title: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ ÐºÐ²Ð°Ð·Ð¸ÑÐµÐ·Ð¾Ð½Ð°Ð½ÑÐ½Ð¾Ð³Ð¾ ÑÐ²ÐµÑÐ° Ð² Ð°Ð½ÑÐ°Ð¼Ð±Ð»Ðµ Ð¿ÑÐ¸Ð¼ÐµÑÐ½ÑÑ Ð°ÑÐ¾Ð¼Ð¾Ð² Ð² Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð´Ðµ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Investigation of quasiresonant light propagation in an ensemble of impurity atoms in a waveguide
Creators: name: ÐÑÐ½ Ð¥ÑÑÐ¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: ÐÐ¾Ð»Ð½Ð¾Ð²Ð¾Ð´Ñ
Ð°ÑÐ¾Ð¼Ð½ÑÐµ Ð°Ð½ÑÐ°Ð¼Ð±Ð»Ð¸
ÑÐ¸ÑÑÐµÐ¼Ñ Ð¿Ð¾Ð½Ð¸Ð¶ÐµÐ½Ð½Ð¾Ð¹ ÑÐ°Ð·Ð¼ÐµÑÐ½Ð¾ÑÑÐ¸
Ð¾Ð¿ÑÐ¸ÑÐµÑÐºÐ¸Ð¹ ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾Ñ
Ð»ÑÐ¼Ð±Ð¾Ð²ÑÐºÐ¸Ð¹ ÑÐ´Ð²Ð¸Ð³
ÑÐ¿Ð¾Ð½ÑÐ°Ð½Ð½ÑÐ¹ ÑÐ°ÑÐ¿Ð°Ð´
Ð´Ð¸Ð¿Ð¾Ð»Ñ-Ð´Ð¸Ð¿Ð¾Ð»ÑÐ½Ð¾Ðµ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ
atomic ensembles
systems of reduced dimensionality
optical cavity
lamb shift
spontanenous decay
dipole-dipole interaction

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸Ð·ÑÑÐµÐ½Ð¸Ñ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ ÐºÐ²Ð°Ð·Ð¸ÑÐµÐ·Ð¾Ð½Ð°Ð½ÑÐ½Ð¾Ð³Ð¾ ÑÐ²ÐµÑÐ° Ð² Ð½ÐµÑÐ¿Ð¾ÑÑÐ´Ð¾ÑÐµÐ½Ð½Ð¾Ð¼ Ð°Ð½ÑÐ°Ð¼Ð±Ð»Ðµ Ð¿ÑÐ¸Ð¼ÐµÑÐ½ÑÑ Ð°ÑÐ¾Ð¼Ð¾Ð² Ð² Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð´Ðµ, Ð¸ Ð¾Ð±ÑÐµÐ¹ ÑÐµÐ»ÑÑ ÑÐ°Ð±Ð¾ÑÑ ÑÐ²Ð»ÑÐµÑÑÑ ÑÐ°ÑÑÐµÑ ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½ÑÐ° Ð¿ÑÐ¾Ð¿ÑÑÐºÐ°Ð½Ð¸Ñ Ð°Ð½ÑÐ°Ð¼Ð±Ð»Ñ Ð¿ÑÐ¸Ð¼ÐµÑÐ½ÑÑ Ð°ÑÐ¾Ð¼Ð¾Ð² Ð² Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð´Ðµ. Ð¢ÐµÐ¾ÑÐ¸Ñ ÑÑÐ¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ Ð² Ð¾ÑÐ½Ð¾Ð²Ð½Ð¾Ð¼ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÑ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾-Ð¼Ð¸ÐºÑÐ¾ÑÐºÐ¾Ð¿Ð¸ÑÐµÑÐºÐ¸Ð¹ Ð¿Ð¾Ð´ÑÐ¾Ð´. ÐÑÐ´ÐµÐ¼ ÑÑÐ¸ÑÐ°ÑÑ, ÑÑÐ¾ ÑÑÐµÐ½ÐºÐ¸ Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð´Ð° ÑÐ²Ð»ÑÐµÑÑÑ Ð¸Ð´ÐµÐ°Ð»ÑÐ½Ð¾ Ð¿ÑÐ¾Ð²Ð¾Ð´ÑÑÐµÐ¹, ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÐ° Ð¼Ð¾Ð¶ÐµÑ Ð±ÑÑÑ Ð´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½Ð¾ Ð½Ð¸Ð·ÐºÐ¾Ð¹, ÑÑÐ¾Ð±Ñ Ð¼Ð¾Ð¶Ð½Ð¾ Ð±ÑÐ»Ð¾ Ð¿ÑÐµÐ½ÐµÐ±ÑÐµÑÑ ÑÐ»ÐµÐºÑÑÐ¾Ð½-ÑÐ¾Ð½Ð¾Ð½Ð½ÑÐ¼ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸ÐµÐ¼, Ð° Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ Ð´Ð¸ÑÐ»ÐµÐºÑÑÐ¸ÐºÐ° Ð½Ð° Ð¿ÑÐ¸Ð¼ÐµÑÐ½ÑÐµ Ð°ÑÐ¾Ð¼Ñ ÑÐ²Ð¾Ð´Ð¸ÑÑÑ Ðº ÑÐ»ÑÑÐ°Ð¹Ð½ÑÐ¼ ÑÐ´Ð²Ð¸Ð³Ð°Ð¼ Ð¸Ñ ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÑÐ¾Ð²Ð½ÐµÐ¹. Ð Ð¾Ð±ÑÐµÐ¼ ÑÐ»ÑÑÐ°Ðµ Ð¼Ñ Ð¼Ð¾Ð¶ÐµÐ¼ ÑÑÐ¸ÑÐ°ÑÑ Ð¿ÑÐ¸Ð¼ÐµÑÐ½ÑÐµ Ð°ÑÐ¾Ð¼Ñ ÑÐ¾ÑÐµÑÐ½ÑÐ¼Ð¸ Ð½ÐµÐ¿Ð¾Ð´Ð²Ð¸Ð¶Ð½ÑÐ¼Ð¸ ÑÐ°ÑÑÐµÐ¸Ð²Ð°ÑÐµÐ»ÑÐ¼Ð¸. ÐÑ Ð¿Ð¾Ð»ÑÑÐ¸Ð»Ð¸ Ð¾Ð¿ÐµÑÐ°ÑÐ¾Ñ Ð¿Ð¾Ð»Ñ E Ì(r) Ð² Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð´Ðµ Ð¿ÑÑÐµÐ¼ ÑÐµÑÐµÐ½Ð¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ ÐÐ°ÐºÑÐ²ÐµÐ»Ð»Ð° Ð¸ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿Ð¾Ð»Ñ Ð² Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð´Ðµ Ñ ÑÑÐµÑÐ¾Ð¼ Ð³ÑÐ°Ð½Ð¸ÑÐ½ÑÑ ÑÑÐ»Ð¾Ð²Ð¸Ð¹, Ð° Ð·Ð°ÑÐµÐ¼ Ð²ÑÐ²ÐµÐ»Ð¸ ÐºÐ¾Ð¼Ð¿Ð¾Ð½ÐµÐ½ÑÑ Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð´Ð½Ð¾Ð¹ Ð¼Ð¾Ð´Ñ ÑÐ¸Ð¿Ð° TE (Ð¿Ð¾Ð¿ÐµÑÐµÑÐ½Ð°Ñ ÑÐ»ÐµÐºÑÑÐ¸ÑÐµÑÐºÐ°Ñ) Ð¸Ð»Ð¸ TM (Ð¿Ð¾Ð¿ÐµÑÐµÑÐ½Ð°Ñ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð°Ñ) Ð² Ð½Ð°Ð¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ð¸ x. y. z.Â ÐÑÐµÐ½ÐµÐ±ÑÐµÐ³Ð°Ñ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÐ¼Ð¸ ÑÑÑÐµÐºÑÐ°Ð¼Ð¸ Ð¸ ÑÐµÑÐ°Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð¨ÑÐµÐ´Ð¸Ð½Ð³ÐµÑÐ° Ð´Ð»Ñ Ð°ÑÐ¾Ð¼Ð¾Ð² Ð¸ ÑÐ»ÐµÐºÑÑÐ¾Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ, Ð¼Ñ Ð¿Ð¾Ð»ÑÑÐ°ÐµÐ¼ ÑÐ¸ÑÑÐµÐ¼Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð´Ð»Ñ Ð°Ð¼Ð¿Ð»Ð¸ÑÑÐ´ÑÂ  Ð¾Ð´Ð½Ð¾ÐºÑÐ°ÑÐ½ÑÐµ Ð°ÑÐ¾Ð¼Ð½ÑÐµ Ð²Ð¾Ð·Ð±ÑÐ¶Ð´ÐµÐ½Ð½ÑÐµ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ, Ð¿ÑÐ¸ÑÐµÐ¼ ÑÐ²ÑÐ·Ñ Ð¼ÐµÐ¶Ð´Ñ Ð°ÑÐ¾Ð¼Ð°Ð¼Ð¸ Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÐµÑÑÑ ÑÐ°Ðº Ð½Ð°Ð·ÑÐ²Ð°ÐµÐ¼Ð¾Ð¹ Ð¼Ð°ÑÑÐ¸ÑÐµÐ¹ ÐÑÐ¸Ð½Ð°. ÐÐ°ÑÑÐ¸ÑÐ° ÐÑÐ¸Ð½Ð° Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÑÐµÑ ÑÐ¾Ð±Ð¾Ð¹ Ð¼Ð°ÑÑÐ¸ÑÑ 3N*3N. ÐÑ ÑÐ°ÑÑÑÐ¸ÑÑÐ²Ð°ÐµÐ¼ Ð¼Ð°ÑÑÐ¸ÑÑ ÐÑÐ¸Ð½Ð° Ð¿ÑÑÐµÐ¼ ÑÑÐ¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐµÐ·Ð¾Ð½Ð°Ð½ÑÐ½ÑÑ Ð¾Ð´Ð½Ð¾ÑÐ¾ÑÐ¾Ð½Ð½ÑÑ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ð¸ "g" Ð¸ Ð½ÐµÑÐµÐ·Ð¾Ð½Ð°Ð½ÑÐ½Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ Ñ Ð´Ð²ÑÐ¼Ñ Ð²Ð¾Ð·Ð±ÑÐ¶Ð´ÐµÐ½Ð½ÑÐ¼Ð¸ Ð°ÑÐ¾Ð¼Ð°Ð¼Ð¸ Ð¸ Ð¾Ð´Ð½Ð¸Ð¼ ÑÐ¾ÑÐ¾Ð½Ð¾Ð¼ "ee". ÐÐ°ÑÐµÐ¼ Ð½Ð°Ð¼ Ð½ÑÐ¶Ð½Ð¾ Ð²ÑÑÐ¸ÑÐ»Ð¸ÑÑÂ  ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½ÑÐ° Ð¿ÑÐ¾Ð¿ÑÑÐºÐ°Ð½Ð¸Ñ, Ð´Ð»Ñ ÑÐµÐ³Ð¾ Ð¼Ñ Ð¿ÑÐµÐ´Ð¿Ð¾Ð»Ð°Ð³Ð°ÐµÐ¼ ÑÑÑÐµÑÑÐ²Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸: Â«Ð°ÑÐ¾Ð¼-Ð´ÐµÑÐµÐºÑÐ¾ÑÂ», ÐºÐ¾ÑÐ¾ÑÑÐ¹ ÑÐ»Ð°Ð²Ð»Ð¸Ð²Ð°ÐµÑ Ð¸Ð·Ð»ÑÑÐµÐ½Ð¸Ðµ, Ð¸ÑÐ¿ÑÑÐºÐ°ÐµÐ¼Ð¾Ðµ Ð¾ÐºÑÑÐ¶Ð°ÑÑÐµÐ¹ ÑÑÐµÐ´Ð¾Ð¹, Ð½Ð¾ Ð½Ðµ Ð¸ÑÐ¿ÑÑÐºÐ°ÐµÑ Ð¿Ð¾Ð²ÑÐ¾ÑÐ½Ð¾ ÑÐ¾ÑÐ¾Ð½Ñ. ÐÐ¾ÑÐºÐ¾Ð»ÑÐºÑ Ð¼Ñ Ð¿Ð¾Ð»ÑÑÐ°ÐµÐ¼ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ðµ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾Ð¹ Ð°Ð¼Ð¿Ð»Ð¸ÑÑÐ´Ñ Ð²Ð¾ Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ð¹ Ð¾Ð±Ð»Ð°ÑÑÐ¸, ÑÐ¾ Ð´Ð»Ñ Ð¿ÐµÑÐµÑÐ¾Ð´Ð° Ð² ÑÐµÐ¶Ð¸Ð¼ ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½ÑÐ¹ Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼Ð¾ Ð¾ÑÐºÐ°Ð·Ð°ÑÑÑÑ (Ð¸ÑÐºÑÑÑÑÐ²ÐµÐ½Ð½Ð¾) Ð¾Ñ Ð¾Ð±ÑÐ°ÑÐ½Ð¾Ð³Ð¾ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ Ð°ÑÐ¾Ð¼Ð¾Ð² Ð°Ð½ÑÐ°Ð¼Ð±Ð»Ñ Ð½Ð° Ð°ÑÐ¾Ð¼-Ð¸ÑÑÐ¾ÑÐ½Ð¸Ðº. ÐÐ¾Ð´ÐµÐ»Ð¸ÑÑÐµÐ¼ Ð¼Ð¾Ð½Ð¾ÑÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¸Ð·Ð»ÑÑÐµÐ½Ð¸Ðµ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑ Ð¿ÑÐµÐ´ÐµÐ»ÑÐ½ÑÐ¹ Ð¿ÐµÑÐµÑÐ¾Ð´, Ñ. Ðµ. Ð¿ÐµÑÐµÑÐ¾Ð´ ÐºÐ¾Ð³Ð´Ð° ÑÐ¸ÑÐ¸Ð½Ð° Ð»Ð¸Ð½Ð¸Ð¸ ÑÑÑÐµÐ¼Ð¸ÑÑÑ Ðº Ð½ÑÐ»Ñ. ÐÐ¾ Ð¼ÐµÑÐµ Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶ÐµÐ½Ð¸Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð¸ Ðº Ð±ÐµÑÐºÐ¾Ð½ÐµÑÐ½Ð¾ÑÑÐ¸ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ðµ ÐºÐ²Ð°Ð·Ð¸ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ Ð¿Ð¾Ð»ÑÑÐ°ÐµÑÑÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð´Ð²ÑÑ Ð¿ÑÐµÐ´ÐµÐ»ÑÐ½ÑÑ Ð¿ÐµÑÐµÑÐ¾Ð´Ð¾Ð². ÐÐ½ÑÐµÐ½ÑÐ¸Ð²Ð½Ð¾ÑÑÑ ÑÐ²ÐµÑÐ° Ð² ÑÐ¾ÑÐºÐµ Â«Ð°ÑÐ¾Ð¼-Ð´ÐµÑÐµÐºÑÐ¾ÑÂ» Ð¿ÑÐ¾Ð¿Ð¾ÑÑÐ¸Ð¾Ð½Ð°Ð»ÑÐ½Ð° Ð·Ð°ÑÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÐ¸ ÐµÐ³Ð¾ Ð²Ð¾Ð·Ð±ÑÐ¶Ð´ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ, Ð¿Ð¾ÑÑÐ¾Ð¼Ñ Ð¼Ñ Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·ÑÐµÐ¼ ÑÐ°ÑÑÐµÑ ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½ÑÐ° Ð¿ÑÐ¾Ð¿ÑÑÐºÐ°Ð½Ð¸Ñ Ð² ÑÐ°ÑÑÐµÑ Ð½Ð°ÑÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÐ¸ Ð²Ð¾Ð·Ð±ÑÐ¶Ð´ÐµÐ½Ð½ÑÑ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ð¹Â  Â«Ð°ÑÐ¾Ð¼-Ð´ÐµÑÐµÐºÑÐ¾ÑÂ». Ð¡ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Matlab Ð¼Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÑÐµÐ¼ Ð¼Ð°ÑÑÐ¸ÑÑ ÐÑÐ¸Ð½Ð° Ð¸, Ð½Ð°ÐºÐ¾Ð½ÐµÑ, Ð¿Ð¾Ð»ÑÑÐ°ÐµÐ¼ ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½Ñ Ð¿ÑÐ¾Ð¿ÑÑÐºÐ°Ð½Ð¸Ñ T, Ð¸Ð·Ð¼ÐµÐ½ÑÑ Ð´Ð»Ð¸Ð½Ñ Ð¾Ð±ÑÐ°Ð·ÑÐ° Ð¿Ð¾ Ð¾ÑÐ¸ z. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¿Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÑÑ, ÑÑÐ¾ Ð²ÐµÐ»Ð¸ÑÐ¸Ð½Ð° ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½ÑÐ° Ð¿ÑÐ¾Ð¿ÑÑÐºÐ°Ð½Ð¸Ñ Ð¸Ð¼ÐµÐµÑ ÑÐ»Ð¾Ð¶Ð½ÑÑ ÑÑÑÐ¿ÐµÐ½ÑÐ°ÑÑÑ Ð½ÐµÐ¼Ð¾Ð½Ð¾ÑÐ¾Ð½Ð½ÑÑ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÑ Ð¾Ñ Ð¿Ð¾Ð¿ÐµÑÐµÑÐ½ÑÑ ÑÐ°Ð·Ð¼ÐµÑÐ¾Ð² Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð´Ð°.
description: This paper studies the propagation of quasiresonant light in a disordered ensemble of impurity atoms in a waveguide. We obtained the field operator E Ì(r) in the waveguide by solving Maxwells system of equations and quantizing the field in the resonator and waveguide considering the boundary conditions, then deduce the waveguide mode type TE (transverse electric) or TM (transverse magnetic) components in the x. y. z direction. By neglecting the non-linear reactions and solving the SchrÃ¶dinger equation for the atom plus electromagnetic field, we obtain a system of equations whose amplitudes are single-fold atomic excited states and the coupling between the atoms is described by the so-called Greens matrix. The Greens matrix is a 3N*3N matrix. We calculate the Greens matrix by summing the resonant single photon state "g" and the non-resonant state with two excited atoms and one photon "ee". After that we need to solve for the steady-state transmittance, for which we assume the existence of a model, namely: an "atom detector", which senses the radiation emitted by the environment, but does not re-emit photons. Since we obtain a dynamical variation of the quantum amplitude in the time domain, to switch to the stationary mode we need to reject (artificially) the reverse influence of the tethered atoms on the source atoms, using limit transitions, where the transition line width tends to zero and the time tends to infinity, to obtain a description of the quasi-stationary state by using two limit transitions. The intensity of light at the point of the atom detector is proportional to its excited state population. We therefore translate the calculation of transmittance into a calculation of the population of excited states on the atom detector. With the help of Matlab, we programmed the Greens matrix to find the transmittance T most neutrally by varying the length of the sample along the z-axis. The results show that the magnitude of the transmittance has a complex stepwise non-monotonic dependence on the transverse dimensions of the waveguide.