写一个拉盖尔高斯光束的代码

以下是一个Python 代码实现拉盖尔-高斯光束的函数：

import numpy as np
import scipy.special


def laguerre_gaussian_beam(x, y, z, w0, zR, l, p):
    """A function to generate a Laguerre-Gaussian beam

    Args:
        x (ndarray): 2D array of x coordinates
        y (ndarray): 2D array of y coordinates
        z (float): distance from the beam waist
        w0 (float): beam waist radius
        zR (float): Rayleigh range
        l (int): azimuthal index
        p (int): radial index

    Returns:
        ndarray: 2D array of the electric field intensity at each point (x, y)
    """
    k = 2 * np.pi / 1.064e-6  # wavelength of the laser light in air
    R = z + zR**2 / z  # radius of curvature of the wavefront

    # calculate the Laguerre polynomial value for the azimuthal index and radial index
    L = scipy.special.genlaguerre(p, abs(l))(2 * (x**2 + y**2) / w0**2)

    # calculate the phase term of the Laguerre-Gaussian beam
    phase = np.exp(1j * (k * z + l * np.arctan(z / zR) +
                         (2 * p + abs(l) + 1) * np.arctan(z / R)))

    # calculate the Gaussian envelope of the Laguerre-Gaussian beam
    envelope = np.exp(-(x**2 + y**2) / w(z)**2)

    # calculate the electric field intensity of the Laguerre-Gaussian beam
    E = L * phase * envelope

    return np.abs(E)**2


def w(z, zR=0.027):
    """A function to calculate the beam waist radius at a distance z

    Args:
        z (float): distance from the beam waist
        zR (float): Rayleigh range (default 0.027m)

    Returns:
        float: beam waist radius
    """
    return w0(zR) * np.sqrt(1 + (z / zR)**2)


def w0(zR=0.027, P=30e-3):
    """A function to calculate the beam waist radius at the waist

    Args:
        zR (float): Rayleigh range (default 0.027m)
        P (float): laser power (default 30 mW)

    Returns:
        float: beam waist radius
    """
    return np.sqrt(2 * P * zR / (np.pi * 0.0117 * 1.064e-6))

在上面的代码中，`laguerre_gaussian_beam` 函数使用生成拉盖尔-高斯光束的公式计算在每个点（x，y）的电场强度值。该函数采用很多参数，包括位置坐标，束腰，Rayleigh 范围，方位角指数和径向指数。

此外，这里也定义了两个辅助函数来计算梯形和束腰的半径。使用这些函数，您可以轻松生成拉盖尔-高斯光束，尝试不同的参数值并查看其输出。