Layered structures: transfer matrix formalism

Transcription

1 Layered tructure: trafer matrx formalm Iterface betwee LI meda Trafer matrx formalm Petr Kužel Practcally oly oe formula to be kow order to calculate ay tructure Applcato: Atreflectve coatg Delectrc mrror, Chrped mrror Laer output coupler Beam-pltter Beam-plttg mrror Iterferece flter

2 Trafer matrx formalm (tagetal) k t α α k + r y T polarzato x η t + ( ) t α z (tagetal) k k + r η + r ( ) r δ coα π dkz d λ co α te e r δ δ

3 Itroducto of trafer matrx η δ δ δ δ η co co δ δ δ δ m m m m co co Trafer matrx coect tagetal feld o both ed of a layer For -th layer: For the whole tructure: η η η ,,,, tot!

4 Reflecto ad tramo coeffcet + r t, + tot tot η ( r) tt η, + r t m m m tm m t t m m + m + m tm + m + t t m polarato T: polarato T: ormal cdece: co δ ω d co α c α α / ω d co α / ω d / c co δ c δ

5 The formalm alo vald for Geeralzato aborbg layer; -th layer aborb: κ coα α layer where total reflecto occur; total reflecto o -th layer: co α α δ ad become magary; oe troduce: δ ad Γ, where ad Γ are real. The trafer matrx become: ch Γ h h Γ ch

6 Applcato Optcal elemet ad coatg are deged for gve cdece agle Specfc layer thckee are frequetly ued tack: quarter-wave () layer co 4 π α λ π δ λ "$"# % d half-wave (λ/) layer π α λ π δ λ %"$"# co d quarter-wave (-) blayer

7 Atreflectve gle layer Let try -layer (the wave wth λ/ phae delay wll terfere) gf.8 r BK7 gla.5.5 Broadbad R (%) 4 Atreflectve coatg (for 55 m) gla (ot treated) Le effcet (o degree of freedom for ) Wavelegth (m)

8 Atreflectve blayer quarter-wave (-) blayer CeF ZrO.65. r + + BK7 gla.5 V-lke hape (arrow frequecy rage) R (%) 6 4 gla (ot treated).5 Atreflectve coatg (for 55 m) - ore effcet (oe degree of freedom for, ) Wavelegth (m)

9 Broadbad AR coatg trlayer tructure (--) r BK7 gla..5.8

10 Broadbad AR coatg trlayer tructure (-λ/-): mlar to a quarter-wave blayer at the reoat wavelegth half-wave layer help to exted the atreflectve rage λ/.8. r BK7 gla.5

11 Atreflectve coatg: ummary Atreflectve coatg for 55 m 8 - R (%) 6 4 -λ/ -- -λ/-.5 gla (ot treated) Wavelegth (m)

12 Delectrc mrror blayer ( L << ): L blayer: L L L ( ) L ( ) L Reflectvty: L R ( )( L ) ( )( ) L +

13 Delectrc mrror: example R.8.6 Phae chage Waveumber (cm - ).4. Delectrc mrror for 8 m umber of blayer (ZS/gF ): Wavelegth (m)

14 Chrped delectrc mrror The reoat wavelegth learly tued alog the tack of blayer Dfferet wavelegth are reflected at dfferet depth dfferet optcal path Addg or compeatg of a chrp of the pule Departure from the lear phae hft rror for 8 m (5 cm - ) ( blayer) Stadard delectrc mrror Chrped mrror ( m tep) Waveumber (cm - )

15 Laer output coupler R R x < λ 54.5 m R x Reflectve (~ 9%) coatg AR coatg

16 Beampltter % R, d R 45, d, d 8%

17 Beamplttg mrror Separato of harmoc frequece (e.g. d:yag fudametal beam at 64 m ad t ecod harmoc at 5 m) Log-pa or cut-off flter xample of oluto: ) Stack of blayer formg a delectrc mrror for 64 m Thee layer are λ/ for the ecod harmoc o t pae through uchaged ) We add below a AR coatg for 5 m 64 m compoet doe ot peetrate dow to thee layer Reult: 64 m reflected, 5 m tramtted Sometme a detug of a reoat wavelegth ued everal layer of the R coatg: t ca mooth the uwated terferece maxma ad mma.

18 Iterferece bad-pa flter Cota: Stack of hgh-reflectg blayer Atreflectve coatg Fabry-Pérot cavte Detug of the reoat wavelegth alo ofte ued for moothg of the terferece