sim: verification of the independence of Nyquist collision integrals …

…wrt differential beta2

scripts/modules/beta_utils.py

@@ -0,0 +1,8 @@
+import numpy as np
+def beta2rms(beta2a, beta2b):
+    return -np.sqrt(beta2a**2 + beta2b**2)
+
+def beta2_complementary(beta2rms, beta2a):
+    tmp = 2*beta2rms**2-beta2a**2
+    assert(tmp>0)
+    return -np.sqrt(tmp)

scripts/modules/plot_collisions_fig1.py

@@ -3,6 +3,7 @@
 import matplotlib.pyplot as plt
 from matplotlib.ticker import ScalarFormatter
 import os
+from modules.beta_utils import beta2rms, beta2_complementary
 
 formatter = ScalarFormatter()
 formatter.set_scientific(True)
@@ -21,9 +22,13 @@ def plot_illustrative(fiber, pulse, wdm, recompute=False):
     dgd_hi = 100e-15
     dgd_lo = 1e-16
     beta2a = -35e-27  # TODO, check con Marco
-    beta2b = -75e-27  
+    beta2b = -25e-27
+    beta2bar = beta2rms(beta2a, beta2b)
+    LDbar = 1/(pulse.baud_rate**2 * np.abs(beta2bar))
     z = np.linspace(0, fiber.length, 1000)
+
     # 1. the two pulses 
+    # cases are related to single collisions
     cases = [(dgd_hi, beta2a, beta2b, m1), 
              (dgd_hi, beta2a, beta2b, m2),]
     I_list = []
@@ -32,19 +37,24 @@ def plot_illustrative(fiber, pulse, wdm, recompute=False):
         I_list.append(I)
 
     # 2. the set of pulse peaks:
+    # cases are related to set of parameters, not to single collisions
+    print(f"B2A = {beta2a:.2e} | B2B = {beta2b:.2e}  B2complement = {beta2_complementary(beta2a, beta2b)}|")
+    cases_peaks = [(dgd_hi, beta2a, beta2a, m1), 
+                   (dgd_hi, beta2b, beta2_complementary(beta2a, beta2b), m2),]
     zw = 1/(pulse.baud_rate * dgd_hi)
     m_max = fiber.length / zw
     print(f"  > m_max: {m_max}")
     m_axis = -np.array(range(int(round(m_max))))
+    m_axis = m_axis[::5]
     peaks   = np.zeros(2)[np.newaxis, :].repeat(len(m_axis), axis=0)
     z_peaks = np.zeros(2)[np.newaxis, :].repeat(len(m_axis), axis=0)
     #
     if not os.path.exists("results/fig1_peaks.npy") or recompute:
       print("  Computing peaks...")
       for im, m in enumerate(m_axis):
         print(f"  m: {m:>10}")
-        for ic, (dgd, beta2a, beta2b, _) in enumerate(cases):
-          I = np.real(m_th_time_integral_general(pulse, fiber, wdm, (0, 0), (0, 0), 0.0, m, z, dgd_hi, None, beta2a, beta2b))
+        for ic, (dgd, beta2a, beta2b, _) in enumerate(cases_peaks):
+          I = np.real(m_th_time_integral_general(pulse, fiber, wdm, (0, 0), (0, 0), 0.0, m, z, dgd, None, beta2a, beta2b))
           peaks[im, ic]   = np.max(I)
           z_peaks[im, ic] = z[np.argmax(I)]
       np.save("results/fig1_peaks.npy", (peaks, z_peaks))
@@ -53,32 +63,39 @@ def plot_illustrative(fiber, pulse, wdm, recompute=False):
       print("  Loading peaks...")
       peaks, z_peaks = np.load("results/fig1_peaks.npy")
       print("  Done loading peaks.")
+    print(peaks)
 
 
     # 3. Plotting
-    cases = [(dgd_hi, beta2a, beta2a, m1), 
-             (dgd_lo, beta2b, beta2b, m2),]
-    colors = ["blue", "grey"]
+    colors  = ["blue", "grey"]
+    markers = ["x", "o"]
+    lw = 0.5
+    size = 5
     plt.figure(figsize=(4, 3))
     # plotting the pulses
     for I in I_list:
-      plt.plot(z*1e-3, I*1e-12, label=f'try', color="red")
+      plt.plot(z/LDbar, I / pulse.baud_rate, label=f'try', color="red")
     # plotting the peaks
     for ip, (peak, z_peak) in enumerate(zip(peaks, z_peaks)):
-      # print(peak, z_peak)
-      for ic in range(len(cases)):
+      for ic in range(len(cases_peaks)):
         if ip == 0:
-          plt.plot(z_peak[ic]*1e-3, peak[ic]*1e-12, 
-                  marker="x",
-                  markersize=0.1,
+          plt.plot(z_peak[ic]/LDbar, 
+                   peak[ic]/pulse.baud_rate, 
+                  marker=markers[ic],
+                  markersize=size,
                   label='case'+str(ic),
-                  color=colors[ic])
-        plt.plot(z_peak[ic]*1e-3, peak[ic]*1e-12, 
-                marker="x",
-                color=colors[ic])
+                  color=colors[ic],
+                  linewidth=lw)
+        else:
+          plt.plot(z_peak[ic]/LDbar, 
+                  peak[ic]/pulse.baud_rate,  
+                  markersize=size, 
+                  marker=markers[ic],
+                  color=colors[ic],
+                  linewidth=lw)
     plt.legend()
-    plt.xlabel(r'$z \; [\mathrm{km}]$')
-    plt.ylabel(r'$I(z) \; [\mathrm{ps^{-1}}]$')
+    plt.xlabel(r'$z / \bar{L_D}$')
+    plt.ylabel(r'$I(z) \cdot T $')
     plt.gca().yaxis.set_major_formatter(formatter)
     plt.tight_layout()
     plt.savefig("media/1-quovadis.pdf")