,” Phys. Rev. X 2, 011014 (2012).

Hauke, N.

A. Laucht, S. Pütz, T. Günthner, N. Hauke, R. Saive, S. Frédérick, M. Bichler, M. C. Amann, A. W. Holleitner, M. Kaniber, and J. J. Finley, “A waveguide-coupled on-chip single-photon source,” Phys. Rev. X 2, 011014 (2012).

Hennessy, K.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

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H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Holleitner, A. W.

A. Laucht, S. Pütz, T. Günthner, N. Hauke, R. Saive, S. Frédérick, M. Bichler, M. C. Amann, A. W. Holleitner, M. Kaniber, and J. J. Finley, “A waveguide-coupled on-chip single-photon source,” Phys. Rev. X 2, 011014 (2012).

Houdré, R.

M. Minkov, U. P. Dharanipathy, R. Houdré, and V. Savona, “Statistics of the disorder-induced losses of high-Q photonic crystal cavities,” Opt. Express 21, 28233–28245 (2013).
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E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
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W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96, 117401 (2006).
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W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96, 117401 (2006).
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K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Hughes, S.

P. T. Kristensen, R. Ge, and S. Hughes, “Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators,” Phys. Rev. A 92, 053810 (2015).
[Crossref]

P. T. Kristensen and S. Hughes, “Modes and mode volumes of leaky optical cavities and plasmonic nanoresonators,” ACS Photonics 1, 2–10 (2014).
[Crossref]

R.-C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J Phys. 16, 113048 (2014).
[Crossref]

P. T. Kristensen, C. V. Vlack, and S. Hughes, “Generalized effective mode volume for leaky optical cavities,” Opt. Lett. 37, 1649–1651 (2012).
[Crossref] [PubMed]

P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser & Photonics Rev. 4, 499–516 (2010).
[Crossref]

P. Yao and S. Hughes, “Controlled cavity QED and single-photon emission using a photonic-crystal waveguide cavity system,” Phys. Rev. B 80, 165128 (2009).
[Crossref]

V. S. C. Manga Rao and S. Hughes, “Single quantum-dot purcell factor and β factor in a photonic crystal waveguide,” Phys. Rev. B 75, 205437 (2007).
[Crossref]

V. S. C. Manga Rao and S. Hughes, “Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient on chip single photon gun,” Phys. Rev. Lett. 99, 193901 (2007).
[Crossref]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

Hugonin, J. P.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nano-size photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

G. Lecamp, P. Lalanne, and J. P. Hugonin, “Very large spontaneous-emission β factors in photonic-crystal waveguides,” Phys. Rev. Lett. 99, 023902 (2007).
[Crossref]

Imamoglu, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

A. Kiraz, M. Atatüre, and A. Imamoğlu, “Quantum-dot single-photon sources: prospects for applications in linear optics quantum-information processing,” Phys. Rev. A 69, 032305 (2004).
[Crossref]

Javadi, A.

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

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J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser & Photonics Rev. 5, 308–321 (2011).
[Crossref]

Jones, G. A. C.

A. Schwagmann, S. Kalliakos, D. J. P. Ellis, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “In-plane single-photon emission from a L3 cavity coupled to a photonic crystal waveguide,” Opt. Express 20, 28614–28624 (2012).
[Crossref] [PubMed]

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett. 99, 261108 (2011).
[Crossref]

S. J. Dewhurst, D. Granados, D. J. P. Ellis, A. J. Bennett, R. B. Patel, I. Farrer, D. Anderson, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “Slow-light-enhanced single quantum dot emission in a unidirectional photonic crystal waveguide,” Appl. Phys. Lett. 96, 031109(2010).
[Crossref]

Julsgaard, B.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
[Crossref] [PubMed]

Kalliakos, S.

A. Schwagmann, S. Kalliakos, D. J. P. Ellis, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “In-plane single-photon emission from a L3 cavity coupled to a photonic crystal waveguide,” Opt. Express 20, 28614–28624 (2012).
[Crossref] [PubMed]

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett. 99, 261108 (2011).
[Crossref]

Kamp, M.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
[Crossref] [PubMed]

Kaniber, M.

A. Laucht, S. Pütz, T. Günthner, N. Hauke, R. Saive, S. Frédérick, M. Bichler, M. C. Amann, A. W. Holleitner, M. Kaniber, and J. J. Finley, “A waveguide-coupled on-chip single-photon source,” Phys. Rev. X 2, 011014 (2012).

Kira, G.

Kiraz, A.

A. Kiraz, M. Atatüre, and A. Imamoğlu, “Quantum-dot single-photon sources: prospects for applications in linear optics quantum-information processing,” Phys. Rev. A 69, 032305 (2004).
[Crossref]

Kristensen, P. T.

P. T. Kristensen, R. Ge, and S. Hughes, “Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators,” Phys. Rev. A 92, 053810 (2015).
[Crossref]

P. T. Kristensen and S. Hughes, “Modes and mode volumes of leaky optical cavities and plasmonic nanoresonators,” ACS Photonics 1, 2–10 (2014).
[Crossref]

P. T. Kristensen, J. R. de Lasson, and N. Gregersen, “Calculation, normalization, and perturbation of quasinormal modes in coupled cavity-waveguide systems,” Opt. Lett. 39, 6359–6362 (2014).
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R.-C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J Phys. 16, 113048 (2014).
[Crossref]

P. T. Kristensen, C. V. Vlack, and S. Hughes, “Generalized effective mode volume for leaky optical cavities,” Opt. Lett. 37, 1649–1651 (2012).
[Crossref] [PubMed]

Kuramochi, E.

Lai, H. M.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Lalanne, P.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nano-size photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

G. Lecamp, P. Lalanne, and J. P. Hugonin, “Very large spontaneous-emission β factors in photonic-crystal waveguides,” Phys. Rev. Lett. 99, 023902 (2007).
[Crossref]

Laucht, A.

A. Laucht, S. Pütz, T. Günthner, N. Hauke, R. Saive, S. Frédérick, M. Bichler, M. C. Amann, A. W. Holleitner, M. Kaniber, and J. J. Finley, “A waveguide-coupled on-chip single-photon source,” Phys. Rev. X 2, 011014 (2012).

Lecamp, G.

G. Lecamp, P. Lalanne, and J. P. Hugonin, “Very large spontaneous-emission β factors in photonic-crystal waveguides,” Phys. Rev. Lett. 99, 023902 (2007).
[Crossref]

Lee, E. H.

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

Leung, P. T.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Lindskov Hansen, S.

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

Liu, J.

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
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Lodahl, P.

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87, 347 (2015).
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M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
[Crossref] [PubMed]

Lund-Hansen, T.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
[Crossref] [PubMed]

Mahmoodian, S.

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87, 347 (2015).
[Crossref]

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

Maksymov, I. S.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nano-size photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

Manga Rao, V. S. C.

P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser & Photonics Rev. 4, 499–516 (2010).
[Crossref]

V. S. C. Manga Rao and S. Hughes, “Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient on chip single photon gun,” Phys. Rev. Lett. 99, 193901 (2007).
[Crossref]

V. S. C. Manga Rao and S. Hughes, “Single quantum-dot purcell factor and β factor in a photonic crystal waveguide,” Phys. Rev. B 75, 205437 (2007).
[Crossref]

Matsuo, S.

M. D. Birowosuto, H. Sumikura, S. Matsuo, H. Taniyama, P. J. van Veldhoven, R. Nótzel, and M. Notomi, “Fast purcell-enhanced single photon source in 1,550-nm telecom band from a resonant quantum dot-cavity coupling,” Sci. Rep. 2, 321 (2012).
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Minkov, M.

Mitsugi, S.

Noda, S.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
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M. D. Birowosuto, H. Sumikura, S. Matsuo, H. Taniyama, P. J. van Veldhoven, R. Nótzel, and M. Notomi, “Fast purcell-enhanced single photon source in 1,550-nm telecom band from a resonant quantum dot-cavity coupling,” Sci. Rep. 2, 321 (2012).
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M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
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Nótzel, R.

M. D. Birowosuto, H. Sumikura, S. Matsuo, H. Taniyama, P. J. van Veldhoven, R. Nótzel, and M. Notomi, “Fast purcell-enhanced single photon source in 1,550-nm telecom band from a resonant quantum dot-cavity coupling,” Sci. Rep. 2, 321 (2012).
[Crossref] [PubMed]

Olivier, S.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

Patel, R. B.

S. J. Dewhurst, D. Granados, D. J. P. Ellis, A. J. Bennett, R. B. Patel, I. Farrer, D. Anderson, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “Slow-light-enhanced single quantum dot emission in a unidirectional photonic crystal waveguide,” Appl. Phys. Lett. 96, 031109(2010).
[Crossref]

Pütz, S.

A. Laucht, S. Pütz, T. Günthner, N. Hauke, R. Saive, S. Frédérick, M. Bichler, M. C. Amann, A. W. Holleitner, M. Kaniber, and J. J. Finley, “A waveguide-coupled on-chip single-photon source,” Phys. Rev. X 2, 011014 (2012).

Ramunno, L.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

Ritchie, D. A.

A. Schwagmann, S. Kalliakos, D. J. P. Ellis, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “In-plane single-photon emission from a L3 cavity coupled to a photonic crystal waveguide,” Opt. Express 20, 28614–28624 (2012).
[Crossref] [PubMed]

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett. 99, 261108 (2011).
[Crossref]

S. J. Dewhurst, D. Granados, D. J. P. Ellis, A. J. Bennett, R. B. Patel, I. Farrer, D. Anderson, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “Slow-light-enhanced single quantum dot emission in a unidirectional photonic crystal waveguide,” Appl. Phys. Lett. 96, 031109(2010).
[Crossref]

Robert-Philip, I.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

Saive, R.

A. Laucht, S. Pütz, T. Günthner, N. Hauke, R. Saive, S. Frédérick, M. Bichler, M. C. Amann, A. W. Holleitner, M. Kaniber, and J. J. Finley, “A waveguide-coupled on-chip single-photon source,” Phys. Rev. X 2, 011014 (2012).

Sauvan, C.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nano-size photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

Savona, V.

Schwagmann, A.

A. Schwagmann, S. Kalliakos, D. J. P. Ellis, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “In-plane single-photon emission from a L3 cavity coupled to a photonic crystal waveguide,” Opt. Express 20, 28614–28624 (2012).
[Crossref] [PubMed]

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett. 99, 261108 (2011).
[Crossref]

Shields, A. J.

A. Schwagmann, S. Kalliakos, D. J. P. Ellis, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “In-plane single-photon emission from a L3 cavity coupled to a photonic crystal waveguide,” Opt. Express 20, 28614–28624 (2012).
[Crossref] [PubMed]

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett. 99, 261108 (2011).
[Crossref]

S. J. Dewhurst, D. Granados, D. J. P. Ellis, A. J. Bennett, R. B. Patel, I. Farrer, D. Anderson, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “Slow-light-enhanced single quantum dot emission in a unidirectional photonic crystal waveguide,” Appl. Phys. Lett. 96, 031109(2010).
[Crossref]

Shinya, A.

Sigmund, O.

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser & Photonics Rev. 5, 308–321 (2011).
[Crossref]

Sipe, J. E.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

Smith, C. J. M.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

Söllner, I.

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

Song, B.-S.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Song, J. D.

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

Stobbe, S.

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87, 347 (2015).
[Crossref]

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
[Crossref] [PubMed]

Sumikura, H.

M. D. Birowosuto, H. Sumikura, S. Matsuo, H. Taniyama, P. J. van Veldhoven, R. Nótzel, and M. Notomi, “Fast purcell-enhanced single photon source in 1,550-nm telecom band from a resonant quantum dot-cavity coupling,” Sci. Rep. 2, 321 (2012).
[Crossref] [PubMed]

Sünner, T.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
[Crossref] [PubMed]

Tanabe, T.

Taniyama, H.

M. D. Birowosuto, H. Sumikura, S. Matsuo, H. Taniyama, P. J. van Veldhoven, R. Nótzel, and M. Notomi, “Fast purcell-enhanced single photon source in 1,550-nm telecom band from a resonant quantum dot-cavity coupling,” Sci. Rep. 2, 321 (2012).
[Crossref] [PubMed]

Thyrrestrup, H.

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
[Crossref] [PubMed]

van Veldhoven, P. J.

M. D. Birowosuto, H. Sumikura, S. Matsuo, H. Taniyama, P. J. van Veldhoven, R. Nótzel, and M. Notomi, “Fast purcell-enhanced single photon source in 1,550-nm telecom band from a resonant quantum dot-cavity coupling,” Sci. Rep. 2, 321 (2012).
[Crossref] [PubMed]

Varoutsis, S.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

Viasnoff-Schwoob, E.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

Vlack, C. V.

Vuckovic, J.

Waks, E.

Weisbuch, C.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

Winger, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Yao, P.

P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser & Photonics Rev. 4, 499–516 (2010).
[Crossref]

P. Yao and S. Hughes, “Controlled cavity QED and single-photon emission using a photonic-crystal waveguide cavity system,” Phys. Rev. B 80, 165128 (2009).
[Crossref]

Young, J. F.

R.-C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J Phys. 16, 113048 (2014).
[Crossref]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

Young, K.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

ACS Photonics (1)

P. T. Kristensen and S. Hughes, “Modes and mode volumes of leaky optical cavities and plasmonic nanoresonators,” ACS Photonics 1, 2–10 (2014).
[Crossref]

Appl. Phys. Lett. (2)

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett. 99, 261108 (2011).
[Crossref]

S. J. Dewhurst, D. Granados, D. J. P. Ellis, A. J. Bennett, R. B. Patel, I. Farrer, D. Anderson, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “Slow-light-enhanced single quantum dot emission in a unidirectional photonic crystal waveguide,” Appl. Phys. Lett. 96, 031109(2010).
[Crossref]

Laser & Photonics Rev. (2)

P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser & Photonics Rev. 4, 499–516 (2010).
[Crossref]

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser & Photonics Rev. 5, 308–321 (2011).
[Crossref]

Nature (2)

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

New J Phys. (1)

R.-C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J Phys. 16, 113048 (2014).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Photonics and Nanostructures-fundamentals and applications (1)

D. Gerace and L. C. Andreani, “Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs,” Photonics and Nanostructures-fundamentals and applications 3, 120–128 (2005).

Phys. Rev. A (3)

P. T. Kristensen, R. Ge, and S. Hughes, “Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators,” Phys. Rev. A 92, 053810 (2015).
[Crossref]

A. Kiraz, M. Atatüre, and A. Imamoğlu, “Quantum-dot single-photon sources: prospects for applications in linear optics quantum-information processing,” Phys. Rev. A 69, 032305 (2004).
[Crossref]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Phys. Rev. B (2)

P. Yao and S. Hughes, “Controlled cavity QED and single-photon emission using a photonic-crystal waveguide cavity system,” Phys. Rev. B 80, 165128 (2009).
[Crossref]

V. S. C. Manga Rao and S. Hughes, “Single quantum-dot purcell factor and β factor in a photonic crystal waveguide,” Phys. Rev. B 75, 205437 (2007).
[Crossref]

Phys. Rev. Lett. (8)

V. S. C. Manga Rao and S. Hughes, “Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient on chip single photon gun,” Phys. Rev. Lett. 99, 193901 (2007).
[Crossref]

G. Lecamp, P. Lalanne, and J. P. Hugonin, “Very large spontaneous-emission β factors in photonic-crystal waveguides,” Phys. Rev. Lett. 99, 023902 (2007).
[Crossref]

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
[Crossref] [PubMed]

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96, 117401 (2006).
[Crossref] [PubMed]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nano-size photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

Phys. Rev. X (1)

A. Laucht, S. Pütz, T. Günthner, N. Hauke, R. Saive, S. Frédérick, M. Bichler, M. C. Amann, A. W. Holleitner, M. Kaniber, and J. J. Finley, “A waveguide-coupled on-chip single-photon source,” Phys. Rev. X 2, 011014 (2012).

Rev. Mod. Phys. (1)

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87, 347 (2015).
[Crossref]

Sci. Rep. (1)

M. D. Birowosuto, H. Sumikura, S. Matsuo, H. Taniyama, P. J. van Veldhoven, R. Nótzel, and M. Notomi, “Fast purcell-enhanced single photon source in 1,550-nm telecom band from a resonant quantum dot-cavity coupling,” Sci. Rep. 2, 321 (2012).
[Crossref] [PubMed]

Other (1)

We used FDTD solutions from Lumerical: www.lumerical.com .

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Figures (5)

Fig. 1
Fig. 1 (a) & (d) Schematic of an L3 PCN with modified edge holes shown in bold black outline and of a W1 PCW with the h-hole marked in bold black, respectively; mode profiles for the fundamental mode of L3 PCN (b) Real Ex, (c) Real Ey along with 4 different h-holes and their location in the (a1,a2) basis (see text); (e) Band structure of W1 PCW calculated for the even parity mode; intensity of electric field mode profiles for W1 PCW at the spectral location of L3 PCN (kx0 (a/2π)=0.375) (f) x-component and (g) y-component.
Fig. 2
Fig. 2 Schematic of the different coupled geometries studied. The basis vectors (a1 and a2) used to identify each of the geometries are also shown. Note the origin for these vectors is the edge-hole of the cavity. The devices are identified by the position of the h-hole. (a) (a1=2, a2=1); (b) (2, 0), (c) (2, 2).
Fig. 3
Fig. 3 (a) Schematic showing the location of the PML (red) from the h-hole and edge hole for (1,0) device. xc=15a; yc=15ay; xwg=15.5a; ywg ≥ 12.5ay were used for this work. (b) The regularized QNM, real(Ẽy(r)), is also shown for the same device. The vertical white line shows the regularization boundary x0 = 10a. (c) Purcell factor computed for (1,0) device using both QNM and full dipole calculations (see text). The inset shows the zoom in of the curves around the maximum Purcell factor values. 3D Dipole method gave a maximum value of FP as 395.378 at a frequency of 312.12217 THz whereas the QNM method gave the maximum FP value of 394.038 at a frequency shifted by 950MHz (312.12122 THz). (d) Mode volume of the (1,0) device computed using three definitions as a function of x-span. Blue horizontal line shows Vreg [using Eq. (6)], the blue circles show the Vunreg[using Eq. (5)] oscillating around Vreg and gradually increasing and green squares show the rapidly diverging VNM[using Eq. (4)]. (e) As in (d), but for a (2,0) cavity-waveguide system which has a higher Q factor (note the different y scale range).
Fig. 4
Fig. 4 Results: (a–c) Simulated QL factors (left vertical axis) and FP (right vertical axis) values as a function of a2 for the devices along three different diagonals, a1 = 0, 1 and 2, respectively. (d) QL factors for the devices with a1 = 2 for three different rh values. Also shown are schematics for three different coupled structures with a1= 0,1,2 and a2 = 3.
Fig. 5
Fig. 5 Waveguide β factors computed from Eq. (8) are plotted as a function of separation (a2) for the devices along three different diagonals, a1 = 0, 1 and 2. Each subfigure was computed using a different loss rate (a) Qdis=∞, (b) Qdis=105 and (c) Qdis=104.

Equations (8)

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F P = Im [ n G ( r , r , ω ) n ] Im [ n G 0 ( r , r , ω ) n ] ,
G ( r , r , ω ) ω 2 2 ω ˜ c ( ω ˜ c ω ) f ˜ c ( r ) f ˜ c ( r ) f ˜ c | f ˜ c ,
× × f ˜ ( ω ˜ c c ) 2 ε ( r ) f ˜ = 0 ,
f ˜ c | f ˜ c NM = 1 2 V ( ε ( r ) | f ˜ c ( r ) | 2 + c 2 μ 0 2 | h ˜ c ( r ) | 2 ) d r ,
f ˜ c | f ˜ c unreg = 1 2 V [ ε ( r ) f ˜ c ( r ) f ˜ c ( r ) c 2 μ 0 2 h ˜ c ( r ) h ˜ c ( r ) ] d r ,
f ˜ c | f ˜ c reg = I cav + I wg ,
1 V eff = Re ( 1 v Q ) , v Q = f ˜ c | f ˜ c ε ( r 0 ) f ˜ c ( r 0 ) f ˜ c ( r 0 ) ,
β = Q WG 1 Q L 1 + Q dis 1 ,

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