p = np.poly1d((16.89475, 0.0, -319.13216, 0.0, 34.82210, 0.0, -0.992495,
0.0, 0.0010671)[::-1])
q = np.poly1d((1.00000, 0.0, -702.70157, 0.0, 78.28249, 0.0, -2.337086,
0.0, 0.0062267)[::-1])
c = 0.29979 # (micron/fs)
return lambda w: (1 + p(w) / q(w)) * w / c
# -- WRAP PROPAATION CONSTANT
beta_fun = get_beta_fun_ESM()
pc = PropConst(beta_fun)
# -- FIND ZERO DISPERSION POINT
w_Z = pc.find_root_beta2(1.3, 2.2)
print("w_Z = %lf rad/fs" % (w_Z))
# -- FIND GV MATCHED PARTNER FREQUENCY
w_S = 1.5 # (rad/fs)
w_GVM = pc.find_match_beta1(w_S, w_Z, 2.5)
print("w_GVM = %lf rad/fs " % (w_GVM))
# -- GV MISMATCH FOR S AND DW1
w_DW1 = 2.06 # (rad/fs)
dvg = pc.vg(w_DW1) - pc.vg(w_S)
print("dvg = %lf micron/fs" % (dvg))
# -- LOCAL EXPANSION COEFFICIENTS
betas = pc.local_coeffs(w_S, n_max=4)
for n, bn in enumerate(betas):
print("b_%d = %lf fs^%d/micron" % (n, bn, n))
###############################################################################
# Finding group-velocity matched frequencies
# ------------------------------------------
#
# For the desing of propagation scenarios that demonstrate, e.g., the
# interaction of a soliton and a dispersive wave accross a zero-dispersion
# point, it is useful to be able to compute a group-velocity matched partner
# frequency for a give frequency. Using the `PropConst` convenience class this
# can be done as shown below. Consider, e.g., a soliton with center frequency
# :math:`\omega_{\rm{S}}=2.1~\mathrm{rad/fs}`. Then, a group-velocity matched
# frequency in the domain of normal dispersion (for :math:`\omega>2.386`),
# which surely is contained in the interval :math:`\omega\in[2.4,3.0]`, can be
# computed as follows:
w_S = 2.1
w_GVM = pc.find_match_beta1(w_S, 2.4, 3.0)
print('w_GVM = ', w_GVM)
###############################################################################
# We might then reassure us that both frequencies exhibit the same group-velocity
# like so:
print(np.abs(pc.vg(w_S) - pc.vg(w_GVM)) < 1e-6)
###############################################################################
# Computing local expansion coefficients of :math:`\beta(\omega)`
# ---------------------------------------------------------------
#
# Taylor expansion coefficients of the proapgation constant at a specific
# frequency can be computed as shown below. Consider, e.g., the frequency