A Semiconductor Topological Photonic Ring Resonator
M. Jalali Mehrabad, A.P. Foster, R. Dost, E. Clarke, P.K. Patil, I. Farrer, J. Heffernan, M.S. Skolnick, L.R. Wilson
AA Semiconductor Topological Photonic Ring Resonator
M. Jalali Mehrabad, a) A.P. Foster, b) R. Dost, E. Clarke, P.K. Patil, I. Farrer, J. Heffernan, M.S. Skolnick, and L.R. Wilson Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH,UK EPSRC National Epitaxy Facility, University of Sheffield, Sheffield S1 4DE,UK Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield S1 4DE,UK (Dated: 11 February 2020)
Unidirectional photonic edge states arise at the interface between two topologically-distinct photonic crystals.Here, we demonstrate a micron-scale GaAs photonic ring resonator, created using a spin Hall-type topologicalphotonic crystal waveguide. Embedded InGaAs quantum dots are used to probe the mode structure of thedevice. We map the spatial profile of the resonator modes, and demonstrate control of the mode confinementthrough tuning of the photonic crystal lattice parameters. The intrinsic chirality of the edge states makesthem of interest for applications in integrated quantum photonics, and the resonator represents an importantbuilding block towards the development of such devices with embedded quantum emitters.The integration of quantum photonic elements on chippresents a highly promising route to the realisation ofscalable quantum devices. A key requirement of such anapproach is the development of optical waveguides ex-hibiting low loss and negligible back scatter. Recently,topological waveguides have emerged as a new class ofphotonic device enabling the robust propagation of lighton chip.
At the interface between two topologically-distinct photonic crystals (PhCs), counter-propagatingedge states of opposing helicity arise, which are idealfor optical waveguiding.
Significant developmentsin this field include the demonstration of efficient guidingof light around tight corners, robust transport de-spite the presence of defects, and integration with pas-sive optical elements including nanobeam waveguides and grating couplers. Compatibility with embeddedquantum emitters such as quantum dots (QDs) hasbeen demonstrated, and used to probe the waveguidetransmission.
Recently, chiral coupling of a QD to atopological waveguide was demonstrated.
This is aresult of the intrinsic helicity of the edge states and is ofgreat interest for chiral quantum optics. Here, we use a spin Hall-type topological waveguide tocreate a GaAs topological photonic ring resonator, andprobe its mode structure using embedded InGaAs QDs.We map the spatial dependence of the confined modes ofthe resonator, and demonstrate that perturbation of thePhC lattice can be used to tune the lateral confinementof the modes.A schematic of the PhC forming the basis of our topo-logical ring resonator is shown in Fig. 1a. The unitcell of the PhC consists of six triangular air holes ofside length s , etched into a GaAs membrane of thick-ness h . A two-dimensional PhC lattice is created using a) mjalalimehrabad1@sheffield.ac.uk b) andrew.foster@sheffield.ac.uk FIG. 1. (a) Schematic showing the unperturbed photoniccrystal (PhC). The triangles represent air holes. A two-dimensional PhC is formed using a triangular lattice of unitcells, with pitch a . (b) Band structure of the unperturbed lat-tice, revealing a Dirac cone at the Γ point. Points of high sym-metry in the Brillouin zone are shown in the accompanyingschematic. (c,d) Schematic of (c) expanded and (d) shrunkenunit cells. The band structure for a PhC formed from such aunit cell is also shown. In each case a bandgap is opened atthe Γ point. (e) Schematic of an interface formed between ex-panded and shrunken unit cells. Edge modes are seen to crossthe bandgap in this case. The parameters used for the bandstructure calculations were: refractive index = 3.4, h =170nm, s =140nm, a =445nm, R e =156nm and R s =141nm. a hexagonal array of unit cells with period a = s/ . R fromthe origin of the unit cell to the centre of each triangu- a r X i v : . [ phy s i c s . op ti c s ] F e b lar aperture, with a graphene-like structure formed when R = R = a/
3. We model the structure using a commer-cially available 3D finite-difference time-domain (FDTD)electromagnetic simulator, and show that in this casethe PhC band structure exhibits a Dirac cone at the Γpoint, as shown in Fig. 1b.However, when a perturbation is introduced such that R (cid:54) = a/
3, a bandgap is opened at the Γ point. Thisis shown for the case of PhCs formed using either ex-panded ( R e > R ) or shrunken ( R s < R ) unit cellsin Fig. 1c-d. Using FDTD, we determine the band-width of the PhC bandgap for a perturbation of either R e /R = 1 .
05 or R s /R = 0 .
94 to be ∼ ∼ ∼ ∼ h =170nm and s =140nm. It is instructive toconsider the nature of the bands in this case. For ashrunken (expanded) unit cell, the higher energy bandhas d -( p -) like character, and the lower energy band is p -( d -) like. This difference in character has an impor-tant consequence when an interface is realised betweenthe two unit cells (see Fig. 1e). The change in charac-ter of adjacent bands necessitates the formation of edgestates, connecting bands of the same character across theinterface. These can be clearly seen in the interface bandstructure shown in Fig. 1e. The edge states exist withinthe bandgap, and the interface therefore supports con-fined modes which form the basis of a topological pho-tonic waveguide. We harness the interface edge modes to create a pho-tonic ring resonator. A hexagonal array of expanded unitcells ( R e /R = 1 .
05) is embedded within a host array ofshrunken unit cells ( R s /R = 0 . ∼ µm . The hexagonalhost array has an internal side length of 31 unit cells.FDTD simulations of the resonator reveal a characteris-tic spectral mode structure (Fig. 2b), which lies withinthe topological bandgap (determined by monitoring thepower radiated by a dipole source in an expanded-unit-cell PhC). The three most prominent modes have an av-erage quality factor (Q factor) of 1760 (range 1600-1900).Spatial intensity profiles for two different modes (Fig. 2c)confirm that they are confined to the topological inter-face.The topological character of the resonator modes canbe seen in protection against certain defects, and in thehelical nature of the modes. We consider a defect inthe form of a single unit cell missing from the resonatorinterface. This is seen to have little effect on the modespectrum (dashed line in Fig. 2b) and does not affect themode Q factors. To demonstrate helicity of the modes,we position a circularly polarised dipole at the centre ofa unit cell adjacent to the interface, and show that thepropagation direction of the dipole emission is dependenton the handedness of the dipole polarisation (see Fig. 2d).This highlights the potential of the resonator for chiral FIG. 2. (a) Schematic of the ring resonator. The topologicalinterface is indicated by the green line. (b) Mode spectrumat the resonator interface (blue solid line), determined usingFDTD simulation. Resonator modes can be seen within thetopological bandgap (shaded). The mode spectrum is alsoshown for a resonator containing a defect in the form of asingle unit cell omitted from the interface (red dashed line).The inset shows a schematic of one side of the resonator, withand without the defect. (c) Spatially-resolved electric field in-tensity (linear scale) in the plane of the device, for the twomodes numbered in (b) (without a defect). Confinement oflight at the interface is clearly seen. The electric field inten-sity is evaluated within the white dashed region in (a). (d)Spatially-resolved electric field intensity (linear scale) in theplane of the device, for a (upper) σ + or (lower) σ − polariseddipole source (position given by the open circle). The fieldintensity is averaged over the first 200fs of simulation time.Chiral emission is observed, with the direction of propagation(arrows) dependent on the dipole polarisation. The dipole iscoupled to mode 1, as labelled in (b). quantum optics and spin-photon interfaces. Next, we investigate the theoretical dependence of theresonator Q factor, first on the device dimensions, andthen on the PhC perturbation. Fig. 3a shows the modespectra for five different resonators with internal sidelength between 4 and 8 unit cells. The host PhC has aside length of 31 unit cells and the perturbation is 5.5%.The number of modes (mode spacing) increases (de-creases) with increasing resonator size, as is expected fora Fabry-P´erot-type resonator. In each case, the Q fac-tor of a mode near the centre of the distribution (markedwith a star) is calculated. The Q factor is greater than2,000 for the smallest resonator, and decreases slightlywith increasing resonator size. Fixing the internal sizeof the ring at 4 unit cells, we then vary the perturba-tion, and see that the Q factor increases with decreasingperturbation, down to 3.5% perturbation (blue circles inFig. 3b). The dependence of the Q factor on both theresonator size and perturbation can be understood as theresult of the finite propagation length of the waveguide.This is due to scattering of the mode at the Γ point, and
FIG. 3. (a) Simulated resonator Q factor versus side length L (the number of internal unit cells at the interface) for aPhC perturbation of 5.5%. The size of the host PhC is fixedat 31 unit cells. Electric field intensity profiles (linear scale)for L = 4 and L = 8 are shown as insets (scale bars 2 µ m).Mode spectra for each case are shown to the right. The Qfactor is evaluated for the mode marked with a star. (b)Simulated Q factor versus perturbation for a resonator with L = 4. Blue circles (red squares, green diamond) correspondto a host PhC size of 31 (41, 51) unit cells. The inset showsthe relative size of the resonator (black hexagon) and the hostPhC in each case. (c) Simulated spatially-resolved electricfield intensity for waveguides with perturbations of 3.5% to6.5%, on a logarithmic intensity scale. The mode propagatesin the x direction (prop. dir.). The unit cell is expanded(Exp.) above and shrunken (Shr.) below the interface, whichis highlighted by the dashed green line. subsequent coupling to free-space modes, the probabilityof which increases with increasing perturbation. Forthe smallest perturbation of 2.5%, we find that the sizeof the host PhC must be increased to obtain the largestQ factor. Increasing the internal side length of the hostinitially to 41 unit cells (red squares in Fig. 3b) has lit-tle effect for perturbations greater than 2.5%, indicat-ing that in this case the host PhC is already sufficientlylarge. However, for a host PC size of 51 unit cells (greendiamond) a higher Q factor of ∼ FIG. 4. (a) Scanning electron microscope (SEM) overviewof the ring resonator (top) and close up of the waveguideinterface (bottom, scale bar 200nm). (b-e) High power PLspectra for four different excitation locations on the device,as labelled in (a). In each case, the collection spot was fixed onthe left hand side of the resonator (yellow circle labelled ‘Col’in (a)). (f) Spatially-resolved, integrated PL intensity mapsfor four different bandwidths, as numbered and colour-codedin (b-e). The zero of the linear colour scale is transparent.An SEM image of the device is positioned under each map,and the interface highlighted with a dashed green line. Scalebars 2 µ m. The resonator has an internal side length of 8 unit cells,and is embedded in a host PhC with a side length re-stricted to 16 unit cells due to experimental limitations.The simulated Q factor in this case is reduced to amaximum of ∼
870 for a perturbation of 5.5%, due toadditional loss into the membrane. Devices are fabri-cated with perturbation between 2.5% ( R e /R = 1 . R s /R = 0 .
97) and 5.5% ( R e /R = 1 . R s /R = 0 . µ -PL) spectroscopy. We use an excitation wavelength of808nm, and focus the laser to a spot size of ∼ µ m. Highpower excitation is used to generate broadband emis-sion from the QD ensemble. Mirrors in the collectionpath, with motorized adjusters, enable the collection ofPL emission from a location either coincident with, orspatially distinct from, the excitation spot. We first po-sition the excitation laser spot on one side of the ring(region ‘b’ in Fig. 4a), and detect light emitted from a lo-cation on the opposite side of the resonator (region ‘Col’in Fig. 4a). This enables us to detect light coupled tothe interface, whilst rejecting PL which is emitted intofree-space modes. The PL spectrum for a ring resonatorwith a unit cell perturbation of 5.5% is shown in Fig. 4b.Resonator modes with a period of ∼ FIG. 5. Dependence of waveguide mode transverse confine-ment on perturbation. Upper panels: Spatially-resolved, in-tegrated PL intensity maps for different unit cell perturba-tions (as labelled). The integration is for a mode centeredat ∼ µ m. increasing from 2.5% to 5.5%. In each case, the inten-sity map corresponds to a single resonator mode, cen-tered at ∼ ± µ m, transverse to the propagation direction.This value increases to 4.1 ± µ m for a perturbationof only 2.5%. The change in confinement is consistentwith FDTD simulations (see Fig. 3 and Fig. 5b), whichshow that, as the perturbation is decreased, the waveg-uide mode increasingly extends into the bulk PhC. Fromthe simulations, we estimate that the spatial extent ofthe mode normal to the propagation direction increasesfrom ∼ ∼ ∼ µ m.)This suggests a robust method to tune the degree ofevanescent coupling between the ring resonator and anadjoining bus waveguide, for instance in an add-drop fil-ter. The perturbation is dependent on the location of thetriangular apertures forming the PhC. This is simple tocontrol lithographically, unlike the case of devices whichrely on fine tuning of the resonator-waveguide spacing.In conclusion, we have created a GaAs spin Hall topo-logical photonic ring resonator, and used embedded In-GaAs QDs to probe the mode structure of the device.Using spatially resolved PL measurements, we demon-strated that the modes were confined to the PhC inter-face. Furthermore, we showed that by controlling theperturbation of the PhC unit cell, the spatial confine-ment of the modes could be tuned. The resonator rep-resents an important building block in the developmentof integrated photonic devices using embedded quantumemitters.Data supporting this study are openly available fromthe University of Sheffield repository. This work was supported by EPSRC Grant No.EP/N031776/1. C. P. Dietrich, A. Fiore, M. G. Thompson, M. Kamp, andS. 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