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We show that graphene is best described as a slab with finite thickness based on our reflectivity analysis for five different wavelengths. We perform fine-scan angular reflectivity on a single layer graphene on top of SiO2/Si and determine its crossing angle. The experimental data were then compared to the predictions of the three most common models for a single layer graphene. We find that the slab model gives good predictions for the crossing angle in all our experiments. This implies that (1) the real part of the electric permittivity of graphene has a crucial role in the electromagnetic wave propagation, (2) the field across a single layer graphene is continuous, and (3) the dispersionless refractive index of graphite can describe the optical index of graphene in the visible regime.

We calculate the out-of-plane Imbert-Fedorov (IF) shifts of radio waves reflected from the ionosphere. From our calculations, we present the use of IF shifts as potential tool to probe the properties of the ionosphere.

We propose and demonstrate a method for lowering the cost of ghost imaging (GI) setups by employing cheaper devices, such as a commercial projector and a light-dependent resistor. Spatial light modulators and high-quality photodiodes are often used in GI, but the cost of these devices limits its implementation in undergraduate or even graduate optics laboratories. Our proposed imaging system produces good reconstructions of our test object even at 10% spectral coverage that is well within sub-Nyquist sampling. This may be used as an alternative low-cost and easy-to-build imaging system, which we can easily extend for technological applications using wavelengths outside the visible spectrum.

We demonstrate potential molecular monolayer detection using measurements of surface plasmon resonance (SPR) and angular Goos-Hänchen (GH) shift. Here, the molecular monolayer of interest is a benzenethiol self-assembled monolayer (BT-SAM) adsorbed on a gold (Au) substrate. Excitation of surface plasmons enhanced the GH shift which was dominated by angular GH shift because we focused the incident beam to a small beam waist making spatial GH shift negligible. For measurements in ambient, the presence of BT-SAM on a Au substrate induces hydrophobicity which decreases the likelihood of contamination on the surface allowing for molecular monolayer sensing. This is in contrast to the hydrophilic nature of a clean Au surface that is highly susceptible to contamination. Since our measurements were made in ambient, larger SPR angle than the expected value was measured due to the contamination in the Au substrate. In contrast, the SPR angle was smaller when BT-SAM coated the Au substrate due to the minimization of contaminants brought about by Au surface modification. Detection of the molecular monolayer acounts for the small change in the SPR angle from the expected value.

The conductivity of a monolayer graphene at intraband transitions is sensitive on the Fermi level and on the wavelength of the incident beam. Changing conductivity values through these parameters thus may offer better control of light impinging on graphene. In this paper, we investigate reflection, the simplest interaction of light on such surface, by looking at the Goos-Hanchen (GH) shift experienced by the incident light where the wavelength is at terahertz range. With this wavelength range, we assume that the carriers in graphene undergo intraband transition. We calculate that spatial and angular GH shifts can be present. For both GH shifts in general, we find that increasing the Fermi level changes the incident angle at which the maximum GH shifts arise. Moreover, we see that at higher frequencies, the amount of beam shift decreases with the Fermi level. At lower frequencies on the other hand, the shift becomes proportional to the Fermi level. Upon obtaining the measurable shifts, we find that the magnitude of the physical shifts can be easily detected given appropriate experimental parameters. Our results may increase the utility of graphene in optoelectronics devices and applications.

We achieved three-dimensional (3D) computational ghost imaging with multiple photoresistors serving as single-pixel detectors using semi-calibrated lighting approach. We performed imaging in the spatial frequency domain by having each photoresistor obtain the Fourier spectrum of the scene at a low spectral coverage ratio of 5%. To retrieve a depth map of a scene, we inverted, apodized, and applied semi-calibrated photometric stereo (SCPS) to the spectra. At least 93.5% accuracy was achieved for the 3D results of the apodized set of images applied with SCPS in comparison with the ground truth. Furthermore, intensity error map statistics obtained at least 97.0% accuracy for the estimated surface normals using our method. Our system does not need special calibration objects or any additional optical components to perform accurate 3D imaging, making it easily adaptable. Our method can be applied in current imaging systems where multiple detectors operating at any wavelength are used for two-dimensional (2D) imaging, such as imaging cosmological objects. Employing the idea of changing light patterns to illuminate a target scene and having stored information about these patterns, the data retrieved by one detector will give the 2D information while the multiple-detector system can be used to get a 3D profile., Comment: 10 pages, 8 figures, 2 visualizations

We demonstrate the surface plasmon resonance (SPR)-enhanced angular Goos-Hanchen (GH) shift. Typical SPR-enhanced GH shift measurements make use of loosely collimated beams, which enhances only the spatial GH shift (ΔGH). Unlike this scheme, we focused the incident beam to a small beam waist to induce enhancement in the angular GH shift (ΘGH). Although this makes ΔGH negligible, the enhancement of ΘGH is much larger than the decrease in ΔGH. In order to excite surface plasmons, we employ a Kretschmann configuration using a simple gold (Au) film on a substrate. We show that although the efficiency of surface plasmon excitation is decreased by the focused geometry, a significantly large ΘGH was induced. With the simultaneous measurement of reflectivity for SPR and the beam shift for the GH shift used in this work, we experimentally show the potential of measuring enhanced ΘGH toward sensing application when the Au film is exposed to local environmental changes even in the simplest thin film structure.

The orbital angular momentum (OAM) of light has become a central topic in quantum information and optical communication. In applications OAM is typically probed by observing a beam's diffraction through binary amplitude and phase masks. Distinguishing the different OAM states of the beam is usually difficult, though, so here the authors program a digital micromirror array to shift the setup's slit transversely, to exploit the unique phase of an OAM beam. By observing how diffraction varies as the slit changes, one can probe higher OAM values than usual, allowing access to theoretically unlimited OAM states for high-dimensional quantum systems, or for multiplexing in communication.

The orbital angular momentum (OAM) of light are central to different areas of research because they can provide theoretically infinite allowable states. Here, use a movable slit to probe the OAM of Lagguerre-Gaussian beams.

Four-lens paraxial cloak theory is extended to accommodate lenses with different focal lengths. Solutions of this case were found and cloaking was still observed in experiments, with only small background magnification.

In this paper, we show that cloaking region can be achieved with four converging lenses of any focal length by solving the ray transfer matrix of a four lens optical system. It has been shown before that cloaking can be achieved using four converging lenses (so-called Rochester cloaks). However, those cloaks require having 2 sets of 2 lenses with equal focal lengths, which we did not impose. We also discuss in this paper how the separation lengths between the lenses are affected by their focal lengths. In addition, we show how our formulas hold under Rochester cloak conditions.

A Digital Micromirror Device or DMD is an instrument used to encode information on a light beam by modulating its amplitude. This device is composed of an array of tiny mirrors that can be controlled individually and can thus act as binary apertures to control the amplitude of light. DMD’s with a diamond pixel configuration have stretching distortion to the uploaded patterns. Although the patterns can be rescaled before uploading to the DMD, there is no straightforward method to determine the proper scaling factor. Here, we propose a method to find the scaling factor for the DMD by looking at diffraction caustics. We uploaded elliptical slits in the DMD that results in astroids caustics which collapse to a point when the correct scaling is matched. The scaling factor we found corrects both the inherent distortion caused by the DMD and the distortion caused by a slight misalignment of the DMD. This method offers a faster and more sensitive determination of the scale ratio instability of diffraction catastrophes and the very nature of diffraction. This method can be used to determine aspect ratios of other similar devices especially when these devices use differently shaped mirrors or when the device’s orientation is constrained such that when it is tilted.

We examine the effects on the spatial and angular Goos-Hanchen (GH) beam shifts of spherical and cylindrical pores in a thin film. In our calculations, a p-polarized light is incident on a 1-μm thick porous silicon (Si) thin film on a Si substrate. The beam shifts are within the measurement range of usual optical detectors. Our results show that a technique based on GH shift can be used to determine the porosity and pore structure of thin films at a given thickness.

Previous implementations of the phase diffuser used in the multiple-plane phase retrieval method included a diffuser glass plate with fixed optical properties or a programmable yet expensive spatial light modulator. Here a model for phase retrieval based on a digital micromirror device as amplitude diffuser is presented. The technique offers programmable, convenient and low-cost amplitude diffuser for a non-stagnating iterative phase retrieval. The technique is demonstrated in the reconstructions of smooth object wavefronts.

Quadrant detectors (QD) are mainly used in research and industries for displacement measurement purposes due to their high sensitivity and accuracy as compared to other photodiode devices. Their scope extend to sub-nanometer scales and they are also operable at a wide temperature range with fast response frequencies, which make them the best candidate for beam displacement measurements. A growing interest in the field of optics are beams carrying orbital angular momentum (OAM), particularly Laguerre-Gaussian (LG) beams, due to their remarkable applications, which include optical tracking and gravitational wave detection. This study shows the combined effect of using different OAM modes of LG beam and varying angles of inclination of the QD on the sensitivity response and linearity index of the QD. In general, it was observed that a lower OAM value for the LG beam gives a higher sensitivity for the QD and a higher angle of inclination for the QD leads to a higher linearity index. This result gives a larger range of application for the QD.

We demonstrate cloaking with four lenses of different focal lengths. To achieve this, we compute the separation distances between lenses such that the effective ABCD matrix is equal to just a propagation in free space. Previously, calculations using this method are restricted to 2 pairs of lenses with equal focal lengths. Our computations, on the other hand, had no such restrictions: we generalize even with an asymmetric case. We derive expressions that show the dependence of the distances on the lenses and their focal lengths. Furthermore, we propose a way to minimize the length of this cloak. Our equations reduce to the Rochester cloak when its restriction is imposed. A general paraxial cloak could be useful in advanced undergraduate experiments in optics because: 1) the limit imposed by the focal length has been lifted; and 2) there is a pedagogical benefit of doing experiments with lenses beyond the usual imaging experiments such as reinforcing concepts in Gaussian optics., Comment: 10 pages, 4 figures

That the speed of light in free space c is constant has been a pillar of modern physics since the derivation of Maxwell and in Einstein’s postulate in special relativity. This has been a basic assumption in light’s various applications. However, a physical beam of light has a finite extent such that even in free space it is by nature dispersive. The field confinement changes its wavevector, hence, altering the light’s group velocity vg. Here, we report the subluminal vg and consequently the dispersion in free space of Laguerre-Gauss (LG) beam, a beam known to carry orbital angular momentum. The vg of LG beam, calculated in the paraxial regime, is observed to be inversely proportional to the beam’s divergence θ0, the orbital order ℓ and the radial order p. LG beams of higher orders travel relatively slower than that of lower orders. As a consequence, LG beams of different orders separate in the temporal domain along propagation. This is an added effect to the dispersion due to field confinement. Our results are useful for treating information embedded in LG beams from astronomical sources and/or data transmission in free space.

Coherent frequency conversion of structured light, i.e. the ability to manipulate the carrier frequency of a wave front without distorting its spatial phase and intensity profile, provides the opportunity for numerous novel applications in photonic technology and fundamental science. In particular, frequency conversion of spatial modes carrying orbital angular momentum can be exploited in sub-wavelength resolution nano-optics and coherent imaging at a wavelength different from that used to illuminate an object. Moreover, coherent frequency conversion will be crucial for interfacing information stored in the high-dimensional spatial structure of single and entangled photons with various constituents of quantum networks. In this work, we demonstrate frequency conversion of structured light from the near infrared (803 nm) to the visible (527 nm). The conversion scheme is based on sum-frequency generation in a periodically poled lithium niobate crystal pumped with a 1540-nm Gaussian beam. We observe frequency-converted fields that exhibit a high degree of similarity with the input field and verify the coherence of the frequency-conversion process via mode projection measurements with a phase mask and a single-mode fiber. Our results demonstrate the suitability of exploiting the technique for applications in quantum information processing and coherent imaging.

Young's boundary wave theory provides an alternative view of diffraction being an interference of a geometric wave and a boundary wave. Here, we show theoretically and experimentally that the transverse structure of a plane wave diffracted through slits originates solely from the boundary waves. For polygonal slits, we demonstrate that the concept of the ordinary evolute is ill-defined, and we solve this problem by taking the limit of the evolute as the curvature goes to zero. We show that light focuses not on caustic as ordinarily described in catastrophe optics but on regions which we define as second order evolutes. Experimentally, we show that these second order evolutes still correspond to the brightest regions of the diffraction because of the boundary waves at the vertices of the polygon. This research is valuable in the study of diffraction of slits in general and in optical self-healing where the reconstruction of the transverse structure is investigated.

We examine the phase structures of Helico-Conical (HC) Optical Beams produced via computer-generated holograms (CGH). The CGHs of these beams are made such that the reconstruction will have a phase which is a product of a helical and a conical phase. Interference-based phase measurement technique reveals very distinct differences between the phases of the two types of HC Beams (K = 0 and K = 1). Most obvious is the presence of screw dislocations at the center of the beam for K = 1 while no screw dislocations are found at the center for K = 0. We also compare the experimental interference patterns with numerical interference patterns calculated by superimposing a field containing vortices at different positions and a plane wave. A remarkable similarity is seen between the interferograms, which is a good indication of the phase of these beams. Contour plots are drawn to show the phases of these beams. We observe a string of vortices with equal charge in contrast to the assumption that a string of alternating charges should be seen.

The use of structured light beams to detect the velocity of targets moving perpendicularly to the beam's propagation axis opens new avenues for remote sensing of moving objects. However, determining the direction of motion is still a challenge since detection is usually done by means of an interferometric setup which only provides an absolute value of the frequency shift. Here, we put forward a novel method that addresses this issue. It uses dynamic control of the phase in the transverse plane of the structured light beam so that the direction of the particles' movement can be deduced. This is done by noting the change in the magnitude of the frequency shift as the transverse phase of the structured light is moved appropriately. We demonstrate our method with rotating micro-particles that are illuminated by a Laguerre-Gaussian beam with a rotating phase about its propagation axis. Our method, which only requires a dynamically configurable optical beam generator, can easily be used with other types of motion by appropriate engineering and dynamic modulation of the phase of the light beam., Comment: 5 pages, 4 figures

We propose a technique based on spatial mode projection that can access dimensional information of nanofeatures. We demonstrate this by calculating the power of a mode-projected Gaussian beam that has been reflected by a nanocylinder.

We present the dynamics of optical vortices (OVs) that came from the propagation of helico-conical optical beam. This dynamics is investigated numerically by tracking the OVs at several distances using rigorous scalar diffraction theory. To ensure that our numerical calculations are correct, we compare the intensity profiles and their corresponding interferograms taken at different propagation distances between simulations and experiments. We observe that the peripheral isopolar vortices transport radially inward, toward the optical axis along the transverse spatial space as the beam propagates. When the beam has a central vortex, these vortices have significant induced angular rates of motion about the optical axis. These propagation dynamics of vortices influence the internal energy flow and the wave profile reconstruction of the beam, which can be important when deciding their applications., Comment: 18 pages, 9 figures; accepted for publication in Optics Communications

We show that optical beams with orbital angular momentum (OAM) can be generated even with incomplete computer generated holograms (CGHs). These holograms are made such that random portions of them do not contain any information about the beam. We observe that although the beams produced with these holograms are less intense, these beams maintain their transverse intensity profiles. The transverse intensity profiles, as well as a total intensity of the beams, are attenuated by a factor dependent only on the fraction of information retained, f. Also important is that even when f is minute, the topological charge of the beam is not affected. Our result is significant, especially since most methods used to generate beams with OAM for various applications rely on pixelated devices or optical elements with imperfections. Random dead pixels do not affect the transverse intensity and the topological charge. As an extension of our work, we show that superposition of two beams can be created using separate incomplete CGHs interspersed together. Our new method of generating superposed beams may be computationally faster because one only needs to prepare the superposed holograms from already calculated CGHs. It is advantageous for amplitude programmable devices such as a digital micromirror device.

We demonstrate an optical scheme for measuring the thickness of thin nanolayers with the use of light beam ’ s spa- tial modes. The novelty in our scheme is the projection of the beam reflected by the sample onto a properly tailored spatial mode. In the experiment described below, we are able to measure a step height smaller than 10 nm, i.e., one- eightieth ( 1 ∕ 80 ) of the wavelength with a standard error in the picometer scale. Since our scheme enhances the signal-to-noise ratio, which effectively increases the sensitivity of detection, the extension of this technique to the detection of subnanometric layer thicknesses is feasible

A Reply to the Comment by A. K. Pan and P. K. Panigrahi.

We investigate how beams with orbital angular momentum (OAM) behave under total internal reflection. This is studied in two complementary experiments: In the first experiment, we study geometric shifts of OAM beams upon total internal reflection (Goos-H\"anchen and Imbert-Fedorov shifts, for each the spatial and angular variant), and in the second experiment we determine changes in the OAM mode spectrum of a beam, again upon total internal reflection. As a result we find that in the first case, the shifts are independent of OAM and beam focussing, while in the second case, modifications in the OAM spectrum occur which depend on the input OAM mode as well as on the beam focussing. This is investigated by experiment and theory. We also show how the two methods, beam shifts on the one hand, and OAM spectrum changes on the other, are related theoretically., Comment: 9 pages, 4 figures

A one-order-of-magnitude terahertz (THz) emission enhancement in the transmission geometry, over a 0.7-THz broadband range, was observed in semi-insulating gallium arsenide (SI-GaAs) integrated with a subwavelength one-dimensional metal line array (1DMLA). THz emission of the 1DMLA samples showed an intensity increase and exhibited a full-width-at-half-maximum broadening relative to the emission of the bare substrate. Improved index matching could not account for the observed phenomenon. A nonlinear dependence of the integrated THz emission intensity on the number of illuminated lines and on the pump power was observed. The actual origin of the increased THz emission is still under investigation. At present, it is attributed to extraordinary optical transmission.

I present 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. Measuring the Goos-H\"anchen and Imbert-Fedorov shifts is an alternative method to determine graphene's conductivity. I look at beamshifts for different polarization states ($p$, $s$, $45^0$, $\sigma^+$) and I discuss other possible experimental routes to determine these beamshifts and consequently, the graphene's optical conductivity. The Goos-H\"anchen shifts for visible light I calculated are in good agreement with results of a recent experiment., Comment: 8 pages, 3 figures, accepted for publication in Journal of Optics

Weak amplification is a signal enhancement technique which is used to measure tiny changes that otherwise cannot be determined because of technical limitations. It is based on the existence of a special type of interaction which couples a property of a system, i.e., polarization or which-path information, with a separate degree of freedom, i.e., transverse position or frequency. Unfortunately, the weak amplification process is generally accompanied by severe losses of the detected signal, which limits the applicability of the weak amplification concept. However, we will show here that since the weak measurement concept is essentially an interference phenomena, it should be possible to use the degree of interference to get relevant information about the physical system under study in a more general scenario, where the signal is not severely depleted (high-signal regime). This can widen the range of systems where the weak measurement concept can be applied. In this scenario, which can be called generally weak interference, the idea of weak value does not convey any useful information., 7 pages

Weak measurements are a unique tool for accessing information about weakly interacting quantum systems with minimal back action. Joint weak measurements of single-particle operators with pointer states characterized by a two-dimensional Gaussian distribution can provide, in turn, key information about quantum correlations which can be of relevance for quantum information applications. Here we demonstrate that by employing two-dimensional pointer states endowed with orbital angular momentum (OAM), it is possible to extract weak values of the higher order moments of single-particle operators, an inaccessible quantity with Gaussian pointer states only. We provide a specific example that illustrates the advantages of our method both, in terms of signal enhancement, and information retrieval., 5 pages, accepted for publication in Phys. Rev. Lett

It is known that orbital angular momentum (OAM) couples the Goos-Hanchen and Imbert-Fedorov shifts. Here, we present the first study of these shifts when the OAM-endowed LG(l,p) beams have higher-order radial mode index (p>0). We show theoretically and experimentally that the angular shifts are enhanced by p while the positional shifts are not. Since LG(l,p) modes form a complete basis set for paraxial beams, our results can be used to predict beam shifts of arbitrary modes of light., Accepted for publication in Optics Letters

This Letter reports an experimental and theoretical study of the response of a quadrant detector (QD) to an incident vortex beam, specifically a Laguerre-Gaussian (LG) beam. We have found that the LG beam response depends on the vorticity index l. We compare LG beams with hard-ringed beams and find that at higher l values, the QD response to LG beams can be approximated by its response to hard-ringed beams. Our findings are important in view of the increasing interest in optical vortex beams.

We present experiments on Orbital Angular Momentum (OAM) induced beam shifts in optical reflection. Specifically, we observe the spatial Goos-H\"anchen shift in which the beam is displaced parallel to the plane of incidence and the angular Imbert-Fedorov shift which is a transverse angular deviation from the geometric optics prediction. Experimental results agree well with our theoretical predictions. Both beam shifts increase with the OAM of the beam; we have measured these for OAM indices up to 3. Moreover, the OAM couples these two shifts. Our results are significant for optical metrology since optical beams with OAM have been extensively used in both fundamental and applied research., Comment: 7 pages, 7 figures

We show experimentally that the angular Goos-Hanchen (GH) effect can be easily observed, also without employing its resonant enhancement at Brewster incidence. An s-polarized beam was used to decouple the polarization from the propagation dynamics of the beam. We found that, in this case, the angular GH effect can be strongly enhanced by increasing the angular aperture of the Gaussian beam. Our experiments suggest a route toward observing the angular GH effect for true scalar waves, such as acoustic waves and quantum matter waves.

It is well known that reflection of a Gaussian light beam ($\text{TEM}_{00}$) by a planar dielectric interface leads to four beam shifts when compared to the geometrical-optics prediction. These are the spatial Goos-H\"{a}nchen (GH) shift, the angular GH shift, the spatial Imbert-Fedorov (IF) shift and the angular IF shift. We report here, theoretically and experimentally, that endowing the beam with Orbital Angular Momentum (OAM) leads to coupling of these four shifts; this is described by a $4 \times 4$ mixing matrix., Comment: v2 Version accepted for publication in Phys. Rev. A

We achieve controllable noninterferometric rotation of a bored helical beam by introducing a phase shift exclusively to the annular helical region of the phase. We present a derivation based on the decomposition of the beams, which shows that a constant phase shift of DeltaPhi between the bore and the surrounding helical phase with topological charge l will rotate the intensity profile by -DeltaPhi/l about its center. The effect of the phase shifting is verified with experiments. This technique is simple, while it preserves the transverse intensity profiles of the beams. Our report may find applications in optical manipulation and trapping.

In this paper the author demonstrates the feasibility of a novel technique in storing data in a Methyl Red doped Polymer Dispersed Liquid Crystal (PDLC) by holography. Holographic gratings were recorded side by side and its effect on the diffraction efficiencies are noted.

We report the first measurement of the Spin Hall Effect of Light (SHEL) on an air-metal interface. The SHEL is a polarization-dependent out-of-plane shift on the reflected beam. For the case of metallic reflection with a linearly polarized incident light, both the spatial and angular variants of the shift are observed and are maximum for -45/45 deg polarization, but zero for pure s- and p-polarization. For an incoming beam with circular polarization states however, only the spatial out-of-plane shift is present., improved figures;removed redundant discussion;change typo in eqn. 2b

A modification of the helical phase profile obtained by eliminating the on-axis screw-dislocation is presented. Beams with this phase possess a variety of interesting properties different from optical vortex beams. Numerical simulations verify analytic predictions and reveal that beams with this phase have intensity patterns which vary as a function of the phase parameters, as well as the propagation distance. Calculations of the Poynting vector and orbital angular momentum are also performed. Experiments verify the intensity profiles obtained in simulation.

We measure the rotational and translational velocity components of particles moving in helical motion using the frequency shift they induced to the structured light beam illuminating them. Under Laguerre-Gaussian mode illumination, a particle with a helical motion reflects light that acquires an additional frequency shift proportional to the angular velocity of rotation in the transverse plane, on top of the usual frequency shift due to the longitudinal motion. We determined both the translational and rotational velocities of the particles by switching between two modes: by illuminating with a Gaussian beam, we can isolate the longitudinal frequency shift; and by using a Laguerre-Gaussian mode, the frequency shift due to the rotation can be determined. Our technique can be used to characterize the motility of microorganisms with a full three-dimensional movement., 5 pages,5 figures

We present initial results showing the dependence of holographic grating formation on polarization of the writing beams in a methyl red-doped PDLC (E48:PVP) film. Our results depart from previously reported works.