Classical Optics Research Articles

Classical light beams and geometric phases.

We present a study of geometric phases in classical wave and polarization optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarization optics, and the behavior of polarization in the eikonal or ray limit of Maxwell's equations in a transparent medium are considered. The case of a beam of light whose propagation direction and polarization state are both subject to change is dealt with, attention being paid to the validity of Maxwell's equations at all stages. Global topological aspects of the space of all propagation directions are discussed using elementary group theoretical ideas, and the effects on geometric phases are elucidated.

Two-point optical coherency matrix tomography.

The two-point coherence of an electromagnetic field is represented completely by a 4×4 coherency matrix G that encodes the joint polarization-spatial-field correlations. Here, we describe a systematic sequence of cascaded spatial and polarization projective measurements that are sufficient to tomographically reconstruct G--a task that, to the best of our knowledge, has not yet been realized. Our approach benefits from the correspondence between this reconstruction problem in classical optics and that of quantum state tomography for two-photon states in quantum optics. Identifying G uniquely determines all the measurable correlation characteristics of the field and, thus, lifts ambiguities that arise from reliance on traditional scalar descriptors, especially when the field's degrees of freedom are correlated or classically entangled.

Size dependence of electrostatic lens effect in vertical MOSFETs

The size dependence of the electrostatic lens effect in the channel of a nanoscale vertical pillar-type metal–oxide–semiconductor field-effect transistor (V-MOSFET) is studied by quantum dynamics simulation. Our findings indicate that the applicable diameter of the pillar for the efficient current-path control by the electrostatic lens effect on the V-MOSFET is in the range of about 10–30 nm. In the large-diameter pillar (30 nm diameter), the lens effect at the interfaces between the source and the body, and between the body and the source works well owing to the ballistic transport of electrons. On the other hand, in a slim pillar (10 nm diameter or less), the lens effect does not work well, because it is difficult to handle the electron dynamics by the analogy of classical geometrical optics, even though the electrons show ballistic transport. Our results indicate that the proposed technique is applicable for many nanoscale pillar-type devices.

Solar tomography adaptive optics

Conventional solar adaptive optics uses one deformable mirror (DM) and one guide star for wave-front sensing, which seriously limits high-resolution imaging over a large field of view (FOV). Recent progress toward multiconjugate adaptive optics indicates that atmosphere turbulence induced wave-front distortion at different altitudes can be reconstructed by using multiple guide stars. To maximize the performance over a large FOV, we propose a solar tomography adaptive optics (TAO) system that uses tomographic wave-front information and uses one DM. We show that by fully taking advantage of the knowledge of three-dimensional wave-front distribution, a classical solar adaptive optics with one DM can provide an extra performance gain for high-resolution imaging over a large FOV in the near infrared. The TAO will allow existing one-deformable-mirror solar adaptive optics to deliver better performance over a large FOV for high-resolution magnetic field investigation, where solar activities occur in a two-dimensional field up to 60'', and where the near infrared is superior to the visible in terms of magnetic field sensitivity.

Experimental study on modified linear quadratic Gaussian control for adaptive optics

To achieve high-resolution imaging the standard control algorithm used for classical adaptive optics (AO) is the simple but efficient proportional-integral (PI) controller. The goal is to minimize the rms error of the residual wave front. However, using the PI controller, it is not possible to do this. One possible way to minimize the rms error is to use linear quadratic Gaussian (LQG) control. In practice, however, this control algorithm still encounters an unexpected problem that leads to the divergence of control in AO. This paper proposes a modified LQG (MLQG) to solve this issue. The controller is analyzed explicitly. Laboratory tests shows strong stability and high precision compared to the classical control.

Super sub-wavelength patterns in photon coincidence detection

High-precision measurements implemented with light are desired in all fields of science. However, light acts as a wave, and the Rayleigh criterion in classical optics yields a diffraction limit that prevents obtaining a resolution smaller than the wavelength. Sub-wavelength interference has potential application in lithography because it beats the classical Rayleigh resolution limit. Here, we carefully study second-order correlation theory to establish the physics behind sub-wavelength interference in photon coincidence detection. A Young's double slit experiment with pseudo-thermal light is performed to test the second-order correlation pattern. The results show that when two point detectors are scanned in different ways, super sub-wavelength interference patterns can be obtained. We then provide a theoretical explanation for this surprising result, and demonstrate that this explanation is also suitable for the results found for entangled light. Furthermore, we discuss the limitations of these types of super sub-wavelength interference patterns in quantum lithography.

Novel States of Classical Light and Noncontextuality

A new criterion, based on noncontextuality, is derived to discriminate between separable and nonseparable states in classical wave optics where no discreteness is involved. An experiment is proposed to test the violation of noncontextuality by a nonseparable state. Such states have only recently begun to be explored. The significance of their nonseparability or entanglement as well as their similarities with and differences from entangled quantum states are discussed.

Optical properties of titanium dioxide nanotube arrays

We present experimental measurements and a theoretical analysis of the near UV to NIR optical properties of free standing titania nanotube arrays. An improved understanding of the optical physics of this type of nanostructure is important to several next generation solar energy conversion technologies. We measured the transmission, reflection, and absorption of the electromagnetic spectrum from 300 nm to 1000 nm (UV to NIR) of titania nanotube arrays. We measured the total, specular, and diffuse reflection and transmission using both single point detection and an integrating sphere spectrometer. We find that the transmission, but not the reflection, of light (UV to NIR) through the nanotube array is well-explained by classic geometric optics using an effective medium model taking into account the conical geometry of the nanotubes. For wavelengths shorter than ∼500 nm, we find the surprising result that the reflection coefficient for light incident on the open side of the nanotube array is greater than the reflection coefficient for light incident on the closed “floor” of the nanotube array. We consider theoretical models based on the eikonal approximation, photonic crystal band theory, and a statistical treatment of scattering to explain the observed data. We attribute the fact that light with wavelengths shorter than 500 nm is more highly reflected from the open than the closed tube side as being due to disorder scattering inside the nanotube array.

Superresolution Microscopy with Quantum Emitters

The optical diffraction limit imposes a bound on imaging resolution in classical optics. Over the last twenty years, many theoretical schemes have been presented for overcoming the diffraction barrier in optical imaging using quantum properties of light. Here, we demonstrate a quantum superresolution imaging method taking advantage of nonclassical light naturally produced in fluorescence microscopy due to photon antibunching, a fundamentally quantum phenomenon inhibiting simultaneous emission of multiple photons. Using a photon counting digital camera, we detect antibunching-induced second and third order intensity correlations and perform subdiffraction limited quantum imaging in a standard wide-field fluorescence microscope.

Development of a Fiber-Optic Probe Hydrophone for a Cryogenic Liquid

We report the progress of developing a fiber-optic probe hydrophone (FOPH) system applicable to the measurement of local density/pressure fluctuations in a cryogenic liquid. The measurement principle is based on a law of classical optics known as “Fresnel’s reflection loss.” We use this principle at the end-face of a single-mode optical fiber that is immersed in liquid helium. Since the refraction index of liquid 4He is a function of density, and the refraction index of the core of the optical fiber is constant, the pressure can be obtained by measuring the reflectivity. We have succeeded in measuring the temperature dependence of the static density, and we go on to discuss the possibility of application to acoustic pressure measurements.

Goos–Hänchen and Imbert–Fedorov shifts from a quantum-mechanical perspective

We study the classical optics effects known as Goos–Hänchen and Imbert–Fedorov shifts, occurring when reflecting a bounded light beam from a planar surface, by using a quantum-mechanical formalism. This new approach allows us to naturally separate the spatial shift into two parts, one independent on orbital angular momentum (OAM) and the other one showing OAM-induced spatial-versus-angular shift mixing. In addition, within this quantum-mechanical-like formalism, it becomes apparent that the angular shift is proportional to the beams angular spread, namely to the variance of the transverse components of the wave vector. Moreover, we extend our treatment to the enhancement of beam shifts via weak measurements and relate our results to the recent experiments.

Hybrid numerical-asymptotic approximation for high-frequency scattering by penetrable convex polygons

We consider time-harmonic scattering by penetrable convex polygons, a Helmholtz transmission problem. Standard numerical schemes based on piecewise polynomial approximation spaces become impractical at high frequencies due to the requirement that the number of degrees of freedom in any approximation must grow at least linearly with respect to frequency in order to represent the oscillatory solution. High frequency asymptotic methods on the other hand are non-convergent and may be insufficiently accurate at low to medium frequencies. Here, we design a hybrid numerical-asymptotic boundary element approximation space that combines the best features of both approaches. Specifically, we compute the classical geometrical optics solution using a beam tracing algorithm, and then we approximate the remaining diffracted field using an approximation space enriched with carefully chosen oscillatory basis functions. We demonstrate via numerical simulations that this approach permits the accurate and efficient representation of the boundary solution and the far field pattern.

Correction [to "New Insight into the Classical Macdonald Physical Optics Approximation"

Correction [to "New Insight into the Classical Macdonald Physical Optics Approximation"

Photon trajectories, anomalous velocities and weak measurements: a classical interpretation

Recently, Kocsis et al (2011 Science 332 1170) reported the observation of ‘average trajectories of single photons’ in a two-slit interference experiment. This was possible by using the quantum weak-measurement method, which implies averaging over many events, i.e. in fact, a multi-photon limit of classical linear optics. We give a classical-optics interpretation of this experiment and other related problems. It appears that weak measurements of the local momentum of photons made by Kocsis et al represent measurements of the Poynting vector in an optical field. We consider both the real and imaginary parts of the local momentum and show that their measurements have been realized in classical optics using small-probe particles. We also examine the appearance of ‘anomalous’ values of the local momentum: either negative (backflow) or exceeding the wavenumber (superluminal propagation). These features appear to be closely related to vortices and evanescent waves. Finally, we revisit a number of older works and find examples of photon trajectories and anomalous-momentum measurements in various optical experiments.

Role of intensity fluctuations in third-order correlation double-slit interference of thermal light

A third-order double-slit interference experiment with a pseudothermal light source in the high-intensity limit has been performed by actually recording the intensities in three optical paths. It is shown that not only can the visibility be dramatically enhanced compared to the second-order case as previously theoretically predicted and shown experimentally, but also that the higher visibility is a consequence of the contribution of third-order correlation interaction terms, which is equal to the sum of all contributions from second-order correlation. It is interesting that, when the two reference detectors are scanned in opposite directions, negative values for the third-order correlation term of the intensity fluctuations may appear. The phenomenon can be completely explained by the theory of classical statistical optics and is the first concrete demonstration of the influence of the third-order correlation terms.

Classical optics representation of the quantum mechanical translation operator via ABCD matrices

The ABCD matrix formalism describing paraxial propagation of optical beams across linear systems is generalized to arbitrary beam trajectories. As a by-product of this study, a one-to-one correspondence between the extended ABCD matrix formalism presented here and the quantum mechanical translation operator is established.

Effects of uniaxial pressure on polar whispering gallery modes in microspheres

We investigate the detuning of whispering gallery modes (WGMs) in solid polystyrene microspheres (PM) as a function of axisymmetric stress applied to two antipodal points of the microsphere we call poles. We specifically investigate WGMs passing close to these poles, so-called polar WGMs. The applied uniaxial pressure reduces the geometrical circumference of the PM but also increases locally the refractive index at the flattened poles. Our experiments show that the WGMs shift to higher frequencies with increasing pressure and that the magnitude of the strain-induced shift depends on the radial mode number n. Furthermore an energy splitting between azimuthal modes linearly increasing with the pressure is observed. A theoretical model based on a classical ray optics approach is presented which reproduces the main results of our experimental observations.

SURFACE PLASMONS IN COAXIAL METAMATERIAL CABLES

Thanks to Victor Veselago for his hypothesis of negative index of refraction, meta-materials — engineered composites — can be designed to have properties difficult or impossible to find in nature: they can have both electrical permittivity (ϵ) and magnetic permeability (μ) simultaneously negative. The metamaterials — henceforth negative-index materials (NIMs) — owe their properties to subwavelength structure rather than to their chemical composition. The tailored electromagnetic response of the NIMs has had a dramatic impact on classical optics: they are becoming known to have changed many basic notions related with electromagnetism. The present article is focused on gathering and reviewing fundamental characteristics of plasmon propagation in coaxial cables fabricated of the right-handed medium (RHM) (with ϵ > 0, μ > 0) and the left-handed medium (LHM) (with ϵ < 0, μ < 0) in alternate shells starting from the innermost cable. Such structures as conceived here may pave the way to some interesting effects in relation to, for example, optical science exploiting the cylindrical symmetry of coaxial waveguides that make it possible to perform all major functions of an optical fiber communication system in which the light is born, manipulated, and transmitted without ever leaving the fiber environment, with precise control over the polarization rotation and pulse broadening. This review also covers briefly the nomenclature, classification, potential applications, and the limitations (related, for example, to the inherent losses) of the NIMs and their impact on classical electrodynamics in general, and in designing the cloaking devices in particular. A recent surge in efforts on invisibility and the cloaking devices seems to have spoiled the researchers worldwide: proposals include not only a way to hide an object without having to wrap the cloak around it, but also to replace a given object with another, thus adding to the deception even further! All this is attributed as much to the fundamental as to the practical advances made in the fabrication and characterization of NIMs. The article concludes briefly addressing the anticipated implications of plasmon observation in the multicoaxial cables and suggesting future dimensions worth adding to the problem. The background provided is believed to make less formidable the task of future writers of reviews in this field.

Deterministic approximations of random reflectors

Within classical optics, one may add microscopic to a macroscopically flat mirror so that parallel rays of a given angle are reflected at different outgoing angles. Taking the limit (as the roughness becomes increasingly microscopic) one obtains a flat surface that reflects randomly, i.e., the transition from incoming to outgoing ray is described by a probability kernel (whose form depends on the nature of the microscopic roughness). We consider two-dimensional optics (a.k.a. billiards) and show that every random reflector on a line that satisfies a necessary measure-preservation condition (well established in the theory of billiards) can be approximated by deterministic reflectors in this way.

Analysis of an Optical Wireless Receiver Using a Hemispherical Lens With Application in MIMO Visible Light Communications

White lighting LEDs offer great potential for high speed communications, especially for indoor applications. However, for their widespread adoption, two important issues need to be addressed: the lack of diversity in multiple-input multiple output (MIMO) systems, and the small field of view of receivers. In this paper, we describe a design using a hemispherical lens in the receiver that solves these problems. By using classical optics, we derive exact expressions for the channel gain and the optical power density of the projected images. Simulation results of a typical indoor scenario show that the new system has a wide field of view, and provides adequate channel gain for angles of incidence as large as 70 degrees. We present the distribution of optical power on the imaging plane for various receiving positions and tilted receivers over a number of representative indoor scenarios. They show that the images of LEDs are clearly distinguishable. The results demonstrate the presence of low channel correlations between individual transmitters and receivers. Consequently, this confirms that the new technique is capable of providing significant diversity order for MIMO optical wireless applications.