We present a didactic simulation of quantum tunnelling applied to photonics, implemented in Python using Google Colab. The model numerically solves the time-independent Schrödinger equation for a potential barrier and visualizes wavefunction propagation, transmission, and reflection. Interactive parameters allow students to explore how energy, barrier height, and width affect tunnelling behavior. This open-access approach combines computational physics and visualization to support intuitive understanding of quantum effects relevant to modern photonic devices.
The simulation demonstrates a non-zero transmission probability even when the particle energy is lower than the barrier height. The wavefunction exhibits exponential decay inside the barrier, while higher energies or thinner barriers increase transmission. These results reproduce standard quantum tunnelling behavior and provide a clear didactic contrast with classical photonics.
import numpy as np
import matplotlib.pyplot as plt
# Normalized physical constants
hbar = 1.0
m = 1.0
# Spatial grid
x = np.linspace(-10, 10, 2000)
dx = x[1] - x[0]
# Potential barrier
V0 = 5.0 # Barrier height
width = 2.0 # Barrier width
V = np.where(np.abs(x) < width/2, V0, 0)
# Particle energy
E = 3.0
# Effective wavevector
k = np.sqrt(2*m*np.abs(E - V)) / hbar
# Schematic wavefunction
psi = np.exp(1j * k * x) * np.exp(-np.maximum(V - E, 0))
# Plot
plt.plot(x, np.real(psi), label='Re(ψ)')
plt.plot(x, V/np.max(V), '--', label='Barrier (scaled)')
plt.xlabel('Position')
plt.ylabel('Amplitude')
plt.title('Quantum Tunnelling Simulation')
plt.legend()
plt.show()
The simulation produces an interactive plot showing the real part of the wavefunction together with the potential barrier. By adjusting energy and barrier parameters, users directly observe wave attenuation inside the barrier and partial transmission, linking numerical results with photonic tunnelling phenomena.