Abstrak |
: |
ABSTRAK Penelitian ini bertujuan menganalisis distribusi medan dan relasi dispersi gelombang elektromagnetik pada antaramuka gradasi Right handed material-left handed metamaterial (RH-LH) menggunakan Asymptotic Iteration Method (AIM). Analisis distribusi medan dan relasi dispersi gelombang melalui struktur RH-LH dikerjakan dengan pemodelan. Sifat gradasi RH-LH didesain dari fungsi spatial hiperbolik dengan variasi gradasi. Persamaan diferensial gelombang elektromagnetik dalam antarmuka dibangun menggunakan Persamaan Maxwell untuk media nonkonduktor (tanpa rapat muatan) dengan permetivitas dan permeabilitas tak homogen. Selanjutnya persamaan diferensial tersebut dikonversi ke persamaan diferensial biasa orde dua homogen dalam kasus satu dimensi sehingga persamaan Maxwell dapat diselesaikan secara analitik dalam domain ini. Penelitian dilaksanakan melalui studi literatur untuk menyelesaikan persamaan diferensial biasa orde dua homogen. Terdapat banyak cara untuk mendapatkan solusi eksak antara lain dengan menggunakan penyelesaian hipergeometri, metode supersimetri mekanika kuantum (SUSY QM), metode Nikiforov-Uvarov (N.U) dan baru-baru ini telah digunakan AIM. Secara khsus penyelesaian analitik distribusi medan (egenfunction) dan relasi dispersi (eigenvalue) dapat diperoleh menggunakan AIM jika Hamiltonian sistem berbentuk seperti osilator harmonik. Penyelesaian persamaan diferensial menggunakan AIM telah diperoleh untuk berbagai kasus antarmuka gradasi RH-LH antara lain: gradasi epsilon, gradasi mu, gradasi matched medium, gradasi nonmatched medium. Secara umum solusi distribusi medan dan relasi dispersi gelombang elektromagnetik diberikan pada limit domain antarmuka RH-LH dekat dengan titik ordinary. Kata Kunci: antarmuka garadsi, right handed, left handed, metamaterial, asymptotic iteration method, transverse magnetic ABSTRACT This study aimed to analyze the field distribution and relation dispersion of electromagnetic waves at the graded interface Right Handed-Left Handed metamaterial (RH-LH) using Asymptotic Iteration Method (AIM). Analysis of field distribution and dispersion relation waves through the structure of the RH-LH is done with modeling. RH-LH gradation properties of functions designed with a hyperbolic spatial variation of gradation. Furthermore, differential equations are converted into second order homogeneous ordinary differential equations in the case of one-dimensional, so the Maxwell equations can be solved analytically in this domain. The research was conducted through the study of literature to solve second order homogeneous ordinary differential equations. There are many ways to get the exact solution, such as using hypergeometry, supersymmetric quantum mechanics (SUSY QM), Nikiforov-Uvarov (NU) and recently has been used AIM. In particular, the analytic solution of the field distribution (egenfunction) and the dispersion relation (eigenvalue) can be obtained using AIM if the Hamiltonian system shaped like a harmonic oscillator. Solutions of differential equations using AIM has been obtained for various cases of gradation RH-LH interfaces include: gradation epsilon, mu, matched medium and non-matched medium. In general, the solution of field distribution and dispersion relation of electromagnetic waves given on the domain limit RH-LH interface close to ordinary point. Key words: graded interface, right handed, left handed, metamaterial, asymptotic iteration method, transverse magnetic |