Photonic Crystal Cavity Modes Research Articles

Transmissible topological edge states based on Su–Schrieffer–Heeger photonic crystals with defect cavities

Abstract Topological photonic crystals have great potential in the application of on-chip integrated optical communication devices. Here, we successfully construct the on-chip transmissible topological edge states using one-dimensional Su–Schrieffer–Heeger (SSH) photonic crystals with defect cavities on silicon-on-insulator slab. Different coupling strengths between the lateral modes and diagonal modes in photonic crystal defect cavities are used to construct the SSH model. Furthermore, two photonic SSH-cavity configurations, called α and β configurations, are designed to demonstrate the topological edge states. Leveraging the capabilities of photonic crystal transverse electric modes with on-chip transmission, we introduced a waveguide to excite a boundary defect cavity and found that the transmission peak of light, corresponding to the topological edge state, can be received in another boundary defect cavity, which is caused by the tunnel effect. Moreover, the position of this peak experiences a blue shift as the defect cavity size increases. Therefore, by tuning the size of the SSH defect cavity, on-chip wavelength division multiplexing function can be achieved, which is demonstrated in experiments. The ultrafast response time of one operation can be less than 20 fs. This work harmonizes the simplicity of one-dimensional SSH model with the transmissibility of two-dimensional photonic crystals, realizing transmissible on-chip zero-dimensional topological edge states. Since transmission peaks are highly sensitive to defect cavity size, this configuration can also serve as a wavelength sensor and a reconfigurable optical device, which is of substantial practical value to on-chip applications of topological photonics.

A very high-resolution refractive index sensor based on hybrid topology of photonic crystal cavity and plasmonic nested split-ring resonator

In this paper, an optical refractive index (RI) sensor based on a photonic crystal and plasmonic (PhC-P) hybrid topology is designed. The sensor's structure is composed of nested circular metallic split-ring resonators (NCMSRR), which are embedded inside a hexagonal cavity in a rod-type photonic crystal (PhC) structure. The finite-difference time-domain (FDTD) method is used for the numerical simulation of the sensor. The obtained results show that by the cooperative coupling between the surface plasmon polaritons (SPP) induced by the NCMSRR and resonant PhC cavity modes, a hybrid PhC-P mode is created. The hybrid mode provides unique opportunities, not only for incrementing the sensitivity but also for obtaining a much higher figure of merit (FoM) compared to modes belonging to purely plasmonic or purely PhC sensors. The simulation results demonstrate a fairly high sensitivity of 1250 nm/RIU and an excellent FoM of 2083 RIU−1 when the proposed sensor is exposed to hazardous gases. These results show considerable improvement compared to the works published in the literature. Accordingly, the sensor proposed in this paper has tremendous potential to be used for high-sensitivity and high-resolution sensing applications at optical communication wavelengths.

Modal Properties of Photonic Crystal Cavities and Applications to Lasers.

Photonic crystal cavities enable strong light–matter interactions, with numerous applications, such as ultra-small and energy-efficient semiconductor lasers, enhanced nonlinearities and single-photon sources. This paper reviews the properties of the modes of photonic crystal cavities, with a special focus on line-defect cavities. In particular, it is shown how the fundamental resonant mode in line-defect cavities gradually turns from Fabry–Perot-like to distributed-feedback-like with increasing cavity size. This peculiar behavior is directly traced back to the properties of the guided Bloch modes. Photonic crystal cavities based on Fano interference are also covered. This type of cavity is realized through coupling of a line-defect waveguide with an adjacent nanocavity, with applications to Fano lasers and optical switches. Finally, emerging cavities for extreme dielectric confinement are covered. These cavities promise extremely strong light–matter interactions by realizing deep sub-wavelength mode size while keeping a high quality factor.

(Invited) Exciton Dynamics in Air-Suspended Carbon Nanotubes Coupled to Nanobeam Cavities

Air modes in photonic crystal nanobeam cavities offer efficient coupling to air-suspended carbon nanotubes [1,2]. Here we investigate exciton dynamics in the time domain at room temperature. The cavities are fabricated from silicon-on-insulator wafers, and nanotubes are synthesized over the cavities by chemical vapor deposition. Time-resolved photoluminescence measurements are performed on individual nanotubes, and we compare the bright exciton lifetime with and without coupling to the cavity. Purcell enhancement of the exciton recombination is observed [3].Work supported in part by MIC (SCOPE 191503001), RIKEN (Incentive Research Projects), JSPS (KAKENHI JP16H05962), and MEXT (Nanotechnology Platform). H.M. is supported by JSPS Research Fellowship. We thank the Advanced Manufacturing Support Team at RIKEN for technical assistance.[1] R. Miura, S. Imamura, R. Ohta, A. Ishii, X. Liu, T. Shimada, S. Iwamoto, Y. Arakawa, Y. K. Kato, Nat. Commun. 5, 5580 (2014).[2] H. Machiya, T. Uda, A. Ishii, Y. K. Kato, Appl. Phys. Lett. 112, 021101 (2018).[3] H. Machiya, A. Ishii, Y. K. Kato, in preparation.

A Cratered Photonic Crystal Cavity Mode for Nonlocal Exciton–Photon Interactions

AbstractOptical nanocavities for coherent interfaces usually have their electric field maximum at the center point, which normally benefits interactions with small local quantum emitters. Here, a partial thickness modulation on 2D slab photonic crystal cavities for a cratered cavity mode function to improve nonlocal interactions is proposed. The thickness modulation is applied around the central region, and has little effect on the fringe electric field, which determines the coupling to waveguides or other cavities. Furthermore, the partial modulation enhances the cratered electric field at positions that are distant from the center point. Therefore, interactions with multiple separated emitters are simultaneously enhanced, and the interaction with a large emitter beyond the dipole approximation is also doubled. The improvement of the nonlocal interactions demonstrates a great potential for the cratered cavity mode profile for applications in quantum photonic networks.

Topological whispering gallery modes in two-dimensional photonic crystal cavities

Utilizing the robust transport properties of the topological photonic crystal interface, we experimentally realize two-dimensional topological photonic crystal cavities, where discrete whispering gallery modes can propagate unidirectionally along the cavity circumference. Different from traditional cavities, these topological whispering galley modes are insensitive to cavity shapes. Our microwave demonstration has a good agreement with numerical simulations. Using pure dielectrics, by scaling down to the optical wavelength, an optical directional coupler based on the same topological photonic crystal scheme is also proposed. We here show that topological photonics can provide more novel designs for optical devices.

Hybrid photonic–plasmonic crystal nanocavity sensors

We have investigated a hybrid photonic–plasmonic crystal nanocavity consisting of a silicon grating nanowire adjacent to a metal surface with a gain gap between them. The hybrid plasmonic cavity modes are highly confined in the gap due to the strong coupling of the photonic crystal cavity modes and the surface plasmonic gap modes. Using finite-element method (FEM), guided modes of the hybrid plasmonic waveguide (WG) were numerically determined at a wavelength of 1550 nm. The modal characteristics such as WG confinement factors and modal losses of the fundamental hybrid plasmonic modes were obtained as a function of groove depth at various gap heights. Furthermore, the band structure of the hybrid crystal modes corresponding to a wide band gap of 17.8 THz is revealed. To enclose the optical energy effectively, a single defect was introduced into the hybrid crystal. At a deep subwavelength defect length as small as 270 nm, the resonant mode exhibits a high quality factor of 567 and an ultrasmall mode volume of 1.9 × 10− 3 (λ/neff)3 at the resonance wavelength of 1550 nm. Compared to conventional photonic crystal nanowire cavities in the absence of a metal surface, the factor Q/Vm is significantly enhanced by about 15 times. The designed hybrid photonic–plasmonic cavity sensors exhibit distinguished characteristics such as sensitivity of 443 nm/RIU and figure of merit of 129. The proposed nanocavities open new possibilities for various applications with strong light–matter interaction, such as biosensors and nanolasers.

Narrow-linewidth carbon nanotube emission in silicon hollow-core photonic crystal cavity.

Polymer-sorted semiconducting single-walled carbon nanotubes (SWNTs) provide room-temperature emission at near-infrared wavelengths, with potential for large volume production of high-quality solutions and wafer-scale deposition. These features make SWNTs a very attractive material for the realization of on-chip light sources. Coupling SWNT into optical microcavities could enhance and guide their emission, while enabling spectral selection by cavity resonance engineering. This could allow the realization of bright, narrowband sources. Here, we report the first demonstration of coupling SWNTs into the resonant modes of Si hollow-core photonic crystal cavities. We exploit the strong evanescent field in these resonators to interact with SWNT emission, coupling it into an integrated access waveguide. Based on this concept, we demonstrate narrowband SWNT emission resonantly coupled into a Si bus waveguide with a full width at half-maximum of 0.34nm and an off-resonance rejection exceeding 5dB.

A novel proposal for OR/NOR logic gates based on dipole-induced transparency

This paper proposes a novel structure for realization of the OR/NOR logic gates. The structure, consists of a Λ-type 3-level quantum dot localized in a single mode photonic crystal cavity and coupled symmetrically to two different parallel waveguides. The probe field is guided by the two waveguide while the control field is applied vertically to the photonic crystal cavity. Absence of the control field results propagation of the probe field in waveguide and mutually, in the presence of the control field, probe field switches to the other waveguide. Two data stream are combined by a coupler and it constructs the control filed. The finite-difference time-domain algorithm are used for solving coupled Heisenberg equations. Simulations and results show that the proposed logic gates can operate at the range of up to 5Gb/s.

Study on the similarity of photonic crystal ring resonator cavity modes and whispering-gallery-like modes in order to design more efficient optical power dividers

In this study, we discuss the wave pattern characteristics of confined cavity modes inside photonic crystal ring resonators (PCRRs). Despite different physical origins, these cavity modes are analogous to the whispering-gallery (WG-like) modes. Because of the absence of perfectly circular symmetry in our PC cavity, the WG-like modes are not degenerate, but they form a close doublet in which the field pattern of each of these doublets repeats itself by $$180^{\circ }/m$$180?/m where "m" is the azimuthal index number of WG-like modes. The cavity modes are named according to their symmetric field pattern, and WG-like ones are named by their azimuthal mode numbers "m." Based on the study of these similarities, we propose a $$1\times 2$$1×2 and a $$1\times 4$$1×4 T-junction- like power dividers. Through study of the similar properties of these cavity modes with WG-like modes, we have enhanced the output power of both dividers to 49.6 and 24.5 %, respectively. The permittivity of the hexagonal photonic crystal rod is $$\varepsilon _{h}= 12.04$$?h=12.04 surrounded by air as the background medium. For our PCRR, the dominant resonating mode is the cavity mode with hexapole field pattern or equivalently WG-like mode with azimuthal mode number of $$m\,=\,6$$m=6. The normalized frequencies for this mode and its doublet are $$a/\lambda = 0.348066$$a/?=0.348066 and 0.348301, respectively. The photonic band structure, PC waveguide guided mode and electric field patterns of the confined cavity modes inside the PCRR are calculated using the PWE method, and the transmission spectra are calculated by means of 2D-FDTD simulation method.

Effects of location and polarization of a dipole source on the excitation of a photonic crystal H1 cavity

The integration of photonic crystal cavity with quantum dot paves the way for photonic-based quantum information processing. Photonic crystal cavity has a high-quality factor and small mode volume, which can be utilized to enhance the interaction between light and matter. Two degenerate fundamental modes with orthogonal polarizations exist in photonic crystal H1 cavity. Entangled photon pairs can be generated with a single quantum dot coupled to degenerate H1 cavity modes. Therefore a coupling system comprised of quantum dot and photonic crystal H1 cavity is a promising platform to implement quantum information processing. The excitations of cavity modes are mostly affected by the location of the single quantum dot, namely a dipole source. For the two degenerate photonic crystal H1 cavity modes, the location of the dipole source determines which mode is excited. In this paper, the effects of location and polarization of a dipole source on the excitation of photonic crystal H1 cavity are investigated with the finite-difference time-domain method, a numerical analysis technique for computing the electrodynamics. We first design a photonic crystal slab structure patterned with hexagonal lattice of air holes. Combining the light modulation by the period lattice in the slab plane and the total internal reflection in the perpendicular direction, photonic bandgap is generated, which inhibits the propagation of photon with certain frequencies. By removing one of the air holes from the photonic crystal slab, an H1 cavity is formed with two degenerate fundamental modes. One mode is x-polarized, and the other one is y-polarized. Next, a dipole source is used to excite the H1 cavity modes. When the dipole source is located at the left to the H1 cavity center, only y-polarized mode is excited. While locating the dipole source above the H1 cavity center, only x-polarized mode is excited. Therefore each degenerate mode of H1 cavity can be selectively excited with the diploe source located at different positions in the cavity. Following that, the H1 cavity modes excited with the dipole sources with different polarizations are also studied. The x-polarized dipole source can only excite the cavity mode with x-polarization, while the y-polarized dipole source can only excite the y-polarized cavity mode accordingly. It can be seen that the dipole source with specific polarization can only excite the modes with corresponding polarization. The effects of location and polarization of a dipole source on the excitation of a photonic crystal H1 cavity are important for understanding the fundamental physics of entangled photon generation with a coupled quantum dot and photonic crystal system.

Lorenz–Mie theory for 2D scattering and resonance calculations

This PhD tutorial is concerned with a description of the two-dimensional generalized Lorenz–Mie theory (2D-GLMT), a well-established numerical method used to compute the interaction of light with arrays of cylindrical scatterers. This theory is based on the method of separation of variables and the application of an addition theorem for cylindrical functions. The purpose of this tutorial is to assemble the practical tools necessary to implement the 2D-GLMT method for the computation of scattering by passive scatterers or of resonances in optically active media. The first part contains a derivation of the vector and scalar Helmholtz equations for 2D geometries, starting from Maxwell’s equations. Optically active media are included in 2D-GLMT using a recent stationary formulation of the Maxwell–Bloch equations called steady-state ab initio laser theory (SALT), which introduces new classes of solutions useful for resonance computations. Following these preliminaries, a detailed description of 2D-GLMT is presented. The emphasis is placed on the derivation of beam-shape coefficients for scattering computations, as well as the computation of resonant modes using a combination of 2D-GLMT and SALT. The final section contains several numerical examples illustrating the full potential of 2D-GLMT for scattering and resonance computations. These examples, drawn from the literature, include the design of integrated polarization filters and the computation of optical modes of photonic crystal cavities and random lasers.

Polarization properties and disorder effects in H3 photonic crystal cavities incorporating site-controlled, high-symmetry quantum dot arrays

We report on the effects of optical disorder on breaking the symmetry of the cavity modes of H3 photonic crystal cavities incorporating site-controlled pyramidal quantum dots (QDs) as the internal light source. The high in-plane symmetry of the polarization states of the pyramidal QDs simplifies the analysis of the polarization states of the H3 cavities. It is shown that the optical disorder induced by fabrication imperfections lifts the degeneracy of the two quadrupole cavity modes and tilts the elongation axes of the cavity mode patterns with respect to the ideal, hexagonal symmetry case. These results are useful for designing QD-cavity structures for polarization-entangled photon sources and few-QD lasers.

Dynamically controlling the emission of single excitons in photonic crystal cavities.

Single excitons in semiconductor microcavities represent a solid state and scalable platform for cavity quantum electrodynamics, potentially enabling an interface between flying (photon) and static (exciton) quantum bits in future quantum networks. While both single-photon emission and the strong coupling regime have been demonstrated, further progress has been hampered by the inability to control the coherent evolution of the cavity quantum electrodynamics system in real time, as needed to produce and harness charge–photon entanglement. Here using the ultrafast electrical tuning of the exciton energy in a photonic crystal diode, we demonstrate the dynamic control of the coupling of a single exciton to a photonic crystal cavity mode on a sub-nanosecond timescale, faster than the natural lifetime of the exciton. This opens the way to the control of single-photon waveforms, as needed for quantum interfaces, and to the real-time control of solid-state cavity quantum electrodynamics systems.

Heralded preparation and readout of entangled phonons in a photonic crystal cavity.

We propose a realistic protocol for the preparation and readout of mechanical Bell states in an optomechanical system. The proposal relies on parameters characterizing a photonic crystal cavity mode, coupled to two localized flexural modes of the structure, but equally applies to other optomechanical systems in the same parameter range. The nonclassical states are heralded via optical postselection and revealed in specific interference patterns characterizing the emission at the cavity frequency.

Demonstration of temperature resilient properties of 2D silicon carbide photonic crystal structures and cavity modes

In this paper, photonic crystal (PhC) based on two dimensional (2D) square and hexagonal lattice periodic arrays of Silicon Carbide (SiC) rods in air structure have been investigated using plane wave expansion (PWE) method. The PhC designs have been optimized for telecommunication wavelength (λ=1.55μm) by varying the radius of the rods and lattice constant. The result obtained shows that a photonic band gap (PBG) exists for TE-mode propagation. First, the effect of temperature on the width of the photonic band gap in the 2D SiC PhC structure has been investigated and compared with Silicon (Si) PhC. Further, a cavity has been created in the proposed SiC PhC and carried out temperature resiliency study of the defect modes. The dispersion relation for the TE mode of a point defect A1 cavity for both SiC and Si PhC has been plotted. Quality factor (Q) for both these structures have been calculated using finite difference time domain (FDTD) method and found a maximum Q value of 224 for SiC and 213 for Si PhC cavity structures. These analyses are important for fabricating novel PhC cavity designs that may find application in temperature resilient devices.

Grating-coupled mid-infrared light emission from tensilely strained germanium nanomembranes

Mechanically stressed nanomembranes are used to demonstrate mid-infrared interband light emission from Ge within the 2.1–2.5 μm atmospheric transmission window. Large biaxial tensile strain is introduced in these samples to convert Ge into a (near-) direct-bandgap semiconductor and to red-shift its luminescence. A diffractive array of Ge pillars is used to outcouple the long-wavelength interband radiation, which is otherwise primarily emitted in the sample plane. An order-of-magnitude strain-induced enhancement in radiative efficiency is also reported, together with the observation of luminescence signatures associated with photonic-crystal cavity modes. These results are promising for the development of silicon-compatible lasers for mid-infrared optoelectronics applications.

Energy-efficient utilization of bipolar optical forces in nano-optomechanical cavities

Nanoscale all-optical circuits driven by optical forces have broad applications in future communication, computation, and sensing systems. Because human society faces huge challenges of energy saving and emission reduction, it is very important to develop energy-efficient nano-optomechanical devices. Due to their high quality (Q) factors, resonance modes of cavities are capable of generating much larger forces than waveguide modes. Here we experimentally demonstrate the use of resonance modes of double-coupled one-dimensional photonic crystal cavities to generate bipolar optical forces. Attractive and repulsive forces of -6.2 nN and 1.9 nN were obtained with respective launching powers of 0.81 mW and 0.87 mW in the waveguide just before cavities. Supported by flexible nanosprings (spring constant 0.166 N/m), one cavity is pulled to (pushed away from) the other cavity by 37.1 nm (11.4 nm). The shifts of the selected resonance modes of the device are mechanically and thermally calibrated with an integrated nanoelectromechanical system actuator and a temperature-controlled testing platform respectively. Based on these experimentally-obtained relations, probe mode shifts due to the optomechanical effect are decoupled from those due to the thermo-optic effect. Actuated by the third-order even pump mode, the optomechanical shift of the second-order even probe mode is found to be about 2.5 times its thermal shift, indicating a highly efficient conversion of light energy to mechanical energy.

MODE TUNING IN PHOTONIC CRYSTAL CAVITIES USING GEOMETRY OF FIRST NEIGHBORING LAYER

The relation between position of optical source and excitation of photonic crystal cavity modes are investigated. For multimode cavities, the source position considerably affects the modes' excitation. The frequency distributions of local density of photonic states in a multimode cavity differ for source positions at structural symmetric locations and nonsymmetrical ones. It was also found that the geometry of cavity's neighboring layers has strong influence on the spatial and spectral distributions of modes. The results also show that the shifts of various cavity modes in frequency domain have different sensitivity with respect to geometrical tolerance. This can be used in various applications which need mode tuning.

First-principles method for high-Q photonic crystal cavity mode calculations

We present a first-principles method to compute radiation properties of ultra-high quality factor photonic crystal cavities. Our Frequency-domain Approach for Radiation (FAR) can compute the far-field radiation pattern and quality factor of cavity modes ~ 100 times more rapidly than conventional finite-difference time domain calculations. We explain how the radiation pattern depends on the perturbation used to create the cavity and on the Bloch modes of the photonic crystal.