Far-field Intensity Distribution Research Articles

Numerical simulation of deep ultraviolet LED, micro-LED, and nano-LED with different emission wavelengths based on FDTD.

The current low external quantum efficiency (EQE) of deep ultraviolet (DUV) LEDs and micro-LEDs is largely attributed to their low light extraction efficiency (LEE). To address this issue and increase the LEE of DUV devices, various strategies such as reducing size, modifying surface with nanostructures and roughening substrates have been proposed. While some studies have investigated the effects of nanopillar and size on DUV LED, there remains a lack of systematic research on the LEE enhancement mechanism across different wavelengths and sizes of DUV LEDs, micro-LEDs, and nano-LEDs. Therefore, in this study, we employed the numerical simulation method to explore the LEE, near-field intensity distribution, and far-field light intensity distribution from various angles for DUV LEDs, micro-LEDs, and nano-LEDs with wavelengths of 255 nm, 260 nm, and 275 nm, respectively. Our findings reveal a significant improvement in the LEE of DUV nano-LEDs and micro-LEDs, accompanied by reduced divergence angles. Moreover, we observe that longer wavelengths correspond to higher LEE values for devices with similar size. This enhancement in LEE is attributed to factors such as increased sidewall emission and reduced p-GaN absorption. Our investigation indicates that as the size of the DUV device decreases, the sidewall LEE for both transverse electric (TE) and transverse magnetic (TM) modes increases, with TM mode exhibiting a larger enhancement. This enhancement is mainly attributed to the reduction of total reflection within the DUV LEDs and micro-LEDs resulting from size reduction. Despite this, TE mode remains the main contributor to overall LEE. Additionally, our study reveals a reduction in p-GaN absorption of DUV light with decreasing device size, further contributing to the enhancement of LEE in DUV micro-LEDs and nano-LEDs. The increased LEE and reduced divergence angles of small-size DUV micro-LEDs and nano-LEDs not only promote lower power consumption but also enable easier optical system coupling. Consequently, these advancements have significant potential in optical wireless communication, charge management and high-precision lithography.

Measuring the orbital angular momentum of generalized higher-order twisted partially coherent beams

Recently a new family of partially coherent fields incorporating generalized inseparable cross-coupled phases named generalized higher-order twisted partially coherent beams (GHTPCBs) have been introduced. The twist factor u is a key parameter that not only quantifies the strength of the generalized cross-coupled phase for a given order, but also determines the amount of the concomitant orbital angular momentum (OAM). In this paper, we propose a simple and reliable method to measure the factor u using a two-pinhole mask. Without need of complicated optical system, it only requires to capture the far-field diffraction intensity distribution of the GHTPCB passing through the mask. By analyzing the Fourier spectrum of the intensity distribution, the value of twist factor can be derived nearly in real time. The influence of the separation distance between two pinholes and the pinholes’ diameter and position on the measurement accuracy are thoroughly studied both in theory and experiment. The experimental results agree well with the theoretical results. Our methodology can also be extended to measure the sole factor of similar position dependent phases such as the topological charge of a vortex phase.

General error analysis of matrix-operation-mode decomposition technique in few-mode fiber laser

The mode decomposition based on matrix operation (MDMO) is one of the fastest mode decomposition (MD) techniques, which is important to the few-mode fiber laser characterization and its applications. In this paper, the general error of the MDMO technique was analyzed, where different influencing factors, such as position deviation of the optical imaging system, coordinate deviation of the image acquisition system, aberrations, and mode distortion were considered. It is found that the MDMO technique based on far-field intensity distribution is less affected by optical imaging system position deviation, coordinate deviation of the image acquisition system, and mode distortion than those based on direct near-field decomposition. But far-field decomposition is more affected by aberration than those based on near-field decomposition. In particular, the numerical results show that the deviation of the coordinate axis direction is an important factor limiting the accuracy of MD. In addition, replacing the ideal eigenmode basis with a distorted eigenmode basis can effectively suppress the decrease in mode decomposition accuracy caused by fiber bending. Moreover, based on detailed numerical analysis results, fitting formulas for estimating the accuracy of the MDMO technique with imperfections are also provided, which provides a comprehensive method for evaluating the accuracy of the MDMO technique in practical engineering operations.

Monolithically integrated multimode interference coupler-based master oscillator power amplifier with dual-wavelength emission around 830 nm

A monolithically integrated dual-wavelength multimode interference coupler-based master oscillator power amplifier is presented. It consists of two shallowly etched, laterally separated ridge waveguide laser cavities as master oscillators with individual distributed Bragg reflector gratings as cavity mirrors. A deeply etched coupling section containing S-bend shaped waveguides and a multimode interference coupler is used to couple the laser emission of the master oscillators into a shallowly etched single waveguide serving as power amplifier. Changing the etch depth for the coupling section enables a compact device layout. In addition, increased radiation angles of modes not coupled into the power amplifier help to suppress beam steering, otherwise indicated by laterally separated far-field intensity distributions. The device provides 0.5 W of dual-wavelength emission around 830 nm in individual and common operation. As designed, both emission wavelengths are separated by 0.5 nm with spectral widths below 20 pm, limited by the spectral resolution of the spectrometer. Both peak wavelengths remain within spectral windows of 50 pm within the available power range. This enables full flexibility selecting operating points for applications such as shifted excitation Raman difference spectroscopy and the generation of THz emission by photomixing. The emission wavelengths can additionally be non-continuously tuned by applying a heater current to resistors implemented next to the distributed Bragg reflector gratings. As an example, selected spectral distances of 0.5 nm, 1.0 nm, 1.5 nm, and 2.0 nm are demonstrated. Near field widths of 5 μm and far field angles of 17° result in beam propagation ratios of 1.4 (1/e2) in all operation modes and enable easy beam shaping or optical single-mode fiber coupling.

Propagation properties of elegant modified Bessel Gaussian beams.

A kind of optical beam with a radially parabolic propagating manner and intensity decay inversely proportional to propagating distance in the far field is investigated. The initial complex amplitudes of this kind of beam have the form of a Gaussian function multiplied by a m/2-order modified Bessel function and a helical phase factor with topological charge m. The arguments for Bessel and Gauss parts in the propagating solutions of these beams are complex and symmetric as elegant Laguerre and Hermite Gaussian beams. As a result, the beams can be referred to as elegant modified Bessel Gauss (EMBG) beams. Similar to non-diffractive beams such as Bessel and Airy beams, the EMBG beams also carry infinite power due to a transversely slowly decaying tail of complex amplitude. The EMBG beams demonstrate intermediate propagating properties between non-diffractive and finite-power beams. Unlike non-diffractive beams that never spread their power and finite-power beams that always diverge in a linear manner and spread their power by inversely square law in the far field, the EMBG beams demonstrate a far-field parabolic propagating manner and decay their power by inversely linear law. In addition, the EMBG beams have total Gouy phase, which is only half of that of elegant Laguerre Gauss beams with the same topological charge, and have far-field intensity distributions regardless of the beam waist radius in the initial plane. The propagating and focusing properties of EMBG beams represent an intermediate status between the non-diffractive and finite-power beams.

Fourier reciprocity between generalized elliptical Gaussian and elegant elliptical Hermite-Gaussian beams carrying orbital angular momenta.

We explore two distinct families of orbital angular momentum carrying light beams, which we refer to as generalized elliptical Gaussian and elegant elliptical Hermite-Gaussian vortex beams, respectively. We show that the fields of the two vortex families are related via a Fourier transform. Hence, one family can be viewed as a source of the far-field intensity distribution of the other and vice versa. We also examine the orbital angular momentum evolution of both beam families on their free space propagation and establish a relationship between the orbital angular momentum, TC, and beam ellipticity factors. Our results may find applications to optical communications and imaging with structured light.

Generation of Vortex Beams via All-Dielectric Spin-Multiplexed Coding Metamaterials

The vector vortex beams are generated by the single-phase modulation of metasurfaces, which severely limits the freedom of design. We use the combination of the propagation phase and the geometric phase to construct a transmissive all-dielectric encoded metasurface. Under two orthogonal circularly polarized incidence conditions, vortex beams with different topological charge can be generated. We utilize the hybrid-order Poincaré sphere to characterize various polarization states of Poincaré vortex beams. Based on the near-field and far-field intensity distribution and phase distribution properties of the vortex beam, the design accuracy of the Poincaré vortex beam is confirmed. In order to improve the degree of freedom of control of vortex beams, we introduce the Fourier convolution principle in digital signal processing. The convolution operation of the encoding array and the phase gradient sequence is performed to construct a new encoding metasurface sequence, and the scattering angle of the vortex beam can be adjusted. Using the principle of coded convolution, functions with arbitrary deflection and beam splitting of vortex beams can be realized.

Hybrid control method for generating airy beam in wavefront sensorless adaptive optics system

In order to reduce the complexity of Airy beams generation based on adaptive optics with a wavefront sensor, a wavefront sensorless adaptive optics system, which employs a camera to measure the far-field intensity distribution as the feedback for optimizing the control voltages of the deformable mirror, is proposed for generating high-quality Airy beams. A hybrid control method combining hill-climbing algorithm and open-loop control method is developed to correct the aberrations of the system and produce the cubic phases. High-quality tunable Airy beams were generated successfully. The properties of the generated Airy beams, such as non-diffraction, self-acceleration and self-healing, were verified. The experimental results coincide with the theoretical results, showing the proposed method has potential applications such as Airy beam light-sheet microscope and optical manipulation.

Grism fabricated on the end-face of an optical fiber.

We designed and fabricated grism structures on the end-face of an optical fiber and experimentally characterized them. A UV-curable ionic-liquid polymer resin, well-suited for nanoimprinting, was used to fabricate the grism structures with grating pitches of 1.8-3 µm and prism apex angle reaching 30-40°. The structures can propagate 1st order of diffraction peaks along the fiber axis at 520, 660, and 830 nm wavelengths. The experimental and numerically simulated results of far-field intensity distribution revealed high agreement. Hence, based on the numerical simulation, we proposed grism structure designs for in-line propagation of first-order diffraction at wavelengths of λ = 1300 - 2000 nm utilizing chalcogenide glass fibers.

Optical link acquisition for the LISA mission with in-field pointing architecture

We present a comprehensive simulation of the spatial acquisition of optical links for the LISA mission in the in-field pointing architecture, where a fast pointing mirror is used to move the line-of-sight of the optical transceiver, which was studied as an alternative scheme to the baselined telescope pointing architecture. The simulation includes a representative model of the far-field intensity distribution and the beam detection process using a realistic detector model, and a model of the expected platform jitter for two alternative control modes with different associated jitter spectra. For optimally adjusted detector settings and accounting for the actual far-field beam profile, we investigate the dependency of acquisition performance on the jitter spectrum and the track-width of the search spiral, while scan speed and detector integration time are varied over several orders of magnitude. Results show a strong dependency of the probability for acquisition failure on the width of the auto-correlation function of the jitter spectrum, which we compare to predictions of analytical models. Depending on the choice of scan speed, three different regimes may be entered which differ in failure probability by several orders of magnitude. We then use these results to optimize the acquisition architecture for the given jitter spectra with respect to failure rate and overall duration, concluding that the full constellation could be acquired on average in less than one minute. Our method and findings can be applied to any other space mission using a fine-steering mirror for link acquisition.

Design and Theoretical Investigation of an on Chip Two-Dimensional Newton’s Ring-like Plasmonic Sensor for Differentiating the Chirality of Circularly Polarized Lights

In this paper, an on chip two-dimensional Newton’s ring-like plasmonic sensor is designed for differentiating the chirality of circularly polarized lights (CPLS). The structure of the plasmonic sensor consists of a circular arc slit and an array of periodic rectangular nano-grooves that are etched into a silver film. When the sensor is illuminated by CPLS with a given chirality, the surface plasmon polariton waves generated by the slit and nano-groove array will selectively interfere with each other in the near field, which results in two different transmitted light intensity distributions in the far field. The generated far-field light intensity distributions are utilized as criteria to qualitatively differentiate the concrete chirality of the incident CPLS. The finite difference time domain method is utilized to theoretically investigate the function of the designed plasmonic sensor. The simulated results indicated that the proposed sensor has the ability to visually display the chirality information in the far field, and can provide a tool to conveniently and qualitatively differentiate the chirality of CPLS in the far field.

Generating high-energy densities by sidelobe suppression in the far-field of phase-locked lasers

Laser beams with high-energy densities are desired for both fundamental research and applied applications. We present a numerical study on the generation of high-energy densities by sidelobe suppression in the far-field intensity distribution of phase-locked lasers. The method relies on modifying the combined field distribution of phase-locked lasers to obtain uniform amplitude and phase distributions in a near-field plane, which enables the formation of a high-energy density main central lobe (zeroth order) in the far field. The method is applied to various one-dimensional (1D) and two-dimensional (2D) array geometries, such as square, triangular, Kagome, random, and 1D ring. The results show that for in-phase-locked lasers in 2D array geometries, the diffraction efficiency of the high-energy density region (zeroth-order lobe) can be increased in the range of 90%–95%. For in-phase-locked lasers in a 1D ring array, the maximum diffraction is found to be ∼ 75 % . Further, the effects of the range of phase locking, system size, as well as topological defects are examined on diffraction efficiency. The method is also applied to an out-of-phase-locked laser in the square array, and a high-energy density output beam is obtained.

Ceramic surface relief gratings imprinted on an optical fiber tip.

We report on the fabrication, experimental measurement, and numerical simulation of sol-gel diffraction grating structures deposited on the end-face of a single mode optical fiber. Using the imprint method, we manufactured surface relief grating structures in four configurations with different grating-relative-to-fiber arrangements. We demonstrate the high quality of the fabricated structures based on atomic force microscopy imaging and their operational characteristics, presenting measured and simulated far-field intensity distributions. Using a numerical model, we simulated the diffraction patterns in the far-field. We obtained strong agreement between the results of the simulations and the experiments in terms of the angular positions of the diffraction peaks. We also investigated the tolerance of fabricated structures to high-power lasers. Among the proposed structures, the most intriguing is the grism fabricated on a fiber end-face using sol-gel imprint technology for the first time, to the best of our knowledge.

Acoustic far-field prediction based on near-field measurements by using several different holography algorithms.

Near-field acoustical holography (NAH) is a useful tool for sound field reconstruction and sound source identification. In NAH, a basis model is first selected to represent the physical sound field, and then a near-field measurement is made with a microphone array. Next, the parameters in the selected model can be estimated based on the measurements by using an inverse approach, resulting in the sound field near the source being reconstructed so that the sound source location can be identified. But, in addition to being able to reconstruct the near-field of a source, the far-field can also be predicted with the identified sound source model. A significant amount of work has been performed to study the near-field reconstruction capability of different NAH algorithms, but there has been a limited number of publications in which the far-field prediction accuracy, based on the near-field measurement constructed model, has been considered. In the present experimental work, two multi-transducer loudspeakers were placed side-by-side to create a multi-component sound source, and two sets of measurements were conducted: an intensity probe scanned the sound field generated by the loudspeakers in both the near-field (0.05 m) and far-field (0.48 m) such that the true near- and far-field intensity spatial distributions and total sound power could be identified. Then, based on the near-field pressure measurements, four acoustical holography algorithms, statistically optimized near-field acoustical holography, wideband acoustical holography, l1-norm minimization, and a hybrid compressive sampling method were used to predict the near- and far-field sound intensity distributions. The near- and far-field prediction results were compared with the direct measurement, and the sound field reconstruction accuracy was studied. It was found that all of the algorithms were able to reconstruct the near-field well when the near-field measurements were used to construct the model. It was found that with the abovementioned models, far-field reconstructions could correctly predict the spatial sound field distribution, but in all of the cases, the total sound power was underestimated.

Optical dipole orientation of interlayer excitons in MoSe2−WSe2 heterostacks

We report on the far-field photoluminescence intensity distribution of interlayer excitons in ${\mathrm{MoSe}}_{2}\text{\ensuremath{-}}{\mathrm{WSe}}_{2}$ heterostacks as measured by back focal plane imaging in the temperature range between 1.7 and 20 K. By comparing the data with an analytical model describing the dipolar emission pattern in a dielectric environment, we are able to obtain the relative contributions of the in- and out-of-plane transition dipole moments associated to the interlayer exciton photon emission. We determine the transition dipole moments for all observed interlayer exciton transitions to be $(99\ifmmode\pm\else\textpm\fi{}1)%$ in plane for R- and H-type stacking, independent of the excitation power and therefore the density of the exciton ensemble in the experimentally examined range. Finally, we discuss the limitations of the presented measurement technique to observe correlation effects in exciton ensembles.

Two-dimensional coherent VCSEL arrays with configurable beam emissions

An accurate far-field intensity distribution model of coherent VCSEL array is established based on Fraunhofer diffraction theory, of which the calculated far-field pattern can be configured by tuning the phase distribution of the array. In experiment, configurable beam emissions are achieved in two-dimensional coherent square 2 × 2 VCSEL arrays and triangular 3-element VCSEL arrays by engineering the phase distribution of the array through simply constructing the array structure. Single-lobe beam, double-lobe beam, and four-lobe beam are obtained in these arrays. Besides, beam shape manipulation is also realized by adjusting the ratio of horizontal dimension to vertical dimension of the array. The experimental results are in good agreement with the calculated results from the established theoretical model.

Uniform rectangular distribution of far-field intensity by optical phased array

In this paper, to solve the problem of uneven distribution of far-field intensity of Flash Lidar, a method of amplitude modulation for optical phased array (OPA) is proposed, which makes the far-field intensity distribution close to the uniform rectangular distribution. We use the impulse response sequence of Finite Impulse Response (FIR) digital filter designed by the window functions to modulate the amplitude of the OPA. This kind of uniform intensity distribution can simultaneously detect a wide range with the same intensity. The modulation sequence can also be extended to two-dimensional situation. In the case of considering the radiation pattern of optical waveguide, the amplitude modulation sequence can also be modified to obtain the far-field pattern that is close to the uniform rectangular distribution.

Broadband decoupling of intensity and polarization with vectorial Fourier metasurfaces

Intensity and polarization are two fundamental components of light. Independent control of them is of tremendous interest in many applications. In this paper, we propose a general vectorial encryption method, which enables arbitrary far-field light distribution with the local polarization, including orientations and ellipticities, decoupling intensity from polarization across a broad bandwidth using geometric phase metasurfaces. By revamping the well-known iterative Fourier transform algorithm, we propose “à la carte” design of far-field intensity and polarization distribution with vectorial Fourier metasurfaces. A series of non-conventional vectorial field distribution, mimicking cylindrical vector beams in the sense that they share the same intensity profile but with different polarization distribution and a speckled phase distribution, is demonstrated. Vectorial Fourier optical metasurfaces may enable important applications in the area of complex light beam generation, secure optical data storage, steganography and optical communications.

Spatio-temporal controlled filamentation using higher order Bessel-Gaussian beams integrated in time.

We demonstrate a new method for a systematic, dynamic, high-speed, spatio-temporal control of femtosecond light filamentation in BK7 as a particular example of nonlinear medium. This method is based on using coherent conjugate asymmetric Bessel-Gaussian beams to control the far-field intensity distribution and in turn control the filamentation location. Such spatio-temporal control allows every femtosecond pulse to have a unique intensity distribution that results in the generation of structured filamentation patterns on demand. The switching speed of this technique is dependent on the rise time of the acousto-optic deflector, which can operate in the MHz range while having the ability to handle high peak power pulses that are needed for nonlinear interactions. The proposed and demonstrated spatio-temporal control of structured filaments can enable generation of large filament arrays, opto-mechanical manipulations of water droplets for fog clearing, as well as engineered radiofrequency plasma antennas.

A Fast Calculation Method of Far-Field Intensity Distribution with Point Spread Function Convolution for High Energy Laser Propagation

The turbulence effect, thermal blooming effect, laser beam aberration, platform jitter, and other effects in the process of high energy laser propagation in the atmosphere will cause serious degradation of laser beam quality, which will have a negative impact on the actual application of laser propagation engineering. It is important in the engineering application of high-energy laser propagation to evaluate the far-field intensity distribution quickly. Based on the optical transfer function (OTF) theory of imaging system, the propagation process of high-energy lasers is modeled as the imaging process of point source. By using the convolution of point spread function (PSF) of jitter, turbulence, thermal blooming, and aberration of emission system, fast calculation of the far-field intensity distribution of high energy laser is realized. The calculation results are compared with those obtained by the 4D wave optics simulation program in different propagation scenarios. The results show that the calculated facula distribution and encircled energy of this method are in good agreement with the simulation results of wave optics, which can realize the fast and accurate evaluation of the far-field intensity distribution of high-energy laser propagation and provide a reference for practical engineering application.