feat: adds a lindhard tranverse function

pyewjn/dielectric/__init__.py

@@ -3,9 +3,13 @@ from pyewjn.dielectric.nam_dielectric_coefficient_approximator import (
 	get_unapproximated_nam_dielectric,
 )
 from pyewjn.dielectric.lindhard_dielectric import get_lindhard_dielectric
+from pyewjn.dielectric.lindhard_dielectric_transverse import (
+	get_lindhard_dielectric_transverse,
+)
 
 __all__ = [
 	"get_nam_dielectric",
 	"get_lindhard_dielectric",
+	"get_lindhard_dielectric_transverse",
 	"get_unapproximated_nam_dielectric",
 ]

pyewjn/dielectric/lindhard_dielectric_transverse.py

@@ -0,0 +1,69 @@
+import numpy as np
+from pyewjn.baskets import CalculationConstants, CalculationParams
+
+TRANSVERSE_THRESHOLD = 1e4
+
+
+class LindhardDielectricTransverse(object):
+	def __init__(
+		self,
+		params: CalculationParams,
+		constants: CalculationConstants = CalculationConstants(),
+		thres=TRANSVERSE_THRESHOLD,
+	):
+
+		self.series_threshold = thres
+		self.omega = params.omega
+		self.v_f = params.v_f
+		self.omega_p = params.omega_p
+		self.tau = params.tau
+		self.c_light = constants.c_light
+
+		self.s = 1 / (self.tau * self.omega)
+		self.prefactor = 3 * (self.omega_p**2) / (self.omega**2)
+
+	def get_eps(self):
+		def eps_lindhard(u_inverse_wavelength: float) -> complex:
+			"""the lindhard dielectric function
+
+			:param u_inverse_wavelength: u is in units of the reciprocal vacuum wavelength (omega / c_light)
+			:return: returns the value of epsilon, dimensionless
+			"""
+
+			# converts u from inverse vacuum wavelength to inverse mean free path
+			# want to convert to q = vf k, where k is wavevector in SI units
+			q = u_inverse_wavelength * (self.v_f * self.omega) / (self.c_light)
+
+			if u_inverse_wavelength < self.series_threshold * self.v_f / self.omega:
+				return eps_series(q)
+			else:
+				return eps_full_lindhard(q)
+
+		def eps_series(q: float) -> complex:
+			pass
+
+		def eps_full_lindhard(q: float) -> complex:
+
+			return internal_eps_t_full(q, 1 / self.tau, self.omega_p, self.omega)
+
+		return eps_lindhard
+
+
+def internal_eps_t_full(
+	q: float,
+	nu: float,
+	wp: float,
+	w: float,
+):
+	s = nu / w
+	qtw = q / w
+
+	log_val = np.log((1 + qtw + 1j * s) / (1 - qtw + 1j * s))
+	parens = 1 + 1j * s - (((1 + 1j * s) ** 2 - qtw**2) / (2 * qtw)) * log_val
+	return 1 - (3 / 2) * ((wp) / (w)) ** 2 * (1 / (qtw**2)) * parens
+
+
+def get_lindhard_dielectric_transverse(
+	params: CalculationParams, constants: CalculationConstants = CalculationConstants()
+):
+	return LindhardDielectricTransverse(params, constants).get_eps()