Three-dimensional Coupled-wave Theory Research Articles

Simulation of Photonic-Crystal Surface-Emitting Lasers with Air-Hole and Air-Pillar Structures

Photonic-crystal surface-emitting lasers (PC-SELs), with and without regrowth, are theoretically simplified as air-hole and air-pillar structures, respectively. In this paper, square-latticed air-hole and air-pillar PC-SELs are simulated by a three-dimensional coupled-wave theory model and the design guideline is illustrated with a PC basis of a right isosceles triangular and double circular shapes. The optimum PC filling factor is determined by infinite PC cavity analysis and the slope efficiency of finite-size PC-SEL is then calculated for the lowest threshold band-edge mode. In comparison with air-hole PC-SEL, air-pillar PC-SEL exhibits lower threshold gain, larger gain discrimination but lower slope efficiency. To achieve slope efficiency of comparable value, the cavity area of air-pillar PC-SEL is about four times larger than that of air-hole PC-SEL.

Modulated photonic-crystal surface-emitting laser with elliptical lattice points for two-dimensional coupling enhancement

Modulated photonic-crystal surface-emitting lasers (M-PCSELs) are new semiconductor lasers that can emit a laser beam in arbitrary directions. Therefore, they can be regarded as a next-generation light source for light detection and ranging. In this manuscript, we numerically investigate the characteristics of M-PCSELs, including one- and two-dimensional optical coupling constants and radiation constants, by using three-dimensional coupled wave theory. We also carry out lattice point designs and show that the two-dimensional optical coupling can be enhanced by more than four times over our previous M-PCSEL devices by employing elliptical lattice points. Moreover, we find that two-dimensional optical coupling can be maintained even when large lattice point position modulations are introduced for large radiation constants. These results indicate that more stable two-dimensional oscillation and a higher slope efficiency are expected in M-PCSELs with elliptical lattice points.

Erratum: Comprehensive analysis of photonic-crystal surface-emitting lasers via time-dependent three-dimensional coupled-wave theory [Phys. Rev. B 99 , 035308 (2019)

Received 8 April 2019DOI:https://doi.org/10.1103/PhysRevB.99.169904©2019 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNanophotonicsPhotonic crystalsPhysical SystemsIII-V semiconductorsPhotonic crystal lasersTechniquesElectromagnetic field calculationsCondensed Matter, Materials & Applied Physics

Comprehensive analysis of photonic-crystal surface-emitting lasers via time-dependent three-dimensional coupled-wave theory

We develop a time-dependent three-dimensional coupled-wave theory (3D-CWT) for the transient analysis of photonic-crystal surface-emitting lasers (PCSELs). Our model takes into account the temporal evolution of both the photon and carrier distribution inside PCSELs, which enable the analysis of various above-threshold lasing characteristics including the relaxation oscillation, spatial hole burning, and multimode lasing. With the developed time-dependent 3D-CWT, we perform transient analysis of the high-power, high-beam-quality PCSELs with double-lattice photonic crystals and reproduce the experimental results of near-field patterns and lasing spectra under high current injection. Our theory enables the comprehensive understanding of the device physics of PCSELs toward the realization of higher-power continuous-wave lasing and short-pulse lasing.

Three-dimensional coupled-wave theory for the guided mode resonance in photonic crystal slabs: TM-like polarization.

A general coupled-wave theory is presented for the guided resonance in photonic crystal (PhC) slabs with TM-like polarization. Numerical results based on our model are presented with finite-difference time-domain validations. The proposed analysis facilitates comprehensive understanding of the physics of guided resonance in PhC slabs and provides guidance for its applications.

Three-dimensional coupled-wave analysis for triangular-lattice photonic-crystal surface-emitting lasers with transverse-electric polarization

Three-dimensional coupled-wave theory is extended to model triangular-lattice photonic-crystal surface-emitting lasers with transverse-electric polarization. A generalized coupled-wave equation is derived to describe the sixfold symmetry of the eigenmodes in a triangular lattice. The extended theory includes the effects of both surface radiation and in-plane losses in a finite-size laser structure. Modal properties of interest including the band structure, radiation constant, threshold gain, field intensity profile, and far-field pattern (FFP) are calculated. The calculated band structure and FFP, as well as the predicted lasing mode, agree well with experimental observations. The effect of air-hole size on mode selection is also studied and confirmed by experiment.

Three-dimensional coupled-wave theory analysis of a centered-rectangular lattice photonic crystal laser with a transverse-electric-like mode

A general coupled-wave theory analysis is presented for centered-rectangular lattice photonic crystal (PC) lasers with transverse-electric-like polarization. This analysis affords a realistic approach to the treatment of the full three-dimensional structure of the laser devices by incorporating surface emission and high-order coupling effects. Band structures and radiation constants of band-edge modes are calculated and discussed for different lattice angles, and their accuracies are verified via experiments and numerical simulations. Thus, the proposed analysis facilitates comprehensive understanding of the physics of PC surface-emitting lasers (PC-SELs), and it reveals extra degrees of structural flexibility for developing novel PC-SEL devices.

Three-dimensional coupled wave study for finite-sized anisotropic volume holographic gratings under ultrashort pulsed beam readout

The three-dimensional coupled wave theory is extended to systematically investigate the diffraction properties of finite-sized anisotropic volume holographic gratings (VHGs) under ultrashort pulsed beam (UPB) readout. The effects of the grating geometrical size and the polarizations of the recording and readout beams on the diffraction properties are presented, in particular under the influence of grating material dispersion. The wavelength selectivity of the finite-sized VHG is analyzed. The wavelength selectivity determines the intensity distributions of the transmitted and diffracted pulsed beams along the output face of the VHG. The distortion and widening of the diffracted pulsed beams are different for different points on the output face, as is numerically shown for a VHG recorded in a LiNbO3 crystal. The beam quality is analyzed, and the variations of the total diffraction efficiency are shown in relation to the geometrical size of the grating and the temporal width of the readout UPB. In addition, the diffraction properties of the finite-sized and one-dimensional VHG for pulsed and continuous-wave readout are compared. The study shows the potential application of VHGs in controlling spatial and temporal features of UPBs simultaneously.

Polarizing properties of crossed-beam volume holographic gratings

Abstract The polarizing properties of crossed-beam volume holographic gratings recorded by arbitrary polarization plane waves are considered, using the three-dimensional coupled wave theory. Simple analysis expressions for the amplitude profiles of the transmitted and diffracted waves are obtained. Detailed diffraction characteristics for the case of a finite plane wave of uniform amplitude distribution are presented. We discuss the influence of the polarized azimuths of the incident wave both at recording and at reconstruction on the amplitude profiles of the transmitted and diffracted waves.