|dc.description.abstract||Coupled-mode theory has been applied to various fields of endeavor from waveguide splitters/combiners and molecular sensing to light-matter interactions. Metamaterials, engineered periodic or aperiodic structures, are employed to sense molecular vibrational fingerprints in the mid to long infrared wavelengths. A metasurface, a 2D metamaterial, can be designed such that it has a resonance at a molecular vibrational frequency. Mode splitting results from the coupling of two electromagnetic field distributions, or modes, spatially and/or temporally. Metamaterial and molecular resonance coupling is a result of near field interaction. Fano resonances have an asymmetric line-shape that results from the coupling of a continuum and a discrete state in a quantum description or a bright and dark mode in a classical description. Analogous to the atomic system, a bright mode exhibits a broad resonance or short lifetime that couples strongly with incident far field radiation while, on the other hand, a dark mode provides a sharp quality factor, Q, resonance or a long lifetime that couples weakly with an excitation far field. Polaritons are quasiparticles that result from strong coupling of light and matter. Surface plasmon polaritons (SPPs) result from the coupling between plasmons, or free electrons in a noble metal, and electromagnetic waves. The SPP mode exists as a tightly bound transverse magnetic (TM) surface mode on a metal/dielectric interface. However, SPPs only exist in a spectrum from the ultraviolet to the near infrared (IR) for a noble metal. For polariton applications in the mid to long infrared range phonon polaritons are required. Surface phonon polaritons (SPhPs), similar to SPPs, are a surface TM mode on a polar dielectric/dielectric interface. However, SPhPs only exist in a spectral region known as the reststrahlen band where the polar dielectric acts like a metal, i.e., negative real permittivity. Hexagonal boron nitride (hBN) is a van der Waals crystal with naturally occurring hyperbolic dispersion hat has been shown to support phonon polaritons in two distinct reststrahlen bands. The upper reststrahlen band, ranging from 1630cm-1 (6.135 μm) to 1360 cm-1 (7.353 μm), provides highly volume-confined phonon polaritons. The lower reststrahlen band, ranging from 825 cm-1 (12.12 μm) to 760 cm-1 (13.16 μm), exhibits a negative index (or negative dispersion) and provides ultra-slow sub-diffraction volume-confined phonon polaritons. The subdiffraction confinement and ultra-slow nature of the type I hyperbolic phonon polaritons (HPhPs) are desirable properties for mid to long IR wavelength sensing.
In this dissertation, a carbonyl oxide bond vibrational resonance in poly(methyl methacrylate) (PMMA) will be used as an analyte. A wide-field-of-view perfectly absorbing metamaterial (PAMM) is then designed such that the metamaterial resonance couples to a molecular vibrational resonance in the analyte. Tuning the relationship between internal (absorption) and external (scattering) damping or loss in the PAMM results in both electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) response in the PAMM-analyte coupled system. Next, Fano resonance metamaterials (FRMM) coupled to the PMMA molecular resonance are investigated. FRMM’s asymmetric reflection spectrum is a result of hybridization of symmetric (bright) and asymmetric (dark) plasmon modes supported by the metamaterial’s geometry. The addition of the analyte results in multi-mode coupling between the FRMM’s modes and molecular resonance. Multi-mode coupling via a FRMM has advantages in selectivity and sensitivity by the tailoring of the metamaterial resonance prior to the introduction of the molecular resonance.
In addition to metamaterial-based sensing, different hybrid phononic waveguide geometries are investigated in this dissertation. The first geometry considered is a 4H-SiC (silicon carbide) substrate with a GaN spacer material and GaAs tracer. The results presented in this dissertation using a 4H-SiC substrate are the first practical analysis of a hybrid phononic waveguide in the mid to long IR. The 4H-SiC enhanced hybrid waveguide geometry is then used to create two fundamental optical waveguiding devices: an optical directional coupler (ODC) and a Mach-Zehnder interferometer (MZI). The phonon polariton enhanced ODC and MZI in the mid to long IR presented in this dissertation are both original contributions. Hyperbolic phonon polariton enhance waveguides using hBN in the mid to long IR of similar confident of approximately 5x10-2(λ0/2)2 have been shown to provide propagation lengths of 58 λ0 and 20 λ0 for type I and II HPhP enhanced waveguiding respectively. Unique and novel coupling between ultraslow negatively dispersive type I HPhP modes and positive dispersive high index waveguide modes are analyzed. The coupling between the type I HPhP modes and high index waveguide modes result in upper hybrid modes with forward and backward propagating modes that inherited the type I HPhP’s slow waves with group velocities ranging from 0.065c to 0.03c.||en_US