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We study the Goos-Hanchen (GH) effect in a graphene-substrate system comprehensively by using the transfer matrix method. It is revealed that the magnitude and sign of GH shifts are closely related to the imaginary part of graphene conductivity in the case of the fixed refractive index of substrate, while the Brewster angle position is largely influenced by the real part of conductivity. Further studies show that the position of Brewster angle keeps invariable when the Fermi energy exceeds 0.4 eV, and the magnitude and sign of GH shifts at a certain Brewster angle are changed only by Fermi energy. On the basis of these findings, a scheme to control the positive and negative GH shifts precisely is proposed and demonstrated by instances. We first adjust the refractive index of substrate to control the Brewster angle position under the condition of the Fermi energy exceeding 0.4 eV, and then adjust the Fermi energy to make the GH shift approach target value. Finally, we apply these precise control properties of GH shift to design a refractive index detector with adjustable sensitivity coefficient. These researches may have potential applications in refractive index sensor with high sensitivity and precise measurement of graphene parameters.

We investigate the spin-dependent splitting systematically by considering spin Hall effect of light and in-plane spin separation of light simultaneously, when a Gaussian beam is reflected from an air-glass interface. It is revealed that there exhibits a spin-dependent splitting rotation with the increase of the polarization angle, and the rotation direction and speed can be controlled by the incident angle. Remarkably, with the polarization angle increasing from 0 $^\circ$ to 90 $^\circ$ , the splitting rotates 180 $^\circ$ clockwise in total when the incident angle is less than Brewster angle, whereas it rotates an angle under 90 $^\circ$ counterclockwise first and then clockwise return to the original position when the incident angle is larger than Brewster angle. Their initial rotation speeds of splitting to $x_r$ direction both become larger as the incident angle approaches to Brewster angle, therefore when the incident angle is equal to Brewster angle, the splitting only forms a 90 $^\circ$ clockwise rotation. These general laws of spin-dependent splitting rotation are demonstrated by instances, and the rotation behaviors are considered as a result of various proportions of transverse spin separation and in-plane spin separation. This research provides a feasible way to manipulate the photon spin in optical nanodevice.

We investigate the spin-dependent splitting systematically by considering spin Hall effect of light and in-plane spin separation of light simultaneously, when a Gaussian beam is reflected from an air-glass interface. It is revealed that there exhibits a spin-dependent splitting rotation with the increase of the polarization angle, and the rotation direction and speed can be controlled by the incident angle. Remarkably, with the polarization angle increasing from 0° to 90°, the splitting rotates 180° clockwise in total when the incident angle is less than Brewster angle, whereas it rotates an angle under 90° counterclockwise first and then clockwise return to the original position when the incident angle is larger than Brewster angle. Their initial rotation speeds of splitting to xr direction both become larger as the incident angle approaches to Brewster angle, therefore when the incident angle is equal to Brewster angle, the splitting only forms a 90° clockwise rotation. These general laws of spin-dependent splitting rotation are demonstrated by instances, and the rotation behaviors are considered as a result of various proportions of transverse spin separation and in-plane spin separation. This research provides a feasible way to manipulate the photon spin in optical nanodevice.

A novel approach is presented for waveguide mode selection by using thin-film spatial filters embedded in multimode waveguides. The waveguide modes are allowed to pass through the spatial filters if and when their mode angles fall within the angle-domain bandwidth of the filters. Consequently the waveguide modes are selectable with varied angle-domain bandwidth of the spatial filters. This approach is relatively simple, cost-effective and features good suppression effect of high-order modes, and is suitable for high-power laser systems.

We studied the electromagnetic scattering from cylindrical cloaks with a quantity of discrete homogeneous layers. The scattering cross sections (SCS) of electromagnetic cloaks designed by different coordinate transformation function are discussed by using a polynomial transform function. The results show that besides the inner boundary, the interfaces between the adjacent discrete anisotropic layers inside the cloak also affect its performance. Through the proper design of the coordinate transformation order, the electromagnetic field distribution insides the cloak can be optimized and the invisible performance of the cloak could be improved with minimization of SCS. These results provide a better way of designing the cloak to achieve low scattering with only a few layers of anisotropic metamaterials.

By using the spatial properties of zero-index gaps in one-dimensional metamaterial photonic crystals, we have designed low-pass spatial filters with small angle-domain bandwidth less than 10 degrees. It is demonstrated by transfer matrix method that the small angle-domain bandwidth and roll-off factor of the spatial filters can be adjusted by changing the structure parameters of the metamaterial photonic crystals. In addition, the spatial filters have absolute polarization-independent properties compared with previous photonic crystal spatial filters. These spatial filters with small angle-domain bandwidth may be applied to the laser science in the future, and decrease the space occupied by the traditional spatial filters.

Based on the transfer matrix theory, general conditions of polarization-independent transmissions in one-dimensional photonic crystals are derived. It is shown that the polarization-independent transmissions are obtained in photonic crystals consisting of two alternating layers with the same refraction index and optical thickness as well as the mutually reciprocal wave impedance. By using two different photonic crystals satisfying the above relation to constitute the light quantum-well structures, the structures have polarization-independent transmission properties. When a defective layer with wave impedance of 1 is introduced in the photonic crystals, the defective photonic crystals also have the polarization-independent transmission properties. In addition, polarization-independent low-pass spatial filters are achieved based on these photonic crystal structures.

The symmetrical confined states are found in photonic quantum-well structures with single-negative materials, in which the photonic barrier is based on the zero-effective-phase gap. The number and frequencies of the symmetrical confined states can be tuned by varying the period number and thicknesses of the well photonic crystal, respectively. Furthermore, the symmetrical confined states of the structures are less sensitive to the incident angle and polarization, compared with previous confined states of photonic quantum-well structures based on the Bragg or zero-average-index gap. The structures open a promising way to fabricate symmetrically tunable and omnidirectional multichannel filters for future dense wavelength division multiplexing applications.

A new application of one-dimensional photonic crystals containing negative-index materials is proposed as low-pass spatial filters. Through optimizing the parameters of defect layer, a series of polarization-independent defect modes in the zero-average-index gap of the photonic crystals are obtained with the increase of the incident angle. Based on these defect modes, polarization-independent low-pass spatial filters are designed. The spatial-frequency bandwidth of the spatial filters can be adjusted by changing the period number of the defective photonic crystal structures. In addition, the effect of the losses of negative-index materials on the spatial filters is considered.

Observation of photonic spin Hall effect (SHE) manifested by spin-dependent splitting of light in a dielectric-based birefringent metasurface is reported experimentally. By designing the metasurface with homogeneous phase retardation but space-variant optical axis directions, we govern the photonic SHE via space-variant Pancharatnam-Berry phase originated from the local polarization manipulation of the metasurface, essentially, the spin-orbit interaction between the light and the metasurface. Modulating the polarization distribution of the incident light and/or the structure geometry of the metasurface, the photonic SHE could be tunable. This type of metasurface offers an effective way to manipulate the spin-polarized photons and a route for spin-controlled nanophotonic applications.

We propose a new type of wavelength division demultiplexer composed of a photonic crystal waveguide with asymmetric corrugated exit surface. The focus displacement for different symmetric corrugated surfaces is relative to the intensity of the excited surface mode. By systematically investigating the effects of the parameters of the corrugated surface on the focus shift, we demonstrate an on-axis focus by a photonic crystal waveguide with an asymmetric corrugated exit surface at a specific wavelength. The precise equivalences of surface modes at each side of the exit surface are broken. Thus, for the light source with other wavelengths, the emerging beams are off-axis focused at different directions, similar to the function of a wavelength division demultiplexer.