def test_gauss_opt():
mat = RayTransferMatrix(1, 2, 3, 4)
assert mat == Matrix([[1, 2], [3, 4]])
assert mat == RayTransferMatrix(Matrix([[1, 2], [3, 4]]))
assert [mat.A, mat.B, mat.C, mat.D] == [1, 2, 3, 4]
d, f, h, n1, n2, R = symbols('d f h n1 n2 R')
lens = ThinLens(f)
assert lens == Matrix([[1, 0], [-1 / f, 1]])
assert lens.C == -1 / f
assert FreeSpace(d) == Matrix([[1, d], [0, 1]])
assert FlatRefraction(n1, n2) == Matrix([[1, 0], [0, n1 / n2]])
assert CurvedRefraction(R, n1, n2) == Matrix([[1, 0],
[(n1 - n2) / (R * n2),
n1 / n2]])
assert FlatMirror() == Matrix([[1, 0], [0, 1]])
assert CurvedMirror(R) == Matrix([[1, 0], [-2 / R, 1]])
assert ThinLens(f) == Matrix([[1, 0], [-1 / f, 1]])
mul = CurvedMirror(R) * FreeSpace(d)
mul_mat = Matrix([[1, 0], [-2 / R, 1]]) * Matrix([[1, d], [0, 1]])
assert mul.A == mul_mat[0, 0]
assert mul.B == mul_mat[0, 1]
assert mul.C == mul_mat[1, 0]
assert mul.D == mul_mat[1, 1]
angle = symbols('angle')
assert GeometricRay(h, angle) == Matrix([[h], [angle]])
assert FreeSpace(d) * GeometricRay(h, angle) == Matrix([[angle * d + h],
[angle]])
assert GeometricRay(Matrix(((h, ), (angle, )))) == Matrix([[h], [angle]])
assert (FreeSpace(d) * GeometricRay(h, angle)).height == angle * d + h
assert (FreeSpace(d) * GeometricRay(h, angle)).angle == angle
p = BeamParameter(530e-9, 1, w=1e-3)
assert streq(p.q, 1 + 1.88679245283019 * I * pi)
assert streq(N(p.q), 1.0 + 5.92753330865999 * I)
assert streq(N(p.w_0), Float(0.00100000000000000))
assert streq(N(p.z_r), Float(5.92753330865999))
fs = FreeSpace(10)
p1 = fs * p
assert streq(N(p.w), Float(0.00101413072159615))
assert streq(N(p1.w), Float(0.00210803120913829))
w, wavelen = symbols('w wavelen')
assert waist2rayleigh(w, wavelen) == pi * w**2 / wavelen
z_r, wavelen = symbols('z_r wavelen')
assert rayleigh2waist(z_r, wavelen) == sqrt(wavelen * z_r) / sqrt(pi)
a, b, f = symbols('a b f')
assert geometric_conj_ab(a, b) == a * b / (a + b)
assert geometric_conj_af(a, f) == a * f / (a - f)
assert geometric_conj_bf(b, f) == b * f / (b - f)
assert geometric_conj_ab(oo, b) == b
assert geometric_conj_ab(a, oo) == a
s_in, z_r_in, f = symbols('s_in z_r_in f')
assert gaussian_conj(s_in, z_r_in,
f)[0] == 1 / (-1 / (s_in + z_r_in**2 /
(-f + s_in)) + 1 / f)
assert gaussian_conj(
s_in, z_r_in, f)[1] == z_r_in / (1 - s_in**2 / f**2 + z_r_in**2 / f**2)
assert gaussian_conj(
s_in, z_r_in, f)[2] == 1 / sqrt(1 - s_in**2 / f**2 + z_r_in**2 / f**2)
l, w_i, w_o, f = symbols('l w_i w_o f')
assert conjugate_gauss_beams(
l, w_i, w_o, f=f)[0] == f * (-sqrt(w_i**2 / w_o**2 - pi**2 * w_i**4 /
(f**2 * l**2)) + 1)
assert factor(conjugate_gauss_beams(
l, w_i, w_o,
f=f)[1]) == f * w_o**2 * (w_i**2 / w_o**2 -
sqrt(w_i**2 / w_o**2 - pi**2 * w_i**4 /
(f**2 * l**2))) / w_i**2
assert conjugate_gauss_beams(l, w_i, w_o, f=f)[2] == f
z, l, w_0 = symbols('z l w_0', positive=True)
p = BeamParameter(l, z, w=w_0)
assert p.radius == z * (pi**2 * w_0**4 / (l**2 * z**2) + 1)
assert p.w == w_0 * sqrt(l**2 * z**2 / (pi**2 * w_0**4) + 1)
assert p.w_0 == w_0
assert p.divergence == l / (pi * w_0)
assert p.gouy == atan2(z, pi * w_0**2 / l)
assert p.waist_approximation_limit == 2 * l / pi
p = BeamParameter(530e-9, 1, w=1e-3, n=2)
assert streq(p.q, 1 + 3.77358490566038 * I * pi)
assert streq(N(p.z_r), Float(11.8550666173200))
assert streq(N(p.w_0), Float(0.00100000000000000))
def test_gauss_opt():
mat = RayTransferMatrix(1, 2, 3, 4)
assert mat == Matrix([[1, 2], [3, 4]])
assert mat == RayTransferMatrix( Matrix([[1, 2], [3, 4]]) )
assert [mat.A, mat.B, mat.C, mat.D] == [1, 2, 3, 4]
d, f, h, n1, n2, R = symbols('d f h n1 n2 R')
lens = ThinLens(f)
assert lens == Matrix([[ 1, 0], [-1/f, 1]])
assert lens.C == -1/f
assert FreeSpace(d) == Matrix([[ 1, d], [0, 1]])
assert FlatRefraction(n1, n2) == Matrix([[1, 0], [0, n1/n2]])
assert CurvedRefraction(
R, n1, n2) == Matrix([[1, 0], [(n1 - n2)/(R*n2), n1/n2]])
assert FlatMirror() == Matrix([[1, 0], [0, 1]])
assert CurvedMirror(R) == Matrix([[ 1, 0], [-2/R, 1]])
assert ThinLens(f) == Matrix([[ 1, 0], [-1/f, 1]])
mul = CurvedMirror(R)*FreeSpace(d)
mul_mat = Matrix([[ 1, 0], [-2/R, 1]])*Matrix([[ 1, d], [0, 1]])
assert mul.A == mul_mat[0, 0]
assert mul.B == mul_mat[0, 1]
assert mul.C == mul_mat[1, 0]
assert mul.D == mul_mat[1, 1]
angle = symbols('angle')
assert GeometricRay(h, angle) == Matrix([[ h], [angle]])
assert FreeSpace(
d)*GeometricRay(h, angle) == Matrix([[angle*d + h], [angle]])
assert GeometricRay( Matrix( ((h,), (angle,)) ) ) == Matrix([[h], [angle]])
assert (FreeSpace(d)*GeometricRay(h, angle)).height == angle*d + h
assert (FreeSpace(d)*GeometricRay(h, angle)).angle == angle
p = BeamParameter(530e-9, 1, w=1e-3)
assert streq(p.q, 1 + 1.88679245283019*I*pi)
assert streq(N(p.q), 1.0 + 5.92753330865999*I)
assert streq(N(p.w_0), Float(0.00100000000000000))
assert streq(N(p.z_r), Float(5.92753330865999))
fs = FreeSpace(10)
p1 = fs*p
assert streq(N(p.w), Float(0.00101413072159615))
assert streq(N(p1.w), Float(0.00210803120913829))
w, wavelen = symbols('w wavelen')
assert waist2rayleigh(w, wavelen) == pi*w**2/wavelen
z_r, wavelen = symbols('z_r wavelen')
assert rayleigh2waist(z_r, wavelen) == sqrt(wavelen*z_r)/sqrt(pi)
a, b, f = symbols('a b f')
assert geometric_conj_ab(a, b) == a*b/(a + b)
assert geometric_conj_af(a, f) == a*f/(a - f)
assert geometric_conj_bf(b, f) == b*f/(b - f)
assert geometric_conj_ab(oo, b) == b
assert geometric_conj_ab(a, oo) == a
s_in, z_r_in, f = symbols('s_in z_r_in f')
assert gaussian_conj(
s_in, z_r_in, f)[0] == 1/(-1/(s_in + z_r_in**2/(-f + s_in)) + 1/f)
assert gaussian_conj(
s_in, z_r_in, f)[1] == z_r_in/(1 - s_in**2/f**2 + z_r_in**2/f**2)
assert gaussian_conj(
s_in, z_r_in, f)[2] == 1/sqrt(1 - s_in**2/f**2 + z_r_in**2/f**2)
l, w_i, w_o, f = symbols('l w_i w_o f')
assert conjugate_gauss_beams(l, w_i, w_o, f=f)[0] == f*(
-sqrt(w_i**2/w_o**2 - pi**2*w_i**4/(f**2*l**2)) + 1)
assert factor(conjugate_gauss_beams(l, w_i, w_o, f=f)[1]) == f*w_o**2*(
w_i**2/w_o**2 - sqrt(w_i**2/w_o**2 - pi**2*w_i**4/(f**2*l**2)))/w_i**2
assert conjugate_gauss_beams(l, w_i, w_o, f=f)[2] == f
z, l, w = symbols('z l r', positive=True)
p = BeamParameter(l, z, w=w)
assert p.radius == z*(l**2*z**2/(pi**2*w**4) + 1)
assert p.w == w*sqrt(l**2*z**2/(pi**2*w**4) + 1)
assert p.w_0 == w
assert p.divergence == l/(pi*w)
assert p.gouy == atan2(z, pi*w**2/l)
assert p.waist_approximation_limit == 2*l/pi