To the best of our knowledge, at the present time there is no answer to the fundamental question stated in the title that provides a complete and satisfactory physical description of the structured nature of Hermite-Gauss beams. The purpose of this manuscript is to provide proper answers supported by a rigorous mathematical-physics framework that is physically consistent with the observed propagation of these beams under different circumstances. In the process we identify that the paraxial approximation introduces spurious effects in the solutions that are unphysical. By removing them and using the property of self-healing, that is characteristic to structured beams, we demonstrate that Hermite-Gaussian beams are constituted by the superposition of four traveling waves.

As a laser beam passes through a multimode fiber (MMF), a speckle pattern is generated, which is sensitive to temperature, thereby making the MMF a temperature-sensing element. A deep learning technique is employed to the MMF-based temperature sensor, to obtain high-precision temperature sensing. We designed an MMF-based temperature-sensing configuration and developed a dual-output Convolutional Neural Network (CNN) for predicting both the temperature and the position of the heating point, and we constructed a dataset. It was shown that the location prediction accuracy reached 100%, while the temperature prediction accuracy (within a ±1 °C error margin) was 100% and 95.12% in the two experiments, respectively. The precision of the predicting heating point was less than 1 cm. Different types of MMFs were used in temperature measurements, showing that the accuracy remained quite high. This non-contact, high-precision MMF-based temperature measurement method, driven by deep learning, is suitable for applications in hazardous environments.

Phase error induced by the scanning error of piezoelectric transducer and vibration in white-light interference signal (WLIS) impose limitations on measurement accuracy. In this paper, two techniques are investigated to eliminate phase error cooperatively. A monochromatic interferometer owning the same optical path as the white-light scanning interferometer (WLSI) is employed to detect and compensate the phase error. Due to the incomplete consistency between the detected phase error and its actual distribution, an algorithm is introduced to further enhance the measurement accuracy. The simulation is given to prove the proposed method is available in different magnitude of noise. In the experiment, the front surface of wedged window is measured, whose maximum fluctuations are reduced to 28.8 nm and 3.0 nm from 62.7 nm with the gradual application of two technologies, and the repeatability reach 5.0 nm and 0.4 nm from 16.8 nm, respectively. The root mean square height S _q and maximum height S _z ultimately decrease to 1.3 nm and 1.6 nm. The measurement of step with height of about 3.0 μm also has the good accuracy and repeatability after phase error elimination. Since the different reflectivity of measured surfaces in the wavelength range of light source will also bring the measurement error, its influences are analyzed by simulation. The proposed techniques provide a phase error insensitive method for WLSI that has potential on measurement in the complex environment.

When a coherent beam transmits through a scattering medium, a random intensity distribution known as speckle is generated. Generally, such speckles can be modulated by feedback-based wavefront shaping, as exemplified by the generation of a bright focal spot. However, it is more challenging to generate a specific focal pattern with uniform intensity distribution. In this study, the Hadamard–Genetic algorithm (HGA), namely a hybrid phase modulation scheme of Hadamard encoding algorithm (HEA) and genetic algorithm (GA), is proposed to face these challenges. This algorithm takes advantages of the high intensity of HEA and the high uniformity of GA and outperforms traditional optimization schemes, especially in suppressing intensity fluctuations of the focal pattern. This research is expected to be applied in the field of laser processing and particle manipulation.

Inaccurate wavelength calibration for spectraldomain optical coherence tomography (SD-OCT) generates a depth-dependent broadening of coherence peak. In this paper, a simple technique is proposed to eliminate the wavelength calibration error by the spectral-resolved interference signal correction. Utilizing the nonlinear component of phase distribution in wavenumber domain and the optimization algorithm, an optimized coefficient is obtained and used to improve the axial resolution. The simulation was carried out to verify the principle of the proposed method. In experiment, a sample of reflecting mirror was used to obtain the nonlinear phase and the optimized coefficient for correcting the spectralresolved interference signals of tapes and chicken breast. In the measurement of a layer of tape with a thickness of about 1.5 mm, two full width half maximum (FWHM) of amplitude generated from the front and rear surfaces dropped to 7.73 μm and 9.99 μm from 33.57 μm and 55.36 μm after the signal correction. A selfmade sample containing 6 layers of tape and a part of chicken breast were tested, whose sharpness metric grow larger than 12.8% after signal correction. This method provides a simple way to improve the image quality of SD-OCT in improper wavelength calibration.

We present a single-shot, common-path Fizeau interferometer for high-precision micro-displacement measurement. By integrating a wire-grid polarizer with a pixelated polarization camera, the system implements spatial polarization phase-shifting for real-time phase retrieval. The common-path configuration and single-exposure acquisition significantly enhance robustness against environmental vibrations and air turbulence. The polarization-multiplexing scheme enables single-exposure measurement, granting the system the capability for real-time dynamic displacement monitoring. Experimental results demonstrate that the proposed method is capable of measuring displacements as small as 2 nm with high repeatability. This compact, vibration-insensitive design offers a robust solution for dynamic nanometric metrology in precision engineering.