RESONANCE ENERGY TRANSFER BETWEEN TWO ATOMS IN THE PRESENCE OF a MULTILAYERED CYLINDRICAL WAVEGUIDE

45B, 2020 k tranminhhien@iuh.edu.vn Keywords RESONANCE ENERGY TRANSFER BETWEEN TWO ATOMS IN THE PRESENCE OF A MULTILAYERED-CYLINDRICAL WAVEGUIDE Abstract Resonance energy transfer (RET) between quantum emitters is an important process in many different physical systems, as well as in chemistry and biology Considering the nature of this process and the potential to control it is a matter of widespread interest today We already know that radiative processes of any quantum emitters are affected by the environment Resonance energy transfer of two atoms is the exchange of excitation between them mediated by the quantum electromagnetic field; it can be significantly influented by environment We consider the resonance energy transfer rate of atoms positioned inside of a multilayered-cylindrical waveguide The configuration studied is a Bragg-distributed mirror type The dependence of resonance energy transfer on the distance of the atoms-surface as well as the frequency dependence of the emitted photon will be considered The results show that the amplification or annihilation is very strong when the Bragg coditions are satisfied Keywords Bragg-distributed mirror, Cylindrical waveguide, Resonance energy transfer T (RET) RET RET có g thơng qua photon, V R T R [2] nh [4 © 2020 Thành 91 6] 7] t ó mode (2018) [8] nguyên nguyên S n c a v t ch t tán s c h p th b t k th trình sau [9] (1) H (r ) hai (r , ) c2 (r , ) (2) chi 6] W W0 | d DG (rD , rA , )d A |2 | d DG0 (rD , rA , )d A |2 (3) rA , rD W0 dA l thái u K © 2020 Thành 92 dj Re , j( ) ( j ) , (4) 2.1 K hàm vector sóng M e on f N e ngồi G (11) (r , r , ) A Khi on f hàm Green i n (2 dh ) C111H M o(1)n (h) M e (1) ( h) n e n o C111H N o(1)n (h) N e (1) ( h) C211H N o(1)n (h)M e (1) ( h) C211V M o(1)n (h) N e (1) ( h) n n n e K o e o e o (5) rong i G ( NN ) (r , r , ) n (2 dh n ) (1) (1) C3NN H M o n ( h) M e n ( h) e N o N (1) (1) NN (1) (1) NN (1) (1) C3NN V N o n ( h) N e n ( h) C4 H N o n (h) M e n ( h) C4V M o n (h) N e n ( h) e N o N e N o N e N o N (6) A6) (A7) A9) C1(11H ,V ) T12( H ,V )T23( H ,V ) T13( H ,V )T22( H ,V ) T11( H ,V )T22( H ,V ) T12( H ,V )T21( H ,V ) 11 C2( H ,V ) T13( H ,V )T21( H ,V ) T11( H ,V )T23( H ,V ) T11( H ,V )T22( H ,V ) T12( H ,V )T21( H ,V ) NN 3( H ,V ) T31( H ,V )T22( H ,V ) T32( H ,V )T21( H ,V ) T11( H ,V )T22( H ,V ) T12( H ,V )T21( H ,V ) C (7) T41( H ,V )T22( H ,V ) T42( H ,V )T21( H ,V ) T11( H ,V )T22( H ,V ) T12( H ,V )T21( H ,V ) [Tij( k )( H ,V ) ]4 x TN( H1,V )TN( H2,V ) Tk( H1 ,V )Tk( H ,V ) C4(NNH ,V ) (8) H L , xen k ng N (khơng trình bày 3.1 Chúng tơi gi s ng t o nên kh i tr dày h u h n c t o nên b i l p Si/SiO2 xen k v ih s ng , ng c a bu ng c ng có kh n x t t Tuy nhiên, v n cho phép m ng h u h n photon ngồi © 2020 Thành 93 Hình 2: T D A d 0,1 - d g d - -b - Si / SiO2 xen k Trên hình 2, g cách g - xanh, g - nguyên g g cách xa [7] Các g g mode W W W g - - g N r , g cách - hác, © 2020 Thành 94 W C ) g A A /3 - - A d /6 - Trên hình 3, mơi C g / 6, A / , A - - © 2020 - Thành A /6 /3- 95 3.2 D A d 0,1 - d 0 g d - - Si / SiO2 xen k Trên hình 4, u g - bé, - kh © 2020 Thành 96 g A A /3 - A d - g /6 - Trên hình 5, - A / 6- ln theo K chân không H N (s 1, 2, , N ) © 2020 (f Thành 1,2, , N ) 97 r G fs r r G( f 1) s , G fs f (A1) r G( f 1) s , (A2) f G fs G0e Gesfs G fs (r, r ) G0e (r, r ) s f Gesfs (r, r ) (A3) Hàm Green không biên G0e rr (r r' ) G0e (r, r' ) i k s2 M (1) ( h) M' e e on s on s Me on s Gesfs (r, r' ) i s n ( h) N (1) (h)N' e e on s on s (h) (1 fs s )C1H M e n (1 (1) N f )N e on f (h) (1 fs s )C1V N e n (1 (1) N f )N o en f (h) (1 fs s )C2 H M e n s (1 (1) N f )M o en f (h) (1 fs s )C2V N e n s (1 f )M e n ( h) (1 fs s )C3 H M e n s (1 f )N e n f (h) (1 fs s )C3V N e n (1 f )N o n f (h) (1 fs s )C4 H M e n s (1 f )M o n ( h) (1 fs s )C4V N e n s o o e e f f r' (h)N' e(1) ( h) r r' on s o o ( h) (1 s o o o o o o ( h) (1 s s fs N (1) s )C'1H M e n o fs (1) N s )C'1V N e n o s ( h) fs N (1) s )C' H M e n ( h) (1 fs N (1) s )C' 2V N e n ( h) (1 fs N (1) s )C'3 H M e n ( h) (1 o o s o fs N (1) s )C'3V N e n o s fs N (1) s )C' H M e n ( h) (1 fs N (1) s )C'4V N e n o N s ( h) ( h) s ( h) ( h) ( h) (1 o ( h) s ( h) (1 f C1fsH , C1Vfs (A4) s (1) N f )M e on f (1 r n) (2 n ( h) on s on s (h)M' e(1) ( h) N e dh n) (2 dh s s ( h) ( h) , N s A1) (A2 A5) M e on f N e on f i [11] © 2020 Thành (A5) 98 M (1) e on f Z n(1) ( j rA )sicons (n )eihz z ( h) nZ n(1) ( j rA ) sin cos ( n r N (1) e ( h) on f h h sin ( n r n 2f )r )r e , (1) cos f Z n ( j rA )sin (n )z eihz Z n(1) ( j rA ) Z n(1) ( j rA ) k 2f k 2f f f f kf f h2 ) (A7) ihn (1) Z n ( j rA )sin cos (n ) r A6) (A7 f sin (n r ihz cos Z n(1) ( j rA )sin (n )eihz z n 2f Z n(1) ( j rA ) cos 2 (A6) Z n(1) ( j rA ) cos , f (A8) , f f C (A5 V , (A9) C H ,V C fs N f 1 s C1fsH ,V N f N s C'1fsH ,V N f 1 s C2fsH ,V N f N s C'2fsH ,V 1 f 1 s C3fsH ,V 1 f N s C'3fsH ,V 1 f 1 s C4fsH ,V 1 f N s C'4fsH ,V A1 © 2020 0 0 0 Thành ; (A10) 0 , A2 0 0 ; (A11) 99 (A12a) (A12b) am m 1,2, , N j j , j j ihn , kj j j kj (A13) Trong (A12a) (A12 (A5) cho hàm Green (A9 [1] Edited by Andrews D L and Demidov A A (1999), Resonant Energy transfer , Wiley, New York [2] Chem Phys 167, 229 [3] H van Amerongen, L Valkunas, and R van Grondelle, Photosynthetic Excitons Singapore: World Scientific (2000) [4 Phys Rev 69,674 [5] Ho Trung Dung, Knöll L and Welsch D.-G (2002), Intermolecular energy transfer in the presence of dispersing and absorbing media , Phys Rev A 65, (043813) [6] Marocico C A and Knoester J (2009), Intermolecular resonance energy transfer in the presence of a dielectric cylinder , Phys Rev A 79, (053816) [7 -mediated radiative transfer between two distant Phys Rev A 72, (063815) © 2020 Thành 100 [8] Phys Rev A 98, (013849) [9] S Y Buhmann and D.-G Welsch, "Born expansion of the Casimir Polder interaction of a ground-state atom with dielectric bodies", Appl Phys B: Lasers Opt 82, 189 (2006) [10] L.-W Li, M.-S Leong, T.-S Yeo, and P.Journal of Electromagnetic Waves and Applications, Vol 14, 961-985, pp.961972 nd edition, IEEE Press, Piscataway, New Jersey, 1994 Ngày nh n bài:17/03/2020 Ngày ch p nh © 2020 Thành 13/10/2020 ... L and Welsch D.-G (2002), Intermolecular energy transfer in the presence of dispersing and absorbing media , Phys Rev A 65, (043813) [6] Marocico C A and Knoester J (2009), Intermolecular resonance. .. (2009), Intermolecular resonance energy transfer in the presence of a dielectric cylinder , Phys Rev A 79, (053816) [7 -mediated radiative transfer between two distant Phys Rev A 72, (063815) © 2020... C'4fsH ,V A1 © 2020 0 0 0 Thành ; (A1 0) 0 , A2 0 0 ; (A1 1) 99 (A1 2a) (A1 2b) am m 1,2, , N j j , j j ihn , kj j j kj (A1 3) Trong (A1 2a) (A1 2 (A5 ) cho hàm Green (A9 [1] Edited by Andrews D L and Demidov