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We formulate a scattering-matrix-based numerical method to calculate the optical transmission properties and quasiguided eigenmodes in a two-dimensionally periodic photonic crystal slab ͑PCS͒ of finite thickness. The square symmetry ͑point group C 4v) is taken for the illustration of the method, but it is quite general and works for any point group symmetry for one-dimensional ͑1D͒ and 2D PCS's. We show that the appearance of well-pronounced dips in the transmission spectra of a PCS is due to the interaction with resonant waveguide eigenmodes in the slab. The energy position and width of the dips in transmission provide information on the frequency and inverse radiative lifetime of the quasiguided eigenmodes. We calculate the energies, linewidths, and electromagnetic fields of such quasiguided eigenmodes, and analyze their symmetry and optical activity. The electromagnetic field in such modes is resonantly enhanced, which opens possibilities for use in creating resonant enhancement of different nonlinear effects.

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Optical spectra in the visible and uv regions are investigated in layer-type perovskite compounds (C H2 + &NH3)PbI4 with n =4, 6, 8, 9, 10, and 12. The spacing between the PbI4 layers changes from 15.17 A for n =4 to 24.51 A for n =12. In spite of these different spacings, the optical spectra are almost the same for these compounds, which means that the interaction between the layers is weak. The lowest exciton is located at 2.56 eV at 1.6 K, and its oscillator strength and binding energy are 0.7 per formula unit and 320 meV, respectively. These values are very large compared with those in a three-dimensional analog PbI2. The large oscillator strength and binding energy can be explained by the small dielectric constant of the alkylammonium "barrier layer, " which strengthens the Coulomb interaction between an electron and a hole.

We demonstrate a promising nanofabrication method, used to fabricate fine patterns beyond the diffraction limit, by employing surface plasmon polariton (SPP) resonance. Sub-100 nm lines were patterned photolithographically using surface plasmon polaritonic interference in the optical near field excited by a wavelength of 436 nm. The unperforated metallic mask approach which has corrugated surfaces on both sides is proposed for arbitrary patterning. The corrugated surface of the metallic mask on the illuminated side collects light through SPP coupling, and SPP on the exit side of metallic mask redistributes the light into nanoscale spatial distribution, which can be used to fabricate nanostructures. Preliminary numerical simulations support the experimental results.

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