Direct experimental evidence for free-space fractional optical vortex transmutation.

The emergence of vortex transmutation has opened new ways for vorticity modulation of optical vortices. Although several approaches have been proposed to realize vortex transmutation, fractional optical vortex (FOV) transmutation remains elusive owing to a lack of effective generation and detection methods. Here we report quantitative experimental evidence for a free-space FOV transmutation rule. The key idea is to combine the advantages of a single optical element, termed as fractional spiral polygonal lenses (FSPLs), with a deep learning approach. The desired wavefront is simultaneously generated and manipulated at the focal plane of the FSPL, and the fractional output vorticity is measured by analyzing a single far-field diffraction pattern. Especially, a deep learning scheme using a Bayesian optimization method is developed for output vorticity prediction with a data recovery rate up to 98.2%. The average error of recognized fractional orbital angular momentum modes is as small as 0.02. We clearly observe the intriguing phenomenon that the central vorticity of FOV is changed following a modulo-n transmutation rule in free space. Our results have important implications for fundamental understanding of FOV systems in free space, and offer a technological foundation for potential applications such as quantum information processing and particle manipulation and transportation.

Toward generalized forked gratings via deep learning.

We extend the concept of forked gratings to include the ability of high diffraction orders suppression of a single pair of vortex beams. The main idea is to appropriately distribute rectangular holes over each open space of a conventional forked grating. We further introduce the deep convolutional neural network algorithm to assist us in reconstructing and obtaining the optimal parameter of generalized forked grating. The recovery rate of our neural network is 92.3%. The 3rd order diffracted light intensity can be as low as 0.067% of the desired 1st order diffracted light intensity. The verification experiment results are also presented, confirming the helical phase structures with multitopological charges. The high diffraction orders suppression properties of the generalized forked gratings hold promise for broad applications, such as imaging, microscopy, and fundamental physics observation.

Superposition of two fractional optical vortices and the orbital angular momentum measurement by a deep-learning method.

We propose a single diffractive optical element called the composite fractional spiral zone plates to generate superimposed fractional optical vortices. Such an element is composed of two fractional spiral zone plates (FSZPs) through logical AND operation, and the produced beam carries superimposed fractional orbital angular momentum (OAM) states. By controlling the topological charge of the superimposed FSZPs, denoted by l1 and l2, one can flexibly obtain the desired superimposed fractional OAM modes of the generated beam. Especially, a deep-learning model with a densely connected convolutional neural network architecture is utilized to accurately predict the superimposed fractional OAM states of SFOVs. The average recovery rate of the superimposed fractional OAM states based on the training model is over 99%, and the average error is as small as 0.02. This work may pave the way for wide-ranging applications such as smart OAM communication, particle transmission, and even quantum entanglement.

Increased phenolic acid and tanshinone production and transcriptional responses of biosynthetic genes in hairy root cultures of Salvia przewalskii Maxim. treated with methyl jasmonate and salicylic acid.

The purpose of this study is to reveal the impact of the plant hormone salicylic acid (SA) and methyl jasmonate (MeJA) on the growth, effective components accumulation, and related gene expression of the hairy root of Salvia przewalskii Maxim. Various concentrations of SA (0, 25, 50, 100, 200 µM) or MeJA (0, 50, 100, 200, 400, 600 µM) were added to the culture medium of Salvia przewalskii Maxim. Low concentrations of SA promoted the growth of hairy root, while a high concentration inhibited it. 0 to 400 µM MeJA promoted the growth of hairy root, but 600 µM MeJA starts to inhibit its growth. 50 µM SA and 400 µM MeJA significantly enhanced the production of caffeic acid, rosmarinic acid, salvianolic acid B, cryptotanshinone, and tanshinone IIA. In general, 50 µM SA can be used to accumulate of tanshinone in hairy roots of S. przewalskii with 6 days. 400 µM MeJA can be used to accumulate of phenolic acids in hairy roots of S. przewalskii with 3 days. The selected genes in the tanshinone and phenolic acid biosynthetic pathway were upregulated with elicitation. To obtain a higher yield and content of secondary metabolites, it is advisable to use 50 µM SA or 400 µM MeJA as the optimal doses to cultivate the hairy root of S. przewalskii. This study provides, for the first time, an efficient tanshinone and phenolic acid production method for S. przewalskii.