Уравнения Максвелла в комплексной форме

ɉɪɟɢɦɭɳɟɫɬɜɚ ɨɬ ɩɪɢɦɟɧɟɧɢɹ ɜɨɥɨɤɨɧɧɨ-ɨɩɬɢɱɟɫɤɢɯɥɢɧɢɣ ɫɜɹɡɢ (ȼɈɅɋ) ɧɚɫɬɨɥɶɤɨ ɡɧɚɱɢɬɟɥɶɧɵ, ɱɬɨ ɜ ɧɚɫɬɨɹɳɟɟɜɪɟɦɹ ɷɬɢ ɥɢɧɢɢ ɫɜɹɡɢ ɨɱɟɧɶ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɥɹ ɩɟɪɟɞɚɱɢ ɢɧɮɨɪɦɚɰɢɢ.Ɂɧɚɱɟɧɢɟ ɭɪɚɜɧɟɧɢɣ Ɇɚɤɫɜɟɥɥɚ ɤɚɤ ɨɫɧɨɜɚɧɢɣ ɬɟɨɪɢɢ ɷɥɟɤɬɪɨɦɚɝɧɟɬɢɡɦɚ ɱɪɟɡɜɵɱɚɣɧɨ ɜɟɥɢɤɨ. Ⱦɥɹ ɢɧɠɟɧɟɪɚ ɜ ɩɟɪɜɭɸɨɱɟɪɟɞɶ ɜɚɠɧɨ, ɱɬɨ ɭɪɚɜɧɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ ɞɚɸɬ ɜɨɡɦɨɠɧɨɫɬɶ ɢɫɫɥɟɞɨɜɚɬɶ ɥɸɛɵɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɩɪɨɰɟɫɫɵ.1.2.

ɍɪɚɜɧɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ1.3. ɍɪɚɜɧɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ ɜ ɤɨɦɩɥɟɤɫɧɨɣ ɮɨɪɦɟɁɚɩɢɲɟɦ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ Ɇɚɤɫɜɟɥɥɚ, ɤɨɬɨɪɵɟ ɜɤɥɸɱɚɸɬɜ ɫɟɛɹ ɨɫɧɨɜɚɧɢɟ ɬɟɨɪɢɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯɜɨɥɧ ɢ ɹɜɥɹɸɬɫɹ ɩɨɫɬɭɥɚɬɚɦɢ ɬɟɨɪɢɢ:∂Brot E = −,(1.1)∂t∂Drot H =+j,(1.2)∂tdiv B = 0 ,(1.3)div D = ρ .(1.4)Ɂɞɟɫɶ ȿ - ɜɟɤɬɨɪ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, D - ɜɟɤɬɨɪɷɥɟɤɬɪɢɱɟɫɤɨɣ ɢɧɞɭɤɰɢɢ, ȼ - ɜɟɤɬɨɪ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ, ɇ ɜɟɤɬɨɪ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, j - ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ ɩɪɨɜɨɞɢɦɨɫɬɢ, ρ - ɨɛɴɟɦɧɚɹ ɩɥɨɬɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɡɚɪɹɞɨɜ.Ɏɨɪɦɭɥɵ (1.1)-(1.4) ɜɵɪɚɠɚɸɬ ɭɪɚɜɧɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ ɜ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣ ɮɨɪɦɟ.ɍɪɚɜɧɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ ɞɨɩɨɥɧɹɸɬɫɹ ɫɥɟɞɭɸɳɢɦɢ ɭɪɚɜɧɟɧɢɹɦɢ:D = ε ε0 E ,(1.5)B = µ µ0 H ,(1.6)Ɋɚɫɫɦɨɬɪɢɦ ɩɨɥɹ, ɦɟɧɹɸɳɢɟɫɹ ɩɨ ɝɚɪɦɨɧɢɱɟɫɤɨɦɭ ɡɚɤɨɧɭ:E = E 0 cos(ωt − kr) ,(1.8)H = H 0 cos(ωt − kr).Ɂɞɟɫɶ ȿ -ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɇ- ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, k - ɜɨɥɧɨɜɨɣ ɜɟɤɬɨɪ, r - ɪɚɞɢɭɫ-ɜɟɤɬɨɪɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɬɨɱɤɢ.ɂɫɩɨɥɶɡɭɟɦ ɦɟɬɨɞ ɤɨɦɩɥɟɤɫɧɵɯ ɚɦɩɥɢɬɭɞ.

ȼ ɪɚɦɤɚɯ ɷɬɨɝɨɦɟɬɨɞɚ ɜɟɤɬɨɪɚɦ ȿ ɢ ɇ ɩɪɢɜɟɞɟɦ ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɤɨɦɩɥɟɤɫɧɵɟ . ɉɪɢ ɷɬɨɦɱɢɫɥɚ E ɢ H =E ei ωt ,E(1.9)j = σ E + jɫɬ ,(1.7)Ɂɞɟɫɶ ε 0 - ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ, µ 0 -ɦɚɝɧɢɬɧɚɹ ɩɨɫɬɨɹɧɧɚɹ,ε -ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɫɪɟɞɵ, µ - ɦɚɝɧɢɬɧɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɫɪɟɞɵ, σ - ɭɞɟɥɶɧɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ, jɫɬ - ɩɥɨɬɧɨɫɬɶ ɫɬɨɪɨɧɧɢɯ ɬɨɤɨɜ.

(ȼ ɬɚɤɨɣ ɡɚɩɢɫɢ ɫɬɨɪɨɧɧɢɟ ɬɨɤɢ ɫɱɢɬɚɸɬɫɹ ɡɚɞɚɧɧɵɦɢ. Ɉɧɢ ɜɨɡɛɭɠɞɚɸɬ ɩɨɥɹ, ɧɨ ɧɟ ɩɨɪɨɠɞɚɸɬɫɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɦɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɦɢ ɩɨɥɹɦɢ). Ɏɨɪɦɭɥɚ (1.7) ɹɜɥɹɟɬɫɹɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣ ɮɨɪɦɨɣ ɡɚɩɢɫɢ ɡɚɤɨɧɚ Ɉɦɚ.11m =H ei ω t .HmɁɧɚɱɟɧɢɹ ɪɟɚɥɶɧɵɯ ɜɟɤɬɨɪɨɜ ȿ ɢ ɇ ɧɚɯɨɞɹɬɫɹ ɤɚɤ ɞɟɣɫɬɜɢɬɟɥɶɧɵɟ ɱɚɫɬɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɤɨɦɩɥɟɤɫɧɨɝɨ ɜɟɤɬɨɪɚ: ei ω t } ,E = Re {E(1.10)miωtH = Re {H e } .m ɢ H ɧɚɡɵɜɚɸɬɫɹ ɤɨɦɩɥɟɤɫɧɵɦɢ ɚɦɩɥɢȼɟɥɢɱɢɧɵ Emmɬɭɞɚɦɢ ɜɟɤɬɨɪɨɜ ȿ ɢ ɇ. Ʉɨɦɩɥɟɤɫɧɵɟ ɚɦɩɥɢɬɭɞɵ ɡɚɜɢɫɹɬ ɬɨɥɶɤɨ ɨɬ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ ɤɨɨɪɞɢɧɚɬ ɢ ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɜɪɟɦɟɧɢ: =E ( x , y, z ) ( x , y, z )E, H =HmmmmȾɥɹ ɨɛɨɡɧɚɱɟɧɢɹ ɤɨɦɩɥɟɤɫɧɨɣ ɚɦɩɥɢɬɭɞɵ ɛɭɞɟɦ ɫɬɚɜɢɬɶ ɬɨɱɤɭɜɜɟɪɯɭ ɢ ɧɢɠɧɢɣ ɢɧɞɟɤɫ m.ɉɪɢɦɟɪ. Ɋɚɫɫɦɨɬɪɢɦ ɩɥɨɫɤɭɸ ɜɨɥɧɭ, ɪɚɫɩɪɨɫɬɪɚɧɹɸɳɭɸɫɹ ɜɞɨɥɶ ɨɫɢ Oz.

ɉɨɫɬɚɜɢɦ ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɷɬɨɣ ɜɨɥɧɟ (z) = E ⋅ e −ikz . Ⱦɥɹ ɩɟɪɟɯɨɞɚɤɨɦɩɥɟɤɫɧɭɸ ɚɦɩɥɢɬɭɞɭ Em120ɤ ɪɟɚɥɶɧɨɦɭ ɜɟɤɬɨɪɭ ȿ ɧɚɣɞɟɦ ɞɟɣɫɬɜɢɬɟɥɶɧɭɸ ɱɚɫɬɶ ɨɬɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɤɨɦɩɥɟɤɫɧɨɝɨ ɜɟɤɬɨɪɚ:E = Re {E 0 ⋅ e −ikz ⋅ e iωt } = Re {E 0 ⋅ e i (ωt − kz ) } == Re {E 0 cos(ωt − kz) − i sin(ωt − kz)} = E 0 cos(ωt − kz) .ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɢɥɨɫɶ ɯɨɪɨɲɨ ɢɡɜɟɫɬɧɨɟ ɭɪɚɜɧɟɧɢɟɩɥɨɫɤɨɣ ɜɨɥɧɵ, ɪɚɫɩɪɨɫɬɪɚɧɹɸɳɟɣɫɹ ɜ ɩɨɥɨɠɢɬɟɥɶɧɨɦɧɚɩɪɚɜɥɟɧɢɢ ɨɫɢ Oz.ȼ ɦɟɬɨɞɟ ɤɨɦɩɥɟɤɫɧɵɯ ɚɦɩɥɢɬɭɞ ɨɩɟɪɚɰɢɢ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɹ ɩɨ ɜɪɟɦɟɧɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɭɦɧɨɠɟɧɢɸ ɧɚ iω:∂→ iω .(1.11)∂tɉɨɞɫɬɚɜɢɦ ɤɨɦɩɥɟɤɫɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ (1.9) ɜ ɭɪɚɜɧɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ.

ɋ ɭɱɟɬɨɦ (1.11) ɭɪɚɜɧɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ (1.1-1.2) ɦɨɠɧɨɡɚɩɢɫɚɬɶ ɜ ɤɨɦɩɥɟɤɫɧɨɣ ɮɨɪɦɟ:rot E m = − i ωB m ,(1.12) =iωD +j ,rot Hmmm(1.13) , B , H , j - ɤɨɦɩɥɟɤɫɧɵɟ ɚɦɩɥɢɬɭɞɵ ɫɨɨɬɜɟɬɫɬ , Dɝɞɟ Emmmmmɜɭɸɳɢɯ ɜɟɤɬɨɪɨɜ. Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɣ Ɇɚɤɫɜɟɥɥɚ ɜ ɤɨɦɩɥɟɤɫɧɨɣ ɮɨɪɦɟ ɡɚɱɚɫɬɭɸ ɹɜɥɹɟɬɫɹ ɛɨɥɟɟ ɩɪɨɫɬɵɦ, ɬɚɤ ɤɚɤ ɜ ɡɚɩɢɫɢɭɪɚɜɧɟɧɢɣ ɨɬɫɭɬɫɬɜɭɸɬ ɩɪɨɢɡɜɨɞɧɵɟ ɩɨ ɜɪɟɦɟɧɢ. Ⱦɥɹ ɩɟɪɟɯɨɞɚɤ ɧɚɛɥɸɞɚɟɦɵɦ ɜɟɤɬɨɪɚɦ ȿ ɢ ɇ ɞɨɫɬɚɬɨɱɧɨ ɧɚɣɬɢ ɞɟɣɫɬɜɢɬɟɥɶɧɭɸ ɱɚɫɬɶ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɤɨɦɩɥɟɤɫɧɨɝɨ ɜɟɤɬɨɪɚ.ɉɪɢɦɟɱɚɧɢɟ. Ʉɨɦɩɥɟɤɫɧɵɟ ɚɦɩɥɢɬɭɞɵ ɦɨɠɧɨ ɜɜɟɫɬɢ ɢ ɞɪɭɝɢɦ ɫɩɨɫɨɛɨɦ, ɫɨɩɨɫɬɚɜɥɹɹ ɜɟɤɬɨɪɚɦ ȿ ɢ ɇ ɤɨɦɩɥɟɤɫɧɵɟ ɱɢɫɥɚ1.4. Ʉɨɦɩɥɟɤɫɧɚɹ ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶɉɪɟɨɛɪɚɡɭɟɦ ɩɪɚɜɭɸ ɱɚɫɬɶ ɭɪɚɜɧɟɧɢɹ (1.13).

ɉɨɞɫɬɚɜɢɦɜɦɟɫɬɨ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ jm ɡɚɤɨɧ Ɉɦɚ ɜ ɜɢɞɟ (1.7), ɡɚɦɟɧɹɹ ɜɟɤɬɨ ɢ jm:ɪɵ ȿ ɢ j ɤɨɦɩɥɟɤɫɧɵɦɢ ɚɦɩɥɢɬɭɞɚɦɢ Emσɫɬ + j =i ωε ε E + j ɫɬ == i ω ε 0 (ε − ii ωD)Emm0 m + σ E m + jmmmε0 ω + j ɫɬ .(1.15)= i ω ε ε E0mmɁɞɟɫɶ ɜɜɟɞɟɧɨ ɧɨɜɨɟ ɨɛɨɡɧɚɱɟɧɢɟ:ε - ɤɨɦɩɥɟɤɫɧɚɹ ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ.σε = ε − i(1.16)ε0 ωɢɥɢε = ε′ − ε′′ ,ɝɞɟ ε′ ɢ ε′′ - ɞɟɣɫɬɜɢɬɟɥɶɧɚɹ ɢ ɦɧɢɦɚɹ ɱɚɫɬɶ ɤɨɦɩɥɟɤɫɧɨɣ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.ɋ ɭɱɟɬɨɦ ɜɜɟɞɟɧɧɨɣ ɤɨɦɩɥɟɤɫɧɨɣ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ (1.15) ɢ ɫ ɭɱɟɬɨɦ ɫɜɹɡɢ ɜɟɤɬɨɪɨɜ ȼ ɢ ɇ ɡɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ (1.12) ɢ (1.13) ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ: = − i ωµ µ H ,rot Em0mrot H m = i ω ε 0 ε E m + jm ɫɬ .(1.17)(1.18)Ɍɨɝɞɚ ɜ ɭɪɚɜɧɟɧɢɹɯ Ɇɚɤɫɜɟɥɥɚ ɜ ɤɨɦɩɥɟɤɫɧɨɣ ɮɨɪɦɟ ɢɡɦɟɧɹɬɫɹɡɧɚɤɢ ɩɟɪɟɞ ɦɧɨɠɢɬɟɥɟɦ iω.Ɇɵ ɜɢɞɢɦ, ɱɬɨ ɤɨɦɩɥɟɤɫɧɚɹ ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɨɡɜɨɥɹɟɬ ɭɱɟɫɬɶ ɡɚɜɢɫɢɦɨɫɬɶ ɷɥɟɤɬɪɨɞɢɧɚɦɢɱɟɫɤɢɯɫɜɨɣɫɬɜ ɫɪɟɞɵ ɨɬ ɱɚɫɬɨɬɵ, ɬɨ ɟɫɬɶ ɟɟ ɞɢɫɩɟɪɫɢɸ. Ɉɞɧɨɜɪɟɦɟɧɧɨɜɜɟɞɟɧɢɟ ε ɭɱɢɬɵɜɚɟɬ ɡɚɩɚɡɞɵɜɚɧɢɟ ɜɟɤɬɨɪɚ D ɨɬɧɨɫɢɬɟɥɶɧɨɜɟɤɬɨɪɚ ȿ ɜ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɯ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɩɨɥɹɯ.ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɧɚɥɢɱɢɟ ɦɧɢɦɨɣ ɱɚɫɬɢ ɭ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɝɨɜɨɪɢɬ ɨ ɧɚɥɢɱɢɢ ɡɚɬɭɯɚɧɢɹ ɜ ɫɪɟɞɟ.Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɱɟɪɟɡ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ εɜɵɪɚɠɚɟɬɫɹ ɜɨɥɧɨɜɨɣ ɜɟɤɬɨɪ k.

ɇɚɩɨɦɧɢɦ: ɜɨɥɧɨɜɨɣ ɜɟɤɬɨɪ kɨɩɪɟɞɟɥɹɟɬ ɧɚɩɪɚɜɥɟɧɢɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɩɥɨɫɤɨɣ ɦɨɧɨɯɪɨɦɚ-1314 =E e −i ω t ,EmH = H e −i ω t .m(1.14)ɬɢɱɟɫɤɨɣ ɜɨɥɧɵ. Ɇɨɞɭɥɶ ɜɨɥɧɨɜɨɝɨ ɜɟɤɬɨɪɚ k ɧɚɡɵɜɚɟɬɫɹ ɜɨɥɧɨɜɵɦ ɱɢɫɥɨɦk = 2π/λ ,(1.19)ɝɞɟ λ - ɞɥɢɧɚ ɜɨɥɧɵ. ȼɨɥɧɨɜɨɟ ɱɢɫɥɨ ɦɨɠɧɨ ɜɵɪɚɡɢɬɶ ɬɚɤɠɟ ɱɟɪɟɡ ɮɚɡɨɜɭɸ ɫɤɨɪɨɫɬɶ ɜɨɥɧɵ:Ɇɧɨɠɢɬɟɥɶ e −i k′′z ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɜɨɥɧɚ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɡɚɬɭɯɚɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɤɨɨɪɞɢɧɚɬɵ z. ɉɨɷɬɨɦɭ ɦɧɢɦɭɸɱɚɫɬɶ k ′′ ɢɧɨɝɞɚ ɧɚɡɵɜɚɸɬ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɡɚɬɭɯɚɧɢɹ.ȼɵɜɨɞɵk = ω / v.(1.20)ɋɤɨɪɨɫɬɶ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɨɥɧɵ ɜ ɫɪɟɞɟ ɧɚɯɨɞɢɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:v = c/n ,(1.21)ɝɞɟ ɫ - ɫɤɨɪɨɫɬɶ ɫɜɟɬɚ ɜ ɜɚɤɭɭɦɟ, n - ɩɨɤɚɡɚɬɟɥɶ ɩɪɟɥɨɦɥɟɧɢɹɫɪɟɞɵ.ȼ ɫɜɨɸ ɨɱɟɪɟɞɶ,n = εµ ,(1.22)ɉɪɢɦɟɧɟɧɢɟ ɭɪɚɜɧɟɧɢɣ Ɇɚɤɫɜɟɥɥɚ ɜ ɤɨɦɩɥɟɤɫɧɨɣ ɮɨɪɦɟ ɜɨɦɧɨɝɢɯ ɫɥɭɱɚɹɯ ɩɨɡɜɨɥɹɸɬ ɨɛɥɟɝɱɢɬɶ ɢɯ ɪɟɲɟɧɢɟ ɡɚ ɫɱɟɬ ɭɩɪɨɳɟɧɢɹ ɨɩɟɪɚɰɢɢ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɹ ɩɨ ɜɪɟɦɟɧɢ ɢ ɩɨ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɦ ɤɨɨɪɞɢɧɚɬɚɦ.

ȼɜɟɞɟɧɢɟ ɤɨɦɩɥɟɤɫɧɨɝɨ ɜɨɥɧɨɜɨɝɨ ɱɢɫɥɚ ɢ ɤɨɦɩɥɟɤɫɧɨɣ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɩɨɡɜɨɥɹɸɬɭɱɟɫɬɶ ɧɚɥɢɱɢɟ ɩɨɬɟɪɶ ɜ ɫɪɟɞɟ.ɝɞɟ ε ɢ µ - ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɢ ɦɚɝɧɢɬɧɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɫɪɟɞɵ.Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɟɫɥɢ ε ɹɜɥɹɟɬɫɹ ɤɨɦɩɥɟɤɫɧɨɣ, ɬɨ ɢ ɜɨɥɧɨɜɨɟɱɢɫɥɨ k ɬɨɠɟ ɛɭɞɟɬ ɤɨɦɩɥɟɤɫɧɵɦ:1.1. Ɂɚɩɢɲɢɬɟ ɭɪɚɜɧɟɧɢɹ (1.3) ɢ (1.4) ɜ ɤɨɦɩɥɟɤɫɧɨɣ ɮɨɪɦɟ. ȼɱɟɦ ɩɪɟɢɦɭɳɟɫɬɜɨ ɦɟɬɨɞɚ ɤɨɦɩɥɟɤɫɧɵɯ ɚɦɩɥɢɬɭɞ?1.2. ɑɬɨ ɬɚɤɨɟ ɜɨɥɧɨɜɨɣ ɜɟɤɬɨɪ?1.3. Ʉɚɤɢɟ ɫɜɨɣɫɬɜɚ ɫɪɟɞɵ ɩɨɡɜɨɥɹɟɬ ɭɱɟɫɬɶ ɜɜɟɞɟɧɢɟ ɤɨɦɩɥɟɤɫɧɨɣ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ?1.3. Ɉɛɴɹɫɧɢɬɟ, ɱɬɨ ɨɩɪɟɞɟɥɹɸɬ ɞɟɣɫɬɜɢɬɟɥɶɧɚɹ ɢ ɦɧɢɦɚɹ ɱɚɫɬɶɜɨɥɧɨɜɨɝɨ ɱɢɫɥɚ?1.4.

ȼɵɛɟɪɢɬɟ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ɜɪɟɦɟɧɢ ɜ ɩɥɨɫɤɨɣ ɜɨɥɧɟ ɜ ɜɢɞɟe −i ωt . Ɂɚɩɢɲɢɬɟ ɭɪɚɜɧɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ (1.1 - 1.2) ɜ ɤɨɦɩɥɟɤɫɧɨɣ ɮɨɪɦɟ ɞɥɹ ɞɚɧɧɨɣ ɜɪɟɦɟɧɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ. (ɍɤɚɡɚɧɢɟ: ɫɨɩɨɫɬɚɜɶɬɟ ɜɟɤɬɨɪɚɦ ȿ ɢ ɇ ɤɨɦɩɥɟɤɫɧɵɟ ɱɢɫɥɚ =H =E e −i ω t , H e −i ω t ).Eω(1.23)ε µ = k ′ − i k ′′ .cɇɚɥɢɱɢɟ ɦɧɢɦɨɣ ɱɚɫɬɢ k ′′ ɝɨɜɨɪɢɬ ɨ ɡɚɬɭɯɚɧɢɢ ɜɨɥɧɵ ɜ ɫɪɟɞɟ.Ⱦɟɣɫɬɜɢɬɟɥɶɧɚɹ ɱɚɫɬɶ k' ɨɩɪɟɞɟɥɹɟɬ ɮɚɡɨɜɭɸ ɫɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɜɨɥɧɵvɮ = ω / k′ .(1.24)k=ɉɪɢɦɟɪ. Ɋɚɫɫɦɨɬɪɢɦ ɩɥɨɫɤɭɸ ɜɨɥɧɭ, ɪɚɫɩɪɨɫɬɪɚɧɹɸɳɭɸɫɹ ɜ ɩɨɥɨɠɢɬɟɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɨɫɢ Oz.

Ɂɚɩɢɲɟɦɭɪɚɜɧɟɧɢɟ ɜɨɥɧɵ ɜ ɤɨɦɩɥɟɤɫɧɨɣ ɮɨɪɦɟ: = E ⋅ e i ( ωt −kz ) .E0ɍɱɬɟɦ ɧɚɥɢɱɢɟ ɭ ɜɨɥɧɨɜɨɝɨ ɜɟɤɬɨɪɚ k ɞɟɣɫɬɜɢɬɟɥɶɧɨɣ ɢɦɧɢɦɨɣ ɱɚɫɬɢ, ɩɨɞɫɬɚɜɢɜ ɜɵɪɚɠɟɧɢɟ (1.23): = E ⋅ e −i k′′z e i ( ωt − k′z )E015(1.25)ȼɨɩɪɨɫɵ ɢ ɡɚɞɚɱɢmm1.5. ɇɚɣɬɢ ɩɚɪɚɦɟɬɪɵ k' ɢ k'' ɩɥɨɫɤɨɣ ɨɞɧɨɪɨɞɧɨɣ ɜɨɥɧɵ, ɪɚɫɩɪɨɫɬɪɚɧɹɸɳɟɣɫɹ ɜ ɩɥɚɜɥɟɧɨɦ ɤɜɚɪɰɟ ɧɚ ɱɚɫɬɨɬɟ 108 Ƚɰ( ε = 3,8 , σ = 10 −16 Cɦ / ɦ ).ɉɊɂɆȿɑȺɇɂȿ: ɜ ɤɨɧɰɟ ɤɨɧɫɩɟɤɬɚ ɥɟɤɰɢɣ ɩɪɢɜɟɞɟɧɵ ɨɬɜɟɬɵɧɚ ɧɟɤɨɬɨɪɵɟ ɜɨɩɪɨɫɵ, ɚ ɬɚɤɠɟ ɨɬɜɟɬɵ ɤɨ ɜɫɟɦ ɡɚɞɚɱɚɦ.ɇɟɤɨɬɨɪɵɟ ɡɚɞɚɱɢ ɫɧɚɛɠɟɧɵ ɩɨɞɪɨɛɧɵɦ ɪɟɲɟɧɢɟɦ.16.