O. Sydoruk

The refractive index of human hemoglobin in the visible range

Because the refractive index of hemoglobin in the visible range is sensitive to the hemoglobin concentration, optical investigations of hemoglobin are important for medical diagnostics and treatment. Direct measurements of the refractive index are, however, challenging; few such measurements have previously been reported, especially in a wide wavelength range. We directly measured the refractive index of human deoxygenated and oxygenated hemoglobin for nine wavelengths between 400 and 700 nm for the hemoglobin concentrations up to 140 g l(-1). This paper analyzes the results and suggests a set of model functions to calculate the refractive index depending on the concentration. At all wavelengths, the measured values of the refractive index depended on the concentration linearly. Analyzing the slope of the lines, we determined the specific refraction increments, derived a set of model functions for the refractive index depending on the concentration, and compared our results with those available in the literature. Based on the model functions, we further calculated the refractive index at the physiological concentration within the erythrocytes of 320 g l(-1). The results can be used to calculate the refractive index in the visible range for arbitrary concentrations provided that the refractive indices depend on the concentration linearly.

Analytical formulation for the resonant frequency of split rings

A simple approximate expression is derived for the resonant frequency of a singly split single ring that is among the first microwave resonators designed to be small relative to the wavelength. In addition to the usual gap capacitance the concept of surface capacitance is introduced. The surface capacitance is determined analytically by two different methods, first using analytical expressions for the electric field of a split cylinder, and second by using conformal mapping. Taking two practical examples the resonant frequency, found analytically, is shown to agree with that obtained by numerical simulations. The model could be used for studies of the resonant properties of split rings in the terahertz region.

Phonon-like dispersion curves of magnetoinductive waves

The dispersion characteristics of magnetoinductive (MI) waves for a one-dimensional array of metamaterial elements are investigated for the case where the element properties vary in a bi-periodic manner. It is shown that, by this means (analogously to acoustic waves in a solid), a variety of dispersion curves can be obtained including those displaying an “optical” branch. The flexibility of the metamaterial design makes it possible to apply this approach for obtaining specified dispersion properties. A design permitting parametric amplification is proposed.

Mechanism of subwavelength imaging with bilayered magnetic metamaterials: Theory and experiment

We present a theoretical and experimental study of a bilayered metamaterial structure for subwavelength imaging of magnetic field. The simplest version of such a structure consists of one or two linear arrays of capacitively loaded split pipe resonators. Its subwavelength physics is governed by strongly anisotropic magnetic coupling between individual resonators and by propagation of magnetoinductive waves with wavelength much shorter than the wavelength of the electromagnetic radiation in free space. It is shown that magnetoinductive waves propagating in the lateral direction are undesirable because they spread the image. Good subwavelength imaging is achieved when, due to the strong interlayer coupling, a stop band in the vicinity of the resonant frequency appears in the dispersion characteristics. The imaging properties of the single and double lens are compared and it is shown that the double lens has a superior performance. Excellent agreement is obtained between experimental and theoretical results ...

Rotational resonance of magnetoinductive waves : Basic concept and application to nuclear magnetic resonance

Magnetoinductive waves propagating along a set of resonant metamaterial elements are studied under the condition when the wave travels round a closed circular path and the total phase shift is an integral multiple of 2π. The resonant frequency of the circulating wave is shown to be related to the resonant frequency of the element via the known dispersion relationship. The currents in the elements are determined with the aid of the impedance matrix when the excitation is by a rotating magnetic dipole located at the center of the structure. It is shown that the power taken out from one element in the loop may approach N times that from a single element, where N is the number of elements, provided the quality factor of the individual elements is sufficiently high and suitable modifications are made to nearby elements. Potential applications to magnetic resonance spectroscopy are discussed.

Refractive index of solutions of human hemoglobin from the near-infrared to the ultraviolet range: Kramers-Kronig analysis

Abstract. Because direct measurements of the refractive index of hemoglobin over a large wavelength range are challenging, indirect methods deserve particular attention. Among them, the Kramers-Kronig relations are a powerful tool often used to derive the real part of a refractive index from its imaginary part. However, previous attempts to apply the relations to solutions of human hemoglobin have been somewhat controversial, resulting in disagreement between several studies. We show that this controversy can be resolved when careful attention is paid not only to the absorption of hemoglobin but also to the dispersion of the refractive index of the nonabsorbing solvent. We present a Kramers-Kroning analysis taking both contributions into account and compare the results with the data from several studies. Good agreement with experiments is found across the visible and parts of near-infrared and ultraviolet regions. These results reinstate the use of the Kramers-Kronig relations for hemoglobin solutions and provide an additional source of information about their refractive index.

Slow waves on magnetic metamaterials and on chains of plasmonic nanoparticles: Driven solutions in the presence of retardation

Slow waves on chains or lattices of resonant elements offer a unique tool for guiding and manipulating the electromagnetic radiation on a subwavelength scale. Applications range from radio waves to optics with two major classes of structures being used: (i) metamaterials made of coupled ring resonators supporting magnetoinductive waves and (ii) plasmonic crystals made of nanoparticles supporting waves of near-field coupling. We derive dispersion equations of both types of slow waves for the case when the interelement coupling is governed by retardation effects, and show how closely they are related. The current distribution is found from Kirchhoff’s equation by inverting the impedance matrix. In contrast to previous treatments power conservation is demonstrated in a form relevant to a finite structure: the input power is shown to be equal to the radiated power plus the powers absorbed in the Ohmic resistance of the elements and the terminal impedance. The relations between frequency and wave number are de...

Distributed gain in plasmonic reflectors and its use for terahertz generation

Semiconductor plasmons have potential for terahertz generation. Because practical device formats may be quasi-optical, we studied theoretically distributed plasmonic reflectors that comprise multiple interfaces between cascaded two-dimensional electron channels. Employing a mode-matching technique, we show that transmission through and reflection from a single interface depend on the magnitude and direction of a dc current flowing in the channels. As a result, plasmons can be amplified at an interface, and the cumulative effect of multiple interfaces increases the total gain, leading to plasmonic reflection coefficients exceeding unity. Reversing the current direction in a distributed reflector, however, has the opposite effect of plasmonic deamplification. Consequently, we propose structurally asymmetric resonators comprising two different distributed reflectors and predict that they are capable of terahertz oscillations at low threshold currents.

Interacting waves on chains of split-ring resonators in the presence of retardation

Wave propagation is studied experimentally in a one-dimensional periodic chain of magnetically coupled split-ring resonators with a spacing of about one tenth of the resonant wavelength. Retardation leads to a strong interaction between magnetoinductive and free-space waves. Two kinds of guided modes are observed: a slow backward wave which propagates far outside the light cone, and a fast forward wave close to the light cone. The two merge in a region of zero group velocity. The results are relevant for all one- and two-dimensional periodic systems interacting with waves of the surrounding space.

Terahertz instability of optical phonons interacting with plasmons in two-dimensional electron channels

A terahertz (THz) instability can occur when optical phonons interact with drifting solid-state plasmas. We developed a theoretical model for the optical-phonon instability in two-dimensional electron channels. The paper derives the dispersion relation and analyzes the instability using parameters measured in InSb. As the calculations show, strong instability occurs around the longitudinal optical-phonon frequency, and both the growth rate and the unstable frequency band are larger for higher electron densities and lower drift velocities. The results demonstrate the potential of the optical-phonon instability for active THz devices.