Lecture 35. Diffraction and Aperture Antennas

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Emerald Reed
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1 ctu 35 Dictin nd ptu ntnns In this lctu u will ln: Dictin f lctmgntic ditin Gin nd ditin pttn f ptu ntnns C 303 Fll 005 Fhn Rn Cnll Univsit Dictin nd ptu ntnns ptu ntnn usull fs t (mtllic) sht with hl ( n ptu) f sm shp thugh which ditin cms ut Th ntul spding f lctmgntic wvs in f spc whn mnting fm suc is clld dictin Incming ditin Qustins Wht hppns n this sid? w ds th ditin cming ut f th ptu ls li whn th dimnsins f th hl f th d f th wvlngth? Wht is th ditin pttn? C 303 Fll 005 Fhn Rn Cnll Univsit 1

2 ptu ntnns in Pctic: Rctngul Wvguids w ds ditin cming ut f ctngul wvguid ls li? Mtl ctngul wvguid P σ Dictin σ Sm fctin f th incidnt pw is flctd fm th pn nd nd sm is ditd ut Rditin cming ut f ctngul ptu C 303 Fll 005 Fhn Rn Cnll Univsit ptu ntnns in Pctic: Dilctic Wvguids Opticl fib Dictin Rditin cming ut f cicul ptu Intgtd Phtnics (dilctic wvguids n chip) Dictin Rditin cming ut f intgtd dilctic wvguid (.g. smicnduct ls) C 303 Fll 005 Fhn Rn Cnll Univsit

3 ssumptin nd Gl Incidnt ditin ssumptin: ssum tht w nw th fild f ll tim ight t th ptu ( 0 t ) This w culd nw f mpl fm u nwldg f th incidnt (nd flctd) filds bhind th ptu Gl: T find th fild f > 0 ( t )? C 303 Fll 005 Fhn Rn Cnll Univsit K -fild nd Sufc Cunt Dnsit Bund Cnditin Fist cll th sufc cunt bund cnditin f th -fild (nw in vct fm): 1 n n ( ) K 1 F lft-ight smmtic pblm: K 1 n 1 n K C 303 Fll 005 Fhn Rn Cnll Univsit 3

4 Pincipl f quivlnc (ugns Pincipl) Pincipl f quivlnc ss tht if n nws th ditin - nd -filds t v pint n n imgin clsd sufc thn th ditin utsid th clsd sufc cn b dscibd s th ditin gntd fm sufc cunt dnsit tht flws n th clsd sufc s quivlnt K s s pblm??? ( ) s s ( ) ( ) s K s ( ) n ( ) Pincipl f quivlnc is mthmticl sttmnt f th ld ugns Pincipl tht sid tht v pint n wv-fnt cn b cnsidd suc f ditin C 303 Fll 005 Fhn Rn Cnll Univsit ptu ntnn nd th quivlnt Pblm ssumptin: Knwing th -fild nd -fild phss t th ptu llws us t cnsid th quivlnt pblm f ditin b cunt sht dnsit ( 0 ) ( ) ( ) ( 0 ) K( ) ( ) ( ) ( ) ( ) δ C 303 Fll 005 Fhn Rn Cnll Univsit 4

5 5 C 303 Fll 005 Fhn Rn Cnll Univsit δ 4 dv µ Knwing th cunt dnsit us th suppsitin intgl f th vct ptntil t clcult th filds: M th f-fild ( th Funh) ppimtin: 4. dv µ Cmput th -fild in th f-fild ppimtin: ptu ntnns: nlsis [ ] [ ] 4. fild in f dv c ω ω. Nt tht in th f-fild: C 303 Fll 005 Fhn Rn Cnll Univsit Rctngul ptus: Gnl Cs 0 δ f & thwis [ ] 4. dv Us th fmuls: [ ] T gt:. d d d d O: F-fild is pptinl t th D Fui tnsfm f th fild t th ptu + + +

6 6 C 303 Fll 005 Fhn Rn Cnll Univsit Rctngul ptus with Unifm Fild t th ptu 0 δ f & thwis d d F-fild is pptinl t th D Fui tnsfm f th shp f th ptu O: d d C 303 Fll 005 Fhn Rn Cnll Univsit Fui Tnsfms nd th Rctngul ptu F-Fild Cnsid th 1D b functin FT f th 1D b functin 1 FT: d f F IFT: d F f f F F d d Th f-fild -fild is pptinl t th D FT f th ptu shp Width f min lb in -spc 4

7 Rctngul ptu: F-Fild ( ) ( ) ( φ ) cs cs ( ) ( ) -fild mplitud n pln ppndicul t th -is is plttd C 303 Fll 005 Fhn Rn Cnll Univsit Rctngul ptu: ngul Widths f th Min b cs( ) ( ) F: null ngul width f min lb in vticl dictin is gvnd b th functin: ( ) ( ( ) ) ( ) Th ngul hlf-width is dtmind b whn th tm insid th functin bcms ± ( null ) ± ± C 303 Fll 005 Fhn Rn Cnll Univsit 7

8 Rctngul ptu: ngul Widths f th Min b ( ) cs( φ ) ( φ ) F: φ φ φ null ngul width f min lb in hintl dictin is gvnd b th functin: ( ) ( ( φ ) ) ( φ ) Th ngul hlf-width is dtmind b whn th tm insid th functin bcms ± ( φ null ) ± ± C 303 Fll 005 Fhn Rn Cnll Univsit Rctngul ptu: Rditin Pttn p( φ ) φ φ 0 4 p( φ ) C 303 Fll 005 Fhn Rn Cnll Univsit 8

9 Wht Cuss th Nulls in th Dictin Pttn? φ null ( ) null φ slit C 303 Fll 005 Fhn Rn Cnll Univsit Nulls in th Dictin Pttn: Intfnc in Dictin F th fist null in th φ dictin n must hv wvs cming fm n hlf f th slit intf dstuctivl with th wvs cming fm th th hlf f th slit: Cn u guss wht ind f intfnc is spnsibl f th scnd null? Th thid null?.. ( φ ) ( φ ) φ ( φ ) slit C 303 Fll 005 Fhn Rn Cnll Univsit 9

10 Rctngul ptu: F-Fild Intnsit Intnsit n pln ppndicul t th -is is plttd v S t ( ) ( ) ( ) ( ) 1 C 303 Fll 005 Fhn Rn Cnll Univsit 3 Rctngul ptu: F-Fild Intnsit Intnsit n pln ppndicul t th -is is plttd Th lbs wid in th dictin in which th ptu dimnsin is smll v S t ( ) ( ) ( ) ± ± ( ) null ( ) ( ) 1 φ null ± ± C 303 Fll 005 Fhn Rn Cnll Univsit 10

11 v S Rctngul ptu: Ttl Rditd Pw t ( ) ( ) cs( φ ) cs( ) ( ) ( ) 1 Ttl pw ditd: Clcult ight t th ptu Pd S 00 1 ( t ). ( ) d dφ C 303 Fll 005 Fhn Rn Cnll Univsit Gin: G ( φ ) ptu ntnns: Gin nd ctiv v S ( t ). d Pd 4 4 ( ) ( ) ( ) d 4 ( φ ) ctiv : ( φ ) ( ) Mimum ctiv : ( φ ) ( ) ( ) d m φ { ptu } Mimum pssibl ctiv f n ptu ntnn (f n shp) is qul t its ctul phsicl d d C 303 Fll 005 Fhn Rn Cnll Univsit 11

Study Material with Classroom Practice solutions. To Electromagnetic Theory CONTENTS. 01 Static Fields Maxwell Equations & EM Waves 06 11

Study Material with Classroom Practice solutions. To Electromagnetic Theory CONTENTS. 01 Static Fields Maxwell Equations & EM Waves 06 11 Pg No. Stud Mtil with lssoom Pctic solutions To lctomgntic Tho ONTNTS hpt No. Nm of th hpt Pg No. Sttic Filds 5 Mwll qutions & M Wvs 6 Tnsmission ins Wvguids 5 6 5 lmnts of ntnns 7 hpt. ns: V cos cos î