Due to the rapid development of laser optics, the application of optical methods in photoacoustics, photoacoustic imaging, biomedicine photonics, and other fields has received widespread attention presently. As is known, it is significant to study the propagation behaviors of lasers in biological tissue to understand the interaction mechanism between the laser and biological tissue. Up to now, a large number of researchers have studied the polarization behavior of laser beams propagating through different media, such as ocean turbulence, atmospheric turbulence, and free space. In addition, the circular edge dislocation beam belongs to a typical singular beam with a circular notch in the transverse plane along the transmission direction, which undergoes a π mutation in the phase across the notch (dislocation line), and the basic research about the polarization state of circular edge dislocation beams in biological tissue transmission has not been reported yet. In order to promote the application of singularity optics in biomedical disease diagnosis and treatment and the development of tissue imaging technology, the basic research on the polarization behavior of circular edge dislocation beams in biological tissue transmission has been studied in this work, and the effects of different beam parameters (wavelength, number of dislocations, and spatial self-correlation length) on the changes in polarization state for different field points have been analyzed and compared in detail. We hope that the obtained results in this work will provide theoretical and experimental guidance for the selection of laser parameters in different applications and enhance the development of tissue imaging technology.

By introducing the Schell term, the cross spectral density matrix of partially coherent circular edge dislocation beams is obtained by the field distribution of the circular edge dislocation beams at the source. Based on the generalized Huygens-Fresnel principle, the analytical expression of the cross spectral density matrix element of partially coherent circular edge dislocation beams propagating biological tissue is derived with the help of the properties of the Hermite function and the complex integration. By means of the unified theory of coherence and polarization, the change in the degree of polarization, orientation angle, and ellipticity of partially coherent circular edge dislocation beams in biological tissue transmission can be investigated by numerical simulation, respectively. Meanwhile, the effects of different beam parameters (beam wavelength, number of dislocations, and spatial self-correlation length) can be analyzed during the transmission process.

Numerical calculations show that the magnitude of wavelength and dislocations number of partially coherent circular edge dislocation beams do not affect the initial value of the beam polarization state (Figs. 1-6), while the initial polarization state of beams with different spatial self-correlation length is different (Figs. 7-9). With the increment of propagation distance, the value of the polarization state of the same field point will eventually tend to be consistent with the initial one after experiencing obvious fluctuations, and those between two different field points will eventually move to a fixed one that is different from the initial value (Figs. 1-9), respectively, which may due to the impact of biological tissue turbulence on polarization behaviors. By comparing the changes in polarization between two situations, both the initial and final values show that the difference between two different field points is greater than that of the same field point (Figs. 1, 4, and 7). Far infrared light is prone to resonance in biological tissue transmission, and the polarization state remains almost constant over a certain transmission distance. Ultraviolet light is strongly absorbed by the tissue, and the polarization state of the beam is relatively small. The polarization changes of visible light and near-infrared light are moderate and can be used as probe beams for biomedical disease diagnosis and treatment (Figs. 1-3). A larger dislocation number indicates a greater distance between the extreme values of each polarization characteristic parameter (Figs. 4-6). The relative size of spatial self-correlation length will play a big role in the size and change trend of the polarization state (Figs. 7-9). It can be seen that beams with different beam parameters will have different turbulence resistance abilities, and different beams should be applied in different fields.

In the present study, based on the generalized Huygens-Fresnel principle and the unified theory of coherence and polarization, the influence of different beam parameters on the change in polarization state between two kinds of field points is numerically simulated. The obtained results indicate that compared with far-infrared and ultraviolet light, both visible light and near-infrared light are more suitable as probe beams for biomedical disease diagnosis and treatment. Affected by the turbulence of biological tissue, the polarization state of the beam undergoes evident fluctuations. The beams with different beam parameters have different turbulence resistance abilities, so beams with different parameters will be selected for different applications. The research results obtained in this work will provide a theoretical and experimental guide for the selection of laser parameters and are of great significance for the development of tissue imaging technology.