12. Hands-On Calculations and Code

import numpy as np
 
# Transmitter
P_tx_dBm = 1.0           # launch power per channel (0 dBm typical)
# Fiber
alpha_dB_per_km = 0.20   # standard SMF at 1550 nm
L_km = 100.0
fiber_loss = alpha_dB_per_km * L_km
# Connectors and splices
N_connectors = 4
loss_per_connector = 0.30
N_splices = 8
loss_per_splice = 0.05
# Margin
margin = 3.0
 
P_rx_dBm = (
    P_tx_dBm
    - fiber_loss
    - N_connectors * loss_per_connector
    - N_splices * loss_per_splice
    - margin
)
 
print(f"Fiber loss:        {fiber_loss:5.2f} dB")
print(f"Connector loss:    {N_connectors*loss_per_connector:5.2f} dB")
print(f"Splice loss:       {N_splices*loss_per_splice:5.2f} dB")
print(f"Margin:            {margin:5.2f} dB")
print(f"Received power:    {P_rx_dBm:5.2f} dBm")
# A 100G coherent receiver needs around -18 dBm; 200G coherent needs -15 dBm.

import numpy as np
import matplotlib.pyplot as plt
 
lam_nm = np.linspace(800, 1700, 901)
lam_um = lam_nm / 1000.0
 
# Rayleigh scattering: ~1/lambda^4
A_rayleigh_um4 = 0.85   # empirical coefficient (dB/km * um^4)
rayleigh = A_rayleigh_um4 / (lam_um**4)
 
# IR absorption tail
ir = 7.81e11 * np.exp(-48.48 / lam_um)
 
# UV absorption tail (small in this band)
uv = 154 * np.exp(-4.63 / lam_um)
 
# OH peak around 1383 nm
oh_peak_nm = 1383.0
oh = 2.0 * np.exp(-((lam_nm - oh_peak_nm) / 12.0)**2)
 
total = rayleigh + ir + uv + oh
 
plt.figure(figsize=(7,4))
plt.plot(lam_nm, total, 'k', lw=2, label='total')
plt.plot(lam_nm, rayleigh, '--', label='Rayleigh ~1/λ⁴')
plt.plot(lam_nm, ir, '--', label='IR tail')
plt.plot(lam_nm, oh, '--', label='OH⁻ peak')
plt.axvline(850, color='gold', alpha=0.4)
plt.axvline(1310, color='skyblue', alpha=0.4)
plt.axvline(1550, color='coral', alpha=0.4)
plt.xlabel('wavelength (nm)')
plt.ylabel('attenuation (dB/km)')
plt.ylim(0, 4)
plt.legend()
plt.title('Silica fiber attenuation vs wavelength')
plt.grid(True, alpha=0.3)
plt.savefig('fiber_attenuation.png', dpi=150)

import numpy as np
import matplotlib.pyplot as plt
 
# Setup
fs = 100e9                        # 100 GS/s sampling
T_bit = 1 / 10e9                  # 10 Gbps
samples_per_bit = int(fs * T_bit)
n_bits = 4096
bits = np.random.randint(0, 2, n_bits)
 
# NRZ baseband with pulse shaping (rectangular for simplicity)
pulse = np.ones(samples_per_bit)
signal = np.repeat(bits, samples_per_bit).astype(float)
 
# Modulate onto an "optical" complex baseband
optical = signal.astype(complex)
 
# Apply chromatic dispersion: multiply spectrum by exp(-j*beta2*omega^2*L/2)
N = len(optical)
freqs = np.fft.fftfreq(N, 1/fs)
omega = 2 * np.pi * freqs
 
D = 17e-6        # 17 ps/nm/km in s/m^2
lam = 1550e-9
c = 3e8
beta2 = -D * lam**2 / (2 * np.pi * c)    # in s^2/m
L = 80e3                                  # 80 km
 
H = np.exp(-1j * beta2 * omega**2 * L / 2)
disp_optical = np.fft.ifft(np.fft.fft(optical) * H)
 
# Direct-detect: square-law photodiode
detected = np.abs(disp_optical)**2
 
# Build eye diagram by overlapping bit windows
eye_window = 2 * samples_per_bit
plt.figure(figsize=(7,4))
for i in range(100, n_bits - 100):
    start = i * samples_per_bit
    plt.plot(np.arange(eye_window), detected[start:start+eye_window],
             'b', alpha=0.05)
plt.xlabel('sample index within 2-bit window')
plt.ylabel('photocurrent (a.u.)')
plt.title('Eye diagram after 80 km of standard SMF (10 Gbps NRZ)')
plt.grid(True, alpha=0.3)
plt.savefig('eye.png', dpi=150)