Matrix Formulation for IsotropicLayered Media
Matrix Formulation for Isotropic Layered Media
2X2 Matrix Formulation For a Thin Film. The dielectric structure is described byx<0,(n1)A之0<x<d,n(×) =3n2,min2n3d<x(n3)AiA2A2A3.The electric field can beB1B'2B2B'3xwritten asx=0x=dE = E(x)ei(αt-βz)
2Χ2 Matrix Formulation For a Thin Film • The dielectric structure is described by • The electric field can be written as
2X2 Matrix Formulation For a Thin Film The electric field E(x) consists of a right-travelingwave and a left-traveling wave and can be writtenAzasmn2n3E(x) = Re-ikxx + Leikxx = A(x) + B(x)A2A2A'3A Let A(x) represent the amplitudeB1B2B2B'3of the right-traveling wave andXx=0x=dB(x) be that of the left-travelingone
2Χ2 Matrix Formulation For a Thin Film • The electric field E(x) consists of a right-traveling wave and a left-traveling wave and can be written as • Let A(x) represent the amplitude of the right-traveling wave and B(x) be that of the left-traveling one
2X2 Matrix Formulation For a Thin Film. To illustratethe matrix method, we defineAi = A(0-) B1 = B(0-)42nin3n2A2 = A(0+) B2 = B(0+)A'3A2A24A2 = A(d-) B2 = B(d-)B2B2B'3Bxx=0x=dA3 = A(d+) B3 = B(d+)
2Χ2 Matrix Formulation For a Thin Film • To illustrate the matrix method, we define
2X2 Matrix Formulation For a Thin Film If we represent the two amplitudes of E(x) ascolumn vectors, the column vectors arerelated by(A2)(A2(A1)D12D1D一?(B1)(B2)(B2 )(A2)(A2eio,A0B(B2)e-i02(B2(B20(A3)(A3)(A2D231D3D3(B3 )(B3)(B2)
2Χ2 Matrix Formulation For a Thin Film • If we represent the two amplitudes of E(x) as column vectors, the column vectors are related by