This simulation visualizes the double-slit experiment using a purely classical wave model for light, interacting with a discrete detector screen, inspired by the semi-classical approach (e.g., Rashkovskiy, SPIE 9570, 2015).
The left canvas shows the calculated classical wave amplitude propagating from two slits (white openings) in a barrier (black). Amplitude is color-coded (Red=positive, Blue=negative, Black=zero). The rightmost column simulates a detector screen. When a "detection" occurs at a specific vertical position (y), a ■ red square appears momentarily. The right canvas plots a histogram (black bars on white background) of these detection events versus y, showing the interference pattern emerging over time.
Adjust `alpha` to control the frequency of ■ detection events. High `alpha` leads to faster pattern buildup.
This simulation follows a semi-classical approach where light is a continuous classical wave, and the detector screen behaves quantum-mechanically (registering discrete events). See S.A. Rashkovskiy, SPIE 2015 for background.
1. Classical Wave Calculation: At any point (x, y) past the barrier (x > barrierX) and at time t, the wave amplitude is the sum (superposition) of waves from each slit:
Where A1 and A2 are the amplitudes from slit 1 (at y1) and slit 2 (at y2) respectively, modeled as cylindrical waves spreading in 2D:
Here:
A0 is the initial Source Amplitude.ri = √((x - barrierX)² + (y - yi)²) is the distance from slit i.1/√ri represents the amplitude decay for a 2D wave.k = 2π/λ is the wave number (where λ is the Wavelength).ω = c*k is the angular frequency (where c is the Wave Speed).cos(...) describes the wave oscillation in space and time.2. Classical Intensity: The classical intensity I of the wave at point (x, y) is proportional to the square of the total amplitude:
3. Detection Probability: The detector screen (at x = W-1) consists of discrete elements. The probability Pdetect that an element at height y registers a "hit" (■) in a single simulation frame (representing a small time step Δt) is proportional to the instantaneous classical intensity at that point. This aligns with Fermi's Golden Rule where the transition rate is proportional to intensity.
Here, α (alpha, the Detection Prob Scale parameter) is a proportionality constant that combines the intrinsic sensitivity of the detector elements and the effective duration (Δt) of a simulation frame.
4. Random Event & Histogram: For each frame and each y on the detector, a random number between 0 and 1 is generated. If Math.random() < Pdetect(y, t), a detection event is registered at that y, marked by a red square, and the count for that y in the histogram is incremented. Over many frames, the histogram statistically builds up the interference pattern corresponding to the time-averaged classical intensity profile.