本文主要是介绍qutip+mayavi可视化波片对光偏振态的影响，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！
半波片对偏振态的影响：
import numpy as np
import qutip# 这是半波片对应的SU(2)操作
def hwp(state, theta):rn_mat = -1*qutip.Qobj([[np.cos(2*theta),np.sin(2*theta)],[np.sin(2*theta),-np.cos(2*theta)]])r_state = (rn_mat*state)*((rn_mat*state).dag())return(r_state)# state = qutip.rand_ket(2)
h = qutip.Qobj([[1],[0]])
d = (1/np.sqrt(2))*qutip.Qobj([[1],[1]])
r = (1/np.sqrt(2))*qutip.Qobj([[1],[(0+1j)]])points = 100
ran = np.pi/2
sx1 = []
sy1 = []
sz1 = []
for delta in range(points):r_rho = hwp(h, (float(delta)/points)*ran)sx1.append((qutip.sigmax()*r_rho).tr())sy1.append((qutip.sigmay()*r_rho).tr())sz1.append((qutip.sigmaz()*r_rho).tr())print(float(delta))sx2 = []
sy2 = []
sz2 = []
for delta in range(points):r_rho = hwp(d, (float(delta)/points)*ran)sx2.append((qutip.sigmax()*r_rho).tr())sy2.append((qutip.sigmay()*r_rho).tr())sz2.append((qutip.sigmaz()*r_rho).tr())# print(sy2)
sx3 = []
sy3 = []
sz3 = []
for delta in range(points):r_rho = hwp(r, (float(delta)/points)*ran)sx3.append((qutip.sigmax()*r_rho).tr())sy3.append((qutip.sigmay()*r_rho).tr())sz3.append((qutip.sigmaz()*r_rho).tr())#下面是画图的函数
#################################################################
import mayavi.mlab as mlab
import matplotlib.colors as colors
import moviepy.editor as mpy
from new_bloch3d import new_Bloch3dduration= 4
fps = 25fig_myv = mlab.figure(1, size=[800, 800],bgcolor=colors.colorConverter.to_rgb('white'),fgcolor=colors.colorConverter.to_rgb('black'))b3d = new_Bloch3d(fig=fig_myv)
# 使用MoviePy把这个图片创建为一个动画，并保存
def make_frame(t):mlab.clf() # clear the figure (to reset the colors)b3d.clear()p_color1 = (189.0/255, 122.0/255, 192.0/255)s_color1 = p_color1p_color2 = (111.0/255, 128.0/255, 240.0/255)s_color2 = p_color2p_color3 = (244.0/255, 106.0/255, 98.0/255)s_color3 = p_color3v_color = (255/255, 130.0/255, 71.0/255)index = round(t*fps)print(index)# b3d.add_states(hwp(h, (float(index)/points)*ran), s_color1)b3d.add_points([sx1[:index+1], sy1[:index+1], sz1[:index+1]],p_color1)b3d.add_vectors([sx1[index], sy1[index], sz1[index]], s_color1)b3d.add_points([sx2[:index+1], sy2[:index+1], sz2[:index+1]],p_color2)b3d.add_vectors([sx2[index], sy2[index], sz2[index]], s_color2)b3d.add_points([sx3[:index+1], sy3[:index+1], sz3[:index+1]],p_color3)b3d.add_vectors([sx3[index], sy3[index], sz3[index]], s_color3)b3d.make_sphere()f = mlab.gcf()f.scene._lift()return mlab.screenshot() #antialiased=Trueanimation = mpy.VideoClip(make_frame, duration=duration)
animation.write_videofile("HWP_on_bloch.mp4", fps=fps)需要先将以下代码保存到相同路径（命名为new_bloch3d.py）：
__all__ = ['new_Bloch3d']import numpy as np
from qutip.qobj import Qobj
from qutip.expect import expect
from qutip.operators import sigmax, sigmay, sigmazclass new_Bloch3d():"""Class for plotting data on a 3D Bloch sphere using mayavi.Valid data can be either points, vectors, or qobj objectscorresponding to state vectors or density matrices. fora two-state system (or subsystem).Attributes----------fig : instance {None}User supplied Matplotlib Figure instance for plotting Bloch sphere.font_color : str {'black'}Color of font used for Bloch sphere labels.font_scale : float {0.08}Scale for font used for Bloch sphere labels.frame : bool {True}Draw frame for Bloch sphereframe_alpha : float {0.05}Sets transparency of Bloch sphere frame.frame_color : str {'gray'}Color of sphere wireframe.frame_num : int {8}Number of frame elements to draw.frame_radius : floats {0.005}Width of wireframe.point_color : list {['r', 'g', 'b', 'y']}List of colors for Bloch sphere point markers to cycle through.i.e. By default, points 0 and 4 will both be blue ('r').point_mode : string {'sphere','cone','cube','cylinder','point'}Point marker shapes.point_size : float {0.075}Size of points on Bloch sphere.sphere_alpha : float {0.1}Transparency of Bloch sphere itself.sphere_color : str {'#808080'}Color of Bloch sphere.size : list {[500,500]}Size of Bloch sphere plot in pixels. Best to have both numbers the sameotherwise you will have a Bloch sphere that looks like a football.vector_color : list {['r', 'g', 'b', 'y']}List of vector colors to cycle through.vector_width : int {3}Width of displayed vectors.view : list {[45,65]}Azimuthal and Elevation viewing angles.xlabel : list {['|x>', '']}List of strings corresponding to +x and -x axes labels, respectively.xlpos : list {[1.07,-1.07]}Positions of +x and -x labels respectively.ylabel : list {['|y>', '']}List of strings corresponding to +y and -y axes labels, respectively.ylpos : list {[1.07,-1.07]}Positions of +y and -y labels respectively.zlabel : list {['|0>', '|1>']}List of strings corresponding to +z and -z axes labels, respectively.zlpos : list {[1.07,-1.07]}Positions of +z and -z labels respectively.Notes-----The use of mayavi for 3D rendering of the Bloch sphere comes witha few limitations: I) You can not embed a Bloch3d figure into amatplotlib window. II) The use of LaTex is not supported by themayavi rendering engine. Therefore all labels must be defined usingstandard text. Of course you can post-process the generated figureslater to add LaTeX using other software if needed."""def __init__(self, fig):# ----check for mayavi-----try:from mayavi import mlabexcept:raise Exception("This function requires the mayavi module.")# ---Image options---self.fig = Noneself.user_fig = None# check if user specified figure or axes.if fig:self.user_fig = fig# The size of the figure in inches, default = [500,500].self.size = [500, 500]# Azimuthal and Elvation viewing angles, default = [45,65].self.view = [45, 65]# Image background colorself.bgcolor = 'white'# Image foreground color. Other options can override.self.fgcolor = 'black'# ---Sphere options---# Color of Bloch sphere, default = #808080self.sphere_color = '#808080'# Transparency of Bloch sphere, default = 0.1self.sphere_alpha = 0.1# ---Frame options---# Draw frame?self.frame = True# number of lines to draw for frameself.frame_num = 8# Color of wireframe, default = 'gray'self.frame_color = 'black'# Transparency of wireframe, default = 0.2self.frame_alpha = 0.05# Radius of frame linesself.frame_radius = 0.005# --Axes---# Axes colorself.axes_color = 'black'# Transparency of axesself.axes_alpha = 0.4# Radius of axes linesself.axes_radius = 0.005# ---Labels---# Labels for x-axis (in LaTex), default = ['$x$','']self.xlabel = ['|+>', '|->']# Position of x-axis labels, default = [1.2,-1.2]self.xlpos = [1.07, -1.07]# Labels for y-axis (in LaTex), default = ['$y$','']self.ylabel = ['|L>', '|R>']# Position of y-axis labels, default = [1.1,-1.1]self.ylpos = [1.07, -1.07]# Labels for z-axisself.zlabel = ['|H>', '|V>']# Position of z-axis labels, default = [1.05,-1.05]self.zlpos = [1.07, -1.07]# ---Font options---# Color of fonts, default = 'black'self.font_color = 'black'# Size of fonts, default = 20self.font_scale = 0.08# ---Vector options---# Object used for representing vectors on Bloch sphere.# List of colors for Bloch vectors, default = ['b','g','r','y']self.vector_color = ['r', 'g', 'b', 'y']self.v_color = []# Transparency of vectorsself.vector_alpha = 1.0# Width of Bloch vectors, default = 2self.vector_width = 2.0# Height of vector headself.vector_head_height = 0.15# Radius of vector headself.vector_head_radius = 0.075# ---Point options---# List of colors for Bloch point markers, default = ['b','g','r','y']self.point_color = ['r', 'g', 'b', 'y']self.p_color = []# Size of point markersself.point_size = 0.03# Shape of point markers# Options: 'cone' or 'cube' or 'cylinder' or 'point' or 'sphere'.# Default = 'sphere'self.point_mode = 'sphere'# ---Data lists---# Data for point markersself.points = []# Data for Bloch vectorsself.vectors = []# Number of times sphere has been savedself.savenum = 0# Style of points, 'm' for multiple colors, 's' for single colorself.point_style = []# clear coneself.ccs = []def __str__(self):s = ""s += "Bloch3D data:\n"s += "-----------\n"s += "Number of points: " + str(len(self.points)) + "\n"s += "Number of vectors: " + str(len(self.vectors)) + "\n"s += "\n"s += "Bloch3D sphere properties:\n"s += "--------------------------\n"s += "axes_alpha: " + str(self.axes_alpha) + "\n"s += "axes_color: " + str(self.axes_color) + "\n"s += "axes_radius: " + str(self.axes_radius) + "\n"s += "bgcolor: " + str(self.bgcolor) + "\n"s += "fgcolor: " + str(self.fgcolor) + "\n"s += "font_color: " + str(self.font_color) + "\n"s += "font_scale: " + str(self.font_scale) + "\n"s += "frame: " + str(self.frame) + "\n"s += "frame_alpha: " + str(self.frame_alpha) + "\n"s += "frame_color: " + str(self.frame_color) + "\n"s += "frame_num: " + str(self.frame_num) + "\n"s += "frame_radius: " + str(self.frame_radius) + "\n"s += "point_color: " + str(self.point_color) + "\n"s += "point_mode: " + str(self.point_mode) + "\n"s += "point_size: " + str(self.point_size) + "\n"s += "sphere_alpha: " + str(self.sphere_alpha) + "\n"s += "sphere_color: " + str(self.sphere_color) + "\n"s += "size: " + str(self.size) + "\n"s += "vector_alpha: " + str(self.vector_alpha) + "\n"s += "vector_color: " + str(self.vector_color) + "\n"s += "vector_width: " + str(self.vector_width) + "\n"s += "vector_head_height: " + str(self.vector_head_height) + "\n"s += "vector_head_radius: " + str(self.vector_head_radius) + "\n"s += "view: " + str(self.view) + "\n"s += "xlabel: " + str(self.xlabel) + "\n"s += "xlpos: " + str(self.xlpos) + "\n"s += "ylabel: " + str(self.ylabel) + "\n"s += "ylpos: " + str(self.ylpos) + "\n"s += "zlabel: " + str(self.zlabel) + "\n"s += "zlpos: " + str(self.zlpos) + "\n"return sdef add_points(self, points, p_color, meth='s'):"""Add a list of data points to bloch sphere.Parameters----------points : array/listCollection of data points.p_color : 元组(RGB)指定点的颜色是什么,例如(1.0,0,0)meth : str {'s','m'}Type of points to plot, use 'm' for multicolored."""self.p_color.append(p_color)if not isinstance(points[0], (list, np.ndarray)):points = [[points[0]], [points[1]], [points[2]]]points = np.array(points)if meth == 's':if len(points[0]) == 1:pnts = np.array([[points[0][0]], [points[1][0]], [points[2][0]]])pnts = np.append(pnts, points, axis=1)else:pnts = pointsself.points.append(pnts)self.point_style.append('s')else:self.points.append(points)self.point_style.append('m')def add_states(self, state, s_color, kind='vector'):"""Add a state vector Qobj to Bloch sphere.Parameters----------state : qobjInput state vector.kind : str {'vector','point'}Type of object to plot."""# self.v_color.append(s_color)if isinstance(state, Qobj):state = [state]for st in state:if kind == 'vector':vec = [expect(sigmax(), st), expect(sigmay(), st),expect(sigmaz(), st)]self.add_vectors(vec, s_color)elif kind == 'point':pnt = [expect(sigmax(), st), expect(sigmay(), st),expect(sigmaz(), st)]self.add_points(pnt, s_color)def add_vectors(self, vectors, v_color):"""Add a list of vectors to Bloch sphere.Parameters----------vectors : array/listArray with vectors of unit length or smaller.v_color : 元组(RGB)指定箭头的颜色是什么,例如(1.0,0,0)"""self.v_color.append(v_color)if isinstance(vectors[0], (list, np.ndarray)):for vec in vectors:self.vectors.append(vec)else:self.vectors.append(vectors)def plot_vectors(self):"""Plots vectors on the Bloch sphere."""from mayavi import mlabfrom tvtk.api import tvtkimport matplotlib.colors as colorsii = 0# print(self.vectors, self.v_color)for k in range(len(self.vectors)):vec = np.array(self.vectors[k])norm = np.linalg.norm(vec)theta = np.arccos(vec[2] / norm)phi = np.arctan2(vec[1], vec[0])vec -= 0.5 * self.vector_head_height * \np.array([np.sin(theta) * np.cos(phi),np.sin(theta) * np.sin(phi), np.cos(theta)])# color = colors.colorConverter.to_rgb(# self.vector_color[np.mod(k, len(self.vector_color))])color = self.v_colormlab.plot3d([0, vec[0]], [0, vec[1]], [0, vec[2]],name='vector' + str(ii), tube_sides=100,line_width=self.vector_width,opacity=self.vector_alpha,color=color[k])cone = tvtk.ConeSource(height=self.vector_head_height,radius=self.vector_head_radius,resolution=100)cone_mapper = tvtk.PolyDataMapper(input_connection=cone.output_port)prop = tvtk.Property(opacity=self.vector_alpha, color=color[k])cc = tvtk.Actor(mapper=cone_mapper, property=prop)cc.rotate_z(np.degrees(phi))cc.rotate_y(-90 + np.degrees(theta))cc.position = vecself.ccs.append(cc)# print(self.fig)self.fig.scene.add_actor(self.ccs[k])# print(self.ccs)# self.fig.scene.remove_actors()def clear(self):"""Resets the Bloch sphere data sets to empty."""from mayavi import mlabfrom tvtk.api import tvtkself.points = []self.vectors = []self.point_style = []if self.fig != None:self.fig.scene.remove_actors(self.ccs)self.ccs = []# return(self.fig)# mlab.clf()def plot_points(self):"""Plots points on the Bloch sphere."""from mayavi import mlabimport matplotlib.colors as colorsfor k in range(len(self.points)):num = len(self.points[k][0])dist = [np.sqrt(self.points[k][0][j] ** 2 +self.points[k][1][j] ** 2 +self.points[k][2][j] ** 2) for j in range(num)]if any(abs(dist - dist[0]) / dist[0] > 1e-12):# combine arrays so that they can be sorted together# and sort rates from lowest to highestzipped = sorted(zip(dist, range(num)))dist, indperm = zip(*zipped)indperm = np.array(indperm)else:indperm = range(num)if self.point_style[k] == 's':# color = colors.colorConverter.to_rgb(# self.point_color[np.mod(k, len(self.point_color))])# ############### color = (1.0,1.0,0)# print(color)##############mlab.points3d(self.points[k][0][indperm], self.points[k][1][indperm],self.points[k][2][indperm], figure=self.fig,resolution=100, scale_factor=self.point_size,mode=self.point_mode, color=self.p_color[k])elif self.point_style[k] == 'm':# pnt_colors = np.array(self.point_color * np.ceil(# num / float(len(self.point_color))))# pnt_colors = pnt_colors[0:num]# pnt_colors = list(pnt_colors[indperm])print('ok')pnt_colors = [(1.0,1.0,0),(1.0,0,1.0)]for kk in range(num):mlab.points3d(self.points[k][0][indperm[kk]], self.points[k][1][indperm[kk]],self.points[k][2][indperm[kk]], figure=self.fig, resolution=100,scale_factor=self.point_size, mode=self.point_mode,color=pnt_colors[kk])def make_sphere(self):"""Plots Bloch sphere and data sets."""# setup plot# Figure instance for Bloch sphere plotfrom mayavi import mlabimport matplotlib.colors as colorsif self.user_fig:self.fig = self.user_figelse:self.fig = mlab.figure(1, size=self.size,bgcolor=colors.colorConverter.to_rgb(self.bgcolor),fgcolor=colors.colorConverter.to_rgb(self.fgcolor))sphere = mlab.points3d(0, 0, 0, figure=self.fig, scale_mode='none', scale_factor=2,color=colors.colorConverter.to_rgb(self.sphere_color),resolution=100, opacity=self.sphere_alpha, name='bloch_sphere')# Thse commands make the sphere look bettersphere.actor.property.specular = 0.45sphere.actor.property.specular_power = 5sphere.actor.property.backface_culling = True# make frame for sphere surfaceif self.frame:theta = np.linspace(0, 2 * np.pi, 100)for angle in np.linspace(-np.pi, np.pi, self.frame_num):xlat = np.cos(theta) * np.cos(angle)ylat = np.sin(theta) * np.cos(angle)zlat = np.ones_like(theta) * np.sin(angle)xlon = np.sin(angle) * np.sin(theta)ylon = np.cos(angle) * np.sin(theta)zlon = np.cos(theta)mlab.plot3d(xlat, ylat, zlat,color=colors.colorConverter.to_rgb(self.frame_color),opacity=self.frame_alpha, tube_radius=self.frame_radius)mlab.plot3d(xlon, ylon, zlon,color=colors.colorConverter.to_rgb(self.frame_color),opacity=self.frame_alpha, tube_radius=self.frame_radius)# add axesaxis = np.linspace(-1.0, 1.0, 10)other = np.zeros_like(axis)mlab.plot3d(axis, other, other,color=colors.colorConverter.to_rgb(self.axes_color),tube_radius=self.axes_radius, opacity=self.axes_alpha)mlab.plot3d(other, axis, other,color=colors.colorConverter.to_rgb(self.axes_color),tube_radius=self.axes_radius, opacity=self.axes_alpha)mlab.plot3d(other, other, axis,color=colors.colorConverter.to_rgb(self.axes_color),tube_radius=self.axes_radius, opacity=self.axes_alpha)# add data to sphereself.plot_points()self.plot_vectors()# #add labelsmlab.text3d(0, 0, self.zlpos[0], self.zlabel[0],color=colors.colorConverter.to_rgb(self.font_color),scale=self.font_scale)mlab.text3d(0, 0, self.zlpos[1], self.zlabel[1],color=colors.colorConverter.to_rgb(self.font_color),scale=self.font_scale)mlab.text3d(self.xlpos[0], 0, 0, self.xlabel[0],color=colors.colorConverter.to_rgb(self.font_color),scale=self.font_scale)mlab.text3d(self.xlpos[1], 0, 0, self.xlabel[1],color=colors.colorConverter.to_rgb(self.font_color),scale=self.font_scale)mlab.text3d(0, self.ylpos[0], 0, self.ylabel[0],color=colors.colorConverter.to_rgb(self.font_color),scale=self.font_scale)mlab.text3d(0, self.ylpos[1], 0, self.ylabel[1],color=colors.colorConverter.to_rgb(self.font_color),scale=self.font_scale)return(self.fig)def show(self):"""Display the Bloch sphere and corresponding data sets."""from mayavi import mlabself.make_sphere()mlab.view(azimuth=self.view[0], elevation=self.view[1], distance=5)if self.fig:mlab.show()def save(self, name=None, format='png', dirc=None):"""Saves Bloch sphere to file of type ``format`` in directory ``dirc``.Parameters----------name : strName of saved image. Must include path and format as well.i.e. '/Users/Paul/Desktop/bloch.png'This overrides the 'format' and 'dirc' arguments.format : strFormat of output image. Default is 'png'.dirc : strDirectory for output images. Defaults to current working directory.Returns-------File containing plot of Bloch sphere."""from mayavi import mlabimport osself.make_sphere()mlab.view(azimuth=self.view[0], elevation=self.view[1], distance=5)if dirc:if not os.path.isdir(os.getcwd() + "/" + str(dirc)):os.makedirs(os.getcwd() + "/" + str(dirc))if name is None:if dirc:mlab.savefig(os.getcwd() + "/" + str(dirc) + '/bloch_' +str(self.savenum) + '.' + format)else:mlab.savefig(os.getcwd() + '/bloch_' + str(self.savenum) +'.' + format)else:mlab.savefig(name)self.savenum += 1if self.fig:mlab.close(self.fig)
1/4波片对偏振态的影响：（hwp改成qwp即可）
def qwp(state, theta):rn_mat = (1/np.sqrt(2)) * qutip.Qobj([[1 + (0+1j)* np.cos(2*theta),(0+1j)*np.sin(2*theta)],[(0+1j)*np.sin(2*theta),1 - (0+1j)* np.cos(2*theta)]])r_state = (rn_mat*state)*((rn_mat*state).dag())return(r_state)最终效果：
可视化波片对光子偏振态的影响
一键三连一下呗：可视化波片对光子偏振态的影响_哔哩哔哩_bilibili
这篇关于qutip+mayavi可视化波片对光偏振态的影响的文章就介绍到这儿，希望我们推荐的文章对编程师们有所帮助！
