Optical implementation of a deep neural network via phase-modulating diffractive layers
Rodion Akinzhala, Ibragimova Ksenia

D2NN (Diffractive Deep Neural Network) is an all-optical computing architecture in which learned parameters are encoded as phase profiles on physical diffractive masks. Free-space wave propagation between masks performs the nonlinear field transformation, enabling inference at the speed of light with no electronic computation at test time.

The forward pass through $N$ layers is:

$$A_{\text{out}} = \mathcal{P}_{d_N} \circ e^{i\varphi_N} \circ \mathcal{P}_{d_{N-1}} \circ \cdots \circ e^{i\varphi_1} \circ \mathcal{P}_{d_0} [{A_{\text{in}}} ]$$

where $P_d$ denotes free-space Angular Spectrum Propagation over distance $d$, and $e^{i\varphi_m}$ is the phase modulation at layer $m$. The classifier reads the output intensity $I(x,y) = |A_{\text{out}}(x,y)|^2$ at a segmented detector plane.

Trainable parameters: phase profiles ${\varphi_1, \ldots, \varphi_N}$
Fixed parameters: inter-layer distances ${d_1, \ldots, d_{N-1}}$

• Novel Gerchberg–Saxton initialization. A modified Gerchberg–Saxton algorithm is developed to produce physically structured initial phase masks, replacing the standard $\mathcal{U}[-\pi,\pi]$ random initialization. The procedure minimizes $|{|B^{(k)}|} - |A_{\text{out}}||_2^2$ via alternating projections onto constraint sets and is proven to converge monotonically. This yields faster training convergence and higher final accuracy compared to random initialization.

• Robustness characterization. Systematic evaluation of model sensitivity to (i) source wavelength variation and (ii) proportional Gaussian phase noise $\delta \sim \mathcal{N}(0,, \alpha^2\varphi^2)$, establishing practical tolerances.

The proposed Gerchberg–Saxton initialization consistently outperforms random phase initialization in both convergence speed and final classification accuracy. Robustness experiments show that the trained model retains accuracy above 80% under source wavelength deviations of up to ±2%, confirming tolerance to realistic spectral fluctuations. Under proportional Gaussian phase noise, accuracy degrades monotonically with noise level $\alpha$ and remains robust in the low-noise regime, establishing practical fabrication tolerances for physical implementation.

D2NN/
├── code/       # Simulation, training, and analysis scripts
└── results/    # Presentation materials and figures
└── articles/   # Library of materials