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