File:Poincare-sphere stokes.svg

Summary

Description
English: Drawing of a Poincaré sphere, which illustrates the space of possible polarisations of electromagnetic waves. The sphere is drawn with three great circles and labels for six basic polarisations H (linear horizontal), V (linear vertical), D (linear diagonal), A (linear antidiagonal), R (right-hand circular) and L (left-hand circular). Additionally the coordinate system of Stokes vectors with components S₁, S₂ and S₃ is drawn in the center of the sphere.
Deutsch: Zeichnung einer Poincaré-Kugel, die den Raum der möglichen Polarisationen elektromagnetischer Wellen darstellt. Die Kugel ist mit drei Großkreisen gezeichnet und mit Zeichen für die sechs Basispolarisationen H (linear horizontal), V (linear vertikal), D (linear diagonal), A (linear antidiagonal), R (rechtshändig zirkular) and L (linkshändig zirkular). Zusätzlich befindet sich im Zentrum der Kugel das Koordinatensystem aus Stokesvektorkomponenten S₁, S₂ and S₃.
Date
Source Own work
Author Geek3
Other versions Poincare-sphere_arrows.svg (with additional small images of the polarisation vectors)

Source Code

The image is created by the following source-code. Requirements:

python3 source code:

# -*- coding: utf-8 -*-
try:
    import svgwrite as svg
except ImportError:
    print('You need to install svgwrite: http://pypi.python.org/pypi/svgwrite/')
    # documentation at http://pythonhosted.org/svgwrite/
    exit(1)

from math import *

def to_xyz(theta, phi, r=1):
    return r * sin(theta) * cos(phi), r * sin(theta) * sin(phi), r * cos(theta)

def to_theta_phi_r(x, y, z):
    return atan2(z, sqrt(x**2 + y**2)), atan2(x, y), sqrt(x**2+y**2+z**2)
    
def rotx(x, y, z, a):
    y, z = cos(a) * y + sin(a) * z, cos(a) * z - sin(a) * y
    return x, y, z

def ellipse_path(theta, phi, tilt, flip=False):
    t, p, r2 = to_theta_phi_r(*rotx(*(to_xyz(theta, phi, 1) + (tilt,))))
    a = abs(r)
    b = abs(r * sin(t))
    return 'M %f,%f A %f,%f %f %i,%i %f,%f' % (-r*cos(p), -r*sin(p),
        a, b, p*180/pi, 0, {True:1, False:0}[flip], r*cos(p), r*sin(p))
 
 
# document
size = 600, 600
doc = svg.Drawing('poincare-sphere_stokes.svg', profile='full', size=size)
doc.set_desc('poincare-sphere_stokes.svg', '''Drawing of a poincare-sphere with polarisations H, V, D, A, R and L, and a coordinate system of Stokes-Vectors S1, S2 and S3
rights: GNU Free Documentation license,
        Creative Commons Attribution ShareAlike license''')

# settings
dash = '8,6'
col = 'black'
r = 240
tilt = radians(-70)
phi = radians(-25)
cp, sp = cos(phi), sin(phi)

# background
doc.add(doc.rect(id='background', profile='full', insert=(0, 0), size=size, fill='white', stroke='none'))

# arrow markers
arrow_d = 'M -4,0 L 2,-3 L 1,0 L 2,3 L -4,0 z'
arrow1 = doc.marker(id='arrow1', orient='auto', overflow='visible')
arrow1.add(doc.path(d=arrow_d, fill=col, stroke='none',
    transform='rotate(180) scale(0.7)'))
doc.defs.add(arrow1)
arrow2 = doc.marker(id='arrow2', orient='auto', overflow='visible')
arrow2.add(doc.path(d=arrow_d, fill=col, stroke='none',
    transform='scale(0.7)'))
doc.defs.add(arrow2)
arrow3 = doc.marker(id='arrow3', orient='auto', overflow='visible')
arrow3.add(doc.path(d='M 8.7185878,4.0337352 L -2.2072895,0.016013256 L 8.7185884,-4.0017078 C 6.9730900,-1.6296469 6.9831476,1.6157441 8.7185878,4.0337352 z', fill=col, stroke='none',
    transform='scale(0.8) rotate(180)'))
doc.defs.add(arrow3)

# make a group for the sphere
sphere = doc.g(transform='translate(300, 300)', fill='none', stroke=col, stroke_width='2')
sphere['font-family'] = 'DejaVu Sans'
sphere['font-size'] = '42px'
doc.add(sphere)

# back ellipses
sphere.add(doc.path(d=ellipse_path(0, 0, tilt),
    stroke_dasharray=dash, stroke=col))
sphere.add(doc.path(d=ellipse_path(pi/2, phi, tilt, True),
    stroke_dasharray=dash, stroke=col))
sphere.add(doc.path(d=ellipse_path(pi/2, phi+pi/2, tilt),
    stroke_dasharray=dash, stroke=col))

# draw coordinate axes
sphere.add(doc.circle(center=(0, 0), r=5, fill=col, stroke='none'))
for i in range(3):
    xyz = [0, 0, 0]
    xyz[i] = 0.3 * r
    x, y, z = xyz
    x, y, z = rotx(x*cp + y*sp, y*cp - x*sp, z, tilt)
    line = doc.line(start=(0, 0), end=('%f' % x, '%f' % y), stroke=col)
    line['marker-end'] = arrow3.get_funciri()
    sphere.add(line)

# the six defined points
pts = []
for x,y,z in [[0,0,-1], [0,0,1], [0,-1,0], [0,1,0], [-1,0,0], [1,0,0]]:
    x, y, z = rotx(r * (x*cp + y*sp), r * (y*cp - x*sp), r * z, tilt)
    if z >= 0:
        continue
    pts.append((x, y))
    sphere.add(doc.circle(center=('%f' % x, '%f' % y), r=6,
        fill=col, stroke='none'))

# V label
sphere.add(doc.text('V', text_anchor='middle',
    transform='translate(144, -86)', stroke='none', fill=col))

# Stokes-Vector labels
sphere.add(doc.text('P₁', text_anchor='middle',
    transform='translate(-56, 33)', stroke='none', fill=col))
sphere.add(doc.text('P₂', text_anchor='middle',
    transform='translate(63, -2)', stroke='none', fill=col))
sphere.add(doc.text('P₃', text_anchor='middle',
    transform='translate(-29, -59)', stroke='none', fill=col))

# sphere surface
grad1 = doc.defs.add(doc.radialGradient(id='grad1',
    center=(0.375, 0.15), r=0.75, gradientUnits='objectBoundingBox'))
grad1.add_stop_color(offset=0, color='#ffffff', opacity=0.3)
grad1.add_stop_color(offset=1, color='#dddddd', opacity=0.3)
sphere.add(doc.circle(center=(0, 0), r=str(r),
    fill='url(#grad1)', stroke='none'))
grad2 = doc.defs.add(doc.radialGradient(id='grad2',
    center=(0.45, 0.45), r=0.575, gradientUnits='objectBoundingBox'))
grad2.add_stop_color(offset=0.6, color='#cccccc', opacity=0)
grad2.add_stop_color(offset=0.8, color='#cccccc', opacity=0.2)
grad2.add_stop_color(offset=1, color='#333333', opacity=0.2)
sphere.add(doc.circle(center=(0, 0), r=str(r),
    fill='url(#grad2)', stroke='none'))

# the six defined points
for x,y,z in [[0,0,-1], [0,0,1], [0,-1,0], [0,1,0], [-1,0,0], [1,0,0]]:
    x, y, z = rotx(r * (x*cp + y*sp), r * (y*cp - x*sp), r * z, tilt)
    if z < 0:
        continue
    pts.append((x, y))
    sphere.add(doc.circle(center=('%f' % x, '%f' % y), r=6,
        fill=col, stroke='none'))

# H, D, A, R, L labels
sphere.add(doc.text('H', text_anchor='middle',
    transform='translate(-144, 115)', stroke='none', fill=col))
sphere.add(doc.text('D', text_anchor='middle',
    transform='translate(272, 52)', stroke='none', fill=col))
sphere.add(doc.text('A', text_anchor='middle',
    transform='translate(-272, -26)', stroke='none', fill=col))
sphere.add(doc.text('R', text_anchor='middle',
    transform='translate(0, -261)', stroke='none', fill=col))
sphere.add(doc.text('L', text_anchor='middle',
    transform='translate(0, 291)', stroke='none', fill=col))

# front ellipses
sphere.add(doc.path(d=ellipse_path(0, 0, tilt, True)))
sphere.add(doc.path(d=ellipse_path(pi/2, phi, tilt)))
sphere.add(doc.path(d=ellipse_path(pi/2, phi+pi/2, tilt, True)))

# circle edge
sphere.add(doc.circle(center=(0, 0), r=str(r)))

doc.save()

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
Category:License migration redundant#Poincare-sphere%20stokes.svgCategory:GFDL#Poincare-sphere%20stokes.svg
w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
Category:CC-BY-3.0#Poincare-sphere%20stokes.svg
You may select the license of your choice.
Category:Self-published work
Category:Images with Python source code Category:Polarization (waves) Category:Photos by User:Geek3 Category:Bloch spheres Category:Octants of a sphere Category:Quality images - vector (validity not checked)

Quality image

This image has been assessed using the Quality image guidelines and is considered a Quality image.

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Category:Quality images#Poincare-sphere%20stokes.svg
Category:Bloch spheres Category:CC-BY-3.0 Category:GFDL Category:Images with Python source code Category:License migration redundant Category:Octants of a sphere Category:Photos by User:Geek3 Category:Polarization (waves) Category:Quality images Category:Quality images - vector (validity not checked) Category:Self-published work