Fractal Resonator Research Articles

Novel microstrip low‐pass filters with fractal defected ground structures

AbstractIn this study, three microstrip low‐pass filters (LPFs) containing fractal‐shaped defected ground structures have been designed and manufactured. To improve the performance of microstrip LPF, cascades of inductively coupled fractal resonators have been applied. Simultaneously, to achieve relatively constant microstrip impedance resulting in essentially low reflection losses, a modification of the strip geometry has been introduced. The measured results excellently prove the validity and efficiency of the proposed new solutions. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2473–2477, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24607

Resonant properties of the Sierpinski‐based fractal resonator and its application on low‐loss miniaturized dual‐mode bandpass filter

AbstractIn this article, resonant characteristics of novel microstrip resonators based on the Sierpinski carpet fractal geometries are proposed in detail. With increasing the iteration order of the Sierpinski‐based fractal resonators, the resonant frequency is decreased but the unloaded quality factor is slightly enhanced. The resonant properties are discussed using the RLC equivalent circuit. Additional, the design guide for bandpass filter using the nth order resonator is also developed. Using these fractal resonators, several dual‐mode bandpass filters using different order resonators can be designed and fabricated to verify the advantages of the size and insertion loss reduction. It is also found good agreement between the simulation and measurement is achieved. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 1358–1361, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24321

A Sierpinski‐based resonator applied for low loss and miniaturized bandpass filters

AbstractIn this article, the resonant behaviors of the Sierpinski‐based fractal resonators were investigated first. The design guideline for the filter using the nth order resonator is then developed. A two‐pole filter example centered at 2.2 GHz based on the 3rd order Sierpinski‐based resonators was designed and fabricated. Measured results have a good agreement with the simulated results and verify the advantages of the size and insertion loss reduction as compared with the filter using conventional patch resonators. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 411–413, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24061

Miniaturization of dual-mode resonators by fractal iteration for suppression of second harmonic

We present a miniaturization technique for square dual-mode resonators. By using the Minkowski fractal iteration it is possible to obtain compact resonators. Furthermore, the second harmonic is highly attenuated, thus enhancing the rejection in the upper band. A fourth order filter using two dual-mode fractal resonators has been fabricated to illustrate these results. We use the suspended substrate technology to design these resonators, but the results can be extended to other technologies. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.

Light amplification from Cantor and asymmetric multilayer resonators

The light amplification properties of fractal and asymmetric multilayer resonator structures which contain a light amplifying medium in the middle layer are studied theoretically. The amplitude gain of transmitted light is analyzed by use of two-dimensional plots which we denote gain maps. The gain map, which is plotted against two different structural parameters, illustrates some regularities in the location of gain peaks and bandgaps. Cantor structures exhibit gain peaks at the edges of multiple bandgaps, and those peaks are higher and sharper than those of periodic structures. Asymmetric resonator structures are found to provide more gain than symmetric ones when the gain length is short. A comparison between the gain and the group velocity of light is also presented, together with the electromagnetic energy distributions in the multilayers.

Generalisation of the modified Weyl–Berry conjecture for drums with jagged boundaries

This Letter introduces a generalisation of the modified Weyl–Berry conjecture about fractal resonators, for approximating the DOS of drums with jagged boundaries, fractal or otherwise. The DOS is approximated by considering the effective length of the perimeter, defined as the length of the interior Minkowski sausage whose radius is proportional to the wavelength. Numerical results indicate that the proposed approximation correctly predicts non-asymptotic deviations from the two-term Weyl asymptotic in the densities of states of drums with deterministically fractal, randomly fractal and jagged non-fractal perimeters.

Diffractive origin of fractal resonator modes

The modes of unstable optical resonators possess fractal character. In this paper, the fundamental question of how and why fractals originate in one of the simplest linear optical systems is addressed. The answer is related to the fact that unstable resonator modes consist of a superposition of Fresnel diffraction patterns with effectively random phases. A connection is established between the mode eigenvalues and their fractal dimensions, and the consequent prediction that higher-order modes should exhibit lower fractal dimension is confirmed by numerical demonstration.

Irregular and fractal resonators with Neumann boundary conditions: Density of states and localization

91128 Palaiseau Ce´dex, France~Received 28 May 1996; revised manuscript received 15 October 1996!Vibrations of two-dimensional systems with free irregular or fractal boundaries are studied on specificexamples. The eigenmodes are calculated numerically using an analogy between Helmholtz and diffusionequations. We discuss the influence of the fractal boundary on the low-frequency part of the spectrum and onwave forms. The density of states is increased by the irregularity and exhibits oscillations at special frequencieswhich depend on the geometry. Surprisingly, many states are found to be confined at the fractal boundary.Increasing the perimeter fractality induces increased confinement.@S1063-651X~97!04402-4#PACS number~s!: 61.43.Hv, 43.20.1g, 63.20.Pw, 63.50.1xINTRODUCTION

Vibrations of strongly irregular or fractal resonators.

It is shown on a specific example that fractal boundary conditions drastically alter the properties of wave excitations in space. The low-frequency part of the vibration spectrum of a finite-range fractal drum is computed using an analogy between the Helmoltz equation and the diffusion equation. The irregularity of the frontier is found to influence strongly the density of states at low frequency. The fractal perimeter generates a specific screening effect. Very near the frontier, the decrease of the wave form is related directly to the behavior of the harmonic measure. The possibility of localization of the vibrations is qualitatively discussed and we show that localized modes may exist at low frequencies if the geometrical structures possess narrow paths. Possible application of these results to the interpretation of thermal properties of binary glasses is briefly discussed.

Experimental observation of local modes in fractal drums

It is shown that fractal boundary conditions drastically alter the properties of wave excitations in space. The low-frequency vibration modes of soap bubbles deposited on a fractal contour are observed. There exist localized modes. The vibrations have a singular behavior along the boundary. Consequently fractal resonators are necessarily non-linear resonators and have special damping properties.