Light In Vacuum Research Articles

Special Section Guest Editorial: Slow and Fast Light

The speed of light in vacuum is one of the most fundamental constants in nature, which underlies many of the basic properties of the universe. There is no wonder, therefore, that the first attempts to understand and control the speed of light can be traced back to some of the pioneers of electromagnetic waves theory such as Lorentz, Sommerfeld, and Brillouin. The efforts to understand the fundamental properties of light propagation through slow- and, in particular, fast-light media triggered a plethora of studies, intense debates, and controversies.

Simultaneous guiding of slow elastic and light waves in three-dimensional topology-type phoxonic crystals with a line defect

Phoxonic crystals (PXCs) which exhibit simultaneous phononic and photonic bandgaps are promising artificial materials for optomechanical and acousto-optical devices. In this paper, we theoretically investigate the phononic and photonic guided modes in the three-dimensional topology-type PXCs with a line defect. By varying the geometrical parameters, simultaneous guidance of the slow elastic and light (electromagnetic) waves can be realized. Both elastic and optical energies can be highly confined in and near the defect region. Small elastic and optical group velocities with small group velocity dispersions can be achieved. The group velocities are about 10 and 20 times smaller than the transverse velocity of the elastic waves in silicon and the speed of light in vacuum, respectively.

Extracting surface wave-coupled emission with subsurface dielectric gratings.

Conventional surface plasmons (SPs) or Bloch surface waves (BSWs) have a wave vector exceeding that of light in vacuum, and, therefore, the surface plasmon-coupled emission (SPCE) or Bloch surface wave-coupled emission (BSWCE) cannot escape from the corresponding structures. With the aid of a high-refractive-index prism or an oil-immersion objective, the SPCE or BSWCE can be coupled into free space. But the large volumes of the prism and objective are certainly unfavorable for miniaturization of the optical systems or inconvenient for applications such as the optical displays. Here we experimentally demonstrate a new method to extract the SPCE or BSWCE with a subsurface dielectric grating. The experimental results verify that the chip-like substrate with two decorated sides can bring out the directional fluorescence emission in free space. The emitting direction and emitting patterns can be tuned by the period size and dimensionality of the gratings. Our work provides a new strategy to realize free-space directional fluorescence emission at a very low cost and compact configuration, which has potential applications in fluorescence-based sensing, imaging, light-emitting diodes, optical displays, and other near-field optical devices.

Analogous of Hartman Effect for Relativistic Particles Through “Transparent” Barrier

The phase time in a nonrelativistic monodimensional tunneling is, for short barrier length, greater than the time it takes for the light in vacuum to travel the same path. Nevertheless, if the length is increased to the limit of “opaque” barrier (κL ≫ 1), where κ is the decay constant of the evanescent wave, the phase time becomes independent from the length (Hartman effect), so that apparent superluminal velocities (independently from unresolved questions about their physical meaning) are possible increasing length in this limit. Here is analytically demonstrated that apparent superluminal behavior can be found also in another situation: for highly relativistic particles, in the limit of “transparent barrier” (κL ≪ 1), is found that the phase time is always shorter than the correspondent time for light in vacuum, and that apparent superluminal velocities (following the Hartman definition) are always possible independently from the barrier length.

Structured relativistic particle, helix-type Minkowski diagram, and “more general” relativity

A model of a 3D classical particle built up of micro-scale spinor fragments, hence structured, is proved sufficient (demands no additional postulates) to generate a theory of relativistic motion, provided the velocity of light in vacuum is the speed limit. In this case, the particle’s structure endows a mechanical action with a clear geometric sense and allows for derivation of a Lagrangian function of the same form as in special relativity. But the graphic image of motion becomes a 3D helix instead of a 4D space-time world line. A forced distortion of the helix line (curved and compressed) results in emerging of variable metric components thus leading to an equation of particle motion under the influence of a geometric potential, an equation identical to that of 4D geodesic. The logical line of the theory is traced in detail.

Quantum mutual information of an entangled state propagating through a fast-light medium

Although it is widely accepted that classical information cannot travel faster than the speed of light in vacuum, the behavior of quantum correlations and quantum information propagating through actively-pumped fast-light media has not been studied in detail. To investigate this behavior, we send one half of an entangled state of light through a gain-assisted fast-light medium and detect the remaining quantum correlations. We show that the quantum correlations can be advanced by a small fraction of the correlation time while the entanglement is preserved even in the presence of noise added by phase-insensitive gain. Additionally, although we observe an advance of the peak of the quantum mutual information between the modes, we find that the degradation of the mutual information due to the added noise appears to prevent an advancement of the leading edge. In contrast, we show that both the leading and trailing edges of the mutual information in a slow-light system can be significantly delayed.

Time Contraction: The Possibility of Faster Than Light without Violation of Lorentz Transformation or Causality and the Vacuum Energy Dependent

Faster than light is impossible according to the special relativity theory of Einstein SRT. In this paper I'll propose a new concept in physics called contraction. This concept will solve many problems in physics related to faster than light without violation Lorentz transformation or causality. According to this concept, it is possible measuring the speed of an electromagnetic wave or a particle which owns rest mass greater than zero to be faster than the speed of light in vacuum without violation of Lorentz transformation or causality. Time contraction is proposed by a new understanding to the Lorentz transformation equations depending on the concepts of quantum theory (Copenhagen School). It is a new formulation to the time dilation and the length contraction and the speed of light which are vacuum energy dependent. By this new formulation, I could rescue the special relativity from the Twin paradox, Ehrenfest paradox, Ladder paradox and Bell's spaceship paradox. Furthermore, I could reconcile and interpret the experimental results of quantum tunneling and entanglement (spooky action), —Casimir effect, Hartman effect— with the SRT in this paper.

The Units ppm, ppb, and ppt

Dimensionless quantities, which are also sometimes called quantities of dimension one, are generally defined as the ratio of two quantities of the same kind. Examples are refractive index n (defined as the ratio of the speed of light in vacuum to the speed in a medium, n = c0/c); and mole fraction xi – more properly called amount of substance fraction (defined as the ratio of the amount of a particular substance i in a mixture to the total amount of substance xi = ni /Σ jnj ). Thus the value of a dimensionless quantity is simply a number, and it would seem that no unit is required. The International System of units, the SI, includes no units for dimensionless quantities as it is at present defined.

Exact Analysis of Optical Precursor in Lossless Plasma

When an electromagnetic field propagates through a linear but dispersive medium, the front edge (the launching fringe of the waveform where the field is first turned on) propagates precisely at the speed of light in vacuum by first timing on t1=tfront=（z/c）and the main signal (the main part of the field) follows up with group velocity which is characterized by the frequency-dependent refractive index of medium by second timing on t2=tgroup=(z/vgroup)=[n(φ)z/c] .The distinct wave-packets progress from tfrontto tgroup(i.e. from the front-edge-timing to the main-signal-starting timing) are well known as optical precursors. It was believed that precursors are an ultra-fast phenomena, persisting only for a few optical cycles, and that they have an exceedingly small amplitude and two different kinds of spike-type wave-packet (i.e. Sommerfeld precursor and Brillouin forerunner). Both exact wave shape for electromagnetic wave while it goes into a linear time-invariant, lossless plasma system is reported.

Index of Refraction Measurements Using a Laser Distance Meter

We present a simple method to determine the refractive indices of transparent media using a laser distance meter. Indices of refraction have been obtained by measuring the speed of light in materials.1–6 Some speed of light techniques use time-of-flight measurements in which pulses are emitted by lasers and the time interval is measured for the pulse to travel from the laser to a detector. These experiments are relatively costly and use sophisticated equipment not always available in an educational institution. Our method uses a laser distance meter that can be purchased for under $80. The meter uses the accepted value of the speed of light in vacuum to determine distances based on a measured time of flight. The output is distance in meters or feet.

Quantum optical interferometry via the mixing of coherent and photon-subtracted squeezed vacuum states of light

Hofmann and Ono [Phys. Rev. A76, 031806, (2007)] showed that the mixing of coherent light and single-mode squeezed light at a beam splitter gives good approximation results in a superposition of path-entangled photon number states (so-called N00N states), which can be used for phase-shift measurements by coincident detections at the output of an interferometer. They showed that N00N states for arbitrary photon number N could be produced by this procedure. Afek et al. [Science328, 879 (2010)] have implemented the Hofmann–Ono proposal in the laboratory. In this paper, we show that, for a given coherent state amplitude and a given squeezing parameter, the mixing of coherent states and photon-subtracted squeezed vacuum states at the first beam splitter of an interferometer leads to improved phase-shift measurement sensitivity when using the photon-number detection technique on one of the output beams of the device. We also show that the phase-shift measurements will also be super-resolved to a greater degree than is possible by mixing coherent and squeezed vacuum light of the same field parameters.

Quasi-light Storage for Optical Data Packets

Today's telecommunication is based on optical packets which transmit the information in optical fiber networks around the world. Currently, the processing of the signals is done in the electrical domain. Direct storage in the optical domain would avoid the transfer of the packets to the electrical and back to the optical domain in every network node and, therefore, increase the speed and possibly reduce the energy consumption of telecommunications. However, light consists of photons which propagate with the speed of light in vacuum. Thus, the storage of light is a big challenge. There exist some methods to slow down the speed of the light, or to store it in excitations of a medium. However, these methods cannot be used for the storage of optical data packets used in telecommunications networks. Here we show how the time-frequency-coherence, which holds for every signal and therefore for optical packets as well, can be exploited to build an optical memory. We will review the background and show in detail and through examples, how a frequency comb can be used for the copying of an optical packet which enters the memory. One of these time domain copies is then extracted from the memory by a time domain switch. We will show this method for intensity as well as for phase modulated signals.

Quasi-light Storage for Optical Data Packets

Today's telecommunication is based on optical packets which transmit the information in optical fiber networks around the world. Currently, the processing of the signals is done in the electrical domain. Direct storage in the optical domain would avoid the transfer of the packets to the electrical and back to the optical domain in every network node and, therefore, increase the speed and possibly reduce the energy consumption of telecommunications. However, light consists of photons which propagate with the speed of light in vacuum. Thus, the storage of light is a big challenge. There exist some methods to slow down the speed of the light, or to store it in excitations of a medium. However, these methods cannot be used for the storage of optical data packets used in telecommunications networks. Here we show how the time-frequency-coherence, which holds for every signal and therefore for optical packets as well, can be exploited to build an optical memory. We will review the background and show in detail and through examples, how a frequency comb can be used for the copying of an optical packet which enters the memory. One of these time domain copies is then extracted from the memory by a time domain switch. We will show this method for intensity as well as for phase modulated signals.

Parametric wave interaction in media exhibiting quadratic and cubic nonlinearities under high-frequency pumping conditions

Specific features of parametric interaction in media exhibiting quadratic and cubic nonlinearities under conditions of high-frequency pumping and nonzero detuning from the phase matching are analyzed. It is shown that the presence of two types of nonlinearities and frequency detuning broaden the possibilities of controlling the dynamics of the forming partial pulses by changing the pump power. The possibility of the signal and idler waves’ decay into four frequency-modulated partial wave packets with different values of chirp and velocities of their envelope maximum is established. The envelope maximum velocities of the partial pulses, as well as their walk-off velocities, can reach values exceeding the speed of light in vacuum.

Dynamical Essence of the Basic Relations of the Special Theory of Relativity and the Origin of Fundamental Interactions: Phenomenology

It is shown that the adoption of the hypothesis that the electromagnetic component of physical vacuum, the vacuum of quantum electrodynamics (QED vacuum), undergoes polarization in the vicinity of elementary particles allows us to comprehend, on the phenomenological level, the physical essence of the basic hypotheses of the special theory of relativity, including the nature of the limitation of the velocity of material objects to the velocity of light in vacuum. The QED vacuum here plays the part of the base medium that governs the development of the fundamental strong and gravitational interactions.

UV irradiation induced conductivity improvement in poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) film

We describe a simple method to increase the conductivity of poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) film by exposure to ultraviolet (UV) light in vacuum. Up to four order of conductivity improvement (from 10−3 to 50 S/cm) is achieved by irradiating PEDOT:PSS film with 254 nm ultraviolet (UV) light. Increased conductivity in UV treated PEDOT:PSS film is stable under ambient exposure. The mechanism for conductivity improvement is investigated by current-voltage measurement, atomic force microscopy, and absorption spectrum. Photo-cross-linking of PSS chains is determined as the reason for conductivity improvement. Our result demonstrates that UV treatment is capable of modifying the conductivity of PEDOT:PSS film independent of the process of film formation.

Light Bending by a Temperature Gradient

Because classical electrodynamics is linear, the vacuum is unique and trivial. In a classical vacuum, the speed of light is constant. In quantum electrodynamics, the vacuum expectation value of the electromagnetic current can be non-zero due to non-charge-like sources, like electric fields, magnetic fields, gravitational fields, temperature fields, etc. We consider the velocity shift of light due to the vacuum polarization effect of quantum electrodynamics when the temperature is finite. The speed of light in this non-trivial vacuum is different from that in a trivial vacuum at zero temperature. This means that the index of refraction is not one. We set up a model to find the trajectory and the bending angle of a light ray when the index of refraction has a gradient. We compute the bending angles when the gradient is spherically symmetric and when it is cylindrically symmetric. For a magnetized neutron star, We compare that bending angle with the bending angles caused by gravitation and electromagnetic field.

Electromagnetic waves in an axion-active relativistic plasma non-minimally coupled to gravity

We consider cosmological applications of a new self-consistent system of equations, accounting for a nonminimal coupling of the gravitational, electromagnetic and pseudoscalar (axion) fields in a relativistic plasma. We focus on dispersion relations for electromagnetic perturbations in an initially isotropic ultrarelativistic plasma coupled to the gravitational and axion fields in the framework of isotropic homogeneous cosmological model of the de Sitter type. We classify the longitudinal and transversal electromagnetic modes in an axionically active plasma and distinguish between waves (damping, instable or running), and nonharmonic perturbations (damping or instable). We show that for the special choice of the guiding model parameters the transversal electromagnetic waves in the axionically active plasma, nonminimally coupled to gravity, can propagate with the phase velocity less than speed of light in vacuum, thus displaying a possibility for a new type of resonant particle-wave interactions.

Rotation of the noise ellipse for squeezed vacuum light generated via four-wave mixing

We report the generation of a squeezed vacuum state of light whose noise ellipse rotates as a function of the detection frequency. The squeezed state is generated via a four-wave mixing process in a vapor of ${}^{85}$Rb. We observe that rotation varies with experimental parameters such as pump power and laser detunings. We use a theoretical model based on the Heisenberg-Langevin formalism to describe this effect. Our model can be used to investigate the parameter space and potentially to tailor the ellipse rotation in order to obtain an optimum squeezing angle, for example, for coupling to an interferometer whose optimal noise quadrature varies with frequency.

Semi-empirical model for stopping cross sections of p, α and Li ions

Absolute magnitudes of stopping cross sections (SCS) for H+, He2+ and Li3+ in various stopping media with atomic numbers Z 2 = 2 to 100 are calculated using atomic density functions from Dirac-Hartree-Fock-Slater wave functions in the Lindhard-Schraff theory [J. Lindhard, M. Scharff, Kgl. Danske Videnskab. Selskab. Mat. Fys. Medd. 27, 15 (1953)]. The newly proposed formula, characterizing projectile-specific parameters in the incident energy range considered herein, describes satisfactorily the experimental and SRIM-simulated SCS data from low energies, with projectile velocities nearing v = Z 1 v 0 (with Z 1 as the projectile’s atomic number, v 0 = c / 137, the Bohr velocity and c, the speed of light in vacuum), to high energies up to about 2.5 MeV/u.