11 11 : 5339 () 111345 ACTA OPTICA SIN ICA Vol.,No. 11 November, 3 (, 371) : ;,,, : ; ; : TN53 : A 1,, [13 ] [4 1973, ], g E( r, t) = 5 E( r, t), 1974 5 t + 5 P ( r, t) 5 t, (1) Marcuse [5 ], P ( r, t) = P ( r, t) + P pert ( r, t), () 1981,Lam Garside [6 ], P ( r, t) = [( r) - ] E ( r, t), (3) [6 ] E ( r, t), ( r),, P pert ( r, t) (), 1996, Engan [7 ] () (3) (1),,, Lam g E t ( r, t) - ( r) 5 E t ( r, t) Garside 1998, 5 t = [8 ] 5 [ P pert ( r, t) ] t,, 5 t, (4),, t 1999 Kashyap [9 ], [5, ] : E t ( r, t) = a t ( r) exp [i ( t - ) ], (5) 3 (699776) H t ( r, t) = (138511) bh t ( r) exp [i ( t - ) ], (6) t ( r) exp [i ( t - ) ] Email :liaobangquan @eyou. com, :35 ; :47 [4 ], 1995-4 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
11 : 1341,( r) g { t ( r) exp [i ( t - ) ]} - ( r) 5 { t ( r) exp [i ( t - ) ]} 5 t =, (7) = n ( r) (5) (4), 5 a 5 t ( r) exp [i ( t - ) ] + 5 a 5 ( - i ) t ( r) exp [i ( t - ) ], (8) 5 a 5 a 5 ν 5 5 a 5 ( - i ) t ( r) exp [i ( t - ) ] 5 [ P = pert ( r, t) ] t 5 t, (8), (9) 5 [ P pert ( r, t) ] t = 5 t, (1) (1) h 3 t, e ( ),, [5 ], e ( t h 3 t) rd rd < = S P 3, (11) [1 (, ] ) d a exp [i ( t + ) ] - d d a exp [i ( t - d ) ] = - i 4 5 P5 t e { [ P pert ( r, t) ] t h 3 t} rd rd <, (1) (11) ; ; S, ( r) = n ( r), (13), S= 1, 3 P ( r) = ( r) +( r). (14), (1) () (3) t ( r),, - P pert ( r, t) =( r) E ( r, t) =,, + (1) n ( r) E ( r, t), (15),n ( r), (5) (15) 3 [ P pert ( r, t) ] t = n ( r) a t ( r) exp [i ( t - ) ], (16) (16) (1),, d a exp [i ( t + d ) ] - 5 P5 t - i 4 d a exp [i ( t - d ) ] = e ( n ( r) a t ( r) exp [i ( t - ) ] 5 [n ( r) aexp (i t) ]/ 5 t = - n ( r) aexp (i t), d a exp [i ( t + d ) ] - P d a exp [i ( t - d ) ] = i e 4 ( n ( r) a t ( r) exp [i ( t - ) ] 1995-4 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved. h 3 t ( r) ) h 3 t ( r) ) rd rd <, (17) rd rd <, (18)
134 (18), n ( r),, n ( r) n ( r) n ( r)n ( r) n ( r)ncos(/ ) = n ( r, <)n [exp (i/ ) + exp ( - i / ) ], (18) a exp (i k s - i ) (= ), (19) / -, () (18) a exp (i ) d a d,, = i 4 P a e ({ n ( r, <)n exp [i ( / - ) ] t ( r) } h 3 t ( r) ) rd rd <. (1) n ( r) a a : = i 4 d a / d = a exp [ - i ( ) ], () P e = - /, (4) { [ n ( r, <)n t ( r) ] h 3 t ( r) } rd rd <, (3) d a / d = 3 a exp [i ( ) ]. (5) (, t) = () cosh[( - L ) ], (3) cosh ( L ) (5) (8) (9), [69 ], 4 A, a, () a (5) d A / (d ) = ab exp [ - i ( ) ], (6) /. (35) d / (d ) = aba 3, <, exp [i ( ) ], (7), () ( ) =,A ( L ) = (6) (7) = / (33), ( ) ( L ) / ( ) ( / c) n eff, n eff A (, t) exp (i ) =, i ab exp (i/ ) () - sinh ( SL ) + i Scosh ( SL ) sinh[ S ( - L ) ], (8) (, t) exp ( - i ) = exp ( - i/ ) () - sinh ( SL ) + i Scosh ( SL ) { sinh[ S ( - L ) ] + i Scosh[ S ( - L ) ]}, (9) S = - ( ), ab. (3) = ( L ) A (, t) = () ab sinh[( - L ) ], (31) cosh ( L ) = i S = / i - [ ( ) - ], (33) ( ) -, (34) = i - ( n eff / c) (- ), (36) =, ( ) - = c n eff - = n eff - =, (37) = n eff, (38), [11,1 ] 1995-4 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved. (8) R eff A () () =
11 : 1343 sinh [ ( - ) 1/ L ] - + cosh [ ( - ) 1/ L ], (39) [, ] (34) (35) (8) (9) ( L ) + A () = n eff = 1, (4) - = - n ( + ) eff, (41) () () -, (4) T + R = 1 R eff = sinh ( L - {n eff / [ ( + ) ]} ) - [n eff / ( + ) ] + cosh ( L - {n eff / [ ( + ) ]} ), (4), (Advantest = : Q8383) 1 ( R eff ) peak = sinh ( L ) cosh = ( L ) 1 - [cosh ( L ) ] -, (43) (43) < R eff < 1 - / + / n, (44) eff 1 (44) ( ) max1 1 - =, = - n eff ( ) max1 / { [ ( ) max1 + ] }, 1 - cosh - n eff ( ) max L (45), (48) ( ) gap - 1, ( ) max1 ( ) max ( ) gap /, ( R eff ) peak 1 - cosh - n eff ( ) gap L. (49) (49) John Wiley and Sons, 1989 5 [6 ] Lam D K W, Garside K. Characteriation of singlemode optical fiber filters. A ppl. Opt., 1981, (3) :44445 [ 7 ] Engan H E. Analysis of polariationmode coupling by A m., 1996, 13 (1) :11118 8 mm, [8 ] Yu Y, Dong X. Theoretical analysis of optical waves in a Fig. 1 The reflection spectra of F G (45) (43) ( R eff ) peak = 1 - cosh - n eff ( ) max1 L 1. 559m, ( ) gap. 64 nm, n eff = 1. 46,, (46) [ ( ) max1 + ]. 993 (49), ( R eff ) peak ( ) max1. 999,, ( ) max -, ( R eff ) peak = 1 - cosh - n eff ( ) max L, (47) [ ( ) max + ] ( ) max1 ν, ( ) max ν, ( R eff ) peak 1 - cosh - n eff ( ) max1 L 1995-4 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved. [1 ] Hill K O, Malo, Vineberg K A et al.. Efficient mode conversion in telecommunication fiber using externally written gratings. Elect ron. Lett., 199, 6 (16) :17 17 [ ] ennion I, Williams J A R, Zhang L et al.. UVwritten in fibre ragg gratings. Opt. and Quant. Elect ron., 1996, 8 () :93135 [ 3 ] Rao Yunjiang. Recent progress in infiber ragg grating sensors: Applications. Proc. S PI E, 1998, 3555 : 49 441 [ 4 ] Yariv A. Int roduction to Optical Elect ronics. New York : [ 5 ] Marcuse D. Theory of Dielectric Optical W aveguides. New York : Academic press, 1974 acoustic torsional wave in optical fibers. J. Opt. Soc.
1344 :, chirped fiber grating. Proc. S PI E, 1998, 3555 :479484 [ 9 ] Kashyap R. Fiber ragg Gratings. San Diego : Academic press, 1999 [1 ] Zhou Shutong. Fiber Theory and Measurement ( :1996 Engan [ 7 ] ). Shanghai : Fudan University Press, 1988. 334 (in Chinese) [ 11 ] Kersey A D, Davis M A, Patrick H J et al.. Fiber E 3 i,t E k, t d xd y = ik, κs (A1) grating sensors. J. L ightw ave Technol., 1997, 15 (8) : 1999 Kashyap 1441463 [ 9 ] [ 1 ] Liao angquan, Feng Dejun, Zhao Qida et al.. Theoretical and experimental research on fiber ragg 1 e [ t 3 t ]d xd y =, (A) grating electric current sensor. Acta Optica S inica ( ),, (9) :19195 (in Chinese) - - e ( t h 3 t) rd rd < = S P 3 /, [ 1 ] (A3), CoupledMode Theory f or Optical Fiber and Its Appl ication to Fiber ragg Gratings Liao angquan Zhao Qida Feng Dejun Huang Yonglin Li Jie Wang Yue Dong Xiaoyi ( Instit ute of Modern O ptics, N ankai U niversity, Tianjin 371) (Received 5 March ; revised 7 April ) Abstract : The correct orthogonality relation for optical fiber is applied to the perturbed coupled mode t heory, and t he corresponding coupledmode equations for common optical fiber are introduced. Its application to fiber ragg gratings is discussed. The coupling coefficients of t he equations for fiber ragg gratings, being t he distinguished feature for coupledmode t heories, are different from other theories. The solutions of t he equations are discussed, and t he simple formula between the peak reflectivity and the ragg wavelength, the length of the fiber ragg grating is obtained. An experiment of fiber ragg gatings is completed. The peak reflectivity of t he experiment is about. 993, and t he corresponding t heoretical result is. 999. The experimental result coincides with the theory very well. Key words : coupledmode equations ; optical fiber ; perturbance 1995-4 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.