We present an analytical and experimental study of the scattering parameters in a one dimensional (1D) symmetric photonic crystal and their relation to the density of states (DOS). The 1D photonic crystal is constituted by N alternating wires and loops that are either inserted horizontally or attached vertically between the source and load on a transmission line. The complete knowledge of the scattering matrix coefficients (S i j ) allows us to access the DOS and eigenvalues of the finite periodic structure as well as the DOS and dispersion curves of an infinite periodic system. We show the usefulness of the transmission and reflection delay times and highlight their similarities and differences with respect to the DOS, in particular as a function of the absorption strength in the system. For both horizontal and vertical geometries, we show analytically that in a lossless structure, the DOS is proportional to the Friedel phase, namely the derivative of the argument of the determinant of the scattering matrix S. For a low loss system, this proportionality remains still valid with a good approximation and can be used as a practical tool to derive the DOS and therefore the dispersion curves from experimental data. Also, the absorption can be accurately extracted from the measurement of the modulus of the determinant of S. However, for increasing strength of dissipation, we show how and why these relationships cease to be valid. Still, the transmission delay time can remain an efficient tool to derive DOS even at relatively high dissipation strength. Additionally, we show that in the vertical geometry the transmission and reflection delay times exhibit negative delta peaks which are related directly to the eigenmodes of the finite system with different boundary conditions on its extremities. Our theoretical results are obtained by means of the Green's function approach, whereas the experimental demonstrations are performed using standard coaxial cables in the radio-frequency domain.

The concept of bound states in the continuum (BICs) in a simple cavity attracts much interest in recent works in wave physics. The BICs are perfectly confined modes with an infinite lifetime that reside inside the continuous spectrum of radiative modes, but they remain totally decoupled from it. There exist several types of BICs based on their physical origin: one of the most interesting types is Friedrich-Wintgen (FW) BICs which result from the destructive interference of two resonant modes belonging to the same cavity. Here, we investigate theoretically and experimentally the existence of FW BICs in a side-coupled loop. The cavity is made of a loop of length 2d = d 2 + d 3 connected to a stub of length d 4 . The whole cavity is attached vertically to two semi-infinite waveguides by a wire of length d 1 . We demonstrate that the BICs can be induced either by the loop-stub system or by the two arms of lengths d 2 and d 3 of the loop for specific geometrical parameters. When a perturbation in the system produces a deviation from the BIC condition, the latter transforms to either electromagnetically induced transparency (EIT) or reflection (EIR) or Autler-Townes splitting (ATS) resonances. Both EIT and ATS exhibit similar features in the transmission spectrum, namely, a transparency window; however, they have different physical origins. Therefore, EIT and ATS resonances are fitted with corresponding analytical model expressions, revealing good agreements. The Akaike's information criterion is then used to quantitatively discern EIT from ATS and the transition from ATS to EIT is also carried out. Our theoretical results are obtained by means of the Green's function method which enables us to obtain the transmission and reflection coefficients, dispersion relations, as well as density of states and scattering matrix. An experimental validation of all these results is performed in the radio-frequency domain using coaxial cables.

We study analytically and numerically the design of plasmonic demultiplexers based on Fano and plasmonic induced transparency (PIT) resonances. The demultiplexers consist of T-shaped structures with an input waveguide and two output waveguides. Each output contains two waveguide stubs grafted either at the same position or at two different positions far from the input waveguide. We derive closed form analytical expressions of the geometrical parameters allowing a selective transfer of a single mode in one waveguide without affecting the other one. This is performed by implementing the Fano and PIT resonances which are characterized by a resonance placed near an antiresonance or placed between two antiresonances respectively. In particular, we show the possibility of trapped modes, also called bound in continuum (BIC) modes. These modes appear as resonances with zero width in the transmission spectra for appropriate lengths of the stubs. Then, by detuning slightly the stubs, BICs transform to PIT or Fano resonances. The existence of a full transmission besides a transmission zero, enables to filter a given wavelength on one output waveguide, by vanishing both the transmission on the second waveguide as well as the reflection in the input waveguide. The demultiplexer is capable to separate two fundamental optical windows (i.e. 1310 and 1550 nm). The performance of the demultiplexer platform is measured using the crosstalk of the two outputs and quality factor. The lowest value of the crosstalk −96.8 dB with an average of −84.7 dB is achieved and a maximum quality factor 45 is obtained. The maximum transmission reaches a high value of 85% despite the large metallic losses. These values are suitable for integrated photonic circuits in the optical communication. The analytical results are obtained by means of the Green’s function method which enables us to deduce the transmission and reflection coefficients, as well as the delay times and density of states. These results are confirmed by numerical simulations using a 2D finite element method. The analytical analysis developed in this work represent a predictive method to understand deeply different physical phenomena in more complex plasmonic devices.

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We investigate both analytically and numerically the existence of localized surface modes, the so-called plasmonic Tamm states (PTSs), in a new and versatile platform based on a periodic array of metal-insulator-metal (MIM) stubs grafted along a MIM waveguide. By considering a semi-infinite structure in which we modify the length of the segment at the surface, we show the existence of surface states inside the bandgaps of the periodic structure and investigate the dependence of the localized modes as a function of the geometrical parameters and the boundary conditions applied at the surface. Three types of surface boundary conditions are considered, namely, two limiting cases of zero surface impedance (or perfect electric conductor), infinite surface impedance (or perfect magnetic conductor), and a third case where the structure is in contact with a real metal. In the latter case, we show that the existence of the interface state can be demonstrated based on topological arguments using the Zak phase. We also demonstrate that if a finite size comb-crystal is vertically grafted along a horizontal waveguide, the PTSs can be detected from the dips in the amplitudes of transmission and reflection coefficients as well as from the peaks in their delay times and the local density of states (LDOS). Our theoretical study is first performed analytically with the help of a Green’s function method, which allows the calculation of the dispersion relations of the bulk and surface modes and the LDOS, as well as the transmission and reflection coefficients of the plasmonic comb-like structure. Then, these results are confirmed by a numerical simulation utilizing a 2D finite element method. Besides providing a deep physical analysis of the PTSs, our work demonstrates the capability of the analytical method as a predictive approach in more complex structures. The proposed designs in this paper can be useful to realize highly sensitive plasmonic nanosensors.