Speckle statistics in a chaotic multimode fiber

Experimental study of speckle patterns generated by low-coherence semiconductor laser light

Speckle is a wave interference phenomenon that has been studied in various fields, including optics, hydrodynamics, and acoustics. Speckle patterns contain spectral information of the interfering waves and of the scattering medium that generates the pattern. Here, we study experimentally the speckle patterns generated by the light emitted by two types of semiconductor lasers: conventional laser diodes, where we induce low-coherence emission by optical feedback or by pump current modulation, and coupled nanolasers. In both cases, we analyze the intensity statistics of the respective speckle patterns to inspect the degree of coherence of the light. We show that the speckle analysis provides a non-spectral way to assess the coherence of semiconductor laser light.

Silicon photonic physical unclonable function

Physical unclonable functions (PUFs) serve as a hardware source of private information that cannot be duplicated and have applications in hardware integrity and information security. Here we demonstrate a photonic PUF based on ultrafast nonlinear optical interactions in a chaotic silicon micro-cavity. The device is probed with a spectrally-encoded ultrashort optical pulse, which nonlinearly interacts with the micro-cavity. This interaction produces a highly complex and unpredictable, yet deterministic, ultrafast response that can serve as a unique "fingerprint" of the cavity and as a source of private information for the device's holder. Experimentally, we extract 17.1-kbit binary keys from six different photonic PUF designs and demonstrate the uniqueness and reproducibility of these keys. Furthermore, we experimentally test exact copies of the six photonic PUFs and demonstrate their unclonability due to unavoidable fabrication variations.

Lossy chaotic electromagnetic reverberation chambers: Universal statistical behavior of the vectorial field

The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a first step, the distribution of wave intensities in chaotic systems with varying opening in the weak coupling limit for scalar quantum waves is derived by means of random matrix theory. In this limit the only parameters are the modal overlap and the number of open channels. Using the extended effective Hamiltonian, we describe the intensity statistics of the vectorial electromagnetic eigenmodes of lossy reverberation chambers. Finally, the typical quantity of interest in such chambers, namely, the distribution of the electromagnetic response, is discussed. By determining the distribution of the phase rigidity, describing the coupling to the environment, using random matrix numerical data, we find good agreement between the theoretical prediction and numerical calculations of the response.

Regular modes in a mixed-dynamics-based optical fiber

A multimode optical fiber with a truncated transverse cross section acts as a powerful versatile support to investigate the wave features of complex ray dynamics. In this paper, we concentrate on the case of a geometry inducing mixed dynamics. We highlight that regular modes associated with stable periodic orbits present an enhanced spatial intensity localization. We report the statistics of the inverse participation ratio whose features are analogous to those of Anderson localized modes. Our study is supported by both numerical and experimental results on the spatial localization and spectral regularity of the regular modes.

Enhanced pump absorption efficiency in coiled and twisted double-clad thulium-doped fibers

Results of the first experimental demonstration of the recently proposed technique for improvement of the pump absorption in double-clad fibers by their simultaneous coiling and twisting are reported. The peak absorption (14 dB) of 3-m long hexagonal thulium-doped fiber was increased by 8 dB by its simultaneous coiling and twisting. Explanation of the effect is given by numerical modelling of the pump absorption in hexagonal and panda-type double-clad fibers. Improvement of fiber laser performance was also proved. The slope efficiency increased from 19.6% of the straight fiber to 23.9% of the coiled only fiber and 29.4% of the simultaneously coiled and twisted fiber.

Effect of geometry on the classical entanglement in a chaotic optical fiber

The effect of boundary deformation on the classical entanglement which appears in the classical electromagnetic field is considered. A chaotic billiard geometry is used to explore the influence of the mechanical modification of the optical fiber cross-sectional geometry on the production of classical entanglement within the electromagnetic fields. For the experimental realization of our idea, we propose an optical fiber with a cross section that belongs to the family of Robnik chaotic billiards. Our results show that a modification of the fiber geometry from a regular to a chaotic regime can enhance the transverse mode classical entanglement.

Dielectric square resonator investigated with microwave experiments

We present a detailed experimental study of the symmetry properties and the momentum space representation of the field distributions of a dielectric square resonator as well as the comparison with a semiclassical model. The experiments have been performed with a flat ceramic microwave resonator. Both the resonance spectra and the field distributions were measured. The momentum space representations of the latter evidenced that the resonant states are each related to a specific classical torus, leading to the regular structure of the spectrum. Furthermore, they allow for a precise determination of the refractive index. Measurements with different arrangements of the emitting and the receiving antennas were performed and their influence on the symmetry properties of the field distributions was investigated in detail, showing that resonances with specific symmetries can be selected purposefully. In addition, the length spectrum deduced from the measured resonance spectra and the trace formula for the dielectric square resonator are discussed in the framework of the semiclassical model.

All-fiber spectrometer based on speckle pattern reconstruction

A standard multimode optical fiber can be used as a general purpose spectrometer after calibrating the wavelength dependent speckle patterns produced by interference between the guided modes of the fiber. A transmission matrix was used to store the calibration data and a robust algorithm was developed to reconstruct an arbitrary input spectrum in the presence of experimental noise. We demonstrate that a 20 meter long fiber can resolve two laser lines separated by only 8 pm. At the other extreme, we show that a 2 centimeter long fiber can measure a broadband continuous spectrum generated from a supercontinuum source. We investigate the effect of the fiber geometry on the spectral resolution and bandwidth, and also discuss the additional limitation on the bandwidth imposed by speckle contrast reduction when measuring dense spectra. Finally, we demonstrate a method to reduce the spectrum reconstruction error and increase the bandwidth by separately imaging the speckle patterns of orthogonal polarizations. The multimode fiber spectrometer is compact, lightweight, low cost, and provides high resolution with low loss.

Experimental phase-space-based optical amplification of scar modes

Wave billiards which are chaotic in the geometrical limit are known to support nongeneric spatially localized modes called scar modes. The interaction of the scar modes with gain has been recently investigated in optics in microcavity lasers and vertical-cavity surface-emitting lasers. Exploiting the localization properties of scar modes in their wave-analogous phase-space representation, we report experimental results of scar mode selection by gain in a doped D-shaped optical fiber.

Controlled excitation of scar modes in passive and active multimode chaotic fiber

A multimode optical fiber with a D-shaped cross section is an experimental paradigm of a wave system with chaotic ray dynamics. We show that seldom but usable modes, called scar modes, localized along some particular direction of the geometric trajectories, can be selectively excited. We report numerical simulations that demonstrate the importance of the so-called self-focal point in the scar mode selection process. We use a localized illumination in a passive fiber, or a localized gain in a ytterbium-doped fiber, located in the vicinity of this special point to control scar mode selection.

Fiber cross-sectional imaging by manually controlled low coherence light sources

We couple a variable-coherence light beam into a multimode optical fiber and observe the fiber cross-sectional images. The variation in the fiber imaging is explored as we change the degree of optical coherence of the incident light. Low coherence light is shown to be capable of improving the quality of the fiber images. Various mode patterns of a multimode optical fiber are also shown numerically and experimentally to elucidate the fiber coupling characteristics.

Superscars in billiards: a model for doorway states in quantum spectra

In a unifying way, the doorway mechanism explains spectral properties in a rich variety of open mesoscopic quantum systems, ranging from atoms to nuclei. A distinct state and a background of other states couple to each other which sensitively affects the strength function. The recently measured superscars in the barrier billiard provide an ideal model for an in-depth investigation of this mechanism. We introduce two new statistical observables: the full distribution of the maximum coupling coefficient to the doorway and directed spatial correlators. Using random matrix theory and random plane waves, we obtain a consistent understanding of the experimental data.

Selective amplification of scars in a chaotic optical fiber

In this Letter we propose an original mechanism to select scar modes through coherent gain amplification in a multimode D-shaped fiber. More precisely, we demonstrate the selective amplification of scar modes by positioning a gain region in the vicinity of the self-focal point of the shortest periodic orbit in the transverse motion.

Air-clad fibers: pump absorption assisted by chaotic wave dynamics?

Wave chaos is a concept which has already proved its practical usefulness in design of double-clad fibers for cladding-pumped fiber lasers and fiber amplifiers. In general, classically chaotic geometries will favor strong pump absorption and we address the extent of chaotic wave dynamics in typical air-clad geometries. While air-clad structures supporting sup-wavelength convex air-glass interfaces (viewed from the high-index side) will promote chaotic dynamics we find guidance of regular whispering-gallery modes in air-clad structures resembling an overall cylindrical symmetry. Highly symmetric air-clad structures may thus suppress the pump-absorption efficiency eta below the ergodic scaling law etainfinity Ac/Acl, where Ac and Acl are the areas of the rare-earth doped core and the cladding, respectively.

Illumination and fluorescence collection volumes for fiber optic probes in tissue

Optical fibers can deliver light to, and collect it from, regions deep in tissue. However, reported illumination and fluorescence collection volumes adjacent to the fiber tip have been inconsistent, and systematic data on this topic are not available. Illumination and fluorescence collection profiles were characterized with high spatial resolution for different optical fibers in tissue and various fluids using two-photon flash photolysis and excitation. We confirm that illumination and fluorescence collection volumes for optical fibers are near identical. Collection volume is determined by the core dimensions and numerical aperture (NA) of the fiber and the scattering properties of the medium. For a multimode optical fiber with 100 microm core diam and NA=0.22, 80% of the total fluorescence is collected from a depth of 170 microm in tissue and 465 microm in nonscattering fluid. A semiempirical mathematical description of photon flux adjacent to the fiber tip was also developed and validated. This was used to quantify the extent of temporal blurring associated with propagation of a wavefront of altered fluorescence emission across the region addressed by fiber optic probes. We provide information that will facilitate the design of optical probes for tissue imaging or therapeutic applications.

Statistical properties of experimental coherent waves in microcavity lasers: analogous study of quantum billiard wave functions

We use a microcavity laser to explore the properties of experimental coherent waves as an analogous study of the chaotic wave functions in quantum billiards. With the eigenstate expansion method, the experimental high-order chaotic coherent waves are well reconstructed. The reconstructed wave functions are employed to calculate the field and intensity correlations. It is found that the spreading of k-space (momentum space) distribution leads to not only wave localization in coordinate space but also enhancement of long-range correlations.

Experiments on elastomechanical wave functions in chaotic plates and their statistical features

We measure the amplitude of the elastomechanical displacement at a fine grid of points on a free plate having the shape of a Sinai stadium. The obtained displacement field formally corresponds to a wave function in a quantum system. While the distribution of the squared amplitudes agrees with the prediction of random matrix theory (RMT), there is a strong deviation of the spatial correlator from the standard prediction for quantum chaotic systems. We show that this is due to the presence of two modes, leading to a beating phenomenon. We construct a proper extension of the spatial correlator within the framework of RMT.

Localization of wave patterns on classical periodic orbits in a square billiard

The connection between wave functions and classical periodic trajectories in a square billiard is analytically constructed by using the representation of SU(2) coherent states. The analytical function form is modified to show that the wave patterns can be apparently localized on the classical periodic trajectories by superposing a few nearly degenerate eigenfunctions. Based on the analogy between the Schrödinger and Helmholtz equations, the features of wave functions are experimentally studied from the transverse pattern formation in a laterally confined microcavity laser. The experimental transverse pattern in a square-shaped microcavity agrees very well with the constructed wave pattern concentrated along classical periodic orbits.