Light-matter interaction in nanostructured materials by Kristensen, Philip Trøst PDF

By Kristensen, Philip Trøst

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Extra info for Light-matter interaction in nanostructured materials

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PXX = pF F = 0º ÌÝÔ ÐÐݸ ÓÖ Ð Ø¹Ñ ØØ Ö Ð ÙÐ Ø ÓÒ× Ò ØÓÑ Ô Ý× ×¸ Ø ×ÝÑÑ ØÖÝ Ó Ø Ð ØÖÓÒ Û Ú ÙÒ Ø ÓÒ× Ö Ù× ØÓ Ö Ù Ø Ø Ø × × Ø × º Ì × Ð ¹ ×× Ñ Ð É × Ö ÒÓØ ×Ô Ö ÐÐÝ ×ÝÑÑ ØÖ ¸ Ò ×Ó Ø × Ö ÙÑ ÒØ Ó × ÒÓØ ÓÐ º ÀÓÛ Ú Ö¸ Û Ö Ø Ò Ø ØÛÓ Ø ÓÒ Ð Ø ÖÑ׸ Ø × ÛÓÙÐ Ú Ö ×ÙÐØ Ò Ø ÖÑ× Ò Ø ÒØ Ö¹ Ø ÓÒ Ô ØÙÖ À Ñ ÐØÓÒ Ò Ó× ÐÐ Ø Ò Ø Ø Ò ÙÐ Ö Ö ÕÙ Ò Ý ωµ Ò Ø Ù× ÛÓÙÐ Ú Ò ÖÓÔÔ Ò Ø ÖÓØ Ø Ò Û Ú ÔÔÖÓÜ Ñ Ø ÓÒº Ð×Ó¸ Ø × Ø ÖÑ× ÛÓÙÐ ÒÓØ ÔÔ Ö Û ÜÔ Ò Ø ÒØ Ö Ø ÓÒ À Ñ ÐØÓÒ Ò Ò Ø ÓÒ ¹ Ü Ø Ø ÓÒ ×Ù ×Ô ¸ × Ò Ø Ý ÓÖÖ ×ÔÓÒ ØÓ Ø ÔÖÓ ×× Ó ÒÒ Ð Ø ÓÒ ÓÖ Ö Ø ÓÒ Ó Ô ÓØÓÒ Û Ø ÓÙØ Ø Ö Ø ÓÒ ÓÖ ÒÒ Ð Ø ÓÒ Ó Ò Ü ØÓÒº ¿¿ ÔØ Ö ¾º Ì ÓÖÝ Ó Ð Ø Ø¹Ñ ØØ Ö ÒØ Ö Ø ÓÒ ÏØ Ø ÒØ Ö Ø ÓÒ Ô ØÙÖ À Ñ ÐØÓÒ Ò¸ ÓÒ Ø × ÑÔÐ ÓÖÑ c˙Áx = i Õº ´¾º ½µ¸ Ø ÕÙ Ø ÓÒ× Ó ÑÓØ ÓÒ cÁµ gµ e−i∆µ t ´¾º ¾ µ µ c˙Áµ = i cÁx gµ∗ ei∆µ t , ´¾º ¾ µ ÖÓÑ Û Û Ò ¸ Ý ÒØ Ö Ø ÓÒ Ó Õº ´¾º ¾ µ Ò Ò× ÖØ ÓÒ ÒØÓ Ø ÕÙ Ø ÓÒ Ó ÑÓØ ÓÒ ÓÖ Ø ÜÔ Ò× ÓÒ Ó ÒØ cÁx c˙Áx = − µ |gµ |2 t 0 Õº ´¾º ¾ µ¸ cÁx (t )e−i∆µ (t−t ) dt .

Pex (r , ω)dr , Ö Ò³× Ø Ò×ÓÖ ÓÖ Ø ÕÙ Ø ÓÒ Ñ Ø Ö Ð ×Ý×Ø Ñº Ì ∇ × ∇ × G(r, r , ω) − k02 Ö (r)G(r, r , ω) = Iδ(r − r ), ´¾º½½µ ½ ÔØ Ö ¾º Ì ÓÖÝ Ó Ð Ø¹Ñ ØØ Ö ÒØ Ö Ø ÓÒ ×Ù Ø ØÓ Ø ËÓÑÑ Ö Ð Ö Ø ÓÒ ÓÒ Ø ÓÒ ½ ¸ Ò Ö× Ô Ò Ò ÓÒ Ø Ñ Ò× ÓÒ Ð Øݺ × Ñ Ð Ö ÕÙ Ø ÓÒ Ò ×Ø Ñ Ò Ø Ð Ö Ò³× Ø Ò×ÓÖº Ï Û ÐÐ ÛÓÖ ÓÒÐÝ Û Ø Ø Ð ØÖ Ð Ú Ö× ÓÒ Ò Û Û ÐÐ Ö Ö ØÓ Ø × × Ø Ð ¹ ØÖÓÑ Ò Ø Ö Ò³× Ø Ò×ÓÖ ØÓ ÑÔ × Þ Ø Û Ú Ò ØÙÖ Ó Ø Ð º ÔÔ Ò Ü Ò Ö ÒØ Ñ Ò× ÓÒ׺ Ô ÖØ ÖÓÑ ÓÑÓ¹ Ð ×Ø× G(r, r , ω) ÓÖ ÓÑÓ Ò ÓÙ× Ñ Ò ÓÙ× Ñ Ø Ö Ð׸ ÐÓ× ÓÖÑ ÜÔÖ ×× ÓÒ× ÓÖ Ø Ö Ò³× Ø Ò×ÓÖ Ö Ö ×ØÖ Ø ØÓ Ð Ñ Ø × Ø Ó × ÑÔÐ ÓÑ ØÖ × ×Ù × ×Ô Ö ÐÐÝ Ð Ý Ö ×ØÖÙ ØÙÖ × ¾ Ò ×ØÖ Ø¹ Ñ ¿¸ º ÓÑÔÖ Ò× Ú Ø ÓÖ Ø Ð ØÖ ØÑ ÒØ Ó Ð ØÖ Ò Ñ Ò Ø Ð Ö Ò³× Ø Ò×ÓÖ× Ò Ú Ö ÓÙ× ÓÑ ØÖ × × Ú Ò Ý Ì º Ì Ò Ø ÓÒ Ó Ø Ö Ò³× Ø Ò×ÓÖ Ò Õº ´¾º½½µ × ÓÒ× ×Ø ÒØ Û Ø Ø Ø Ó Ê ×º ¸ ¼¸ º ÁØ Ö× Ö Ò³× Ø Ò×ÓÖ Ò Ê º Ò Ý ØÓÖ Ó k02 ÖÓÑ Ý ØÓÖ Ó (−1) ÖÓÑ Ø Ø Ø Ó Ê ×º ¸ º Ì ÒØ ÖÔÖ Ø Ø ÓÒ Ó Ø Ö Ò³× Ø Ò×ÓÖ ÓÑ × Ð Ö Û Ù× Õº ´¾º½¼µ ØÓ Ð ÙÐ Ø Ø Ð ÖÓÑ ÔÓ ÒØ ×ÓÙÖ ¸ Pex (r, ω) = d(ω)δ(r − r )¸ × E(r, ω) = G(r, r , ω) k02 0 = G(r, r , ω) k02 d(ω)δ(r − r )dr ´¾º½¾µ d(ω), 0 Û × ÓÛ× Ø Ø Ø Ð ØÖ Ð Ør Ù ÓÖ Ú Ò Ñ Ø ÜÔ Ò ÓÒ Ø i³Ø ÓÐÙÑÒ Ó Ø Ö Ò³× Ø Ò×ÓÖ Ñ Ý ÒØ ÖÔÖ Ø ×Ø ØÓ ÔÓ ÒØ ×ÓÙÖ Ø r ÓÖ ÒØ ÒØ Ö Ø ÓÒ ei º Ö Ò³× Ø Ò×ÓÖ Ñ Ý Ö Ð ×Ý×Ø Ñ¸ × Ò Ý Ö (r)¸ Ø ÒÑÓ × Ó Ø Û Ú ÕÙ Ø ÓÒ × ¼¸ G(r, r , ω) = c2 µ fµ (r)fµ∗ (r ) , ωµ2 − (ω + iη)2 Û Ö Ø Ò Ò Ø × Ñ Ð ÙØ ÔÓ× Ø Ú Ñ Ò ÖÝ Ô ÖØ iη Ò×ÙÖ × Ö Ò³× Ø Ò×ÓÖ º Õº ´¾º½¿µ¸ ØÓ Ø Ö Û Ø Ø ÒØ ØÝ lim ÁÑ →0 Ñ Ý Ù× ωµ2 ØÓ Ö Ð Ø Ø 1 − ω2 − i Ù× Ð ØÝ Ó Ø π (δ(ω − ωµ ) − δ(ω + ωµ )) , 2ωµ Ö Ò³× Ø Ò×ÓÖ ØÓ Ø ρx (ω, r) = ¾º¾º¾ Ì = ´¾º½¿µ Ä ÇË × 2ω ÁÑ {ex G(r, r, ω) ex } .

C2 Ù ØÓ Ø ×ÝÑÑ ØÖ × Ó Ø Ð ØØ ¸ ×ÓÐÙØ ÓÒ× Ø Ö ÒØ k ÔÓ ÒØ× Ñ Ý Ú ÒØ Ð Ö ÕÙ Ò ×º Ò Ó Ú ÓÙ× Ü ÑÔÐ × Ø Ñ ¹Ö Ú Ö× Ð ×ÝÑÑ ØÖÝ Û ÓÐ × ÓÖ ÐÐ Ô ÓØÓÒ ÖÝ×Ø Ð× Ó ÒØ Ö ×Ø Ò Ø × ÛÓÖ º ÁØ Ð × ØÓ Ø Ô Ý× ÐÐÝ ÕÙ Ø Ö ×ÓÒ Ð ÓÒ Ø ÓÒ Ø Ø Û Ú × ØÖ Ú Ð Ò Ò Ü Ø ÓÔÔÓ× Ø Ö Ø ÓÒ× Û ÐÐ Ú º ÁÒ ÓÖ Ö ØÓ Ö ÑÓÚ Ö ÙÒ Ò Ý Ù ØÓ ÒØ Ð Ö ÕÙ Ò × ωn (k) = ωn (−k) ×ÝÑÑ ØÖݸ ÒÚ ×Ø Ø ÓÒ× Ö ØÝÔ ÐÐÝ Ö ×ØÖ Ø ØÓ Ø ÓÙÒ Ö × Ó Ø ÖÖ Ù Ð Ö ÐÐÓÙ Ò ÞÓÒ º Ì × × Ò × Ø × Ø Ó ÔÓ ÒØ× Ò Ø Ö ÐÐÓÙ Ò ÞÓÒ ÓÖ Û Ø ×ÓÐÙØ ÓÒ× En,k (r)¸ Û Ø ÓÖÖ ×ÔÓÒ Ò Ò Ö ÕÙ Ò × ωn (k)¸ Ö ÒÓØ Ö Ð Ø ØÓ Ø ×ÓÐÙØ ÓÒ× Ø ÓØ Ö k ÔÓ ÒØ× Ú ÒÝ Ó Ø ×ÝÑÑ ØÖ × Ó Ø Ð ØØ º Ì È Ò ×ØÖÙ ØÙÖ × Ö ØÝÔ ÐÐÝ Ð ÙÐ Ø ×Ø ÒÚ ÐÙ × Ó Ø Ð ¹ ØÖÓÑ Ò Ø Û Ú ÕÙ Ø ÓÒ Û Ø Ô Ö Ó Ô ÖÑ ØØ Ú Øݸ Ö (r) = Ö (r + R)¸ ÙÒ Ö Ø ××ÙÑÔØ ÓÒ Ø Ø Ø ×ÓÐÙØ ÓÒ× Ú ÐÓ ÓÖѸ Õº ´¾º¾ µº ÓÖ Ð ÙÐ Ø ÓÒ× ÓÒ ÒÓÒ¹Ñ Ò Ø Ñ Ø Ö Ð× Ø × × Ö ØÓ ÛÓÖ Û Ø Ø Û Ú ÕÙ Ø ÓÒ ÓÖ Ø Hk (r) Ð Û ¸ ÙÒ Ö Ø ××ÙÑÔØ ÓÒ Hk (r) = exp(ik · r)uk (r)¸ Ö Ù × ØÓ Ø ÓÖÑ ∇ × ∇ × En,k (r) = (ik + ∇) × Ù× Ò ÓÖ ¾º¾º Ð Ö ÔÖÓÔ ¾¾ ω 2 (k) 1 uk (r).

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