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By using a vectorial approach, the validity of paraxial approximation in second harmonic generation (SHG) microscopy under low numerical aperture (NA) is examined when the sample is a collagen fibril Due to the larger value of dzzx and tensorial nature of SHG, the component Ez of the focused field may have strong effect on the radiation pattern of SHG. Numerical results indicate that when the value of NA exceeds 0.3, the effect of Ez can not be neglected, which results in the invalidation of paraxial approximation in SHG microscopy despite the fact that SHG microscopy is still under low NA focusing.

A novel design of a tunable terahertz switch and band-pass filter using liquid-crystal-filled photonic crystal waveguide is demonstrated. The effects of magnetic field on the photonic bandgaps and transmitting properties of a THz wave are investigated by using the plane wave expansion method and finite difference time domain method. The efficient photonic bandgap tuning is predicted such that the two-dimensional liquid-crystal-filled photonic crystal waveguide can serve as a switch and continuously tunable band-pass filter with controlling of the magnetic field.

A new learning scheme using a periodic packet as the neuronal activation function is proposed for invariance extraction and recognition of handwritten digits. Simulation results show that the proposed network can extract the invariant feature effectively and improve both the convergence and the recognition rate.