Predicting physical response of an artificially structured material is of particular interest for scientific and engineering applications. Here we use deep learning to predict optical response of artificially engineered nanophotonic devices. In addition to predicting forward approximation of transmission response for any given topology, this approach allows us to inversely approximate designs for a targeted optical response. Our Deep Neural Network (DNN) could design compact (2.6 × 2.6 μm2) silicon-on-insulator (SOI)-based 1 × 2 power splitters with various target splitting ratios in a fraction of a second. This model is trained to minimize the reflection (to smaller than ~ −20 dB) while achieving maximum transmission efficiency above 90% and target splitting specifications. This approach paves the way for rapid design of integrated photonic components relying on complex nanostructures.

Distribution matching is a fixed-length invertible mapping from a uniformly distributed bit sequence to shaped amplitudes and plays an important role in the probabilistic amplitude shaping framework. With conventional constantcomposition distribution matching (CCDM), all output sequences have identical composition. In this paper, we propose multisetpartition distribution matching (MPDM) where the composition is constant over all output sequences. When considering the desired distribution as a multiset, MPDM corresponds to partitioning this multiset into equal-size subsets. We show that MPDM allows to address more output sequences and thus has lower rate loss than CCDM in all nontrivial cases. By imposing some constraints on the partitioning, a constructive MPDM algorithm is proposed which comprises two parts. A variable-length prefix of the binary data word determines the composition to be used, and the remainder of the input word is mapped with a conventional CCDM algorithm, such as arithmetic coding, according to the chosen composition. Simulations of 64-ary quadrature amplitude modulation over the additive white Gaussian noise channel demonstrate that the block-length saving of MPDM over CCDM for a fixed gap to capacity is approximately a factor of 2.5 to 5 at medium to high signal-to-noise ratios (SNRs).

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In this paper, we examine the performance of several modulation formats in more than four dimensions for coherent optical communications systems. We compare two high-dimensional modulation design methodologies based on spherical cutting of lattices and block coding of a 'base constellation' of binary phase shift keying (BPSK) on each dimension. The performances of modulation formats generated with these methodologies is analyzed in the asymptotic signal-to-noise ratio regime and for an additive white Gaussian noise (AWGN) channel. We then study the application of both types of high-dimensional modulation formats to standard single-mode fiber (SSMF) transmission systems. For modulation with spectral efficiencies comparable to dual-polarization (DP-) BPSK, polarization-switched quaternary phase shift keying (PS-QPSK) and DP-QPSK, we demonstrate SNR gains of up to 3 dB, 0.9 dB and 1 dB respectively, at a BER of 10(-3).

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