Asymmetric Stationary Lasing Patterns in 2D Symmetric Microcavities

Harayama, Takahisa; Fukushima, Tetsuya; Sunada, Satoshi; Ikeda, Kensuke S.

doi:10.1103/physrevlett.91.073903

Cited by 70 publications

(70 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, because of the requirements of mode selection, these applications favor microresonators of mesoscopic dimensions, with size parameters kL = O(100) − O(1000) (where L is the linear size, k = 2π/λ is the wavenumber and λ is the wavelength) which quickly puts these systems out of the reach of numerical simulations. On the other hand, ray-optics predictions of the intricate resonator modes [4,6,9,13,14,15,16,17] can deviate substantially from experimental observations [5,7] and theoretical predictions [5,11,15,16].The purpose of this paper is to develop an amended ray optics (ARO) description which still idealizes beams as rays, but incorporates corrections of the origin and propagation direction of the reflected ray. We identify these corrections by utilizing quantum-phase space representations of the incident and reflected beam [18] and relate them to the recently discovered Fresnel filtering effect [19] and the long-known Goos-Hänchen shift [20].…”

mentioning

confidence: 99%

Correcting Ray Optics at Curved Dielectric Microresonator Interfaces: Phase-Space Unification of Fresnel Filtering and the Goos-Hänchen Shift

Schomerus

Hentschel

2006

Phys. Rev. Lett.

View full text Add to dashboard Cite

We develop an amended ray optics description for reflection at the curved dielectric interfaces of optical microresonators which improves the agreement with wave optics by about one order of magnitude. The corrections are separated into two contributions of similar magnitude, corresponding to ray displacement in independent quantum phase space directions, which can be identified with Fresnel filtering and the Goos-Hänchen shift, respectively. Hence we unify two effects which only have been studied separately in the past.PACS numbers: 05.45. Mt, 42.55.Sa Over the recent years it has become feasible to design optical microresonators that confine photons by means of dielectric interfaces into a small spatial region not larger than a few micrometers [1,2,3]. Two promising lines of research are the amplification of photons by stimulated emission in active media, which yields lasing action [1,2,3,4,5,6,7,8,9,10,11], and the generation and trapping of single photons which can be used as carriers of quantum information [12]. These applications require integration of several components and interfacing with electronics, which are best realized in twodimensional resonator geometries where the main in-and out-coupling directions are confined to a plane, and can be selected via the (asymmetric) resonator geometry. Furthermore, because of the requirements of mode selection, these applications favor microresonators of mesoscopic dimensions, with size parameters kL = O(100) − O(1000) (where L is the linear size, k = 2π/λ is the wavenumber and λ is the wavelength) which quickly puts these systems out of the reach of numerical simulations. On the other hand, ray-optics predictions of the intricate resonator modes [4,6,9,13,14,15,16,17] can deviate substantially from experimental observations [5,7] and theoretical predictions [5,11,15,16].The purpose of this paper is to develop an amended ray optics (ARO) description which still idealizes beams as rays, but incorporates corrections of the origin and propagation direction of the reflected ray. We identify these corrections by utilizing quantum-phase space representations of the incident and reflected beam [18] and relate them to the recently discovered Fresnel filtering effect [19] and the long-known Goos-Hänchen shift [20]. These two effects have only been discussed separately in the past (for applications to microresonators see, e.g., Refs. [5,11,21,22]), and their complementary nature has not been realized. Moreover, their uniform analysis for all angles of incidence is known to pose considerable technical challenges [19,23,24,25]. In the phasespace representation, the Fresnel filtering and Goos-Hänchen corrections are simply determined by the position of maximal phase-space density. For the prototypical case of a Gaussian • is close to the critical angle χ ′ = 41.8• . Conventional ray optics predicts that the beam is specularly reflected at the point of incidence. In this paper we use phase-space representations to obtain a more accurate reflection law, which accounts for (i...

show abstract

mentioning

confidence: 99%

Correcting Ray Optics at Curved Dielectric Microresonator Interfaces: Phase-Space Unification of Fresnel Filtering and the Goos-Hänchen Shift

Schomerus

Hentschel

2006

Phys. Rev. Lett.

View full text Add to dashboard Cite

show abstract

“…[17][18][19][20] Deformed microcavities fabricated on a chip are particularly desired for high-density optoelectronic integration, but they suffer from low Q factors in experiments. The Q factors are typically around or even smaller than ten thousand [21][22][23][24][25][26][27] limited by the large scattering losses from the involuntary surface roughness. The high Q factor is of great importance in fundamental studies and on-chip photonic applications.…”

mentioning

confidence: 99%

Highly Unidirectional Emission and Ultralow‐Threshold Lasing from On‐Chip Ultrahigh‐Q Microcavities

et al. 2012

View full text Add to dashboard Cite

Confi nement and manipulation of photons using microcavities have triggered intense research interest for more than a decade. [ 1 ] Prominent examples are whispering gallery mode (WGM) microcavities, [ 2 , 3 ] which confi ne photons by means of continuous total internal refl ection along a curved and smooth surface. The long photon lifetime (described by high Q factors), strong fi eld confi nement, and in-plane emission characteristics make them promising candidates for novel light sources [4][5][6][7][8][9] and biochemical sensors with the ability of detecting few or even single nanoparticles. [ 10 , 11 ] The principal disadvantage of circular WGM microcavities is their intrinsic isotropy of emission due to their rotational symmetry. In addition to the photonic structures consisting of two or more perfectly spherical microcavities, [ 12 ] one of vital solutions is to use deformed microcavities by breaking the rotational symmetry, [13][14][15][16] which can provide not only the directional emission but also the effi cient and robust excitation of WGMs by a free-space optical beam. [17][18][19][20] Deformed microcavities fabricated on a chip are particularly desired for high-density optoelectronic integration, but they suffer from low Q factors in experiments. The Q factors are typically around or even smaller than ten thousand [21][22][23][24][25][26][27] limited by the large scattering losses from the involuntary surface roughness. The high Q factor is of great importance in fundamental studies and on-chip photonic applications. Here, with a pattern transfer technique and a refl ow process ensuring a nearly atomic-scale microcavity surface, we demonstrate experimentally on-chip undoped silica deformed microcavities which support both nearly unidirectional emission and ultrahigh Q factors exceeding 100 million. Consequently, low-threshold, unidirectional microlasing in such a microcavity with Q factor about 3 million is realized by erbium doping and a convenient free-space excitation.The deformed microcavities are fabricated from a 2-μ mthick layer of silicon dioxide on a silicon wafer. Combining a two-step dry etching process and a laser refl ow process is employed for the fi rst time to transfer patterns and achieve microcavities with designed shapes and ultra-smooth cavity surface. The process details are depicted in Figure 1 a. First, we purposely design the mask patterns with minor modifications from the desired deformed toroidal boundaries R ( ϕ ) by adding an extra 15 μ m in the radius at all polar angles. Through optical lithography followed by buffered HF etching, deformed silica disks are created on the silicon wafer, which inherit the mask patterns well. Subsequently, the resulting silica disks are exposed to XeF 2 gas at 2.7 torr to etch the underneath silicon by about 15 μ m. In this process, the silica disks keep their original shapes and also serve as etching masks for the silicon underneath; consequently a silicon pillar is formed under each disk. Owing to the isotropic dry etching of silicon, ...

show abstract

“…The direction of asymmetric emission oscillates, upwards and downwards alternately. We can expect if the pumping rate increase, this multimodes operation becomes single mode operation resulted from the locking process [15].…”

Section: Dynamical Modeling Of Microdisk Lasermentioning

confidence: 99%

“…Moreover, due to the inherent properties of the dielectric cavities, the existence of quasi-scarred resonance modes [13], which are not supported by any unstable periodic orbit, are suggested and numerically confirmed in a spiralshaped dielectric microdisk. In a nonlinear dynamical model of a stadium-shaped cavity with an active medium, Harayama et al examined laser action on a single spatially chaotic wave function [14] and locking of two resonance modes of different symmetry classes and slightly different frequencies [15].…”

Section: Introductionmentioning

confidence: 99%

Resonance patterns in a stadium-shaped microcavity

et al. 2004

View full text Add to dashboard Cite

We investigate resonance patterns in a stadium-shaped microcavity around nckR ≃ 10, where nc is the refractive index, k the vacuum wavenumber, and R the radius of the circular part of the cavity. We find that the patterns of high Q resonances can be classified, even though the classical dynamics of the stadium system is chaotic. The patterns of the high Q resonances are consistent with the ray dynamical consideration, and appears as the stationary lasing modes with low pumping rate in the nonlinear dynamical model. All resonance patterns are presented in a finite range of kR.

show abstract

Asymmetric Stationary Lasing Patterns in 2D Symmetric Microcavities

Cited by 70 publications

References 20 publications

Correcting Ray Optics at Curved Dielectric Microresonator Interfaces: Phase-Space Unification of Fresnel Filtering and the Goos-Hänchen Shift

Correcting Ray Optics at Curved Dielectric Microresonator Interfaces: Phase-Space Unification of Fresnel Filtering and the Goos-Hänchen Shift

Highly Unidirectional Emission and Ultralow‐Threshold Lasing from On‐Chip Ultrahigh‐Q Microcavities

Resonance patterns in a stadium-shaped microcavity

Contact Info

Product

Resources

About