Strong resonances on periodic arrays of cylinders and optical bistability with weak incident waves

Yuan, Lijun; Lu, Ya Yan

doi:10.1103/physreva.95.023834

Cited by 72 publications

(58 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With C 0 determined such that the system (3.19)-(3.20) has solutions, we can calculate u 22 using the same mixed Chebyshev-Fourier pseudospectral method. As we mentioned in section 3, a unique solution for u 22 can be determined when the solvability condition for u 24 is imposed, and it can be written as u 22 = C 2 u * + u chosen domain. In Fig.…”

Section: Numerical and Perturbation Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Excitation of Bound States in the Continuum via Second Harmonic Generations

Yuan¹,

Lu²

2020

SIAM J. Appl. Math.

Self Cite

View full text Add to dashboard Cite

A bound state in the continuum (BIC) on a periodic structure sandwiched between two homogeneous media is a guided mode with a frequency and a wavenumber such that propagating plane waves with the same frequency and wavenumber exist in the homogeneous media. Optical BICs are of significant current interest, since they have applications in lasing, sensing, filtering, switching, and many light emission processes, but they cannot be excited by incident plane waves when the structure consists of linear materials. In this paper, we study the diffraction of a plane wave by a periodic structure with a second order nonlinearity, assuming the structure has a BIC and the frequency and wavenumber of the incident wave are one half of those of the BIC. Based on a scaling analysis and a perturbation theory, we show that the incident wave may induce a very strong second harmonic wave dominated by the BIC, and also a fourth harmonic wave that cannot be ignored. The perturbation theory reveals that the amplitude of the BIC is inversely proportional to a small parameter depending on the amplitude of the incident wave and the nonlinear coefficient. In addition, a system of four nonlinearly coupled Helmholtz equations (the four-wave model) is proposed to model the nonlinear process. Numerical solutions of the four-wave model are presented for a periodic array of circular cylinders and used to validate the perturbation results.

show abstract

Section: Numerical and Perturbation Resultsmentioning

confidence: 99%

“…Bulgakov et al [18] suggested to use the nonlinear optical Kerr effect [19] to excite the BICs. However, with the Kerr effect, the BICs become nonlinear [20] and the associated diffraction problem exhibits complicated optical bistability and symmetry-breaking phenomena [21,22].…”

mentioning

confidence: 99%

Excitation of Bound States in the Continuum via Second Harmonic Generations

Yuan¹,

Lu²

2020

SIAM J. Appl. Math.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Importantly, a BIC can be regarded as a resonant mode (or resonant state) with an infinite quality factor (Qfactor). This implies that resonant modes with arbi- * Corresponding author: mayylu@cityu.edu.hk trarily high Q-factors can be created by modifying the structure [40] or varying a physical parameter such as a component of the Bloch wavevector [41,42]. Applications of optical BICs include lasing [43], sensing [45], filtering [46,47], switching [48], nonlinear optics [41,49], etc.…”

Section: Introductionmentioning

confidence: 99%

“…This implies that resonant modes with arbi- * Corresponding author: mayylu@cityu.edu.hk trarily high Q-factors can be created by modifying the structure [40] or varying a physical parameter such as a component of the Bloch wavevector [41,42]. Applications of optical BICs include lasing [43], sensing [45], filtering [46,47], switching [48], nonlinear optics [41,49], etc. They are mostly related to the high-Q resonances, and are based on local fields enhanced by the resonances [50,51], or special features in scattering, transmission or other spectra [52,53].…”

Section: Introductionmentioning

confidence: 99%

Bound states with complex frequencies near the continuum on lossy periodic structures

Zhen

Yuan

2020

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

On a lossless periodic dielectric structure sandwiched between two homogeneous media, bound states in the continuum (BICs) with real frequencies and real Bloch wavevectors may exist, and they decay exponentially in the surrounding homogeneous media and do not couple with propagating plane waves with the same frequencies and wavevectors. The BICs are of significant current interest, because they give rise to high-Q resonances when the structure or the Bloch wavevector is slightly perturbed. In this paper, the effect of a small material loss on the BICs is analyzed by a perturbation method and illustrated by numerical results. It is shown that bound states with complex frequencies near the continuum appear, but they behave differently depending on whether the BIC is symmetryprotected or not. The Bloch wavevector of a bound state with a complex frequency can be real if the original BIC is symmetry-protected, and it is usually complex if the original BIC is not symmetryprotected. Our study improves the theoretical understanding on BICs and provides useful insight for their practical applications.

show abstract

“…Example 3:K1 andK2 [defined in Eq (43),. with unit L] as functions of a1 for an ASW on a periodic structure with three arrays of cylinders with radii a1, a2 = 0.3L and a3 = a1.…”

mentioning

confidence: 99%

Perturbation theories for symmetry-protected bound states in the continuum on two-dimensional periodic structures

Yuan

2020

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

On dielectric periodic structures with a reflection symmetry in a periodic direction, there can be antisymmetric standing waves (ASWs) that are symmetry-protected bound states in the continuum (BICs). The BICs have found many applications, mainly because they give rise to resonant modes of extremely large quality-factors (Q-factors). The ASWs are robust to symmetric perturbations of the structure, but they become resonant modes if the perturbation is non-symmetric. The Q-factor of a resonant mode on a perturbed structure is typically O(1/δ 2 ) where δ is the amplitude of the perturbation, but special perturbations can produce resonant modes with larger Q-factors. For twodimensional (2D) periodic structures with a 1D periodicity, we derive conditions on the perturbation profile such that the Q-factors are O(1/δ 4 ) or O(1/δ 6 ). For the unperturbed structure, an ASW is surrounded by resonant modes with a nonzero Bloch wave vector. For 2D periodic structures, the Q-factors of nearby resonant modes are typically O(1/β 2 ), where β is the Bloch wavenumber. We show that the Q-factors can be O(1/β 6 ) if the ASW satisfies a simple condition.

show abstract

Strong resonances on periodic arrays of cylinders and optical bistability with weak incident waves

Cited by 72 publications

References 31 publications

Excitation of Bound States in the Continuum via Second Harmonic Generations

Excitation of Bound States in the Continuum via Second Harmonic Generations

Bound states with complex frequencies near the continuum on lossy periodic structures

Perturbation theories for symmetry-protected bound states in the continuum on two-dimensional periodic structures

Contact Info

Product

Resources

About