We experimentally investigate the propagation of Airy surface plasmon polaritons (Airy SPPs) on a gold film by multiphoton Photoemission Electron Microscopy (PEEM) at different excitation wavelengths and compare the result with rigorous numerical simulations. The typical bent trajectories of the excited two-dimensional beams are observed and analyzed over a wide range of wavelengths. We furthermore investigate the generation bandwidth of the diffraction grating from modal overlap calculations and evaluate the possibility of creating ultrashort Airy plasmon pulses. This provides a viable route to engineer two-dimensional ultrashort non-diffracting pulsed beams in the field of ultrafast nanophotonics.
We investigate numerically the evolution of a particular type of non-diffracting pulsed plasmonic beam called Airy plasmon pulses. A suitable diffraction grating is obtained by optimizing a grating (e.g., [Phys. Rev. Lett. 107, 116802 (2011)10.1103/PhysRevLett.107.116802]) for maximum generation bandwidth and efficiency to excite ultrashort Airy plasmon pulses. The optimization process is based on Airy and non-Airy plasmons contributions from the diffraction grating. The time-averaged Airy plasmon pulse generated from the grating shows a bent trajectory and quasi non-diffracting properties similar to CW excited Airy plasmons. A design-parameter-dependent geometrical model is developed to explain the spatio-temporal dynamics of the Airy plasmon pulses, which predicts the pulse broadening in Airy plasmon pulses due to non-Airy plasmons emerging from the grating. This model provides a parametric design control for the potential engineering of temporally focused 2D non-diffracting pulsed plasmonic beams.
Rectified linear unit (ReLU) activations can also be thought of as gates, which, either pass or stop their pre-activation input when they are on (when the preactivation input is positive) or off (when the pre-activation input is negative) respectively. A deep neural network (DNN) with ReLU activations has many gates, and the on/off status of each gate changes across input examples as well as network weights. For a given input example, only a subset of gates are active, i.e., on, and the sub-network of weights connected to these active gates is responsible for producing the output. At randomised initialisation, the active sub-network corresponding to a given input example is random. During training, as the weights are learnt, the active sub-networks are also learnt, and potentially hold very valuable information.In this paper, we analytically characterise the role of active sub-networks in deep learning. To this end, we encode the on/off state of the gates of a given input in a novel neural path feature (NPF), and the weights of the DNN are encoded in a novel neural path value (NPV). Further, we show that the output of network is indeed the inner product of NPF and NPV. The main result of the paper shows that the neural path kernel associated with the NPF is a fundamental quantity that characterises the information stored in the gates of a DNN. We show via experiments (on MNIST and CIFAR-10) that in standard DNNs with ReLU activations NPFs are learnt during training and such learning is key for generalisation. Furthermore, NPFs and NPVs can be learnt in two separate networks and such learning also generalises well in experiments. In our experiments, we observe that almost all the information learnt by a DNN with ReLU activations is stored in the gates -a novel observation that underscores the need to further investigate the role of gating in DNNs.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.