Transmission of electromagnetic waves in planar, cylindrical, and spherical dielectric layer systems and their applications

Ping, Er-Xuan

doi:10.1063/1.357999

Cited by 31 publications

(15 citation statements)

References 10 publications

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“…For a better understanding, band-structure calculations are performed with the MPB (MIT Photonic Bands) eigenvalue simulation tool, 23 with the aim of obtaining appropriate values for the band edges. As the experimental graphs show that the band gap of the circular gratings coincides with that of the linear one, 15 we applied this tool to a linear 1D structure, i.e. infinite layers with the indices obtained, which yielded a band gap that matches very well with the results of our model (Fig.…”

Section: Modelsupporting

confidence: 74%

“…12,13 The deep etched ones have the advantage of confining light in much smaller volumes, owing to the comparatively large etch depth of their trenches and the resulting strong in-plane effective index modulation. They are generally analyzed using a 2D cylindrical model based on a transfer-matrix method 14 (TMM) by means of Hankel functions [15][16][17] as general solutions of the Maxwell equations.…”

Section: Introductionmentioning

confidence: 99%

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Lasing in a 2D photonic bandgap structure

et al. 2004

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Organic two-dimensional photonic bandgap structures (2D PBG) have been fabricated by spin-coating a thin polymer film onto a nano-patterned SiO 2 circular-grating surface-emitting distributed Bragg reflectors (CG-SE-DBR). When optically pumped and for certain grating parameters, these structures exhibit a peak inside the stop band that leads to lasing with a reduced threshold. An analytical model based on the transfer-matrix method has been developed to investigate the origin of this peak. The theoretical results are in excellent agreement with the experimental findings.

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Section: Modelsupporting

confidence: 74%

Section: Introductionmentioning

confidence: 99%

Lasing in a 2D photonic bandgap structure

et al. 2004

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“…Figure 3 shows the dependences of the E-polarized and H-polarized optical eigenmode photon energies of the cylindrical microcavity as a function of the central cylinder radius « 0 , in the range close to the re¯ector' s stopband. When « 0 is large, the curves for the E-polarized and H-polarized modes are interleaved and correspond closely to the behaviour predicted by the simpli® ed formula (8). T he frequency separation of the di erent branches is given approximately by formulae (9) and (10).…”

Section: Re Su Lts An D Discussionmentioning

confidence: 71%

“…T he solid and dashed lines corresponds to Epolarized and H-polarized modes respectively. T he dotted lines correspond to the results obtained using the approximate formula (8).…”

Section: Re Su Lts An D Discussionmentioning

confidence: 98%

Optical eigenmodes of a cylindrical microcavity

Kaliteevski

Abram

Nikolaev

2000

Journal of Modern Optics

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Abstrac t.T he optical mode structure of a cylindrical microcavity has been investigated using a transfer matrix approach. We derive exact algebraic equations from which the frequencies of the optical eigenmodes of the two polarizations can be obtained, as well as approximate explicit algebraic expressions for those frequencies. In trod u c tionSemiconductor microcavities have attracted increasing interest in the last decade as a result of their application in the investigation of light± matter interactions [1] in low-dimensional systems, and because of their practical use for vertical cavity surf ace emitting lasers [2]. T he typical microcavity consists of two Bragg re¯ectors (which are essentially one-dimensional photonic band gap structures [3]) enclosing a central layer of one or more wavelengths in thickness. T he Bragg re¯ectors provide localization of light only in the dimension which is perpendicular to the layers of the structure, and theref ore the eigenmodes of the microcavity are two-dimensional photonic states.Structures which provide two-dimensional [4] and full three-dimensional localization of light [5] promise to be useful in the development of optoelectronic devices possessing enhanced properties. T wo-dimensional localization by cylindrical multilayered structures has been demonstrated experimentally [6] and the theory of the propagation of electromagnetic waves through cylindrical structures has received some attention [7± 9]. In particular, the present authors, with S okolow ski, have considered the properties of cylindrical Bragg re¯ectors using the transf er matrix technique [9].T he aim of this work is to investigate theoretically the optical eigenmode structure of a multilayered cylindrical microcavity of the type shown in ® gure 1, where light propagates in the plane perpendicular to the axis of symmetry z , but not along the axis as occurs in an optical ® ber [10,11]. However, the formalism can be applied to a wide range of other problems, including the study of non-

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“…One of particular interest is a laser device operated along the axis, such as a laser with quantum well structures in cylindrical geometry. A theory has predicted that an axial magnetic field can modulate the energy levels, or the emission spectrum, of the active cylindrical quantum well [19]. It has been pointed out that spontaneous emission from the recombination of electrons and holes in the cylindrical wells is independent of the azimuthal number due to fundamental selection rules for optical transitions.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Spontaneous Emission in Cylindrical Periodically-Layered Structures

Wang

1999

phys. stat. sol. (a)

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This paper studies the effects of cylindrical dielectric periodically‐layered structures on spontaneous emission from an excited dipole line source. The source is modeled as a forced oscillator with radiative damping. The underlying physics lies in how the oscillator can be driven by the reflected field supported by this structure. To match the boundary conditions of EM waves, the transfer matrix method (TMM) is employed for its simplicity and versatility. Both the frequency shift and modified radiative damping rate are formulated analytically. It is shown that due to interference the wave supported by the structures can affect the source emission significantly. Strong enhancement and inhibition of the emission depend on both the layered structure and the frequency. Different compositions of the structures are achieved by tuning the structure parameters such as the reflective index and the width of layers. Furthermore, the results reveal that the strong enhancement and inhibition are sensitive to the layer width. It is found that strong inhibition is stable against source position variation, whereas strong enhancement is quite unstable. Potential applications in cylindrical quantum well lasers and semiconductor devices and perspective for future work are suggested.

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Transmission of electromagnetic waves in planar, cylindrical, and spherical dielectric layer systems and their applications

Cited by 31 publications

References 10 publications

Lasing in a 2D photonic bandgap structure

Lasing in a 2D photonic bandgap structure

Optical eigenmodes of a cylindrical microcavity

Spontaneous Emission in Cylindrical Periodically-Layered Structures

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