Diffractive optics. Introduction/terminology

Transcription

1 Itroductio ECE 566 OE Syste Desig Diractive optics Itroductio/teriology Classes Diractive optical eleet: Modiicatio o the optical waverot via subdivisio ad idividual odiicatio o the phase ad/or aplitude o the segets. ratig: liear segets uior diractio agle Coputer geerated hologra: A DOE i which the structure has bee calculated uerically Holographic optical eleet: DOE i which the structure is geerated by the itererece o optical waverots. Discretizatio Biary optic: phase or aplitude structure with two levels. Typically created via a sigle etch step. Daa gratig: Biary optics with repetitive patter, geerates N beas (a out) Multilevel optic: Sae as biary but with M etch steps to achieve N M levels. Kioor: Phase DOE with soothly varyig proile (liit o N ) Blazed: ratig with liear (sawtooth) segets Fabricatio Direct achiig: aa rulig or diaod turig, ab via echaical achiig. Ote used or asters. Lithography Direct write: sca laser or e-bea over photoresist Itererece (holography) ic ear ield Mass: grey-scale, ultiple eposure Replicatio O Shea, Diractive Optics: Desig, Fabricatio ad Test 74

2 Diractio gratigs ECE 566 OE Syste Desig Diractio gratigs Basics Real-space Fourier-space z L i d i K i +3 i + K + K + 3K i i E out L j d si( K ) ( ) E ( ) rect e E i i ( ) rect L J ( d ) e jk FT E out ( ) A δ ( ) i A J ( i J d i ) δ ( *sic ( K ) d ) sic L * ( K ) i L What are agles o diracted waves? π siθ + K i π π siθi + Coservatio o trasverse siθ siθ i + ratig equatio 75

3 Diractio gratigs ECE 566 OE Syste Desig Resolvig power aa uber o spots Real-space Fourier-space z + θ blue pea θ red pea i-b K π L i-r θ red ull si red blue K θ blue pea π L red π π L π δ L R N δ si K blue where N Rayleigh resolvability criterio L algebra uber o gratig lies illuiated 76

4 Diractio gratigs ECE 566 OE Syste Desig Estiatio o gratig R Why gratigs are iterestig Holographic gratigs o 8 lp/ are typical i the visible. A bea ad irst-order diractio would yield R 8 8, or a iiu resolvable wavelegth shit o.3 i the visible. For a pris at the iiu deviatio coditio (syetrical icidet ad eit agles) the resolvig power ca be show to be R δ d R B b b b V ( Y ) d R B 7 I the visible a b 5 pris would give resolvig power R 34 Crow Flit S S or δ ~.5 to.7, roughly a order o agitude lower resolutio tha a gratig. w φ b φ S S b + w 77

5 Diractio gratigs ECE 566 OE Syste Desig Badwidth aa Free spectral rage z K K Whe will diractios be coused with the eighborig order? θ red si blue red θ K red blue+ ( + ) + + blue si blue blue K blue Thus irst-order gratig spectroeter could operate ro 4 to 8. 78

6 Diractio gratigs ECE 566 OE Syste Desig Eiciecy Overview by type Thi phase gratig: Typically ay orders, ca t reach % i ay (e.g. siusoidal). h i Siusoidal phase K K i π/ i π π + K i Eceptio: blazed phase gratig: Ca be % i sigle order Thi aplitude gratig: Lossy (by deiitio), typically ay orders. /() Eceptio: Siusoidal aplitude gratig: DC ad +/- orders Thic phase gratig: Bragg selectivity ca give sigle order ad theoretically % DE. BUT, very sesitive to icidet wave (ulie thi). 79

7 Diractio gratigs ECE 566 OE Syste Desig Multilevel DOEs Why you pay or the Phase (ot physical) proiles: / N /4 3/4 N4 N d B D First order diractio eiciecy vs. uber o levels η sic π [ / N ] N 8

8 DOEs as leses ECE 566 OE Syste Desig Diractive les desig Multilevel o-ais Fresel r r + Ferat (reractive) all rays have OPL Diractive all rays have OPL odulo Thus reractive is liit o diractive w/. r Spherical covergig waverot What is the radial locatio o the p th zoe or a th order DOE abricated with N layser? rp + [ + p N ] OPL o each zoe diers by /Ν r p N + p N p p [ ] What is the radius size o the p th zoe? p+ r r p+ r p p r p ( p + ) ( rp+ rp )( rp+ + rp ) r( r ) p N N For >> p N N [ rn ] [ F # N ] Radius o p th ad p+ th zoe Tae dierece Epad Local gratig period Note or iiu eature size, N reduces F/# liearly (ouch). 8

9 DOEs as leses ECE 566 OE Syste Desig Diractive leses depedece o agles Readig a diractive optic at ad order that was desiged or ad order. z θ Local gratig period θ siθ π siθ π siθ π π e siθ e e K K h DOE Chage i agle is perectly aalogous to reractig ito a slab o ide e. Note that this ide ca be <. h siθ h siθ siθ siθ e Deiitio o ocal legth.. Diracts to set o ocii.. For e, each suers spherical aberratio. 8

10 83 ECE 566 OE Syste Desig Diractive leses depedece o eiciecy (/) For a ioor (N ) h() t ( ) t h ( ) ( ) ( ) [ ] ( ) ( ) ( ) t h t h t h S + + OPL by desig is at. Calculate ro proile Substitute h() t Solve or step height. ( ) ( ) S OPL at shited ( ) ( ) S π π φ Phase at ( ) ( ) l j ratig l e T δ π rect Trasissio as ( ) ratig T π δ π sic costat Diractive optics DOEs as leses Which gives us the diracted electric ield vs. agle or a uior E ic

11 DOEs as leses ECE 566 OE Syste Desig Diractive leses depedece o eiciecy (/) Eiciecy o a blazed gratig desiged or wavelegth ad order with ide read at wavelegth ad order with ide η sic π I a blazed gratig has % theoretical DE i the desig order ad (coveietly) % i all other orders. η - - η I / a blazed gratig has 4.5% theoretical DE i the desig order ad a equal aout i the et lowest order. A iiite # o orders are preset

12 DOEs as leses ECE 566 OE Syste Desig Hybrid reractive/does B φ V ( ) φ( ) φ φ R DOE φ B R φy Y Y B Y V DOE R Fro page 8 I used at sae order ( ) Fid chage i power over Fro page 7 Solve or V. This is a) the sae or all DOEs, b) egative ad c) very strog. Let s desig a achroatic 5.4 BK7 siglet: φbk 7 φdoe +, φbk 7 + φdoe φ , φ DOE BK 7 / Achroatic coditios Note the reractive power is early uchaged ad the DOE is quite wea. 85