Laser diodes (LDs) are widely used in optical wireless communication (OWC) and optical networks, and proper theoretical models are needed to precisely describe the complicated beam field of LDs. A novel mathematical model is proposed to describe the vectorial field of nonparaxial LD beams. Laser beam propagation is studied using the vector Rayleigh diffraction integrals, and the stationary phase method is used to find the asymptotic expansion of diffraction integral. The far-field distribution of the LD beam in the plane parallel and perpendicular to the junction is considered in detail, and the computed intensity distributions of the theory are compared with the corresponding measurements. This model is precise for single transverse model beam of LDs and can be applied to describe the LD beams in OWC and optical networks.

Considering that laser diodes (LDs) are the efficient light source and easy to integrate, LD-enabled optical wireless communication (OWC) is an emerging technology for realizing high-confidentiality and high-speed point-to-point (PtP), vehicle-to-vehicle, and white-lighting data access links in free-space communication [

However, the output beam quality of LDs is relatively poor, such as astigmatism, high beam asymmetry, and large beam divergence [

The problem of laser propagation is mainly dealt through paraxial approximation. However, the output facet of LDs is extremely small, and their beams are divergent and asymmetrical. The rigid optical field distributions cannot be calculated from the paraxial approximation, and the longitudinal component in beam propagation direction should be considered. Thus, the vector theory for nonparaxial beams should be used to precisely describe beam fields of LDs. Several models, such as exponential Gaussian function [

Considering that transverse electric modes are usually excited in LD, _{x} is the waveguide width in the _{y} is the waveguide width in the

Beam propagation is governed by the vector Rayleigh diffraction integrals that provide the field expression in the entire half-space

We expand

For large

The corresponding diffraction integral is approximated by [

Letting

Thus,

Substituting equations (

Equation (

The intensity profiles can be given by

The intensity of LD beams can be investigated in two vertical planes. In the plane perpendicular to the junction (i.e.,

Facet of a LD chip and the related coordinate system.

In the plane parallel to the junction (i.e.,

The experiments were performed to examine the theoretical results using three high-power LDs (USHIO HL63391DC, TOSHIBA TOLD9441MC, and USHIO HL63290HD). The parameters are shown in Table

Parameter of LDs.

LDs | Wave model | Operating current (mA) | Wavelength (nm) | Parameter | Parameter |

USHIO HL63391DC | Single transverse model | 225 | 639 | 1.55 × 10^{3} | 2.20 × 10^{4} |

TOSHIBA TOLD9441MC | Single transverse model | 50 | 650 | 335 | 3.05 × 10^{4} |

USHIO HL63290HD | Multitransverse model | 2.4 | 638 | 256 | 1.55 × 10^{4} |

As shown in Figure

Experimental setup.

Figure

Measured and theoretical beam intensity profiles of HL63391DC. (a)

Measured and theoretical beam intensity profiles of TOLD9441MC. (a)

Measured and theoretical beam intensity profiles of HL63290HD. (a)

Compared with the previous models of LD beam, including Hermite–Gaussian model [

A novel theoretical model for the nonparaxial vectorial field of high-power LDs was proposed, and the beam parameters were related to the structure of LDs’ waveguide. High-order approximations of the diffraction integral were calculated on the basis of the vector Rayleigh diffraction integrals, the fields parallel and perpendicular to beam propagation direction were considered, and the beam intensities of three high-power LDs beam were measured. The mathematical model provided a good fit to the experimental data of single transverse model beam of LDs. This mathematical model can be used to describe the beam propagation and shape of LDs in OWC and optical networks.

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (61975158) and Aeronautical Science Foundation of China (20180181).