Machine-learning-assisted single-shot measurement of Orbital-Angular-Momentum Spectrum

Photonic orbital angular momentum (OAM) has attracted considerable research due to its potential in some quantum- and classical-information protocols, such as superresolution quantum measurement. However, the benefits of OAM can only be realized when the high-dimensional OAM complex-valued spectrum can be constructed efficiently. Generally, this spectrum can be realized when the high-dimensional OAM superposition mode is projected onto a spatial modulator containing specific OAM holographic gratings. This method necessitates measuring all observables, which is insufficient and time-consuming as the measurements increase exponentially with the system dimensionality. Additionally, the accuracy of the measured spectrum is affected by the nonuniform coupling efficiency of various OAM modes.

The full construction and characterization of the high-dimensional OAM complex spectrum are still challenging. Several promising candidates have been explored to improve reconstruction efficiency. These methods can be largely divided into two: interference-based spectrum measurement and coordinate transformation. Unfortunately, these methods can only measure the power spectrum of the OAM superpositioning state but fail to measure the interference with the reference wave. Moreover, self-guided state estimation and the rotational Doppler effect can be utilized in the reconstruction of the complex-valued spectrum through multiple measurements.

Recently, the growing popularity of machine learning has attracted research attention due to its ability to process regular and large-scale data and solve complicated optical tasks. Although machine learning has been extended to OAM modes, its capability in reconstructing density matrix or complex-valued spectrum of high-dimensional OAM states remains underexplored. Moreover, whether the spectrum can be fully reconstructed using only single-shot measurement is yet to be answered.

To overcome the above barriers, Dr. Haoxu Guo, Dr. Xiaodong Qiu and Professor Lixiang Chen from Xiamen University employed a diffraction-based deep learning method to realize the full reconstruction of high-dimensional OAM high-valued spectrum. In their approach, only a single-shot measurement was used, while the learning of the single-shot diffraction behaviors was facilitated by adopting a residual convolutional neural network. The experiment involved diffracting the high-dimensional OAM states using a simple aperture of pentagram to break the OAM conjugate symmetry. Their research work is currently published in the journal, Physical Review Applied.

The authors fully reconstructed the high-dimensional OAM complex-valued spectrum using only a single shot measurement. This was attributed to the benefits and advantages of the convolutional neural network. Density matrices of unknown OAM superposition states were reconstructed with extremely high fidelity, over 92.1% and over 97.8% for 15-dimensional mixed state and 15-dimensional pure state, respectively. Compared with other methods, this method was relatively fast, did not require multiple measurements for individual dimensions and was more robust even in noisy environments.

In summary, a simple and highly efficient scheme for full reconstruction of high-dimensional OAM complex-valued spectrum was proposed and validated experimentally. This method successfully overcomes the inherent barriers to achieving a superfast and efficient reconstruction, making it a promising technique for many applications. Specifically, Professor Lixiang Chen, told Advances in Engineering, that their findings could find important applications in high-dimensional information encoding like real-time quantum imaging and sensing.