Journal of Optics

Published by IOP Publishing
Online ISSN: 2040-8986
Print ISSN: 2040-8978
In this paper, we demonstrate a high speed spectral domain optical coherence tomography (SDOCT) system capable of achieving full range complex imaging at 47 kHz line scan rate. By applying beam-offset method, a constant modulation frequency is introduced into each B-scan that enables reconstruction of the full range complex SDOCT images of in vivo tissue samples. To make use of the full capacity of detection camera used in the system, system control software is developed that streams the raw spectral fringe data directly into the computer memory. In order to assess performance of the high speed full range SDOCT system for imaging biological specimen, we present results imaged from the cuticle of fingernail of a human volunteer in vivo, and from the chicken embryos ex vivo. We also show the high sensitivity advantages of full range complex imaging as compared to the conventional SDOCT. To the best of our knowledge, 47,000 A-scan imaging rate is the highest imaging rate ever been reported for full range complex imaging. Notwithstanding, the method reported here has no limitations on the imaging speed, thus offers a useful tool to achieve volumetric imaging of living samples where the high sensitivity region around zero-delay line in the system can be utilized for imaging.
We show that laser-tweezers Raman spectroscopy of eukaryotic cells with a significantly larger diameter than the tight focus of a single beam laser trap leads to optical trapping of the cell by its optically densest part, i.e. typically the cell's nucleus. Raman spectra of individual optically trapped monocytes are compared with location-specific Raman spectra of monocytes adhered to a substrate. When the cell's nucleus is stained with a fluorescent live cell stain, the Raman spectrum of the DNA-specific stain is observed only in the nucleus of individual monocytes. Optically trapped monocytes display the same behavior. We also show that the Raman spectra of individual monocytes exhibit the characteristic Raman signature of cells that have not yet fully differentiated and that individual primary monocytes can be distinguished from transformed monocytes based on their Raman spectra. This work provides further evidence that laser tweezers Raman spectroscopy of individual cells provides meaningful biochemical information in an entirely nondestructive fashion that permits discerning differences between cell types and cellular activity.
Schematic of the LC-PolScope for birefringence imaging. The optical design (left) builds on the traditional polarized light microscope with the conventional compensator replaced by two variable retarders LC-A and LC-B. The polarization analyzer passes circularly polarized light and is typically built from a linear polarizer and a quarter wave plate. Images of the specimen (top row, aster isolated from surf clam egg) are captured at five predetermined retarder settings, which cause the specimen to be illuminated with circularly polarized light (1st, left most image) and with elliptically polarized light of different axis orientations (2nd to 5th image). Based on the raw PolScope images, the computer calculates the retardance image and the slow axis orientation or azimuth image using specific algorithm. The LC-PolScope requires the use of narrow bandwidth ( ≤ 40 nm) or monochromatic light. 
LC-PolScope images of a Siemens star etched into a 50 nm thick aluminum film on cover glass using electron lithography. The cover glass with film was mounted on a microscope slide using Permount. A Average transmittance of the star pattern, which consists of 36 wedge pairs and has an out- side diameter of 75 μ m. Near the outer edge along the circumference the grating period is 6.5 μ m, which decreases continuously towards the smallest period of 0.1 μ m near the inner black disk (dia. 1.2 μ m). Near the white dashed circle, the period is 0.5 λ , and λ near the solid circle, with λ the wavelength of the illuminating light (630 nm). The square outlines the magnified portion in panels B to D. B to D Central portion of the Siemens star imaged with the LC-PolScope in different imaging modes: B Mean transmittance. Gray scale legend between panels A and B indicates mean transmittance and applies to both panels. C Apparent retardance of the central pattern with red lines indicating the slow axis orientation. D Diattenuation of the central pattern with red lines indicating the orientation of the maximum transmittance. In panels C and D lines are drawn for every 3 rd pixel of the original image. Gray scale legend be- 
Polarized light microscopy provides unique opportunities for analyzing the molecular order in man-made and natural materials, including biological structures inside living cells, tissues, and whole organisms. 20 years ago, the LC-PolScope was introduced as a modern version of the traditional polarizing microscope enhanced by liquid crystal devices for the control of polarization, and by electronic imaging and digital image processing for fast and comprehensive image acquisition and analysis. The LCPolScope is commonly used for birefringence imaging, analyzing the spatial and temporal variations of the differential phase delay in ordered and transparent materials. Here we describe an alternative use of the LC-PolScope for imaging the polarization dependent transmittance of dichroic materials. We explain the minor changes needed to convert the instrument between the two imaging modes, discuss the relationship between the quantities measured with either instrument, and touch on the physical connection between refractive index, birefringence, transmittance, diattenuation, and dichroism.
This paper presents a planar waveguide grating sensor integrated with a photodetector (PD) for on-chip optical sensing systems which are suitable for diagnostics in the field and in-situ measurements. III-V semiconductor-based thin-film PD is integrated with a polymer based waveguide grating device on a silicon platform. The fabricated optical sensor successfully discriminates optical spectral characteristics of the polymer waveguide grating from the on-chip PD. In addition, its potential use as a refractive index sensor is demonstrated. Based on a planar waveguide structure, the demonstrated sensor chip may incorporate multiple grating waveguide sensing regions with their own optical detection PDs. In addition, the demonstrated processing is based on a post-integration process which is compatible with silicon complementary metal-oxide semiconductor (CMOS) electronics. Potentially, this leads a compact, chip-scale optical sensing system which can monitor multiple physical parameters simultaneously without need for external signal processing.
Malaria affects over 200 million individuals annually, resulting in 800,000 fatalities. Current tests use blood smears and can only detect the disease when 0.1-1% of blood cells are infected. We are investigating the use of photoacoustic flowmetry to sense as few as one infected cell among 10 million or more normal blood cells, thus diagnosing infection before patients become symptomatic. Photoacoustic flowmetry is similar to conventional flow cytometry, except that rare cells are targeted by nanosecond laser pulses to induce ultrasonic responses. This system has been used to detect single melanoma cells in 10 ml of blood. Our objective is to apply photoacoustic flowmetry to detection of the malaria pigment hemozoin, which is a byproduct of parasite-digested hemoglobin in the blood. However, hemozoin is difficult to purify in quantities greater than a milligram, so a synthetic analog, known as β-hematin was derived from porcine haemin. The specific purpose of this study is to establish the efficacy of using β-hematin, rather than hemozoin, for photoacoustic measurements. We characterized β-hematin using UV-vis spectroscopy, TEM, and FTIR, then tested the effects of laser irradiation on the synthetic product. We finally determined its absorption spectrum using photoacoustic excitation. UV-vis spectroscopy verified that β-hematin was distinctly different from its precursor. TEM analysis confirmed its previously established nanorod shape, and comparison of the FTIR results with published spectroscopy data showed that our product had the distinctive absorbance peaks at 1661 and 1206 cm(-1). Also, our research indicated that prolonged irradiation dramatically alters the physical and optical properties of the β-hematin, resulting in increased absorption at shorter wavelengths. Nevertheless, the photoacoustic absorption spectrum mimicked that generated by UV-vis spectroscopy, which confirms the accuracy of the photoacoustic method and strongly suggests that photoacoustic flowmetry may be used as a tool for diagnosis of malaria infection.
Comparison of calculation time for the GSM rigorous 3D diffraction simulation on CPU and on GPU a 
The article encloses a new Fourier space method for rigorous optical simulation of 3D periodic dielectric structures. The method relies upon rigorous solution of Maxwell's equations in complex composite structures by the Generalized Source Method. Extremely fast GPU enabled calculations provide a possibility for an efficient search of eigenmodes in 3D periodic complex structures on the basis of rigorously obtained resonant electromagnetic response. The method is applied to the homogenization problem demonstrating a complete anisotropic dielectric tensor retrieval.
Schematics of the VO 2 lattice structure and electron energy band structure below and above 
Schematics of the optical pump-probe experimental setup. The output of the amplified 
Sample time-dependent changes in the probe reflection corresponding to various dynamical 
Threshold measurements for the onset and for the full MIT of VO 2 thin films grown on a) 
We investigate the differences in the dynamics of the ultrafast photo-induced metal-insulator transition (MIT) of two VO$_2$ thin films deposited on different substrates, TiO$_2$ and Al$_2$O$_3$, and in particular the temperature dependence of the threshold laser fluence values required to induce various MIT stages in a wide range of sample temperatures (150 K - 320 K). We identified that, although the general pattern of MIT evolution was similar for the two samples, there were several differences. Most notably, the threshold values of laser fluence required to reach the transition to a fully metallic phase in the VO$_2$ film on the TiO$_2$ substrate were nearly constant in the range of temperatures considered, whereas the VO$_2$/Al$_2$O$_3$ sample showed clear temperature dependence. Our analysis qualitatively connects such behavior to the structural differences in the two VO$_2$ films.
Intensity distributions ( γ = 18) for ( a ) the paraxial field of Eq. 3; ( b ) exact field of Eq. 1; ( c ) numerically simulated 1D binary gold grating (of refractive index 0 . 2 + 3 . 44i, thickness 100 nm and slit width to grating period ratio of 0 . 05) illuminated by a normally incident, TE-polarized, monochromatic ( λ = 632 . 8 nm) plane wave; and ( d ) the post-paraxial field as given by Eq. 4. A value of γ = 18 is outside the region of validity for the paraxial approximation, since ( a ) is fundamentally different to ( b ). The fields ( b ), ( c ) and ( d ) exhibit foci (indicated by the white box) which are aberrated compared to ( a ). 
A comparison of foci symmetric about the centre of each image ( γ = 18, M = 9) with colours corresponding to Fig. 1; ( a ) paraxial focus of Eq. 3; ( b ) the exact field of Eq. 1; ( c ) numerically simulated focus according to the parameters of Fig. 1( c ); ( d ) post-paraxial focus of Eq. 5 ( | μ | ≤ 1); ( e ) the Pearcey function Eq. 7; and ( f ) the incomplete Pearcey function ( μ = 0 term of Eq. 5). 
The intensity of ( a ) the exact field, Eq. 1 (normalised by (2[ γ/ 2] + 1)) and ( b ) the post-paraxial field (Eq. 5, summing | μ | ≤ 1) as a function of γ . The dashed line is the approximate location of maximum intensity according to Eq. 8. The dots are the actual maxima of the exact field for integer γ . The solid line is the Talbot distance. 
We present an analysis of self-imaging in a regime beyond the paraxial, where deviation from simple paraxial propagation causes apparent self-imaging aberrations. The resulting structures are examples of aberration without rays and are described analytically using post-paraxial theory. They are shown to relate to, but surprisingly do not precisely replicate, a standard integral representation of a diffraction cusp. Beyond the Talbot effect, this result is significant as it illustrates that the effect of aberration -- as manifested in the replacement of a perfect focus with a cusp-like pattern -- can occur as a consequence of improving the paraxial approximation, rather than due to imperfections in the optical system.
We investigate the capabilities of the effective non-retarded method (ENR) to explore and design nanoparticles composites with specific optical properties. We consider a composite material comprising periodically distributed metallic spheres in a dielectric host matrix. The effective macroscopic dielectric function of the composite medium is obtained by means of the ENR and is used to calculate the electromagnetic response of a slab made of such an inhomogeneous material. This response is compared with that obtained using the Korringa-Kohn-Rostoker wave calculation method (KKR). We analyze the optical properties for different filling fractions, especially in the vicinity of the resonance frequencies of the macroscopic dielectric function. We show that appropriately choosing the parameters of the composite it is possible to achieve a tunable absorber film. The ENR results to be a versatile tool for the design of nanoparticle composite materials with specific properties.
We propose to achieve a strong bistable response of a thin layer of a saturable absorption medium by involving a planar metamaterial specially designed to bear a high-Q trapped-mode resonance in the infrared region.
absorption efficiency of many graphene wrapped dielectric spheres as a function of wavelength under the excitation of the linear polarization incident wave. (a) 7-sphere system in a plane as shown in Inset; (b) 27-sphere system in 3×3×3 packing way as shown in Inset. Here the parameters of graphene wrapped dielectric spheres are taken identical with those in figure 3. The electric polarization E of the incident wave is along longitudinal axis of two adjacent spheres. 
The optical absorption properties of graphene wrapped dielectric particles have been investigated by using Mie scattering theory and exact multi-scattering method. It is shown that subwavelength strong absorption in infrared spectra can take place in such systems due to the excitation of plasmon resonance in graphene. The absorption characteristics and efficiency are tunable by varying Fermi level and damping constant of graphene, or by changing size and dielectric constant of small particles. For a cluster of these particles, the absorption characteristics are also affected by the separation distance between them. These extreme light resonances and absorptions in graphene wrapped nanostructures have great potential for opto-electronic devices.
An exact solution of the Maxwell equations in Rindler coordinates is obtained. The electromagnetic field represents a wave preserving its shape in a relativistic uniformly accelerated frame. The relation with Airy beams is shown explicitly in the non-relativistic limit.
We present a contrast-maximizing optimal linear representation of polarimetric images obtained from a snapshot polarimetric camera for enhanced vision of a polarized light source in obscured weather conditions (fog, haze, cloud) over long distances (above 1 km). We quantitatively compare the gain in contrast obtained by different linear representations of the experimental polarimetric images taken during rapidly varying foggy conditions. It is shown that the adaptive image representation that depends on the correlation in background noise fluctuations in the two polarimetric images provides an optimal contrast enhancement over all weather conditions as opposed to a simple difference image which underperforms during low visibility conditions. Finally, we derive the analytic expression of the gain in contrast obtained with this optimal representation and show that the experimental results are in agreement with the assumed correlated Gaussian noise model.
We experimentally demonstrate a broadband and an ultra-broadband spectral bandwidth polarization rotators. Both polarization rotators have modular design, that is, they are comprised of an array of half-wave plates rotated to a given angle. We show that the broadband and ultra-broadband performance of the polarization rotators is due to the adiabatic nature of the light polarization evolution. In this paper we experimentally investigate the performance of broadband and ultra-broadband polarization rotators comprising of ten multi-order half-wave plates or ten commercial achromatic half-wave plates, respectively. The half-wave plates in the arrays are rotated gradually with respect to each other starting from an initial alignment between the fast polarization axis of the first one and the incoming linearly polarized light, to the desired polarization rotation angle.
m { k } 2: = Maps 0 (red), illustrating at the coordinate the directions origin of for k ˆ = v s ′ k/k ∈ { = 0 . 60 k ˆ x , x 0 . + 62 k ˆ , y 0 . y 70 + , 0 k ˆ . z 90 z } for . Parameter which Im { values: k } = 0 σ (blue) = 5 and and R = 1. 
The Alcubierre spacetime was simulated by means of a Tamm medium which is asymptotically identical to vacuum and has constitutive parameters which are ontinuous functions of the spatial coordinates. Accordingly, the Tamm medium is amenable to physical realization as a nanostructured metamaterial. A comprehensive characterization of ray trajectories in the Tamm medium was undertaken, within the geometric-optics regime. Propagation directions corresponding to evanescent waves were identified: these occur in the region of the Tamm medium which corresponds to the warp bubble of the Alcubierre spacetime, especially for directions perpendicular to the velocity of the warp bubble at high speeds of that bubble. Ray trajectories are acutely sensitive to the magnitude and direction of the warp bubble's velocity, but rather less sensitive to the thickness of the transition zone between the warp bubble and its background. In particular, for rays which travel in the same direction as the warp bubble, the latter acts as a focusing lens, most notably at high speeds.
(Color online) A cross-like (A), a sunflower-like (C) and a hexagram (D) all mimicking a circular cylinder (B) of small radius r 0 = 0.195, that is c 0 = d 0 = 0.195 in equation (18). The inner and outer boundaries of the petals are respectively parts of the ellipses x 2 /0.7 2 + y 2 /0.2 2 and x 2 /0.9 2 + y 2 /0.4 2 rotated by angle 0 or π 2 in (A) or 0, π 4 , π 2 or 3π/4 in (C). The hexagram (D) is generated from an equilateral triangle with side 1.2. The energy corresponding to the plane matter wave incident from the top is E = √ ω = 2πc/λ = 4.58, where λ = 0.3 is the wavelength of a transverse electromagnetic wave in the optics setting with c the celerity of light in vacuum, normalized here to 1.  
(Color online) Left: A hollow parallelogram cylindrical region (A) scatters any incoming plane wave just like a much smaller solid cylinder (B) of the same nature. In (C) the same hollow parallelogram cylinder is designed to have the same response to waves as the small equilateral triangle (D) with side 2 √ 3 5  
Left panel: Modulus of the fundamental eigenstates associated with quantified normalized energy E = √ ω = 2πc/λ = 1.32 (resp. a transverse electric plane wave of wavelength λ = 3.6) for a non-singular cloak shaped as a star (A) and a rabbit (B) both of which mimic a small disc (of normalized radius 0.195, e.g. 195 nanometers) ; Right panel: Matter wave incident from the top on the quantum cloaks with a spatially varying potential V with compact support (i.e. vanishing outside the cloak) and energy E; The large amplitude of the field within the cloak is noted.  
Construction of a generalized cloak with optical space folding for superscattering effect. The transformation with inverse (6) magnifies the region bounded by the two surfaces S 0 and S 2 into the region bounded by S 1 and S 2 . We note that the transform is no longer an isomorphism. The curvilinear metric inside the carpet (here, an orange flower) is described by the transformation matrix T, see (7)-(14). Any quantum object located within the region bounded by the surface S 1 scatters matter waves like a larger object bounded by S 0 (here, a yellow star).  
(A-C)Any obstacle surrounded by a square anti-cloak with square boundaries of sidelengths 1 and 1.4, scatters a plane matter wave of energy E = 4.58 (resp. a transverse electric plane wave of wavelength λ = 0.3 in the context of optics) which is coming from the top like a larger square obstacle of sidelength 1.6. (b-d) Any obstacle surrounded by a circular anti-cloak with circular boundaries of radii 0.2 and 0.4 scatters a plane matter wave of energy E = 4.58 (resp. a transverse electric plane wave of wavelength λ = 0.3) which is coming from the top like a larger square obstacle of sidelength 1. The large field amplitude on the upper boundary of the anti-cloak in (A) and (B) is noted. It can be attributed to some kind of surface matter wave (a surface plasmon polariton in the context of optics).  
We design non-singular cloaks enabling objects to scatter waves like objects with smaller size and very different shapes. We consider the Schrodinger equation which is valid e.g. in the contexts of geometrical and quantum optics. More precisely, we introduce a generalized non-singular transformation for star domains, and numerically demonstrate that an object of nearly any given shape surrounded by a given cloak scatters waves in exactly the same way as a smaller object of another shape. When a source is located inside the cloak, it scatters waves as if it would be located some distance away from a small object. Moreover, the invisibility region actually hosts almost-trapped eigenstates. Mimetism is numerically shown to break down for the quantified energies associated with confined modes. If we further allow for non-isomorphic transformations, our approach leads to the design of quantum super-scatterers: a small size object surrounded by a quantum cloak described by a negative anisotropic heterogeneous effective mass and a negative spatially varying potential scatters matter waves like a larger nano-object of different shape. Potential applications might be for instance in quantum dots probing. Comment: Version 2: 23 pages, 9 figures. More figures added. Misprints corrected. OCIS Codes: (000.3860) Mathematical methods in physics; (260.2110) Electromagnetic theory; (160.3918) Metamaterials; (160.1190) Anisotropic optical materials; (350.7420) Waves; (230.1040) Acousto-optical devices; (160.1050) Acousto-optical materials; (290.5839) Scattering,invisibility; (230.3205) Invisibility cloaks
Propagation of oppositely polarized beams inside a screw dislocated circular waveguide. (i) σ = 1, m = |m|, (ii) σ = −1, m = −|m| with λ(|m| + 1) < b (left) and λ(|m| + 1) > b (right).
We study paraxial beam propagation parallel to the screw axis of a dislocated amorphous medium that is optically weakly inhomogeneous and isotropic. The effect of the screw dislocation on the beam's orbital angular momentum is shown to change the optical vortex strength, rendering vortex annihilation or generation possible. Furthermore, the dislocation is shown to induce a weak \textit{biaxial} anisotropy in the medium due to the elasto-optic effect, which changes the beam's spin angular momentum as well as causing precession of the polarization. We derive the equations of motion of the beam and demonstrate the optical Hall effect in the dislocated medium. Its application with regard to determining the Burgers vector as well as the elasto-optic coefficients of the medium is explained.
Spaser SP population and spectral characteristics in the stationary state. The computations are done for a silver nanoshell with the external radius R 2 = 12 nm; the detuning of the gain medium from the spasing SP mode is ¯ h(ω 21 − ω n ) = −0.02 eV. The other parameters are indicated in section 2. (a) Number N n of plasmons per spasing mode as a function of the excitation rate g (per chromophore of the gain medium). Computations are done for the dipole eigenmode with the spasing frequencies ω s as indicated, which were chosen by the corresponding adjustment of the nanoshell aspect ratio. (b) Population inversion n 12 as a function of the pumping rate g. The color coding of the lines is the same as in panel (a). (c) The spectral width s of the spasing line (expressed as ¯ h s in meV) as a function of the pumping rate g. The color coding of the lines is the same as in panel (a). (d)-(f) Spectra of the spaser for the pumping rates g expressed in the units of the threshold rate g th , as indicated in the panels. The curves are color coded and scaled as indicated.
Bistability in a spaser with a saturable absorber in a stationary spasing state. (a) Dependence of the SP population number N n in the spasing mode on the pumping rate g for different concentrations ρ a of the saturable absorber. The curves are color coded corresponding to ρ a shown in units of the concentration ρ of the active medium chromophores. The black line shows the threshold curve (separatrix) between the bistable and uniquely stable solutions. (b) The dependence of the population inversion n 21 on the pumping rate g for the spasing states. The color coding is the same as in panel (a). Note that the lower branches of the curves in this panel correspond to the upper ones in panel (a) and vice versa. (c) The same as panel (a) but only the stable branches of the curves are displayed, illustrating the physical behavior of the spaser population N n. Note that one of the stable branches coincides with the horizontal axis. The vertical arrows illustrate the hysteretic transitions between the two stable branches for ρ a = 3ρ. (d) The same as panel (c) but for the population inversion n 21. The black curve starting with n 21 = −1 shows a trivial stable solution corresponding to the absence of spasing (N n = 0).
Ultrafast dynamics of the spaser. (a) For a monostable spaser (without a saturable absorber), the dependence of the SP population in the spasing mode N n on time t. The spaser undergoes stationary pumping at a rate of g = 5 × 10 12 s −1. The color coded curves correspond to the initial conditions with the different initial SP populations, as shown in the graphs. (b) The same as (a) but for the temporal behavior of the population inversion n 21. (c) Dynamics of a monostable spaser (no saturable absorber) with the pulsed pumping described as the initial inversion n 21 = 0.65. The coherent SP population N n is displayed as a function of time t. Different initial populations are indicated by color coded curves. (d) The same as (c) but for the corresponding population inversion n 21. (e) The same as (a) but for a bistable spaser with the saturable absorber for the concentration ρ a = 0.66ρ. (f) The same as (b) but for the bistable spaser. (g) The same as (e) but for the pulsed pumping with the initial inversion n 21 = 0.65. (h) The same as (g) but for the corresponding population inversion n 21 .
Nanoplasmonics has recently experienced explosive development with many novel ideas and dramatic achievements in both fundamentals and applications. The spaser has been predicted and observed experimentally as an active element -- generator of coherent local fields. Even greater progress will be achieved if the spaser could function as a ultrafast nanoamplifier -- an optical counterpart of the MOSFET (metal-oxide-semiconductor field-effect transistor). A formidable problem with this is that the spaser has the inherent feedback causing quantum generation of nanolocalized surface plasmons and saturation and consequent elimination of the net gain, making it unsuitable for amplification. We have overcome this inherent problem and shown that the spaser can perform functions of an ultrafast nanoamplifier in two modes: transient and bistable. On the basis of quantum density matrix (optical Bloch) equations we have shown that the spaser amplifies with gain greater than 50, the switching time less or on the order of 100 fs (potentially, 10 fs). This prospective spaser technology will further broaden both fundamental and applied horizons of nanoscience, in particular, enabling ultrafast microprocessors working at 10 to 100 THz clock speed. Other prospective applications are in ultrasensing, ultradense and ultrafast information storage, and biomedicine. The spasers are based on metals and, in contrast to semiconductors, are highly resistive to ionizing radiation, high temperatures, microwave radiation, and other adverse environments. Comment: 4 figures
Temporal and frequency characteristics of the all-fiber PM 
We investigated the effct of pump wavelength on the modal instabilities (MI) in high power linearly-polarized Yb-doped fiber amplifiers. We built a novel semi-analytical model to determine the frequency coupling characteristics and power threshold of MI, which indicates promising MI suppression through pumping at an appropriate wavelength. By pumping at 915nm, the threshold can be enhanced by a factor of 2.36 as compared to that pumped at 976nm. Based on a high power linearly-polarized fiber amplifier platform, we studied the influence of pump wavelength experimentally. The threshold has been increased by a factor of 2 at 915nm, which agrees with the theoretical calculation and verified our theoretical model. Furthermore, we show that MI suppression by detuning the pump wavelength is weakened for fiber with large core-to-cladding ratio.
We present an analytical model for describing complex dynamics of a hybrid system consisting of interacting classical and quantum resonant structures. Classical structures in our model correspond to plasmonic nano-resonators of different geometries, as well as other types of nano- and micro-structures optical response of which can be described without invoking quantum-mechanical treatment. Quantum structures are represented by atoms or molecules, or their aggregates (for example, quantum dots and carbon nanotubes), which can be accurately modelled only with the use of quantum approach. Our model is based on the set of equations that combines well-established density matrix formalism appropriate for quantum systems, coupled with harmonic-oscillator equations ideal for modelling sub-wavelength plasmonic and optical resonators. This model can also be straightforwardly adopted for describing electromagnetic dynamics of various hybrid systems outside the photonics realm, such as Josephson-junction metamaterials, or SQUID elements coupled with an RF strip resonator.
Oblique incidence from lower left at 2D-NRPhC (the region between the two white lines with a number of periods in the z direction 51) sandwiched by air in TM polarization ((a), (b) and (c)) with incidence angle of 26° and TE polarization ((d), (e) and (f)) with incidence angle of 29° . Surface termination at (a), (d) τ = 0; (b), (e) τ = 0.25; and (c), (f) τ = 0.8.  
The investigation of surface termination over the inverse Goos-H\"anchen (GH) shift of two-dimensional (2D) negatively refractive photonic crystal (NRPhC), made by air holes arranged in hexagonal lattice in a dielectric background, shows that the magnitude of the inverse GH shift of 2D-NRPhC depends strongly on the surface termination even for an incident beam with fixed frequency and incidence angle, while the effective index of 2D-NRPhC remains. For surface termination with the outmost row of air holes complete, TM-polarized light is characterized by the inverse GH shift of more than tens of lattices and TE-polarized light by very tiny inverse GH shift. While for surface termination with the outmost row of air holes cut in quarter or so, the situation is just on the opposite. In addition, the reflectivity of 2D-NRPhC as a function of surface termination is also studied, and the result shows that the smaller the reflectivity the larger the inverse GH shifts. The results of this paper will provide technical information for the combination of various functional photonic elements in the design of integrated optical circuits.
It is shown that the photon picture of the electromagnetic field enables one to determine unambiguously the splitting of the total angular momentum of the electromagnetic field into the orbital part and the spin part.
The law of reflection and Snell's law are among the tenets of geometrical optics. Corrections to these laws in wave optics are respectively known as the angular Goos-Hänchen shift and Fresnel filtering. In this paper we give a positive answer to the question of whether the two effects are common in nature and we study both effects in the more general context of optical beam shifts. We find that both effects are caused by the same principle, but have been defined differently. We identify and discuss the similarities and differences that arise from the different definitions.
Representation of the optical elements. 
We prove that a single photon with quantum data encoded in its orbital angular momentum can be manipulated with simple optical elements to provide any desired quantum computation. We will show how to build any quantum unitary operator using beamsplitters, phase shifters, holograms and an extraction gate based on quantum interrogation. The advantages and challenges of these approach are then discussed, in particular the problem of the readout of the results.
This paper is devoted to study the propagation of light beams carrying orbital angular momentum in optically anisotropic media. We first review some properties of homogeneous anisotropic media, and describe how the paraxial formalism is modified in order to proceed with a new approach dealing with a general setting of paraxial propagation along uniaxial inhomogeneous media. This approach is suitable for describing the space-variant-optical-axis phase plates.
We predict a non-thermal magneto-optical effect for magnetic insulators subject to intense light carrying orbital angular momentum (OAM). Using a classical approach to second harmonic generation in non-linear media with specific symmetry properties we predict a significant nonlinear contribution to the local magnetic field triggered by light with OAM. The resulting magnetic field originates from the displacement of electrons driven by the electrical field (with amplitude $E_0$) of the spatially inhomogeneous optical pulse, modeled here as a Laguerre-Gaussian beam carrying OAM. In particular, the symmetry properties of the irradiated magnet allow for magnetic field responses which are second-order ($\sim E_0^2$) and fourth-order ($\sim E_0^4$) in electric-field strength and have opposite signs. For sufficiently high laser intensities, terms $\sim E_0^4$ dominate and generate magnetic field strengths which can be as large as several Tesla. Moreover, changing the OAM of the laser beam is shown to determine the direction of the total light-induced magnetic field, which is further utilized to study theoretically the non-thermal magnetization dynamics.
In this paper we describe how to derive the expressions for the higher nonlinear generation of waves, their transmission and reflection for the case of a normal incidence plane wave by direct superposition of nonlinear dipoles. We describe explicitly that the transmitted and reflected nonlinear harmonic wave can only propagate inside the material if the phase matching condition is fulfilled and show for the case of second-harmonic-generation that our calculation yields similar results with coupled-mode-theory (CMT).
Experimental set-up. WP: Wollaston prism. MO:microscope objective. P: polarizer. HWP: half-wave plate. PBS: polarizing beam splitter. BS: beam splitter. 
a) shows some examples of this procedure, for = E 0 0 , μ = d 10 m and different writing beam intensities I W. Our method for absolute calibration of Δn 0 [9] then allows to convert the initial slope α ∂ ∂t W into v 0. For moderate lattice strengths Δn 0 (which is often valid at short times), Δn 0 is simply proportional to α. In b), we show v 0 as function of I , W for μ = d 10 m, and for a drift-dominated regime (E 0 = 0.8kV cm −1 , squares), and a diffusion-dominated regime ( = E 0 0 , circles). From equation (14), we have Δ δ = − + ∞ ∞ n n I I I ( ) max W W sat , and using equation (11) and ≫ I I W s a t one sees that the initial writing speed is expected to be 
Influence of external parameters on writing efficiency for a 1D lattice of period μ = d 10 m. (a) Determination of initial writing speed v 0 from fits of the modulation coefficient α as function of writing time t W with (10), for = E 0 0 V, and average writing beam intensities = I 0.2, 0.4, 0.86, 1.4 W
Ratio of initial writing speeds for drift ( = E 2 0 kV cm −1 ) and diffusive ( = E 0 0 ) photorefractive mechanisms versus lattice period d, for = I 1 W mW cm −2. The solid line is the theoretical prediction equation (21), with no adjustable parameter.
Intensity of a linear probe beam (and writing beam, in second column) at crystal output in real and Fourier space, for a 1D (upper row), square (middle row) and a diamond lattice (lower row). The probe beam is a plane wave (first two columns) or a narrowly defocusing wave at the crystal input, which expands in the lattice (last two columns). (a), (e) and (i) real space output for a plane wave input probe with lattice period μ = d 27 m (1D lattice) and μ = d 38.5 m (2D lattices) (b), (f) and (j) Fourier images of lattice writing beams (four outside points) and the probe which is a point at = k 0. (c), (g) and (k) real space output for a defocusing probe (discrete diffraction patterns) with μ = d 7 m (1D lattice) and μ = d 10 m (2D lattices). White lines show the ballistic positions ±y L of vertical Bragg components ±k L. (d), (h) and (l) Fourier images of the defocusing probe (Brillouin zone spectroscopy), with μ = d 13.6 m (1D lattice) and μ = d 19.2 m (2D lattices), with vertical Bragg components ±k L shown as white lines.
We experimentally study the writing of one- and two-dimensional photorefractive lattices and the propagation of linear and nonlinear waves inside them. Using plane waves, we perform a time-resolved study of lattice writing and find good agreement with transient and steady-state photorefractive theory. In particular, the ratio of the drift to diffusion terms is proportional to the lattice period. We then analyze various wave propagation schemes. For focussed linear waves with broad transverse spectrum, we note that both the intensity distributions in real space ("discrete diffraction") and Fourier space ("Brillouin zone spectroscopy") reflect the Bragg planes and band structure. For non-linear waves, we observe modulational instability and time-domain discrete solitons formation. We discuss also the non-ideal effects inherent to the photo-induction technique : anisotropy, parasitic nonlinearity, diffusive term, and non-stationarity.
We have introduced a class of spiraling elliptic breathers in saturable nonlinear media with linear anisotropy. Two kinds of evolution behaviors of the breathers, rotating and pendulum-like librating, are both predicted by the variational approach, and confirmed by the numerical simulation.The spiraling elliptic breathers can rotate even though they have no initial orbital angular momentum (OAM). Due to the linear anisotropy of the media, the OAM is no longer conserved. Therefore, the angular velocity is found to be not a constant but a periodic function of the propagation distance. When the linear anisotropy is large enough, the spiraling elliptic breathers can librate like the pendulum. The spiraling elliptic breathers exist in the media with not only the saturable nonlinearity but also the nonlocal nonlinearity, as a matter of fact, they are universal in the nonlinear media with the linear anisotropy.
Wavelength dependences of the magnitude of reflection coefficients of arrays made of two dielectric bars in periodic cell (h 1 = 877 nm and h 2 = 780 nm, line 1) and single dielectric bar which length is 877 nm (line 2) or 780 nm (line 3). Sizes of the periodic cell and the bar cross sections are 975 nm and 195 nm, respectively. The refractive index of the bar dielectric is 5.5. .
Results of research of resonant phenomena in planar periodic structures consisted of dielectric elements are presented. A problem of plane wave diffraction by a structure which a periodic cell is composed of two dielectric bars with different lengths has been solved. For the first time an existence of high Q-factor trapped mode resonances are revealed in these structures. The main difference of studied structure in contrast to the planar structure with a single dielectric bar in the unit cell is appearing of a great red shift of a trapped mode resonant wavelength. The red shift is caused by strong coupling of electromagnetic fields in neighbor dielectric bar resonators. This property is very attractive to design resonant periodic planar structures by using moderate refractive index materials like semiconductors within their transparency window. In the near infrared band, the trapped mode resonances of periodic planar structure with bars made of germanium have been studied. It is shown that decreasing of structure asymmetry degree results in increasing of both red shift and Q-factor of resonance.
We present a theory of the local field corrections to the spontaneous emission rate for the array of silicon nanocrystals in silicon dioxide. An analytical result for the Purcell factor is obtained. We demonstrate that the local-field corrections are sensitive to the volume fill factor of the nanocrystals in the sample and are suppressed for large values of the fill factor. The local-field corrections and the photonic density of states are shown to be described by two different effective permittivities: the harmonic mean between the nanocrystal and the matrix permittivities and the Maxwell-Garnett permittivity.
We have studied harmonic oscillations in an elliptical optical waveguide array in which the coupling between neighboring waveguides is varied in accord with a Kac matrix so that the propagation constant eigenvalues can take equally spaced values. As a result, long-living Bloch oscillation (BO) and dipole oscillation (DO) are obtained when a linear gradient in the propagation constant is applied. Moreover, we achieve a switching from DO to BO or vice versa by ramping up the gradient profile. The various optical oscillations as well as their switching are investigated by field evolution analysis and confirmed by Hamiltonian optics. The equally spaced eigenvalues in the propagation constant allow viable applications in transmitting images, switching and routing of optical signals.
We show that second harmonic generation can be enhanced by Fano resonant coupling of asymmetric plasmonic metal nanostructures. We develop a theoretical model examining the effects of electromagnetic interaction between two metal nanostructures on the second harmonic generation. We compare the second harmonic generation efficiency of a single plasmonic metal nanostructure with that of two coupled ones. We show that second harmonic generation from a single metal nanostructure can be enhanced about 30 times by attaching a second metal nanostructure with a 10 times higher quality factor than that of the first one. The origin of this enhancement is Fano resonant coupling of the two metal nanostructures. We support our findings on Fano enhancement of second harmonic generation by an experimental study of a coupled plasmonic system composed of a silver nanoparticle and a silver nanowire on glass surface in which the ratio of the quality factors are also estimated to be around 10 times.
The real ((a) and (c)) and imaginary ((b) and (d)) parts of the roots of the dispersion relation (f r ) of the layered structure as a function of the atomic density at γ = 0.0008 (left panel) and 0.001 (right panel). The solid (dashed) curve corresponds to the split resonance at the lower (higher) frequency. 
We study a critically coupled cavity doped with resonant atoms with metamaterial slabs as mirrors. We show how resonant atom-cavity interaction can lead to a splitting of the critical coupling dip. The results are explained in terms of the frequency and lifetime splitting of the coupled system.
We investigate the self-Kerr nonlinearity of a four-level N-type atomic system in 87Rb and observe its reversible property with the unidirectional increase of the switching field. For the laser arrangement that the probe field interacts with the middle two states, the slope and the sign of the self-Kerr nonlinearity around the atomic resonance can not only be changed from negative to positive, but also can be changed to negative again with the unidirectional increasing of the switching field. Numerical simulation agrees very well with the experimental results and dressed state analysis is presented to explain the experimental results.
The interference between optical beams of different polarizations plays a fundamental role in reproducing the optical analog of the electron spin weak measurement. The extraordinary point in optical weak measurements is represented by the possibility to estimate with great accuracy the Goos-Haenchen (GH) shift by measuring the distance between the peak of the outgoing beams for two opposite rotation angles of the polarizers located before and after the dielectric block. Starting from the numerical calculation of the GH shift, which clearly shows a frequency crossover for incidence near to the critical angle, we present a detailed study of the interference between s and p polarized waves in the critical region. This allows to determine in which conditions it is possible to avoid axial deformations and reproduce the GH curves. In view of a possible experimental implementation, we give the expected weak measurement curves for Gaussian lasers of different beam waist sizes propagating through borosilicate (BK7) and fused silica dielectric blocks.
(Color online) Transmittance ( T r ) spectra of the blue-green beads shown in Fig. 3 derived as a result of averaging of a number of spectra obtained from similar points on each bead or on a specific segment of the bead at magnification of 600: (1) an intact blue bead (sample 1, Fig. 3 a), (2) a cracked bead at initial phase of destruction (sample 2, Fig. 3 b), (3) a strongly degraded bead (sample 3, blue segments, Fig. 3 c, domain 2), (4) a strongly degraded bead (sample 3, brown-green segments, Fig. 3 c, domain 3) and (5) a disrupted bead (samples 4a and 4b, Fig. 3 d, e). 
A result of subtraction of the spectra (3) to (5) from the spectrum (1) (Δ Tr, see figure 4) plotted as a function of λ −4 and linear fits of fragments of the graphs in the range of the visible light; designations are the same as in figure 4.
LSM images (a), (b) of the cleavage surface of a segmented bead shown in the panel (c); numerous foreign microinclusions are spread throughout the spall area and aggregation of the inclusions is observed in the centres of the images (a) and (b); cracks of various sizes are also observed everywhere on the surface (some of them are marked by the letter 'S') which indicate the presence of a strong strain.
Blue-green historical beads are sometimes referred to as instable ones because of their degradability. At present, the cause of the phenomenon of deterioration of the blue-green beads is unknown. We explore internal microstucture of degrading blue-green historical beads and its evolution in the process of bead deterioration. Investigating transmittance and scattering spectra of visible and near infrared light we observe formation of microscopic internal inhomogeneities with the sizes less than 150 nm in the glass bulk and growth of their density with increase in degree of bead degradation. By means of laser scanning microscopy we also observe numerous microinclusions and microcracks on the cleavage surface of a partially degraded bead. We discuss possible physical factors resulting in destruction of the blue-green beads.
(a) Schematic of the refractive index disordered waveguide lattice with different colors indicating different refractive indices; (b) ballistic mode of propagation through a perfectly ordered lattice; (c) transition to a localized mode after propagation through a 20 mm (L) long 20% disordered lattice.
Variation in the ensemble averaged effective width (ω eff ) of a Gaussian beam (of initial FWHM 12 µm) with propagation through the disordered waveguide lattice. The curves are labeled in terms of the disorder parameter C for three different values of the phase front curvature parameter B. The error bars are the statistical standard deviations for the effective beam widths over 200 realizations.
Comparison of the building up of a central peak (a transition towards the localized state) and suppression of ballistic side lobes from (a)-(c); this clearly indicates a significant effect on the localization transition due to the initial curved phase front of the light beam. Side lobes are more prominent in the case of propagation of an input beam with finite phase fronts.
Localization lengths (l C ) on either side of a localized state have been plotted as a function of the curvature parameter (B) for the same Gaussian input beam profile along a 15 mm long lattice geometry with 60% disorder. Due to the characteristic asymmetry of a localized state around its peak, some difference in the variation of the localization length with B on either side of the peak of the profile is evident from (a) and (b). Bars show possible errors encountered during the curve fitting.
Variation of the ensemble averaged effective width (ω eff ) of a Gaussian beam with two different input FWHMs with propagation through the waveguide lattice for C = 0.2. The error bars are the statistical standard deviations for the effective beam widths over 250 realizations. The chosen input widths cover: (a) about one site of the lattice; (b) ∼18 sites of the lattice.
We investigate the influence of the phase-front curvature of an input light beam on the transverse localization of light by choosing an evanescently coupled disordered one-dimensional semi-infinite waveguide lattice as an example. Our numerical study reveals that a finite phase front curvature of the input beam indeed plays an important role and it could degrade the quality of light localization in a disordered dielectric structure. More specifically, a faster transition from ballistic mode of beam propagation due to diffraction to a characteristic localized state is observed in case of a continuous wave (CW) beam, whose phase-front is plane as compared to one having a curved phase front.
We present a study of radially and azimuthally polarized Bessel-Gauss beams in both the paraxial and nonparaxial regimes. We discuss the validity of the paraxial approximation and the form of the nonparaxial corrections for Bessel-Gauss beams. We show that, independently from the ratio between the Bessel aperture cone angle $\vartheta_0$ and the Gauss beam divergence $\theta_0$, the nonparaxial corrections are always very small and therefore negligible. Explicit expressions for the nonparaxial vector electric field components are also reported.
We study monochromatic, scalar solutions of the Helmholtz and paraxial wave equations from a field-theoretic point of view. We introduce appropriate time-independent Lagrangian densities for which the Euler-Lagrange equations reproduces either Helmholtz and paraxial wave equations with the $z$-coordinate, associated with the main direction of propagation of the fields, playing the same role of time in standard Lagrangian theory. For both Helmholtz and paraxial scalar fields, we calculate the canonical energy-momentum tensor and determine the continuity equations relating "energy" and "momentum" of the fields. Eventually, the reduction of the Helmholtz wave equation to a useful first-order Dirac form, is presented. This work sheds some light on the intriguing and not so acknowledged connections between angular spectrum representation of optical wavefields, cosmological models and physics of black holes.
This work is the second part of an investigation aiming at the study of optical wave equations from a field-theoretic point of view. Here, we study classical and quantum aspects of scalar fields satisfying the paraxial wave equation. First, we determine conservation laws for energy, linear and angular momentum of paraxial fields in a classical context. Then, we proceed with the quantization of the field. Finally, we compare our result with the traditional ones.
We consider two-dimensional (2D) localized vortical modes in the three-wave system with the quadratic ($\chi ^{(2)}$) nonlinearity, alias nondegenerate second-harmonic-generating system, guided by the isotropic harmonic-oscillator (HO) (alias parabolic) confining potential. In addition to the straightforward realization in optics, the system models mixed atomic-molecular Bose-Einstein condensates (BECs). The main issue is stability of the vortex modes, which is investigated through computation of instability growth rates for eigenmodes of small perturbations, and by means of direct simulations. The threshold of parametric instability for single-color beams, represented solely by the second harmonic (SH) with zero vorticity, is found in an analytical form with the help of the variational approximation (VA). Trapped states with vorticities $\left( +1,-1,0\right) $ in the two fundamental-frequency (FF) components and the SH one [the so-called \textit{hidden-vorticity} (HV) modes] are completely unstable. Also unstable are \textit{semi-vortices} (SVs), with component vorticities $% \left( 1,0,1\right) $. However, full vortices, with charges $\left( 1,1,2\right) $, have a well-defined stability region. Unstable full vortices feature regions of robust dynamical behavior, where they periodically split and recombine, keeping their vortical content.
We review optical phenomena associated with the internal energy redistribution which accompany propagation and transformations of monochromatic light fields in homogeneous media. The total energy flow (linear-momentum density, Poynting vector) can be divided into spin part associated with the polarization and orbital part associated with the spatial inhomogeneity. We give general description of the internal flows in the coordinate and momentum (angular spectrum) representations for both nonparaxial and paraxial fields. This enables one to determine local densities and integral values of the spin and orbital angular momenta of the field. We analyse patterns of the internal flows in standard beam models (Gaussian, Laguerre-Gaussian, flat-top beam, etc.), which provide an insightful picture of the energy transport. The emphasize is made to the singular points of the flow fields. We describe the spin-orbit and orbit-orbit interactions in the processes of beam focusing and symmetry breakdown. Finally, we consider how the energy flows manifest themselves in the mechanical action on probing particles and in the transformations of a propagating beam subjected to a transverse perturbation.
I present theoretical calculations of reflection beamshifts, Goos-H\"anchen and Imbert-Fedorov shifts, due to the presence of a monolayer graphene on a dielectric media when using a beam with wavelength in the visible range. Specifically, I look at beamshifts for different polarization states (p, s, $45^0$, $\sigma^+$). The Goos-H\"anchen shifts I calculated are in good agreement with results of a recent experiment. I will discuss other possible experimental routes to determine beamshifts in graphene.
Transverse intensity pattern at the focal plane for a cascade of two biaxial crystals with aligned optic axes obtained from an elliptical input beam. (a) Numerical simulations obtained by using equations (8)-(13). (b) Experimental measurements obtained by using two KGd(WO ) 2 4 biaxial crystals with lengths of = l 28 mm 1 
We present a formalism able to predict the transformation of light beams passing through biaxial crystals. We use this formalism to show both theoretically and experimentally the transition from double refraction to conical refraction, which is found when light propagates along one of the optic axes of a biaxial crystal. Additionally, we demonstrate that the theory is applicable both to non-cylindrically symmetric and non-homogeneously polarized beams by predicting the transformation of input beams passing through a cascade of biaxial crystals.
Omnidirectional light concentration remains an unsolved problem despite such important practical applications as design of efficient mobile photovoltaic cells. Optical black hole designs developed recently offer partial solution to this problem. However, even these solutions are not truly omnidirectional since they do not exhibit a horizon, and at large enough incidence angles light may be trapped into quasi-stationary orbits around such imperfect optical black holes. Here we propose and realize experimentally another gravity-inspired design of a broadband omnidirectional light concentrator based on the cosmological Big Crunch solutions. By mimicking the Big Crunch spacetime via corresponding effective optical metric we make sure that every photon world line terminates in a single point.
(Color online). Schematic of experimental setup for producing narrow-band biphotons with frequency-bin entanglement. The phase-matched paired photons are generated from spontaneous four-wave mixing in laser-cooled 85 Rb atoms with a right-angle pump-coupling geometry. The relevant 85 Rb energy levels are |1 = |5S 1/2 , F = 2, |2 = |5S 1/2 , F = 3, |3 = |5P 3/2 , F = 3, and |4 = |5P 3/2 , F = 2. 
(Color online). (a) The Poincaré sphere. An arbitrary projection state can be rotated to |H with the combination of a half-wave plate and a quarter-wave plate. Blue (red) dashdot line represents rotation axis for half-wave plate (quarterwave plate), and blue (red) arrow curve shows half-wave plate (quarter-wave plate) rotation. (b) The equatorial S1S2-plane view. 
We describe a technique to produce narrow-band photon pairs with frequency-bin entanglement, whose relative phase can be tuned using linear polarization optics. We show that, making use of the polarization-frequency coupling effect, the phase of a complex polarizer can be transferred into the frequency entanglement.
Diagram of the relationship between the pump, signal, and idler momenta, in standard (not necessarily collinear) phase matching.
Plot comparing estimates of the momentum difference probability density \rho ({k}_{-}). The solid (blue) curve with wavy side-bands gives our Sinc-based probability density estimate (29), where we set a = 2 for convenience. The dashed (magenta) Gaussian curve gives our Gaussian-based probability density estimate with matching means and variances.
Plot comparing different estimates of \rho ({x}_{-}). The solid blue wavy curve is our most accurate estimate from the transformed Sinc-based distribution (51). The tall dashed (magenta) curve is the Gaussian distribution obtained from matching momentum means and variances, while the shallow dashed (red) curve is the Gaussian distribution obtained by matching position means and variances. The solid (green) curve gives us a refined Gaussian approximation, by setting the central maximums equal to one another. The flat (gold) line, gives the height of the half maximum of the sinc-based probability density (51) (blue curve). We see that the widths of half maximum are nearly identical (off by less than 0.3\%) for the Sinc-based and refined Gaussian distributions Again, we set a = 2 for convenience.
Plot of the double-Gaussian probability density for {\sigma }_{{x}_{+}}=1 unit and {\sigma }_{{x}_{-}}=0.075 units. The horizontal dotted line indicates a particular value of x2, so that the half-width of the Gaussian along that dotted line is the conditioned half-width {\sigma }_{({x}_{1}| {x}_{2})}. The equivalent sinc-Gaussian distribution will have subtle side bands (at about 5.0\% the maximum intensity) parallel to the long axis of this double-Gaussian as in figure 3.
Idealized diagram of the transverse intensity profile (in both x and y) of the downconverted light just as it exits the crystal. The blue circle encapsulates the region within one standard deviation of the pump photon position (or also approximately the signal or idler photon position) from the beam center. The red circle is centered on a particular downconversion event, and encapsulates the region where the signal and idler photons are likely to be found given that their mean position is known to be at the center of the circle (i.e. one birth zone). For a sense of scale, we let {{\rm{\Delta }}}_{p}/{{\rm{\Delta }}}_{\mathrm{BZ}}=10.
For the purpose of a pedagogical introduction to the spatial aspects of Spontaneous Parametric Downconversion (SPDC), we present here a detailed first-principles derivation of the transverse correlation width of photon pairs in degenerate collinear SPDC. Along the way, we discuss the quantum-optical calculation of the amplitude for the SPDC process, as well as its simplified form for nearly collinear degenerate phase matching. Following this, we show how this biphoton amplitude can be approximated with a Double-Gaussian wavefunction, give a brief discussion of the statistics of such Double-Gaussian distributions, and show how such approximations allow a simple description of the biphoton field over propagation. Next, we use this Double-Gaussian approximation to get a simplified estimation of the transverse correlation width, and compare it to more accurate calculations as well as experimental results. We then conclude with a discussion of the related concept of a biphoton birth zone, using it to develop intuition for the tradeoff between the first-order spatial coherence and bipohoton correlations in SPDC.
In spontaneous parametric down-conversion photons are known to be created coherently and with equal probability over the entire length of the crystal. Then, there is no particular position in the crystal where a photon pair is created. We make the seemingly contradictory observation that we can control the time delay with the crystal position along the propagation direction. We resolve this contradiction by showing that the spatio-temporal correlations critically affect the temporal properties of the pair of photons, when using a finite detector size. We expect this to have important implications for experiments that require indistinguishable photons.
We analyse a multilayer leaky cladding (MLC) fibre using the finite element method and study the effect of the MLC on the bending loss and birefringence of two types of structures: (i) a circular core large-mode-area structure and (ii) an elliptical-small-core structure. In a large-mode-area structure, we verify that the multilayer leaky cladding strongly discriminates against higher order modes to achieve single-mode operation, the fibre shows negligible birefringence, and the bending loss of the fibre is low for bending radii larger than 10 cm. In the elliptical-small-core structure we show that the MLC reduces the birefringence of the fibre. This prevents the structure from becoming birefringent in case of any departures from circular geometry. The study should be useful in the designs of MLC fibres for various applications including high power amplifiers, gain flattening of fibre amplifiers and dispersion compensation. Comment: 18 pages
Top-cited authors
Ebrahim Karimi
  • University of Ottawa
Zubin Jacob
  • Purdue University
Benjamin Eggleton
  • The University of Sydney
Sean J. Molesky
  • Princeton University
Cristian Cortes
  • Argonne National Laboratory