... ``photonics''^1.1

Optronics -- opto-electronics -- is about using modern optical technology along with conventional microelectronics technology. Many times, the terms ``optics'' and ``photonics'' are used interchangeably, and the distinction between them is rather vague. Optics is a quite wide field dealing with light in different contexts, spanning from geometrical optics (dealing with lenses, prisms, free space transmission, etc.) to quantum optics (dealing with light-matter interaction).

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... maximum ^1.2

In a time domain setting, the $Q$ factor is defined as the ratio of the optical power stored in the cavity to the cycle averaged power radiated out of the cavity [37]. Therefore the larger the Q factor, the longer the optical field is trapped inside the cavity.

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... indices ^1.3

Other factors like anisotropy, material attenuation, side wall roughness play a role in real devices, but these are out of scope of the present work.

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... already ^1.4

For the present work, we use 2-D straight waveguide mode solver by Dr. Manfred Hammer. See www.math.utwente.nl/ hammer/Metric/ for further details.

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... modes.^2.1

Partly these notions originate from the use of a ray picture for the description of bent waveguides, or from approximate models in terms of ``equivalent'' leaky straight waveguide profiles. We will avoid these viewpoints in the present work.

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... solved^2.2

In an alternative approach, where one looks at time domain resonances of circular cavities, a similar procedure as outlined here [44,39] leads to precisely the same equation (cf. the remarks in the introduction). In that case, Eq. (2.7) is to be solved for complex valued resonance frequencies $\omega$, for given integer azimuthal mode numbers $\nu$.

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... profiles.^2.3

An approximate orthogonality relation involving complex conjugates of one of the mode profiles is derived in Ref. [91], valid in the limit of large bend radius (i.e. for almost straight waveguides).

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... product^2.4

Cf. the standard variants of orthogonality relations for straight dielectric waveguides made of attenuating materials, as introduced e.g. in Ref. [43]

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... Uranus04^3.1

For comprehensive information about finite difference time domain methods, see www.fdtd.org

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