Far-field Intensity Research Articles

Boundary integral equation method for resonances in gradient index cavities designed by conformal transformation optics

In the case of two-dimensional gradient index cavities designed by the conformal transformation optics, we propose a boundary integral equation method for the calculation of resonant mode functions by employing a fictitious space which is reciprocally equivalent to the physical space. Using the Green’s function of the interior region of the uniform index cavity in the fictitious space, resonant mode functions and their far-field distributions in the physical space can be obtained. As a verification, resonant modes in limaçon-shaped transformation cavities were calculated and mode patterns and far-field intensity distributions were compared with those of the same modes obtained from the finite element method.

Out-of-plane orientation of luminescent excitons in two-dimensional indium selenide

Van der Waals materials offer a wide range of atomic layers with unique properties that can be easily combined to engineer novel electronic and photonic devices. A missing ingredient of the van der Waals platform is a two-dimensional crystal with naturally occurring out-of-plane luminescent dipole orientation. Here we measure the far-field photoluminescence intensity distribution of bulk InSe and two-dimensional InSe, WSe2 and MoSe2. We demonstrate, with the support of ab-initio calculations, that layered InSe flakes sustain luminescent excitons with an intrinsic out-of-plane orientation, in contrast with the in-plane orientation of dipoles we find in two-dimensional WSe2 and MoSe2 at room-temperature. These results, combined with the high tunability of the optical response and outstanding transport properties, position layered InSe as a promising semiconductor for novel optoelectronic devices, in particular for hybrid integrated photonic chips which exploit the out-of-plane dipole orientation.

Surface Shape Detection with a Single Far-Field Intensity by Combined Amplitude and Phase Retrieval

The efficiency of a reflector antenna highly depends on its surface shape. In order to ensure a good convergence, the conventional phase retrieval based shape detection schemes require that several far-field intensities be scanned, focused, or defocused. For large reflector antennas, the scanning process is time consuming. This paper proposes a new shape detection method that requires only single far-field intensity. Unlike existing shape detection methods, it retrieves both the amplitude and the phase, based on the fact that a deformed shape causes change not only in the aperture phase but also in the aperture amplitude. Through even-odd decomposition analysis, it is found that in the case of small and smooth deformation, “odd-phase” and “even-amplitude” can be directly recovered from one focused far-field intensity. This leads to the recovery of both the odd and the even parts of the antenna surface shape simultaneously. By combining amplitude retrieval and phase retrieval, this work achieves for the first time the shape detection with only one scan.

Large Aberration Correction by Magnetic Fluid Deformable Mirror with Model-Based Wavefront Sensorless Control Algorithm.

Magnetic fluid is a stable colloidal suspension of nano-sized, single-domain ferri/ferromagnetic particles dispersed in a liquid carrier. The liquid can be magnetized by the ferromagnetic particles aligned with the external magnetic field, which can be used as a wavefront corrector to correct the large aberrations up to more than 100 µm in adaptive optics (AO) systems. Since the measuring range of the wavefront sensor is normally small, the application of the magnetic fluid deformable mirror (MFDM) is limited with the WFS based AO system. In this paper, based on the MFDM model and the relationship between the second moment (SM) of the aberration gradients and the far-field intensity distribution, a model-based wavefront sensorless (WFSless) control algorithm is proposed for the MFDM. The correction performance of MFDM using the model-based control algorithm is evaluated in a WFSless AO system setup with a prototype MFDM, where a laser beam with unknown aberrations is supposed to produce a focused spot on the CCD. Experimental results show that the MFDM can be used to effectively compensate for unknown aberrations in the imaging system with the proposed model-based control algorithm.

Large-area enhancement of far-field fluorescence intensity using planar nanostructures

While nanoscale local enhancement of fluorescence is a well-studied phenomenon, enhancement of far-field radiation of large-area samples using nanostructures has been explored much less. In this work, we demonstrate planar nanostructures with exceptionally high far-field intensity enhancement factors and in addition show that the enhancement can be made controllable via the polarization state of the pump light. We also find that, counterintuitively, the Purcell effect plays only a small part in the observed far-field enhancement. The results of these studies can be applied, for example, in thin-film optical emitters, fluorescence sensors, and wide-field fluorescence microscopy.

Ultranarrow-waveguide AlGaAs/GaAs/InGaAs lasers

We have designed, fabricated and studied ultranarrow-waveguide heterostructure lasers emitting in the spectral range 1000 – 1100 nm. The lasers have been characterised by current – voltage, light – current, far-field intensity distribution and internal optical loss measurements. The ultranarrow-waveguide lasers have been shown to have a threshold current density of ∼75 A cm−2, internal quantum efficiency near 100 % and internal optical loss near the lasing threshold under 1 cm−1, which corresponds to the level of standard heterostructures. We have demonstrated the possibility of obtaining up to 5 W of output power in continuous mode and up to 30 W in pulsed mode, with a beam convergence (FWHM) of 17.8°. The slope of the internal optical loss as a function of pump current for the ultranarrow-waveguide lasers can be markedly lower than that in lasers with a standard design, but internal quantum efficiency drops to 40 % with increasing pump current. The use of barrier layers in ultranarrow-waveguide lasers makes it possible to substantially reduce the drop in internal quantum efficiency.

Method for calculation and analysis of the weights of grating mosaic errors.

A method to calculate the weight of grating mosaic errors is proposed based on an analytical hierarchy process. An accurate mosaic error tolerance calculation formula is also presented that is useful for large-size grating fabrication by the mosaic method. The grating mosaic error weights and tolerances are analyzed for mosaic echelle gratings. The analytical error weight and tolerance results agree well with the experimental results. The mosaic grating's far-field intensity is 95.8%, which is higher than the 94% value from the simulation results.

Compensation for Laser Beam Depolarization by Spatial Light Modulators

We propose a new method for compensating the thermally induced depolarization of laser radiation, which is based on using spatial light modulators. It is shown that using one modulator, the integral depolarization degree can be reduced by several times, whereas two modulators make it possible to almost completely rule out depolarization, regardless of its nature. The phase front of the laser beam is analyzed and it is shown that this phase front remains qualitatively unchanged when depolarization is compensated by one modulator, while in the case of compensation by two modulators the phase nonuniformity decreases, which leads to an increase in the far-field intensity.

Enhanced superradiance of quantum sources near nanoscaled media

We develop a rigorous theory for nanophotonic cooperative spontaneous emission of an ensemble of quantum emitters near matter, which also incorporates absorption. Such theory is highly requested since one should expect that in the field of nanophotonics the close-by emitters will emit cooperatively simultaneously with strong interaction with the exotic metamaterial complex dielectric function. The closed-form model developed here considers the buildup both of interemitter correlation over time through emitter transitions via the mutual field and of geometry-induced spatial correlation. The presence of matter alters the local density of states (LDOS), resulting in modified decay rate and emission intensity for the entire ensemble relative to values of spontaneous emission in free space. The superradiant total emission is separable into a quantum-mechanical time-dependent part and a classical space-dependent part, both being functions of the LDOS. Two distinct radiative emitter--far-field coupling mechanisms, which together account for the superradiant emission, are obtained---the coupling of every individual emitter with the far field and the coupling of emitter pairs to the far field. The calculations for superradiating emitters near silver and near-zero epsilon (NZE) materials were performed with the following results: the silver sphere augments the superradiant far-field intensity and rate by up to 400 and 1000%, respectively, while the NZE sphere enhances the far-field intensity and rate of the superradiance by approximately 1400 and 400%, respectively.

Coherent fiber-optics-array collimator based on a single unitary collimating lens: proposal design and experimental verification.

In this paper, we propose a design of coherent fiber-optics-array collimator (CFAC) that is mainly composed of a single unitary collimating lens and a prism. The CFAC system is presented conceptually, and corresponding parameters are theoretically analyzed using a geometrical optics method. Then, we set up a proof-of-concept experiment to verify the validity of the CFAC system with three coherent fiber lasers distributed along the symmetry axis through the center of the single unitary lens. After that, we realize the synchronous aberrationless collimating of the three beams with only one collimating lens system and their parallel propagation by utilizing a specific prism array. Finally, we successfully achieve a coherent beam combination of the laterally distributed three beams using a single-frequency dithering algorithm. Through an active piston phase control, the residual phase errors among the laser beams are suppressed below λ/26. By comparing the experimental results with the simulation results, we can see that the distribution of the closed-loop far-field intensity pattern detected by the charge-coupled infrared camera basically matches the ideal intensity distribution.

Position correction in ptychography using hybrid input–output (HIO) and cross-correlation

Ptychography is a form of coherent diffractive imaging; it employs far-field intensity patterns of the object to reconstruct the object. In ptychography, an important limiting factor for the reconstructed image quality is the uncertainty in the probe positions. Here, we propose a new approach which uses the hybrid input–output algorithm and cross-correlation in a way that can correct our estimates of the probe positions. The performance and limitations of the method in the presence of noise, varying overlap, and maximum recoverable error are studied using simulations. A brief comparison with other existing methods is also discussed here.

Binary square axicon with chiral focusing properties for optical trapping

We introduce a novel phase-only diffractive optical element called chiral binary square axicon (CBSA). The CBSA is designed by linearly rotating the square half-period zones of the binary square axicon with respect to one another. A quadratic phase mask (QPM) is combined with the CBSA using modulo-2{\pi} phase addition technique to bring the far-field intensity pattern of CBSA at the focal plane of the QPM and to introduce quasi-achromatic effects. The periodically rotated zones of CBSA produces a whirlpool phase profile and twisted intensity patterns at the focal plane of QPM. The degree of twisting seen in the intensity patterns is dependent upon the angular step size of rotation of the zones. The intensity pattern was found to rotate around the optical axis along the direction of propagation. The phase patterns of CBSA with different angles of zone rotation are displayed on a phase-only spatial light modulator and the experimental results were found to match with the simulation results. To evaluate the optical trapping capabilities of CBSA, an optical trapping experiment was carried out and the optical fields generated by CBSA were used for trapping and rotating yeast cells.

Magnetic Plasmon-Enhanced Second-Harmonic Generation on Colloidal Gold Nanocups

The magnetic plasmons of three-dimensional nanostructures have unique optical responses and special significance for optical nanoresonators and nanoantennas. In this study, we have successfully synthesized colloidal Au and AuAg nanocups with a well-controlled asymmetric geometry, tunable opening sizes, and normalized depths ( h/ b, where h is depth and b is the height of the templating PbS nanooctahedrons), variable magnetic plasmon resonance, and largely enhanced second-harmonic generation (SHG). The most-efficient SHG of the bare Au nanocups is experimentally observed when the normalized depth h/ b is adjusted to ∼0.78-0.79. We find that the average magnetic field enhancement is maximized at h/ b = ∼0.65 and reveal that the maximal SHG can be attributed to the joint action of the optimized magnetic plasmon resonance and the "lightning-rod effect" of the Au nanocups. Furthermore, we demonstrate for the first time that the AuAg heteronanocups prepared by overgrowth of Ag on the Au nanocups can synergize the magnetic and electric plasmon resonances for nonlinear enhancement. By the tailoring of the dual resonances at the fundamental excitation and second-harmonic wavelengths, the far-field SHG intensity of the AuAg nanocups is enhanced 21.8-fold compared to that of the bare Au nanocups. These findings provide a strategy for the design of nonlinear optical nanoantennas based on magnetic plasmon resonances and can lead to diverse applications ranging from nanophotonics to biological spectroscopy.

Complementary transmissive ultra-thin meta-deflectors for broadband polarization-independent refractions in the microwave region

Polarization manipulation is a significant issue for artificial modulation of the electromagnetic (EM) wave, but general mechanisms all suffer the restriction of inherent symmetric properties between opposite handedness. Herein, a strategy to independently and arbitrarily manipulate the EM wave with orthogonal circular polarizations based on a metasurface is proposed, which effectually breaks through traditional symmetrical characteristics between orthogonal handedness. By synthesizing the propagation phase and geometric phase, the appropriate Jones matrix is calculated to obtain independent wavefront manipulation of EM waves with opposite circular polarizations. Two transmissive ultra-thin meta-deflectors are proposed to demonstrate the asymmetrical refraction of transmitted circularly polarized waves in the microwave region. Simulated transmitted phase front and measured far-field intensity distributions are in excellent agreement, indicating that the transmitted wave with different polarizations can be refracted into arbitrary and independent directions within a wide frequency band (relative bandwidth of 25%). The results presented in this paper provide more freedom for the manipulation of EM waves, and motivate the realizations of various polarization-independent properties for all frequency spectra.

Build the Structure of WFSless AO System Through Deep Reinforcement Learning

We report on an aberration correction algorithm for a wavefront sensorless adaptive optics (WFSless AO) system based on deep reinforcement learning. First, it is verified that the reinforcement learning theory can be applied in our system. In addition, the deep deterministic policy gradient algorithm is introduced to build the control structure. After that, deep learning is used to deal with the messy raw images of far-field intensity distribution. We emphatically present how to design a feature extraction with the convolutional neural network in the control structure. To demonstrate the performance of this structure, some comparisons are made with the stochastic parallel gradient descent algorithm and the WFSless AO based on general modes algorithm. The results indicate that the correction speed of our method improves about 9 times and 2.5 times, respectively, for the similar correction effect.

Real-time coherent diffraction inversion using deep generative networks

Phase retrieval, or the process of recovering phase information in reciprocal space to reconstruct images from measured intensity alone, is the underlying basis to a variety of imaging applications including coherent diffraction imaging (CDI). Typical phase retrieval algorithms are iterative in nature, and hence, are time-consuming and computationally expensive, making real-time imaging a challenge. Furthermore, iterative phase retrieval algorithms struggle to converge to the correct solution especially in the presence of strong phase structures. In this work, we demonstrate the training and testing of CDI NN, a pair of deep deconvolutional networks trained to predict structure and phase in real space of a 2D object from its corresponding far-field diffraction intensities alone. Once trained, CDI NN can invert a diffraction pattern to an image within a few milliseconds of compute time on a standard desktop machine, opening the door to real-time imaging.

Effect of refractive index mismatch on forward-to-backward ratios in SHG imaging.

Nonlinear optical imaging in the epi-direction is used to image subresolution features. We find that a refractive index mismatch between the object to be imaged and the background medium can change the far-field intensity image. As an example, we study second harmonic generation (SHG) microscopy where the forward-to-backward (F/B) ratio is used to quantify subresolution features. We show both theoretically and experimentally that the inhomogeneous refractive index in collagen tendon tissue creates near-field effects, which can change the F/B ratio by ∼20%-25%, even though the effect is negligible for most of the individual fibrils in the tissue. This is caused by the sensitivity of the backward signal on phase matching conditions.

Horizontal Plasmonic Ruler Based on the Scattering Far-Field Pattern.

A novel method is proposed to detect the horizontal shift of a specific nanoblock relative to a reference nanoblock using surface plasmon modes at nanometer resolution. To accomplish this task, two orthogonal localized surface plasmon resonances were excited within the air gap region between the silver nanoblocks at the respective wavelengths, 890 nm, and 1100 nm. This technique utilized the scattering far-field intensities of the two block nanostructures at the two specific wavelengths at two specific directional spots. The ratio of the scattering intensities at the two spots changed according to the horizontal shift of the block that moved. Correspondingly, this ratio can be used to provide the precise location of the block. This method can be applied to many fields, including label-free bio-sensing, bio-analysis and alignment during nano-fabrication, owing to the high resolution and simplicity of the process.

Pulse duration of a partially coherent soft X-ray laser estimated from far-field speckle statistics.

A novel method for estimating the pulse duration of partially coherent soft X-ray pulses from a far-field intensity pattern is presented. The method is based on intensity statistics at a single point in space and time, which allows the number of coherent longitudinal modes to be measured. Utilizing the knowledge of the coherence time of the radiation, either from the measurement of the spectral bandwidth or from numerical simulations, the duration of each individual pulse can be evaluated. This method was used to estimate the pulse duration of the laser-driven nickel-like molybdenum soft X-ray laser that is based on amplified spontaneous emission from a narrow plasma column and emits at a wavelength of 18.9nm. By varying the length of the gain medium, a clear dependence of the number of modes caused mainly by the spectral line narrowing was observed. Supported by simulations of radiative transfer and pulse propagation, the pulse duration at the end of a 3mm long gain medium was estimated to be 3.5ps. The experimental data from far-field intensity patterns were also analyzed by applying the generalized van Cittert-Zernike theorem, providing a lower bound of effective source size.

Analyzing modal power in multi-mode waveguide via machine learning.

A machine learning assisted modal power analyzing scheme designed for optical modes in integrated multi-mode waveguides is proposed and studied in this work. Convolutional neural networks (CNNs) are successfully trained to correlate the far-field diffraction intensity patterns of a superposition of multiple waveguide modes with its modal power distribution. In particular, a specialized CNN is trained to analyze thin optical waveguides, which are single-moded along one axis and multi-moded along the other axis. A full-scale CNN is also trained to cross-validate the results obtained from this specialized CNN model. Prediction accuracy for modal power is benchmarked statistically with square error and absolute error distribution. It is found that the overall accuracy of our trained specialized CNN is very satisfactory for thin optical waveguides while that of our trained full-scale CNN remains nearly unchanged but the training time doubles. This approach is further generalized and applied to a waveguide that is multi-moded along both horizontal and vertical axes and the influence of noise on our trained network is studied. Overall, we find that the performance in this general condition keeps nearly unchanged. This new concept of analyzing modal power may open the door for high fidelity information recovery in far field and holds great promise for potential applications in both integrated and fiber-based spatial-division demultiplexing.