研究目的
Investigating light propagation in one-dimensional (1D) photonic crystals (PCs) enclosed in a rectangular waveguide to achieve a complete photonic band gap (PBG) while avoiding the difficulty in fabricating 3D PCs.
研究成果
A complete PBG can exist in quasi-1D PCs, categorized into three types: (1) below the cutoff frequency of the fundamental TE mode, (2) within the PBG of the fundamental TE mode but below the cutoff frequency of the next higher order mode, and (3) within an overlap of the PBGs of either TE modes, TM modes, or both. These results are of general importance and relevance to the dipole radiation or spontaneous emission by an atom in quasi-1D periodic structures and may have applications in future photonic quantum technologies.
研究不足
The study is limited to quasi-1D photonic crystals enclosed in a rectangular waveguide, and the determination of a complete PBG must be carefully conducted and verified. The model might be easier for experimental validation in a millimeter wave frequency range while the optical counterpart might be possibly pursued as well.
1：Experimental Design and Method Selection:
The study employs a transfer matrix approach to discretize the dielectric function profile of the heterostructure and calculates transmission functions by matching boundary conditions at each interface. The band structures are obtained by solving eigenvalue equations with proper periodic boundary conditions following the Bloch theorem.
2：Sample Selection and Data Sources:
The study considers a WR28 (7.11 mm × 3.555 mm) rectangular waveguide, usually used for Ka-band millimeter waves, with periodic dielectric heterostructure arranged along the longitudinal (z) direction to form quasi-1D PCs.
3：11 mm × 555 mm) rectangular waveguide, usually used for Ka-band millimeter waves, with periodic dielectric heterostructure arranged along the longitudinal (z) direction to form quasi-1D PCs.
List of Experimental Equipment and Materials:
3. List of Experimental Equipment and Materials: The dielectric constants used are ε1 = 3.8 (quartz) and ε2 = 1.0 (air), with thicknesses varied as (t1, t2) = (1.00, 3.30), (1.00, 3.60), and (1.00, 3.90) mm.
4：8 (quartz) and ε2 = 0 (air), with thicknesses varied as (t1, t2) = (00, 30), (00, 60), and (00, 90) mm.
Experimental Procedures and Operational Workflow:
4. Experimental Procedures and Operational Workflow: The transmittances for both the TE and TM modes through a periodic multilayer heterostructure in a rectangular waveguide are calculated. The corresponding band structures are obtained by solving the eigenvalue equations with proper periodic boundary conditions.
5：Data Analysis Methods:
The formulas for determining the PDOS are derived to facilitate identifying the photonic band gaps for all the modes residing in the system.
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