Wave chaos enhanced light trapping in optically thin solar cells.

Enhancing the energy output of solar cells increases their competitiveness as a source of energy. Producing thinner solar cells is attractive, but a thin absorbing layer demands excellent light management in order to keep transmission- and reflection-related losses of incident photons at a minimum. We maximize absorption by trapping light rays to make the mean average path length in the absorber as long as possible. In chaotic scattering systems, there are ray trajectories with very long lifetimes. In this paper, we investigate the scattering dynamics of waves in a model system using principles from the field of quantum chaotic scattering. We quantitatively find that the transition from regular to chaotic scattering dynamics correlates with the enhancement of the absorption cross section and propose the use of an autocorrelation function to assess the average path length of rays as a possible way to verify the light-trapping efficiency experimentally.

Chaos: A new mechanism for enhancing the optical generation rate in optically thin solar cells.

The photogenerated current of solar cells can be enhanced by light management with surface structures. For solar cells with optically thin absorbing layers, it is especially important to take advantage of this fact through light trapping. The general idea behind light trapping is to use structures, either on the front surface or on the back, to scatter light rays to maximize their path length in the absorber. In this paper, we investigate the potential of chaotic scattering for light trapping. It is well known that the trajectories close to the invariant set of a chaotic scatterer spend a very long time inside of the scatterer before they leave. The invariant set, also called the chaotic repeller, contains all rays of infinite length that never enter or leave the region of the scatterer. If chaotic repellers exist in a system, a chaotic dynamics is present in the scatterer. As a model system, we investigate an elliptical dome structure placed on top of an optically thin absorbing film, a system inspired by the chaotic Bunimovich stadium. A classical ray-tracing program has been developed to classify the scattering dynamics and to evaluate the absorption efficiency, modeled with Beer-Lambert's law. We find that there is a strong correlation between the enhancement of absorption efficiency and the onset of chaotic scattering in such systems. The dynamics of the systems was shown to be chaotic by their positive Lyapunov exponents and the noninteger fractal dimension of their scattering fractals.

Observation of Mie ripples in the synchrotron Fourier transform infrared spectra of spheroidal pollen grains.

Conceptually, biological cells are dielectric, photonic resonators that are expected to show a rich variety of shape resonances when exposed to electromagnetic radiation. For spheroidal cells, these shape resonances may be predicted and analyzed using the Mie theory of dielectric spheres, which predicts that a special class of resonances, i.e., whispering gallery modes (WGMs), causes ripples in the absorbance spectra of spheroidal cells. Indeed, the first tentative indication of the presence of Mie ripples in the synchrotron Fourier transform infrared (SFTIR) absorbance spectra of Juniperus chinensis pollen has already been reported [Analyst140, 3273 (2015)ANLYAG0365-488510.1039/C5AN00401B]. To show that this observation is no isolated incidence, but a generic spectral feature that can be expected to occur in all spheroidal biological cells, we measured and analyzed the SFTIR absorbance spectra of Cunninghamia lanceolata, Juniperus chinensis, Juniperus communis, and Juniperus excelsa. All four pollen species show Mie ripples. Since the WGMs causing the ripples are surface modes, we propose ripple spectroscopy as a powerful tool for studying the surface properties of spheroidal biological cells. In addition, our paper draws attention to the fact that shape resonances need to be taken into account when analyzing (S)FTIR spectra of isolated biological cells since shape resonances may distort the shape or mimic the presence of chemical absorption bands.

Infrared refractive index dispersion of polymethyl methacrylate spheres from Mie ripples in Fourier-transform infrared microscopy extinction spectra.

We performed high-resolution Fourier-transform infrared (FTIR) spectroscopy of a polymethyl methacrylate (PMMA) sphere of unknown size in the Mie scattering region. Apart from a slow, oscillatory structure (wiggles), which is due to an interference effect, the measured FTIR extinction spectrum exhibits a ripple structure, which is due to electromagnetic resonances. We fully characterize the underlying electromagnetic mode structure of the spectrum by assigning mode numbers to each of the ripples in the measured spectrum. We show that analyzing the ripple structure in the spectrum in the wavenumber region from about 3000 cm-1 to 8000 cm-1 allows us to determine both the unknown radius of the sphere and the PMMA index of refraction, which shows a strong frequency dependence in this infrared spectral region. While in this paper we focus on examining a PMMA sphere as an example, our method of determining the refractive index and its dispersion from infrared extinction spectra is generally applicable for the determination of the index of refraction of any transparent substance that can be shaped into micron-sized spheres.

Recovery of absorbance spectra of micrometer-sized biological and inanimate particles.

In this paper, we first provide an overview of the Mie type scattering at absorbing materials and existing correction methods, followed by a new method to obtain the pure absorbance spectra of biological systems with spherical symmetry. This method is a further development of the recently described iterative algorithm of van Dijk et al. The method is tested on FTIR synchrotron spectra of polymethyl methacrylate (PMMA) microspheres and pollen grains with approximately spherical shape. The imaginary part of the refractive index was successfully recovered for both systems. Good agreement was obtained between the pure absorbance spectra obtained by this method and the measured spectra.

Ghost orbit spectroscopy.

Direct periodic-orbit expansions of individual spectral eigenvalues is a new direction in quantum mechanics. Using a unitary -matrix theory, we present exact, convergent, integral-free ghost orbit expansions of spectral eigenvalues for a step potential in the tunneling regime. We suggest an experiment to extract ghost orbit information from measured spectra in the tunneling regime (ghost orbit spectroscopy). We contrast our unitary, convergent theory with a recently published nonunitary, divergent theory [Yu. Dabaghian and R. Jensen, Eur. J. Phys. 26, 423 (2005)].

Weyl formula: experimental test of ray splitting and corner corrections.

The number of resonances N(f) of a resonator below frequency f is an essential concept in physics. Smooth approximations N(f) are known as Weyl formulas. An abrupt change in the properties of the wave propagation medium in a resonator was predicted by Prange [Phys. Rev. E 53, 207 (1996)] to produce a universal ray-splitting correction to N(f). We confirm this effect experimentally. Our results with a quasi-two-dimensional dielectric-loaded microwave cavity are directly relevant to the ray-splitting correction in two-dimensional quantal ray-splitting billiards. Our experimental spectra have sufficient accuracy and extent to allow, as far as we are aware, the first experimental determination of the corner correction, which we find to agree with theory. We show that our movable-bar setup enhances non-Newtonian periodic orbits, thereby providing an experimental technique for periodic-orbit spectroscopy. This technique, differential spectroscopy, will facilitate the study of non-Newtonian classical physics.

Explicit spectral formulas for scaling quantum graphs.

We present an exact analytical solution of the spectral problem of quasi-one-dimensional scaling quantum graphs. Strongly stochastic in the classical limit, these systems are frequently employed as models of quantum chaos. We show that despite their classical stochasticity all scaling quantum graphs are explicitly solvable in the form E(n) =f (n) , where n is the sequence number of the energy level of the quantum graph and f is a known function, which depends only on the physical and geometrical properties of the quantum graph. Our method of solution motivates a new classification scheme for quantum graphs: we show that each quantum graph can be uniquely assigned an integer m reflecting its level of complexity. We show that a network of taut strings with piecewise constant mass density provides an experimentally realizable analogue system of scaling quantum graphs.

Universal instabilities of radio-frequency traps.

Using standard tools of nonlinear dynamics we analyze recently discovered instabilities of radio-frequency charged-particle traps. In the cw-driven cylindrical Kingdon trap the instabilities occur at the two values eta*(3) =3.6130467...and eta*(4) =4.4311244...of the trap's control parameter eta. Analytical estimates based on the theory of Mathieu functions predict eta*(3) =pi square root of [(363-32 pi(2))/(66 pi square root of (6-48 pi(2))]=3.6923922...and eta*(4) = [(square root of pi)/2) x [(363-32 pi(2))/(square root of (1089+48 pi(2))-12 pi)](1/2) =4.4965466... The kicked Kingdon trap, an analytically solvable model, predicts eta*(3) = 1/3 square root of 105=3.4156502...and eta*(4) = square root of 17=4.1231056... We show that similar instabilities occur in the two-particle Paul trap and the cw-driven spherical Kingdon trap.

Explicit analytical solution for scaling quantum graphs.

We show that scaling quantum graphs with arbitrary topology are explicitly analytically solvable. This is surprising since quantum graphs are excellent models of quantum chaos and quantum chaotic systems are not usually explicitly analytically solvable.

Exact, convergent periodic-orbit expansions of individual energy eigenvalues of regular quantum graphs.

We present exact, explicit, convergent periodic-orbit expansions for individual energy levels of regular quantum graphs in the paper. One simple application is the energy levels of a particle in a piecewise constant potential. Since the classical ray trajectories (including ray splitting) in such systems are strongly chaotic, this result provides an explicit quantization of a classically chaotic system.

Explicitly solvable cases of one-dimensional quantum chaos.

We identify a set of quantum graphs with unique and precisely defined spectral properties called regular quantum graphs. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are explicitly solvable. The proof is constructive: we present exact, convergent periodic orbit expansions for individual energy levels, thus obtaining an analytical solution for the spectrum of regular quantum graphs that is complete, explicit, and exact.

Parametric correlations of the energy levels of ray-splitting billiards.

Parameter-dependent statistical properties of the spectra of ray-splitting billiards are studied experimentally and theoretically. The autocorrelation functions c(x) and c(omega,x) of level velocities as well as the generalized conductance C(0) are calculated for two different classically chaotic ray-splitting billiards. Experimentally a modified Sinai ray-splitting billiard is studied consisting of a thin microwave rectangular cavity with two quarter-circle-shaped Teflon inserts. The length of the cavity serves as the experimentally adjustable parameter. For the theoretical estimates of the parametric correlations we compute the quantum spectrum of a scaling triangular ray-splitting billiard. Our experimental and numerical results are compared with each other and with the predictions of random matrix theory.

Exact trace formulas for a class of one-dimensional ray-splitting systems.

Using quantum graph theory we establish that the ray-splitting trace formula proposed by Couchman et al. [Phys. Rev. A 46, 6193 (1992)] is exact for a class of one-dimensional ray-splitting systems. Important applications in combinatorics are suggested.

Autocorrelation function of level velocities for ray-splitting billiards

We study experimentally and theoretically the autocorrelation function of level velocities c(x) and the generalized conductance C(0) for classically chaotic ray-splitting systems. Experimentally, a Sinai ray-splitting billiard was simulated by a thin microwave rectangular cavity with a quarter-circle Teflon insert. For the theoretical estimates of the autocorrelator c(x) and the conductance C(0) we made parameter-dependent quantum calculations of eigenenergies of an annular ray-splitting billiard. Our experimental and numerical results are compared to theoretical predictions of systems based on the Gaussian orthogonal ensemble in random matrix theory.

Test of semiclassical amplitudes for quantum ray-splitting systems.

We compute semiclassically and numerically the weights of ray-splitting orbits in the density of states of a rectangular and an annular ray-splitting billiard. The agreement between the semiclassical and the numerical results is very good, confirming the necessity of including reflection and transmission coefficients of non-Newtonian ray-splitting orbits in semiclassical expressions for the density of states of ray-splitting systems.

Synchrotron radiation of crystallized beams.

We study the modifications of synchrotron radiation of charges in a storage ring as they are cooled. The pair correlation lengths between the charges are manifest in the synchrotron radiation and coherence effects exist for wavelengths longer than the coherence lengths between the charges. Therefore, the synchrotron radiation can be used as a diagnostic tool to determine the state (gas, liquid, crystal) of the charged plasma in the storage ring. We show also that the total power of the synchrotron radiation is significantly reduced for crystallized beams, both coasting and bunched. This opens the possibility of accelerating particles to ultrarelativistic energies using small-sized cyclic accelerators.