Optimization of the Q factor in photonic crystal microcavities

Vučković, Jelena; Lončar, Marko; Mabuchi, Hideo; Scherer, Axel

doi:10.1109/jqe.2002.1017597

Cited by 238 publications

(150 citation statements)

References 20 publications

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“…The fourier space analysis [3][4], the multi-pole cancelation [5], and the mode matching mechanism [6][7] [8] have been developed to explain the origin of high Qs. The design of PhC cavities, however, is typically based on extensive parameter search and optimization [9]- [13], also known as intuitive design.…”

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confidence: 99%

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Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide

Quan

Deotare

Lončar

2010

Applied Physics Letters

333

268

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A deterministic design of an ultrahigh Q, wavelength scale mode volume photonic crystal nanobeam cavity is proposed and experimentally demonstrated. Using this approach, cavities with Q> 10 6 and on-resonance transmission T>90% are designed. The devices fabricated in Si and capped with low-index polymer, have Q=80,000 and T=73%. This is, to the best of our knowledge, the highest transmission measured in deterministically designed, wavelength scale high Q cavities.Photonic crystal (PhC) The large computational cost, in particular the computation time, needed to perform the simulation of high-Q cavities make this trial based method inefficient. Inverse engineering design, in which the physical structure is optimized by constructing specific target functions and constraints, was also proposed[14] [15]. A design recipe based on the desired field distribution is proposed in [16]. In this letter, we propose and experimentally demonstrate a deterministic method to design an ultrahigh Q, sub-wavelength scale mode volume, PhC nanobeam cavity( Figure.1) that is strongly coupled to the feeding waveguide(i.e. near unity on resonance transmission). The design approach is deterministic in the sense that it does not involve any trial-based hole shifting, re-sizing and overall cavity re-scaling to ensure ultra-high Q cavity. Moreover, the final cavity resonance has less than 2% deviation from a predetermined frequency. Our design method requires only computationally inexpensive, photonic band calculations (e.g. using plane wave expansion method), and is simple to implement.The Q factor of a PhC nanobeam cavity can be maximized by reducing the out-of plane scattering(Q sc ) due to the coupling to the radiation modes. As shown previously [3][16], scattered power (P sc ) can be expressed as an integral of spatial fourier frequencies within a light cone, calculated over the surface above the cavity:. The integral is minimized when major fourier components are tightly localized (in k-space) at the edge of the first Brillioun zone [4]. We start by considering the ideal field distribution on this surface which would minimize P sc . A general property of these nanobeam cavities is that it consists of the waveguide region of length L, that sup- * Electronic address: quan@fas.harvard.edu ports propagating modes, surrounded by infinitely long Bragg mirror on each side( Figure.1a). Without the loss of generality, we consider the TE-like cavity mode with Hz as a major field component. In the case of conventional periodic Bragg mirror, evanescent field inside the mirror can be expressed as sin(β Bragg x) exp(−κx), where κ is attenuation constant. The cavity field inside the waveguide region can be represented as sin(β wg x). As mentioned above, scattering loss decreases in mirror section when β Bragg = π/a, while phase matching between mirror and waveguide [7], β Bragg = β wg , minimizes the scattering loss at cavity-mirror interface. The spatial fourier transform of such cavity field is approximately a Lorentzian in the vicinity of π/a. As ...

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“…As shown previously [3][16], scattered power (P sc ) can be expressed as an integral of spatial fourier frequencies within a light cone, calculated over the surface above the cavity:…”

mentioning

confidence: 99%

Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide

Quan

Deotare

Lončar

2010

Applied Physics Letters

333

268

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“…We first perform a full electromagnetic study of these microcavities with a 3D frequency-domain modal method 10 and emphasize the impact of hole tuning on the Q factors of cavities with several N values. Currently, the theoretical analysis 5,11,12 of PC slab microcavities relies on a complete resolution of the electromagnetic problem with 3D Finite-Difference-Time-Domain methods, followed by an analysis of the cavity-mode pattern through a Fourier (or momentum-space) decomposition method. The approach we develop here is radically different.…”

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Slow-wave effect and mode-profile matching in photonic crystal microcavities

2005

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Abstract:Physical mechanisms involved in the light confinement in photonic crystal slab microcavities are investigated. We first present a full three-dimensional numerical study of these microcavities. Then, to gain physical insight into the confinement mechanisms, we develop a Fabry-Perot model. This model provides accurate predictions and sheds new light on the physics of light confinement. We clearly identify two mechanisms to enhance the Q factor of these microcavities. The first one consists in improving the mode-profile matching at the cavity terminations and the second one in using a slow wave in the cavity.

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“…A tremendous amount of progress has been made both in optimizing cavity properties such as the quality (Q)-factor [1]- [3] and mode volume as well as in developing interesting applications that are intrinsically enabled through a nanoscale dielectric form factor [4]- [6]. Early work in this field showed that localized defect modes can be created by perturbing the periodicity of a photonic lattice, creating highly customizable nanocavities with simple control over mode field patterns, radiation profiles, spectral positioning, and photon lifetime [7], [8].…”

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Electrically Driven Photonic Crystal Nanocavity Devices

Shambat

Ellis

Petykiewicz

et al. 2012

IEEE J. Select. Topics Quantum Electron.

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Abstract-Interest in photonic crystal nanocavities is fueled by advances in device performance, particularly in the development of low-threshold laser sources. Effective electrical control of highperformance photonic crystal lasers has thus far remained elusive due to the complexities associated with current injection into cavities. A fabrication procedure for electrically pumping photonic crystal membrane devices using a lateral p-i-n junction has been developed and is described in this study. We have demonstrated electrically pumped lasing in our junctions with a threshold of 181 nA at 50 K-the lowest threshold ever demonstrated in an electrically pumped laser. At room temperature, we find that our devices behave as single-mode light-emitting diodes (LEDs), which when directly modulated, have an ultrafast electrical response up to 10 GHz corresponding to less than 1 fJ/bit energy operation-the lowest for any optical transmitter. In addition, we have demonstrated electrical pumping of photonic crystal nanobeam LEDs, and have built fiber taper coupled electro-optic modulators. Fibercoupled photodetectors based on two-photon absorption are also demonstrated as well as multiply integrated components that can be independently electrically controlled. The presented electrical injection platform is a major step forward in providing practical low power and integrable devices for on-chip photonics.

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Optimization of the Q factor in photonic crystal microcavities

Cited by 238 publications

References 20 publications

Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide

Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide

Slow-wave effect and mode-profile matching in photonic crystal microcavities

Electrically Driven Photonic Crystal Nanocavity Devices

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