ABSTRAKPenelitian ini bertujuan menganalisis distribusi medan dan relasi dispersi gelombangelektromagnetik pada antaramuka gradasi Right handed material-lefthanded metamaterial (RH-LH) menggunakan Asymptotic Iteration Method (AIM).Analisis distribusi medan dan relasi dispersi gelombang melalui struktur RH-LHdikerjakan dengan pemodelan. Sifat gradasi RH-LH didesain dari fungsi spatialhiperbolik dengan variasi gradasi. Persamaan diferensial gelombang elektromagnetikdalam antarmuka dibangun menggunakan Persamaan Maxwell untuk medianonkonduktor (tanpa rapat muatan) dengan permetivitas dan permeabilitas takhomogen. Selanjutnya persamaan diferensial tersebut dikonversi ke persamaandiferensial biasa orde dua homogen dalam kasus satu dimensi sehingga persamaanMaxwell dapat diselesaikan secara analitik dalam domain ini.Penelitian dilaksanakan melalui studi literatur untuk menyelesaikan persamaandiferensial biasa orde dua homogen. Terdapat banyak cara untuk mendapatkansolusi eksak antara lain dengan menggunakan penyelesaian hipergeometri, metodesupersimetri mekanika kuantum (SUSY QM), metode Nikiforov-Uvarov (N.U)dan baru-baru ini telah digunakan AIM. Secara khsus penyelesaian analitikdistribusi medan (egenfunction) dan relasi dispersi (eigenvalue) dapat diperolehmenggunakan AIM jika Hamiltonian sistem berbentuk seperti osilator harmonik.Penyelesaian persamaan diferensial menggunakan AIM telah diperoleh untukberbagai kasus antarmuka gradasi RH-LH antara lain: gradasi epsilon, gradasi mu,gradasi matched medium, gradasi nonmatched medium. Secara umum solusi distribusimedan dan relasi dispersi gelombang elektromagnetik diberikan pada limitdomain antarmuka RH-LH dekat dengan titik ordinary.Kata Kunci:antarmuka garadsi, right handed, left handed, metamaterial, asymptotic iterationmethod, transverse magneticABSTRACTThis study aimed to analyze the field distribution and relation dispersion of electromagneticwaves at the graded interface Right Handed-Left Handed metamaterial(RH-LH) using Asymptotic Iteration Method (AIM). Analysis of field distributionand dispersion relation waves through the structure of the RH-LH is done withmodeling. RH-LH gradation properties of functions designed with a hyperbolicspatial variation of gradation. Furthermore, differential equations are convertedinto second order homogeneous ordinary differential equations in the case ofone-dimensional, so the Maxwell equations can be solved analytically in thisdomain.The research was conducted through the study of literature to solve second orderhomogeneous ordinary differential equations. There are many ways to get the exactsolution, such as using hypergeometry, supersymmetric quantum mechanics (SUSYQM), Nikiforov-Uvarov (NU) and recently has been used AIM. In particular, theanalytic solution of the field distribution (egenfunction) and the dispersion relation(eigenvalue) can be obtained using AIM if the Hamiltonian system shaped like aharmonic oscillator.Solutions of differential equations using AIM has been obtained for various cases ofgradation RH-LH interfaces include: gradation epsilon, mu, matched medium andnon-matched medium. In general, the solution of field distribution and dispersionrelation of electromagnetic waves given on the domain limit RH-LH interface closeto ordinary point.Key words:graded interface, right handed, left handed, metamaterial, asymptotic iterationmethod, transverse magnetic