Formulas of Agrawal s Fiber-Optic Communication Systems NA n 2 ; n n. NA( )=n1 a

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1 Formula o grawal Fiber-Oti Communiation Sytem Chater (ntroution) 8 / max m M / E nh N h M m J e 9.6 / m log /mw SN / / /, NZ SN log / Z max N E Chater (Otial Fiber) Setion - (Geometrial Oti erition) SF/MMF: n in in n n i ninr N n n n n ini o n n / n N n ; n n GF/MMF: / n / n n / n n SF n n ; <a n( ) a n =n ; >a 8 / n int er, GF n / N( )=n a int er, SF n / n ( ) GF / Setion - (Wave roagation) k / / Ez / or / H K ( ) / ex ; m q q q q SMF E : z, H z z J m( )ex( m )ex( z); a CKm ( q)ex( m )ex( z); a J( ) / J( a) ex( z); a Ey Ex E K( q) / K( qa) ex( z); a V ka( N) ka n n ( / ) a n b V V V ( ) ( / ) ;.5.5 n n / k n / k ( n) n ( ) b n n b n n V / ; l arg e V 4 V / ; mall V GF M, M akn SF

2 Formula o grawal Fiber-Oti Communiation Sytem E ( )ex( / w )ex( z); x y x w a V V V 6 / ,..4 e w a x Ex ore a ex total w E m nx ny / m Setion - (ierion in Single-Moe Fiber) g / v n g / g ( / ) / g v / n nk n / / v n ( n) / n ( n / ) n ( n / ) g i i i / / / g n n M v g M n n g g W ng V ( V b) ng ( V b) n V V W M n( ) M ( Z / );.8 Z. i i i i 4 S S S ( ) G ( ) ( z) ( ) l ex( z / l ) z / l ( ) z ; z l ( ) l ; z l int er GV Setion -4 (ierion-nue imitation) ( ) n( ) / ( ) ( ) ( )... 6

3 Formula o grawal Fiber-Oti Communiation Sytem Gauian ule C t (, t) ex FWHM C (t) t.665 t / (, ) ex C C z t (, ) ex Qz ( ) C t Q( z) C / Q( z) ( C ) z / b C z z min C / zmin C / / C Non-Gauian ule b C V C V ; V S S V 8 V, C,, C, / 4 / 4 V, C / 4 / /4.4 V, C 4 / H( ) ex, / / ; V S

4 Formula o grawal Fiber-Oti Communiation Sytem ln.88 ;, Z Setion -5 (Fiber oe) out / z out in ex( ) (/ k m) log 4.4 in C / ;.7 C.9( / km) m 4 4 ex( / );. a / ( n n ).4 bening Setion -6 (Nonlinear Otial Eet) SS k / k k in / ; k k k k n / / n / g g z z g ( ) g ( ) g / th e th e e e [ ex( )] / SS gthe / e 6 6 w / th SM n / ( e ) XM n n n ( / );, g e z N in e i ; i N N e m / (M ) m Shröinger equation: z z z t 4

5 Formula o grawal Fiber-Oti Communiation Sytem Chater (Otial ranmitter) Setion - (Semionutor aer hyi) int rr nr nr nr rr N CN g ( N) ( N N ) nr g g ( N) g [ ln( N / N )] m n n g int mir av mir ln m m /n g g m Setion - (Single-Moe Semionutor aer) m( / n) Setion - (aer Charateriti) G t N N G G vggm GN( N N) th () ex( / ) t q C n G G v / V N g g N N V N N G vgav th ( N ) th qnth / q th ; th e ( gmir ) h q e h ext th h q E e h g total ext ext V qv qv e th int G G mir mir int N N N N ( G N N) t N ( ) in m b th t t ( t) in( t ) b m m b m m m mm N( t) N n in( t ) b m m m /4 GG Ω N N b N b GN m / q Ω m m / G b N b 5

6 Formula o grawal Fiber-Oti Communiation Sytem G / G th N N b Ω Ω Ω 4 4 Ω G G Ω Ω GG, G / N b N N b b th 4 4 q N N G FN t G S F t GN N N F t t q t t N( ) C ( )ex( ) / / {( N ) GN [ GN ( N / ) N ]} [( ) ][( ) ] / S ( ) ( ) N N, e N i N hv N SNN ; SN b ( ) ( b) [o( ) e o( )] o b /, tan ( / ) ( ) / (4 ) Setion -4 (Otial Signal Generation) ( t) GN ( N N) t 4 Setion -5 (ight-emitting ioe) h q int int / e ext int ext 4 in 4 / n n n / E ext tot ext h qv / extint / ex h q int on h Eg h Eg k.8k v FWHM h 6

7 Formula o grawal Fiber-Oti Communiation Sytem ex ex t t N t N N t b m m b m m b/ q Nb b / q, Nm( m) m H E Nmm E N m m Setion -6 (ranmitter eign) n N 7

8 Formula o grawal Fiber-Oti Communiation Sytem Setion 4- (ai Conet) Chater 4 = in / q h in / q h q [ ex( W )] hv.4 ab in tr in ab / ex( W ) V out (t) V[ ex( t / C)], (ln 9) C. in (ln 9)( ) r tr C =[ ( )] Setion 4- (Common hotoetetor) ie tr W / v C ( S ) C x i / x ( ) i e e h e h M M ( q / h ) Setion 4- (eeiver eign) tr C - ih eie hih eie hih ie( x) ih( x) x k M ex[ ( k ) ] k e r k / h e / e em C e M ( ) M [ ( M ) ] C C, C C C S ' ' ' Vout Z V (t) z ( t t ) ( t ) t out ( ) ( ) ( ) Z ( ) G ( ) G ( ) H ( ) / Y ( ) H ( ) H ( ) H ( ) H ( ) Z ( ) Z () F in out H in( t) hout (t) t ( t) [ o( / )], out ( ), H ( ) H ( ) / H () out H ( ) ( / )ot( / ) NZ Setion 4-4 (eeiver Noie) (t) i (t) i ( t) i ( t ) S ( )ex( ) i ( t) S ( ) q S ( ) = q H S ( ) k / q( ) i i i ( t) S ( ) (4 k / ) ( ) q( ) (4 k / ) F S n (t) (t) (t) (4 / ) n k F 8

9 Formula o grawal Fiber-Oti Communiation Sytem SN in ( in ) 4( / ) n q k F in SN 4k F SN n in in q h / / in 4kF n h 4kF n NE q M in in qm F ( ) in F ( M ) k M ( k )( / M ) SN qm F k F ( M in ) S ( in ) 4( / ) n SN in in qf hf SN ( / 4 k F ) M n in 4kFn km ot ( k) M ot q ( ) in M ot 4kF n kq ( in ) / Setion 4-5 (Coherent etetion) E ex ( t ) E ex[ ( t )] S S S O O O O ( t) o( t ) O S O F O,, S S O O F O (t) ( ) (t) o( ) S O Hom S O O ( t) S ( t) O ( t) ( ) o( t ) Het S O S O F O a () t, q( ), (4 k / ) F S t n SN ; Het O S a O q( O ) O / (q ). S S SN ; Hom O S q h SN 4 N SN Hom Het 9

10 Formula o grawal Fiber-Oti Communiation Sytem ESK hom er N /EFSKhetyn E h er N E er N E SK hom ESK het ayn N ex / SK et yn ex / 4 E h er N h N EFSK hetayn N SK et ayn ex / 4 /4 SK et yn Setion 4-6 (eeiver Senitivity) E () ( ) () ( ) E [( ) ( )] () () / ( ) ( ) ex er er x ( ) ex( y ) x y ( ) ( ) ex er E er 4 er ( ) ( ) ln Q ( ) / ( ) / Q ex( Q / ) E er( ) Q Q M M re ( ), = / qm F ( ) S re (4 k / ) F n M re Q / ( ) re Q qfq M ( ) Q / re min / M ot k k Qq kqq ( re ) ( q / ) Q ( km ot k) / / ( ) ( q / ) qq re ieal m m ex( N ) N / m! E ex( N ) / re Nh / N h E er ( N / )

11 Formula o grawal Fiber-Oti Communiation Sytem Setion 4-7 (Senitivity egraation) r / ex r ex re Q rex re rex Q ( rex ) rex ex log ( r ) log r re ex ex re () rex / ( in ) inr r N( ) Q re / ( ) S / S (4 q re ), r re re ( r ) Q ( ) Q q r Q log [ re ( r ) / re ()] log [ r Q ] i Q ( ) / i [ h () h ( t)], out out i ( i ) ex( ) bi b i ( / 4)( t) b t ( t) ex (4 / 8)( ) i b b /, / re Q b / ( b) b b Q ( / ) / S log ( b ) log b / () ( / ) / re re b b Q

12 Formula o grawal Fiber-Oti Communiation Sytem Setion 5- (Sytem rhiteture) Chater 5 (ightwave Sytem) [( )( C)] N N log N bu N ( / N)( ) tar C Setion 5- (eign Guieline) r tr log re.c C M C on lie Vout (t) V[ ex( t / C)] tr re S H ( ) ( C) r.5 /.5 /.7 / r Z r NZ r tr iber re iber mo al GV ( n / ) mo al SF ( n / 8 ) moal GF GV Setion 5- (ong-haul Sytem): Shroinger equation (age 4) Setion 5-4 (Soure o ower enalty) k / 5log ( Qr ) mn mn n n r N( ) (N) e b / [ ( / ) ] / re i i r Q log ( e ) re r N / (MS) log b rmn ( k / ){ ex[ ( ) ]} 5log [( (8 C / ) (8 / ) ] 5log [ (4 / ) ] 5log [ (8 / ) ] C, V eye eye oening ater tranmiion log. eye oening beore tranmiion Setion 5-5 (Forwar-Error Corretion) G log ( Q / Q) E er( Q / ), E er( Q / )

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Formulas of Agrawal s Fiber-Optic Communication Systems. Section 2-1 (Geometrical Optics Description) NA n 2 ; n n. NA( )=n1 a Formula o grawal Fier-Oti Commuiatio Sytem Chater (troutio 8 max m M E h h M m 4 6.66. J e.6 9 m log mw S, Chater (Otial Fier SFMMF: i i ir Z Setio - (Geometrial Oti eritio i Z S log i h max E ii o ; GFMMF: