Ternary logic in the optical controlled-SWAP gate based on Laguerre-Gaussian modes of light.

The need set by a computational industry to increase processing power, while simultaneously reducing the energy consumption of data centers, became a challenge for modern computational systems. In this work, we propose an optical communication solution, that could serve as a building block for future computing systems, due to its versatility. The solution arises from Landauer's principle and utilizes reversible logic, manifested as an optical logical gate with structured light, here represented as Laguerre-Gaussian modes. We introduced a phase-shift-based encoding technique and incorporated multi-valued logic in the form of a ternary numeral system to determine the similarity between two images through the free space communication protocol.

Differences between the geometric phase and propagation phase: clarifying the boundedness problem.

We show white light interferometer experiments that clearly demonstrate the basic differences between geometric and propagation phases. These experimental results also suggest a way to answer the "boundedness problem" in geometric phase-whether geometric phase is unbounded (i.e., can take on any values without limit) or bounded (i.e., limited to values between -π and +π). We show why the answer to this question is not as easy as it seems, from both a theoretical and an experimental perspective, and explain how the answer depends on one's choice of phase convention. We also hope that the videos provided will be pedagogically useful for explaining geometric phase.

Deciphering Pancharatnam's discovery of geometric phase: retrospective.

While Pancharatnam discovered the geometric phase in 1956, his work was not widely recognized until its endorsement by Berry in 1987, after which it received wide appreciation. However, because Pancharatnam's paper is unusually difficult to follow, his work has often been misinterpreted as referring to an evolution of states of polarization, just as Berry's work focused on a cycle of states, even though this consideration does not appear in Pancharatnam's work. We walk the reader through Pancharatnam's original derivation and show how Pancharatnam's approach connects to recent work in geometric phase. It is our hope to make this widely cited classic paper more accessible and better understood.

Wave description of geometric phase.

Since Pancharatnam's 1956 discovery of optical geometric phase and Berry's 1984 discovery of geometric phase in quantum systems, researchers analyzing geometric phase have focused almost exclusively on algebraic approaches using the Jones calculus, or on spherical trigonometry approaches using the Poincaré sphere. The abstracted mathematics of the former and the abstracted geometry of the latter obscure the physical mechanism that generates geometric phase. We show that optical geometric phase derives entirely from the superposition of waves and the resulting shift in the location of the wave maximum. This wave-based model provides a way to visualize how geometric phase arises from relationships between waves, and from the transformations induced by optical elements. We also derive the relationship between the geometric phase of a wave by itself and the phase exhibited by an interferogram, and provide the conditions under which the two match one another.

Quantum-inspired Fredkin gate based on spatial modes of light.

Insights gained from quantum physics can inspire novel classical technologies. These quantum-inspired technologies are protocols that aim at mimicking particular features of quantum algorithms. They are generally easier to implement and make use of intense beams. Here we demonstrate in a proof-of-concept experiment a quantum-inspired protocol based on the idea of quantum fingerprinting (Phys. Rev. Lett. 87, 167902, 2001).The carriers of information are optical beams with orbital angular momentum (OAM). These beams allow the implementation of a Fredkin gate or polarization-controlled SWAP operation that exchanges data encoded on beams with different OAM. We measure the degree of similarity between waveforms and strings of bits without unveiling the information content of the data.

Perfect Laguerre-Gauss beams.

Perfect vortex beams (PVBs) have intensity distributions independent of their topological charges. We propose an alternative formulation to generate PVBs through Laguerre-Gauss beams (LGBs). Using the connection between Bessel and LGBs, we formulate a modified LGB that mimics the features of a PVB, the perfect LGB (PLGB). The PLGB is closer to the ideal PVB, maintaining a quasi-constant ring radius and width. Furthermore, its number of rings can be augmented with the order of the Laguerre polynomial, showing an outer ring independent of the topological charge. Since the PLGB comprises a paraxial solution, it is closely related to an experimental realization, e.g., using spatial light modulators [Phys. Rev. A100, 053847 (2019)PLRAAN1050-294710.1103/PhysRevA.100.053847].

Cylindrical vector beam generator using a two-element interferometer.

We realize a robust and compact cylindrical vector beam generator that consists of a simple two-element interferometer composed of a beam displacer and a cube beamsplitter. The interferometer operates on the higher-order Poincaré sphere transforming a homogeneously polarized vortex into a cylindrical vector (CV) beam. We experimentally demonstrate the transformation of a single vortex beam into all the well-known CV beams and show the operations on the higher-order Poincaré sphere according to the control parameters. Our method offers an alternative to the Pancharatnam-Berry phase optical elements and has the potential to be implemented as a monolithic device.

Generation of light beams with custom orbital angular momentum and tunable transverse intensity symmetries.

We introduce a novel and simple modulation technique to tailor optical beams with a customized amount of orbital angular momentum (OAM). The technique is based on the modulation of the angular spectrum of a seed beam, which allows us to specify in an independent manner the value of OAM and the shape of the resulting beam transverse intensity. We experimentally demonstrate our method by arbitrarily shaping the radial and angular intensity distributions of Bessel and Laguerre-Gauss beams, while their OAM value remains constant. Our experimental results agree with the numerical and theoretical predictions.

Simple phase shifting by polarizer rotations in a cube beam-splitter interferometer.

A simple and low-cost method for phase-shifting interferometry by the rotation of a polarizer is presented. This proposal takes advantage of the polarization aberration in a cube beam splitter due to its geometry, to the angular dependence with the coating, and to the polarization angle of the input beam. The interferometric setup performs as a two-window common-path interferometer in which the added phase shifting is achieved by simply rotating a polarizer at the interferometer output. The viability of the proposal is sustained with experimental results in which the phase-shift value and the resulting wavefront are calculated with Farrel's technique and the three-step PSI algorithm, respectively.

Technical aspects for counting and timing photons with a digital oscilloscope.

Photon counting and timing are generic tasks in many photonics laboratories. However, the cost of a commercial photon counter system can be a limiting factor to establish a new laboratory. Homemade photon counters can present a cost-saving solution, but they can also present a demanding side project not always part of the main research. Modern digital oscilloscopes are available in most universities and can provide a simple solution to measure photon statistics. Here, we describe the technicalities and limitations for counting and timing photons using a digital oscilloscope.

Geometric phase morphology of Jones matrices.

We demonstrate an innovative technique based on the Pancharatnam-Berry phase that can be used to determine whether an optical system characterized by a Jones matrix is homogeneous or inhomogeneous, containing orthogonal or nonorthogonal eigenpolarizations, respectively. Homogeneous systems have a symmetric geometric phase morphology showing line dislocations and sets of polarization states with an equal geometric phase. In contrast, the morphology of inhomogeneous systems exhibits phase singularities, where the Pancharatnam-Berry phase is undetermined. The results show an alternative to extract polarization properties such as diattenuation and retardance, and can be used to study the transformation of space-variant polarized beams.

Orbital angular momentum of optical vortices from power measurements and the cross-correlation function.

We show that the complex-amplitude cross-correlation function between two beams can be obtained by the global Stokes parameters. We apply this approach to determine the topological charge of a Laguerre-Gaussian (LG) beam by performing power measurements only. Additionally, we study the connection of the cross-correlation function with the degree of polarization for nonuniformly polarized beams, and we obtain closed-form expressions of the cross correlation for LG vector modes and the generalized full Poincaré beams.

Adaptive boundaryless finite-difference method.

The boundaryless beam propagation method uses a mapping function to transform the infinite real space into a finite-size computational domain [Opt. Lett.21, 4 (1996)]. This leads to a bounded field that avoids the artificial reflections produced by the computational window. However, the method suffers from frequency aliasing problems, limiting the physical region to be sampled. We propose an adaptive boundaryless method that concentrates the higher density of sampling points in the region of interest. The method is implemented in Cartesian and cylindrical coordinate systems. It keeps the same advantages of the original method but increases accuracy and is not affected by frequency aliasing.

Quantum-optical coherence tomography with collinear entangled photons.

Quantum-optical coherence tomography (QOCT) combines the principles of classical OCT with the correlation properties of entangled photon pairs [Phys. Rev. A 65, 053817 (2002)]. The standard QOCT configuration is based on the Hong-Ou-Mandel interferometer, which uses entangled photons propagating in separate interferometer arms. This noncollinear configuration imposes practical limitations, e.g., misalignment due to drift and low signal-to-noise. Here, we introduce and implement QOCT based on collinear entangled photons. It makes use of a two-photon Michelson interferometer and offers several advantages, such as simplicity, robustness, and adaptability.

Interference effects in quantum-optical coherence tomography using spectrally engineered photon pairs.

Optical-coherence tomography (OCT) is a technique that employs light in order to measure the internal structure of semitransparent, e.g. biological, samples. It is based on the interference pattern of low-coherence light. Quantum-OCT (QOCT), instead, employs the correlation properties of entangled photon pairs, for example, generated by the process of spontaneous parametric downconversion (SPDC). The usual QOCT scheme uses photon pairs characterised by a joint-spectral amplitude with strict spectral anti-correlations. It has been shown that, in contrast with its classical counterpart, QOCT provides resolution enhancement and dispersion cancellation. In this paper, we revisit the theory of QOCT and extend the theoretical model so as to include photon pairs with arbitrary spectral correlations. We present experimental results that complement the theory and explain the physical underpinnings appearing in the interference pattern. In our experiment, we utilize a pump for the SPDC process ranging from continuous wave to pulsed in the femtosecond regime, and show that cross-correlation interference effects appearing for each pair of layers may be directly suppressed for a sufficiently large pump bandwidth. Our results provide insights and strategies that could guide practical implementations of QOCT.