Hermite Gaussian Research Articles

Calculation of trapping optical forces induced by a focused continuous Hermite Gaussian beam on a nano-dielectric spherical particle

An analytical expression for the intensity distribution of a focused continuous Hermite Gaussian beam after passing through a positive lens has been derived. Analytically, this intensity has been used to derive the gradient force acting on a nano-dielectric spherical particle . It is found that, the beam modes (p, l) have a direct influence on the trap stability, the number of trapping regions, the area of trapping zones and the particle size range.

Integrated optical phased array with on-chip amplification enabling programmable beam shaping

We present an integrated optical phased array (OPA) which embeds in-line optical amplifiers and phase modulators to provide beam-forming capability with gain and beam steering in the 1465–1590 nm wavelength range. We demonstrate up to 21.5 dB net on-chip gain and up to 35.5 mW optical output power. The OPA circuit is based on an InP photonic integration platform and features the highest measured on-chip gain and output power level recorded in an active OPA (i.e., with amplification), to the best of our knowledge. Furthermore, the OPA enables the independent control of both amplitude and phase in its arms and through this we demonstrate programmable beam shaping for two cases. First, we carried out a Gaussian apodization of the power distribution profile in the OPA emitter waveguides, leading to 19.8 dB sidelobe suppression in the far-field beam, which is the highest value recorded for active OPAs, and then we demonstrated beam forming of 0th, 1st, and 2nd order 1D Hermite–Gaussian beams in free-space.

Two-dimensional modulation instability and soliton clusters in nonlocal media with competing cubic–quintic nonlinearities

Using linear-stability analysis, two-dimensional modulation instability (MI) of plane wave is studied in nonlocal media with competing cubic–quintic (CQ) nonlinearities, which shows that MI can be effectively eliminated by strong nonlocality and competing quintic nonlinearity. Furthermore, propagation properties of higher-order soliton clusters, i.e., Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) solitons are also investigated. Bifurcated solutions of these solitons are obtained analytically with variational approach. We also demonstrate in detail the propagation dynamics of the HG and LG solitons with split-step Fourier transform.

MPLC-based low-modal-crosstalk nine-mode-group demultiplexer for DSP-free IM/DD MDM transmission over MMF

Weakly coupled mode-division multiplexing (MDM) transmission over legacy laid multimode fiber (MMF) has great economic efficiency and can enormously enhance the capacity of short-reach optical interconnections. In order to be compatible with cost-efficient intensity-modulation/direct-detection (IM/DD) transceivers, weakly coupled mode-group demultiplexers that can simultaneously receive each mode group of MMFs are highly desired. In this paper, we propose a scalable low-modal-crosstalk mode-group demultiplexer over MMF based on multiplane light conversion (MPLC). Multiple input Hermite–Gaussian (HG) modes of MMF are first converted to bridging modes that are composed of HG00 modes distributed as a right-angle triangle in Cartesian coordinates, and then each HG00 mode belonging to a degenerate mode group is mapped to different overlapped HGn0 modes with vertical orientation for simultaneous detection. With the help of bridging modes, the MPLC-based mode-group demultiplexer can efficiently demultiplex all mode groups in standard MMFs with less than 20 phase masks. A nine-mode-group demultiplexer is further designed for demonstration, and simulation results show that the MPLC-based demultiplexer achieves low modal crosstalk of lower than −22.3dB at 1550 nm and lower than −17.9dB over the C-band for all the nine mode groups with only 16 phase masks.

Optical mode manipulation using deep spatial diffractive neural networks

In this paper, we investigate the theoretical models and potential applications of spatial diffractive neural network (SDNN) structures, with a particular focus on mode manipulation. Our research introduces a novel diffractive transmission simulation method that employs matrix multiplication, alongside a parameter optimization algorithm based on neural network gradient descent. This approach facilitates a comprehensive understanding of the light field manipulation capabilities inherent to SDNNs. We extend our investigation to parameter optimization for SDNNs of various scales. We achieve the demultiplexing of 5, 11 and 100 orthogonal orbital angular momentum (OAM) modes using neural networks with 4, 10 and 50 layers, respectively. Notably, the optimized 100 OAM mode demultiplexer shows an average loss of 0.52 dB, a maximum loss of 0.62 dB, and a maximum crosstalk of -28.24 dB. Further exploring the potential of SDNNs, we optimize a 10-layer structure for mode conversion applications. This optimization enables conversions from Hermite-Gaussian (HG) to Laguerre-Gaussian (LG) modes, as well as from HG to OAM modes, showing the versatility of SDNNs in mode manipulation. We propose an innovative assembly of SDNNs on a glass substrate integrated with photonic devices. A 10-layer diffractive neural network, with a size of 49 mm × 7 mm × 7 mm, effectively demultiplexes 11 orthogonal OAM modes with minimal loss and crosstalk. Similarly, a 20-layer diffractive neural network, with a size of 67 mm × 7 mm × 7 mm, serves as a highly efficient 25-channel OAM to HG mode converter, showing the potential of SDNNs in advanced optical communications.

A symmetric optical cryptosystem based on QZ decomposition and Hermite Gaussian beam speckles

A symmetric optical cryptosystem based on QZ decomposition and Hermite Gaussian beam speckles

The resilience of Hermite–Gaussian and orbital angular momentum modes for free space optical communication in atmospheric turbulence

The resilience of Hermite–Gaussian and orbital angular momentum modes for free space optical communication in atmospheric turbulence

Mode conversion of various solitons in parabolic and cross-phase potential wells

We numerically establish the controllable conversion between Laguerre–Gaussian and Hermite–Gaussian solitons in nonlinear media featuring parabolic and cross-phase potential wells. The parabolic potential maintains the stability of Laguerre–Gaussian and Hermite–Gaussian beams, while the actual conversion between the two modes is facilitated by the cross-phase potential, which induces an additional phase shift. By flexibly engineering the range of the cross-phase potential well, various higher-mode solitons can be generated at desired distances. Beams carrying orbital angular momentum can also be efficiently controlled by this method. In addition, other types of beams, such as sine complex-various-function Gaussian and hypergeometric-Gaussian vortex beams, can be periodically transformed and manipulated in a similar manner. Our approach allows the intricate internal relationships between different modes of beams to be conveniently revealed.

Optimizing terahertz emission with Hermite–Gaussian laser beams in collisional slanted up density plasma

Optimizing terahertz emission with Hermite–Gaussian laser beams in collisional slanted up density plasma

Compressed Hermite–Gaussian differential single-pixel imaging

Traditional single-pixel imaging (SPI) encounters challenges such as high sampling redundancy and poor imaging quality, constraining its widespread application. Despite a range of orthogonal modulation modes have been employed in structured illumination to enhance imaging performance, some encoding issues still persist in information sampling, impeding the further progression of SPI. We propose an SPI method based on orthogonal Hermite–Gaussian (HG) moments, achieving improved imaging reconstruction through differential modulation of HG basis patterns and linear weighting of acquired intensity. Both simulations and experiments confirm superior imaging quality and computation efficiency of proposed Hermite–Gaussian single-pixel imaging (HG-SI), especially at low-measurement levels. Moreover, we incorporate compressed sensing algorithms within the framework of HG-SI, integrating moments-based sampling strategies to optimize imaging capability under sparse measurements. Our research underscores the effectiveness of HG modulation in SPI reconstruction, enabling high-quality outcomes via compressed sampling. This advancement propels the investigation of optical field modulation modes within SPI and holds promise in offering a universal solution for weak-intensity and non-visible light microscopy.

Magnetic field effects in laser wakefield excitation: a study using Hermite–Gaussian laser pulses in homogeneous plasma

Magnetic field effects in laser wakefield excitation: a study using Hermite–Gaussian laser pulses in homogeneous plasma

Weak measurement of the Goos–Hänchen shift for a Hermite–Gaussian laser beam

We report on an experimental investigation of the Goos–Hänchen (GH) optical beam shift in the vicinity of the critical angle of incidence at an air–glass interface using a weak value amplification (WVA) technique for two mutually orthogonal first order Hermite–Gaussian (HG) modes (HG10 and HG01) of a light beam at 633 nm generated by a phase-only reflective spatial light modulator. We have developed a mathematical approach to visualize the beam shaping due to the WVA scheme of beam shifts for the HG modes. The study reveals the angle of incidence dependency of the GH shift in the total internal reflection condition. For both modes, a detailed study of the horizontal and transverse beam shift values with varied post-selection angles is also reported. In addition, a comparison of the beam shift values for both of the selected modes with the fundamental mode (HG00) has been demonstrated. We found a significant enhancement (about two to three times) in the beam shifts for the first order HG10 and HG01 modes compared to the fundamental mode (HG00). Our results clearly demonstrate the advantages of the HG modes of the light beam-exploiting WVA technique and thus may contribute significantly to this field and open up important applications in photonic manipulation and future technologies.

Spatial Mode Division Multiplexing of Free-Space Optical Communications Using a Pair of Multiplane Light Converters and a Micromirror Array for Turbulence Emulation

Multi-plane light converters (MPLC) are a means of deconstructing a wavefront into constituent modes that are focused at specific spatial locations, and the reverse—that specific inputs result in controlled modal output. We have used a pair of MPLCs with 21 Hermite–Gaussian modes to represent a free-space optical connection. The effects of strong atmospheric turbulence (Cn2 = 10−13 m−2/3) are emulated using a micromirror array producing a time sequence of aberrating frames. The modal crosstalk between transmitter and receiver modes induced by the turbulence is presented by measuring the intensity in receiver channels for the same turbulence. Six receiver modes are used for optical communication channels with a rate of 137 Gbits/s displaying the benefits of single input multiple output (SIMO) operation for overcoming the deleterious effects of turbulence.

The uncertainty principle and quantum wave functions that are their own Fourier transforms

We present several variations of a proof of the position-momentum uncertainty principle that are based on the calculus of variations and does not rely on the Cauchy–Schwartz inequality. We show that the stationary uncertainty wave functions are the Hermite–Gaussian solutions to the quantum harmonic oscillator problem, that the minimum uncertainty wave function is the Gaussian, and that stationary uncertainty wave functions must be their own Fourier transforms. We also provide a calculus of variations proof of the Cauchy–Schwartz inequality. Finally, we discuss the properties of wave functions that are their own Fourier transforms and provide examples of such functions that may be of interest to teachers of undergraduate and graduate level quantum mechanics courses.

Study on the Generation of 1.9 μm Mode Superposition Conversion Laser by Double-End Off-Axis Pumping

In this paper, the Laguerre–Gaussian (LG) mode superposition is obtained by using the technology of double-end off-axis pumping Tm:YLF crystal, and the LG mode superposition is achieved by combining the extra-cavity conversion method. The impact of changing the off-axis distance on the order of Hermite–Gaussian (HG) mode and the topological charge of LG mode is studied. The results show that when the off-axis distance of the pump source at both ends is tuned, when the off-axis distance is in the range of 260 μm~845 μm, the single-ended 0~10 order HG mode can be obtained. Subsequently, the mode converter is placed to obtain the LG mode beam, and the double-end simultaneously pumps the crystal to obtain the superimposed LG mode. The tuning off-axis quantity changes the topological charge number. When P = 0, l1=l2, the superimposed LG mode is a single-ring spot, and the vortex beam center’s dark hollow area increases with the topological charge number. When P = 0, l1=−l2, the superimposed LG mode is a petal-like spot. The number of petals differs from the topological charges of two opposite numbers. Finally, in the case of changing the topological charge number of the double-ended LG mode, the output of the vortex array structured beams of the tuning mode order 1.9 μm Tm:YLF is completed in the case of conversion and superposition.

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.

Structurally Invariant Higher-Order Ince-Gaussian Beams and Their Expansions into Hermite-Gaussian or Laguerre-Gaussian Beams

Paraxial beam modes, which propagate in space and focus without changing their transverse intensity pattern, are of great value for multiplexing transmitted data in optical communications, both in waveguides and in free space. The best-known paraxial modes are the Hermite-Gaussian and Laguerre-Gaussian beams. Here, we derive explicit analytical expressions for Ince-Gaussian (IG) beams for several first values of the indices p = 3, 4, 5, and 6. In total, we obtain expressions for the amplitudes of 24 IG beams. These formulae are written as superpositions of the Laguerre-Gaussian (LG) or Hermite-Gaussian (HG) beams, with the superposition coefficients explicitly depending on the ellipticity parameter. Due to simultaneous representation of the IG modes via the LG and HG modes, it is easy to obtain the IG modes in the limiting cases wherein the ellipticity parameter is zero or approaches infinity. The explicit dependence of the obtained expressions for the IG modes on the ellipticity parameter makes it possible to change the intensity pattern at the beam cross-section by continuously varying the parameter values. For the first time, the intensity distributions of the IG beams are obtained for negative values of the ellipticity parameter. The obtained expressions could facilitate a theoretical analysis of properties of the IG modes and could find practical applications in the numerical simulation or generation of such beams with a liquid-crystal spatial light modulator.

Engineering Orbital Angular Momentum in Structured Beams in General Astigmatic Systems via Symplectic Matrix Approach

We studied theoretically and experimentally the propagation of structured Laguerre–Gaussian (sLG) beams through an optical system with general astigmatism based on symplectic ABCD transforms involving geometry of the second-order intensity moments symplectic matrices. The evolution of the coordinate submatrix ellipses accompanying the transformation of intensity patterns at different orientations of the cylindrical lens was studied. It was found that the coordinate submatrix W and the twistedness submatrix M of the symplectic matrix P degenerate in the astigmatic sLG beam with simple astigmatism, which sharply reduces the number of degrees of freedom, while general astigmatism removes the degeneracy. Nevertheless, degeneracy entails a simple relationship between the coordinate element Wxy and the twistedness elements Mxy and Myx of the submatrix M, which greatly simplifies the measurement of the total orbital angular momentum (OAM), reducing the full cycle of measurements of the Hermite–Gaussian (HG) mode spectrum (amplitudes and phases) of the structured beam to the only measurement of the intensity moment. Moreover, we have shown that Fourier transform by a spherical lens enables us to suppress the astigmatic OAM component and restore the original free-astigmatic sLG beam structure. However, with further propagation, the sLG beam restores its astigmatic structure while maintaining the maximum OAM.

Alias Transformation of Structured Beam and Holography in Real and Fourier Space Based on Dielectric Metasurface

AbstractStructured beams are analytical solutions to wave equations that possess specific spatial profiles and rigorous transmission properties. Holography enables wavefront reconstruction by recording objective wavefront information. In this study, comprehensive wavefront control by transforming a structured beam in real space is proposed and experimentally verified, and optical holography is reconstructed in Fourier space. To obtain an arbitrary profile of the structured beam, alias transformation is performed to rebuild the coordinate system to form arbitrary user‐defined shapes. Subsequently, the complex amplitude control of the metasurface to encode the alias‐transformed structured beam accordingly is applied. This allows the conventional standard Hermite–Gaussian and Laguerre–Gaussian modes to be transformed into their corresponding shapes while maintaining their distinct features. Holography is realized based on pure phase modulation by interleaving the information with a structured beam, which fully utilizes the space‐bandwidth product of the metasurface. These distinctive optical phenomena in both spaces expand the definition of conventional structured beams and enable further developments in laser fabrication, optical manipulation, and optical displays.

Dynamics of quadratic phase controlled Hermite-Gaussian beams in fractional systems based on different variable coefficients and potentials

The Hermite-Gaussian (HG) beam has many potential advanced applications in optical communications, electron acceleration, nonlinear optics and bio-optical disease detection, owing to its distinctive mode and intensity distribution. The research on HG beam are significant in the development of optics, medicine and quantum technology. However, the controlling of the evolutions of HG beam with quadratic phase modulation (QPM) in fractional systems under variable coefficients and potentials has been rarely studied. In this work, the propagation dynamic behaviors of the HG beam with QPM are investigated based on the fractional Schrödinger equation (FSE) under different variable coefficients and potentials by using a split-step Fourier algorithm. In the free space, the focusing spot of the beam becomes larger as the positive QPM coefficient increases or the Lévy index decreases. The QPM coefficient has little effect on the focusing amplitude when the Lévy index is 2. When the QPM coefficient is negative, the focusing of the beam disappears. Under the joint action of cosine modulations and QPM, the transmission of the beam oscillates not by the cosine law, but presents a large and a small breathing structure. The positive and the negative coefficient of QPM only alter the breathing sequence. The evolution period and width of the beam decrease as the modulation frequency increases. The trajectory of split beams turns into a parabolic shape under the linear modulation. In the joint influence of linear modulations and QPM, the HG beam exhibits either focusing or not focusing. Furthermore, the focusing position and focal plane of the beam decrease as the Lévy index increases. When the Lévy index is small, the beam keeps a straight-line transmission without distortion at a longer distance under the joint effect of the power function modulation and a positive QPM. The transmission of the beam also stabilizes and the beam width becomes larger with a negative QPM. Under a linear potential, the splitting of the HG beam disappears with the increase of the linear coefficient and shows a periodic evolution. The propagation trajectory of the beam shows a serrated pattern. By adding QPM, the beam is significantly amplified. Additionally, the evolution period of the beam is inversely proportional to the linear coefficient, and the transverse amplitude turns larger as the Lévy index increases. The interference among beams is strong, but it also exhibits an autofocus-defocusing effect under the joint action of a parabolic potential and QPM. In addition, the positive coefficient and the negative coefficient of QPM only affect the focusing time of the beam. The frequency of focusing increases as the Lévy index and parabolic coefficient rise. These features are important for applications in optical manipulations and optical focusing.