Experimental validation of the theoretical prediction for the optical $S$ matrix

Abstract

Scattering of waves is omnipresent in nature in systems with sizes varying from $10^{-15}$ to $10^{25}$ m. Within this 40 orders of magnitude, in a great number of systems, the scattering can be separated in an averaged response that crosses rapidly the scattering region and a fluctuating delayed response. This fact is the basis of the optical model; the averaged response, represented by the optical matrix $⟨S⟩$, is composed with the fluctuating part that can be taken as a random matrix. Although the optical model was developed more than 60 years ago, a theoretical prediction for the optical matrix was obtained until very recently. The validity of such prediction is experimentally demonstrated here. This is done studying the scattering of torsional waves in a quasi-1D elastic system in which a locally periodic system is built; the distribution of the scattering matrix is calculated completely free of parameters. In contradistinction to all previous works, in microwaves and in elasticity, in which the value of $⟨S⟩$ is obtained from the experiment, here the theoretical prediction is used to compare with the experiment. Numerical simulations show that the theoretical value is still valid when strong disorder is present. Several applications of the theoretical expression for the optical matrix in other areas of physics are proposed. Possible extensions of this work are also discussed.

arXiv comment7pages, 5 figures

References in corpus (29)

• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Anomalous Localization in Low-Dimensional Systems with Correlated Disorder
• Random Matrices and Chaos in Nuclear Physics: Nuclear Reactions
• Voltage-probe and imaginary potential models for dephasing in a chaotic quantum dot
• First experimental realization of the Dirac oscillator
• Universal Impedance Fluctuations in Wave Chaotic Systems
• Full transmission and reflection of waves propagating through a maze of disorder
• Distribution of the S-matrix in chaotic microwave cavities with direct processes and absorption
• Distribution of reflection coefficients in absorbing chaotic microwave cavities
• Interference Phenomena in Electronic Transport Through Chaotic Cavities: An Information-Theoretic Approach
• The Single-Channel Regime of Transport through Random Media
• Universal transport properties of open microwave cavities with and without time-reversal symmetry
• Quantum Interference Phenomena in the Local Polarization Dynamics of Mesoscopic Systems: An NMR Observation
• Periodic Chaotic Billiards: Quantum-Classical Correspondence in Energy Space
• Anderson Localization in a String of Microwave Cavities
• Impurity effects on the band structure of one-dimensional photonic crystals: Experiment and theory
• Single-Parameter Scaling and Maximum Entropy inside Disordered One-Dimensional Systems: Theory and Experiment
• Universal spectral properties of spatially periodic quantum systems with chaotic classical dynamics
• Testing quantum transport without decoherence
• Acoustic resonance spectroscopy for the advanced undergraduate laboratory
• Electromagnetic prompt response in an elastic wave cavity
• Transport studies in three-terminal microwave graphs with orthogonal, unitary, and symplectic symmetry
• Equivalence between the mobility edge of electronic transport on disorderless networks and the onset of chaos via intermittency in deterministic maps
• Wave systems with direct processes and localized losses or gains: the non-unitary Poisson kernel
• Exact time-reversal focusing of acoustic and quantum excitations in open cavities: The perfect inverse filter
• Evolution with size in a locally periodic system: Scattering and deterministic maps
• Chaotic scattering with direct processes: A generalization of Poisson's kernel for non-unitary scattering matrices
• Typical length scales in conducting disorderless networks
• Scattering of Elastic Waves in a Quasi-one-dimensional Cavity: Theory and Experiment