Kyosuke Sakai

Sub-wavelength focal spot with long depth of focus generated by radially polarized, narrow-width annular beam

We demonstrate the formation of a sub-wavelength focal spot with a long depth of focus using a radially polarized, narrow-width annular beam. Theoretical analysis predicts that a tighter focal spot (approximately 0.4 lambda) and longer depth of focus (more than 4 lambda) can be formed by a longitudinal electric field when the width of the annular part of the beam is decreased. Experimental measurements using a radially polarized beam from a photonic crystal laser agree well with these predictions. Tight focal spots with long depths of focus have great potential for use in high-tolerance, high-resolution applications in optical systems.

Lasing band-edge identification for a surface-emitting photonic crystal laser

The possibility of single-mode oscillation over a large cavity area for photonic crystal lasers emitting at the photonic band edge has resulted in much interest in such materials for new forms of solid-state laser. In this paper, we measure the photonic bandstructure in our sample and identify the lasing band edge. By mapping out the bandstructure at the /spl Gamma/-point, we have observed fine structure at the band edge. The experimental results are in good agreement with the theoretically predicted bandstructure. Above threshold, we observe a lasing peak at 965 nm at one of the band edges. The far-field distribution of the laser is measured, showing an annular profile and azimuthal polarization. Calculations on the far-field distribution at the lasing band edge suggest the annular profile is due to an anti-symmetric resonant mode.

Two-dimensional coupled wave theory for square-lattice photonic-crystal lasers with TM-polarization

We present a useful framework based on the coupled-wave theory, through which we can survey the resonant modes of TM polarization in 2D photonic-crystal lasers and understand their properties in detail. Through numerical calculations, we clarify their threshold gains, deviations from the Bragg frequency and field distributions. We find that the lasing mode can be selected by manipulating the hole-filling factor or the boundary reflection.

Higher-order vector beams produced by photonic-crystal lasers

We have successfully generated vector beams with higher-order polarization states using photonic-crystal lasers. We have analyzed and designed lattice structures that provide cavity modes with different symmetries. Fabricated devices based on these lattice structures produced doughnut-shaped vector beams, with symmetries corresponding to the cavity modes. Our study enables the systematic analysis of vector beams, which we expect will lead to applications such as high-resolution microscopy, laser processing, and optical trapping.

Coupled-Wave Theory for Square-Lattice Photonic Crystal Lasers With TE Polarization

We present a coupled-wave analysis for square-lattice photonic crystal lasers with transverse electric polarization. A model consisting of eight plane waves coupled by Bragg diffraction is used to describe two-dimensional optical coupling. The resonant frequencies and threshold criteria for the modes of oscillation have been determined for the case of index periodicity with a lattice of circular holes. The spatial intensity distributions of these resonant modes have also been calculated. For the fundamental modes, we have investigated how the intensity distribution varies as a function of coupling strength. The dependence of the threshold gain of these modes on hole size has also been elucidated. This semianalytical approach provides a comprehensive understanding of square-lattice photonic crystal lasers and allows more effective optimization of their cavity design.

Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode

We propose a coupled-wave model for a square-lattice two-dimensional (2D) photonic crystal (PC) with a transverse electric mode. A set of coupled-wave equations is obtained from this model and it is shown that 2D optical coupling occurs between four light waves propagating in the Γ-X direction via higher-order waves propagating in the Γ-M direction. The expressions for the resonant mode frequencies derived from the coupled-wave equations describe the characteristics of experimental results for the band-edge frequencies of the 2D PC laser.

Three-dimensional coupled-wave model for square-lattice photonic crystal lasers with transverse electric polarization: A general approach

A general coupled-wave model is presented for square-lattice photonic crystal (PC) lasers with transverse-electric polarization. This model presents a realistic treatment of the full three-dimensional structure of typical laser devices by incorporating the surface emission and high-order coupling effects. Numerical examples based on our model are presented for various PC structures with different air-hole shapes. The accuracy of the results is verified using three-dimensional finite-difference time-domain simulations. Using this model, we demonstrate that the PC lattice with asymmetric air holes can give rise to a high-output power, efficient device.

Three-dimensional coupled-wave analysis for square-lattice photonic crystal surface emitting lasers with transverse-electric polarization: finite-size effects

We develop a coupled-wave model that is capable of treating finite-size square-lattice photonic crystal surface emitting lasers with transverse-electric polarization. Various properties of interest including threshold gain, mode frequency, field intensity envelope within the device, far-field pattern, as well as polarization and divergence angle of the output beam for the band-edge modes are calculated. Theoretical predictions of the lowest threshold mode and the output beam profile are in good agreement with our experimental findings. In particular, we show that, contrary to the infinite periodic case, the finite length of the device significantly affects surface emission and mode selection properties of the laser device.

Coupled-wave model for triangular-lattice photonic crystal with transverse electric polarization

We present a coupled-wave model for a triangular-lattice two-dimensional (2D) photonic crystal (PC) with a transverse electric (TE) polarization and derive a set of coupled-wave equations. We use these equations to obtain analytic expressions that describe the relations between the resonant mode frequencies and the coupling constants. We calculate the resonant mode frequencies for a PC composed of circular holes. These agree well with the frequencies calculated using the 2D plane wave expansion method. We also evaluate the coupling constants of fabricated samples using their measured resonant mode frequencies. Our analytic expressions allow the design and evaluation of feedback strength in triangular-lattice 2D PC cavities.

Focusing properties of vector vortex beams emitted by photonic-crystal lasers

We experimentally investigate the focusing properties of first- and second-order vector beams and vector vortex beams generated by photonic-crystal lasers. When the azimuthal indices of the vector beam (l) and the phase dependence (n) match, strong intensity appears at the center of focus. Our theoretical analyses agree well with the experimental results and predict that the central intensity has circular polarization.