A degenerate band edge is a resonant dispersive behavior of coupled transmission lines arising from a fourth-order degeneracy due to the coalescence of two propagating and two evanescent modes. It leads to a so-called giant resonance resulting in field enhancement inside the transmission line. In this paper, we propose a SIW periodic line supporting a degenerate band edge and we study the impact of losses. Conductor and dielectric losses are analyzed in the full-wave simulations of the unit cell and of truncated structures.
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Sensitivity of resonance frequency in the detection of thin layer using nano-slit structures
Abstract We derive the formulas for the resonance frequencies and their sensitivity when the nano-slit structures are used in the detection of thin layers. For a thin layer with a thickness of $H$ deposited over the nanostructure, we show quantitatively that for both single and periodic slit structures with slit aperture size $\delta $, the sensitivity of resonance frequency reduces as $H$ increases. Specifically, the sensitivity is of order $O(\delta /H)$ if $H>\delta $ and of order $O(1+\ln H/\delta )$ otherwise. The evanescent wave modes are present along the interface between the thin dielectric film and ambient medium above. From the mathematical derivations, it is observed that the sensitivity of the resonance frequency highly depends on the effect of evanescent wave modes on the tiny slit apertures.
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- NSF-PAR ID:
- 10221166
- Date Published:
- Journal Name:
- IMA Journal of Applied Mathematics
- Volume:
- 86
- Issue:
- 1
- ISSN:
- 0272-4960
- Page Range / eLocation ID:
- 146 to 164
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Subwavelength resonant lattices offer a wide range of fascinating spectral phenomena under broadside illumination. The resonance mechanism relies on the generation of lateral Bloch modes that are phase matched to evanescent diffraction orders. The spectral properties and the total number of resonance states are governed by the structure of leaky modes and the mode count. This study investigates the effect of interface modifications on the band dynamics and bound-state transitions in guided-mode resonant lattices. We provide photonic lattices comprising rectangular Si3N4 rods with a liquid film with an adjustable boundary. The band structures and band flips are examined through numerical simulations using the rigorous coupled-wave analysis (RCWA) method and analyzing the zero-order spectral reflectance as a function of the incident angle. The band structures and band flips are examined through numerical simulations, and the influences of the refractive index and the thickness of the oil layer on the band dynamics are investigated. The results reveal distinct resonance linewidths corresponding to different refractive indices of the oil layer. Furthermore, the effect of the oil thickness on the band dynamics is explored, demonstrating precise control over the number of propagating modes within the lattice structure. Theoretical simulations and experimental results are presented for a subwavelength silicon-nitride lattice combined with a liquid film featuring an adjustable boundary. The presence of a relatively thick liquid waveguiding region enables the emergence of additional modes, including the first four transverse-electric (TE) leaky modes, which produce observable resonance signatures. Through experimental manipulation of the basic lattice’s duty cycle, the four bands undergo quantifiable band transitions and closures. The experimental results obtained within the 1400–1600 nm spectral range exhibit reasonable agreement with the numerical analysis. These findings underscore the significant role played by the interface in shaping the band dynamics of the lattice structure, providing valuable insights into the design and optimization of photonic lattices with adjustable interfaces.
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We present the general conditions to realize a fourth-order exceptional point of degeneracy (EPD) in two uniform (i.e., invariant along z) lossless and gainless coupled transmission lines (CTLs), namely, a degenerate band edge (DBE). Until now the DBE has been shown only in periodic structures. In contrast, the CTLs considered here are uniform and subdivided into four cases where the two TLs support combinations of forward propagation, backward propagation, and evanescent modes (when neglecting the mutual coupling). We demonstrate, for the first time, that a DBE is supported in uniform CTLs when there is proper coupling between: 1) propagating modes and evanescent modes, 2) forward and backward propagating modes, or 3) four evanescent modes (two in each direction). We also show that the loaded quality factor of uniform CTLs exhibiting a fourth-order EPD at k=0 is robust to series losses due to the fact that the degenerate modes do not advance in phase. We also provide a microstrip possible implementation of a uniform CTL exhibiting a DBE using periodic series capacitors with very subwavelength unit-cell length. Finally, we show an experimental verification of the existence DBE for a microstrip implementation of a CTL supporting coupled propagating and evanescent modes.more » « less
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Abstract. A narrow-band sodium lidar provides high temporal and vertical resolution observations of sodium density, atmospheric temperature, and wind that facilitate the investigation of atmospheric waves in the mesosphere and lower thermosphere (80–105 km). In order to retrieve full vector winds, such a lidar is usually configured in a multi-direction observing mode, with laser beams pointing to the zenith and several off-zenith directions. Gravity wave events were observed by such a lidar system from 06:30 to 11:00 UT on 14 January 2002 at Maui, Hawaii (20.7° N, 156.3° W). A novel method based on cross-spectrum was proposed to derive the horizontal wave information from the phase shifts among measurements in different directions. At least two wave packets were identified using this method: one with a period of ∼ 1.6 h, a horizontal wavelength of ∼ 438 km, and propagating toward the southwest; and the other one with a ∼ 3.2 h period, a ∼ 934 km horizontal wavelength, and propagating toward the northwest. The background atmosphere states were also fully measured and all intrinsic wave properties of the wave packets were derived. Dispersion and polarization relations were used to diagnose wave propagation and dissipation. It was revealed that both wave packets propagate through multiple thin evanescent layers and are possibly partially reflected but still get a good portion of energy to penetrate higher altitudes. A sensitivity study demonstrates the capability of this method in detecting medium-scale and medium-frequency gravity waves. With continuous and high-quality measurements from similar lidar systems worldwide, this method can be utilized to detect and study the characteristics of gravity waves of specific spatiotemporal scales.
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/imamat/hxaa041
