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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. [ABSTRACT FROM AUTHOR]

A letter to the editor is presented in response to the article "Weak Measurements with Orbital-Angular-Momentum Pointer States," by G. Puentes, N. Hermosa, and J. P. Torres in the 2012 issue.

We achieved three-dimensional (3D) computational ghost imaging with multiple photoresistors serving as single-pixel detectors using the 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.

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.

We demonstrate the surface plasmon resonance (SPR)-enhanced angular Goos-Hänchen (GH) shift. Typical SPR-enhanced GH shift measurements make use of loosely collimated beams, which enhances only the spatial GH shift (Δ GH ). Unlike this scheme, we focused the incident beam to a small beam waist to induce enhancement in the angular GH shift (Θ GH ). Although this makes Δ GH negligible, the enhancement of Θ GH is much larger than the decrease in Δ GH . 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 Θ GH 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 Θ GH toward sensing application when the Au film is exposed to local environmental changes even in the simplest thin film structure.

Spatial light modulators (SLMs), which are devices used to manipulate the phase of an incident wave front, are prolific in fields such as optical trapping, dynamic diffractive optical elements, and display technology. Of the many challenges inherent to using SLMs, one of the most ubiquitous is the calibration of the device's phase-shifting mechanism. In this paper, we present a new SLM calibration method based on spatial mode projection. We also implement a data processing technique to our data to generate accurate look-up tables from our calibration curves. We then evaluate the success of our method by propagating Laguerre-Gauss beams with computer-generated holograms. Our results show that the qualitative analysis of modes propagated using the SLM is a viable method of assessing performance. On the whole, we show that spatial mode projection provides clear performance improvements in the SLM's phase-modulating capabilities.

We propose a new expression for the response of a quadrant detector using convolution integrals. This expression, exploiting the properties of the convolution, is easier to evaluate by hand. Computationally, it is also practicable to use since a large number of computer programs can evaluate convolutions right away. We use the new expression to obtain an analytical form of the response of a quadrant detector for a Gaussian beam and for Hermite-Gaussian beams in general. We compare this analytic expression for the response for the Gaussian beam with the approximations from previous studies and with the response obtained through simulations. From the response, we also obtained an analytical form for the sensitivity of the quadrant detector to a Gaussian beam. Lastly, we demonstrate the computational ease of using our new expression for the response by calculating the sensitivity of the quadrant detector to the Bessel beam.

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.

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.

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 because detection is usually done by means of an interferometric setup, which only provides an absolute value of the frequency shift. In this Letter, we present 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 microparticles 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.

We measure the rotational and translational velocity components of particles moving in helical motion under a Laguerre-Gaussian mode illumination. The moving particle reflects light that acquires an additional frequency shift proportional to the 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.

One procedure widely used to detect the velocity of a moving object is by using the Doppler effect. This is the perceived change in frequency of a wave caused by the relative motion between the emitter and the detector, or between the detector and a reflecting target. The relative movement, in turn, generates a time-varying phase which translates into the detected frequency shift. The classical longitudinal Doppler effect is sensitive only to the velocity of the target along the line-of-sight between the emitter and the detector (longitudinal velocity), since any transverse velocity generates no frequency shift. This makes the transverse velocity undetectable in the classical scheme. Although there exists a relativistic transverse Doppler effect, it gives values that are too small for the typical velocities involved in most laser remote sensing applications. Here we experimentally demonstrate a novel way to detect transverse velocities. The key concept is the use of structured light beams. These beams are unique in the sense that their phases can be engineered such that each point in its transverse plane has an associated phase value. When a particle moves across the beam, the reflected light will carry information about the particle's movement through the variation of the phase of the light that reaches the detector, producing a frequency shift associated with the movement of the particle in the transverse plane.

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: a) the existence of a weak interaction which couples a property of a system (the system) with a separate degree of freedom (the pointer), and b) the measurement of an anomalously large mean value of the pointer state (weak mean value), after appropriate pre-and post-selection of the state of the system. Unfortunately, the weak amplification process is generally accompanied by severe losses of the detected signal, which limits its applicability. However, we will show here that since weak amplification is essentially the result of an interference phenomena, it should be possible to use the degree of interference (weak 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).

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.