code: def test_polarization():
      assert jones_vector(0, 0) == Matrix([1, 0])
      assert jones_vector(pi / 2, 0) == Matrix([0, 1])
      #################################################################
      assert stokes_vector(0, 0) == Matrix([1, 1, 0, 0])
      assert stokes_vector(pi / 2, 0) == Matrix([1, -1, 0, 0])
      #################################################################
      H = jones_vector(0, 0)
      V = jones_vector(pi / 2, 0)
      D = jones_vector(pi / 4, 0)
      A = jones_vector(-pi / 4, 0)
      R = jones_vector(0, pi / 4)
      L = jones_vector(0, -pi / 4)
  
      res = [
          Matrix([1, 1, 0, 0]),
          Matrix([1, -1, 0, 0]),
          Matrix([1, 0, 1, 0]),
          Matrix([1, 0, -1, 0]),
          Matrix([1, 0, 0, 1]),
          Matrix([1, 0, 0, -1]),
      ]
  
      assert [jones_2_stokes(e) for e in [H, V, D, A, R, L]] == res
      #################################################################
      assert linear_polarizer(0) == Matrix([[1, 0], [0, 0]])
      #################################################################
      delta = symbols("delta", real=True)
      res = Matrix([[exp(-I * delta / 2), 0], [0, exp(I * delta / 2)]])
      assert phase_retarder(0, delta) == res
      #################################################################
      assert half_wave_retarder(0) == Matrix([[-I, 0], [0, I]])
      #################################################################
      res = Matrix([[exp(-I * pi / 4), 0], [0, I * exp(-I * pi / 4)]])
      assert quarter_wave_retarder(0) == res
      #################################################################
      assert transmissive_filter(1) == Matrix([[1, 0], [0, 1]])
      #################################################################
      assert reflective_filter(1) == Matrix([[1, 0], [0, -1]])
  
      res = Matrix(
          [
              [S(1) / 2, S(1) / 2, 0, 0],
              [S(1) / 2, S(1) / 2, 0, 0],
              [0, 0, 0, 0],
              [0, 0, 0, 0],
          ]
      )
      assert mueller_matrix(linear_polarizer(0)) == res
      #################################################################
      res = Matrix(
          [[1, 0, 0, 0], [0, 0, 0, -I], [0, 0, 1, 0], [0, -I, 0, 0]]
      )
      assert polarizing_beam_splitter() == res
  
imports: from sympy.physics.optics.polarization import jones_vector, stokes_vector, jones_2_stokes, linear_polarizer, phase_retarder, half_wave_retarder, quarter_wave_retarder, transmissive_filter, reflective_filter, mueller_matrix, polarizing_beam_splitter
  from sympy.core.numbers import I, pi
  from sympy.core.singleton import S
  from sympy.core.symbol import symbols
  from sympy.functions.elementary.exponential import exp
  from sympy.matrices.dense import Matrix
label_desc: Use image node_id 1 for calling a global function with example usage: test_polarization() without return types