In-fiber acousto-optic interaction

Transcription

1 I-fib acouo-opic iacio Migul V. Adé Laboaoio d Fiba Ópica d la Uividad d Valcia Dpaamo d Fíica Aplicada ICMUV migul.ad@uv. Gal objciv Fabicaio of all-fib dyamic dvic bad o h i-fib acouo-opic iacio A adad opical fib i a idal wavguid fo boh h opical ad h acouic wav ad hi pmi o hav lag iacio lgh Th ampliud ad fqucy of h acouic wav cool h iacio: Dyamic dvic wih a im po of ~ 1 µ Flxual wav R Logiudial wav λ m λ m

2 Co I-fib acouo-opic iacio I. Opical ad acouic mod guidd by a opical fib I.1. Th fudamal acouic mod I.. Co ad claddig opical mod II. Acouo-opic iacio: coupld mod hoy II.1. Th faciv idx pubaio gad by a acouic wav II.. Coupld wav hoy II.3. Flxual wav: Couplig coffici ad baic dvic II.4. Logiudial wav: Couplig coffici ad baic dvic III. Applicaio III.1. Dyamic add & dop muliplx III.. Wavlgh-wichabl all-fib la III.3. Q-wichd fib la III.4. Tuabl ad cofiguabl micowav opical fil IV. Cocluio I. Opical ad acouic mod i a opical fib I.1. Th fudamal acouic mod Th wav quaio fo acouic wav i a ioopic homogou mdium u λ + µ u µ u ρ = λ ad µ a h Lamé coffici: λ = c 1 ad µ = c 44 wh c ij i h iff o ρ i h diy u i h vco diplacm Th vlocii of popagaio of compioal, c D, ad ha wav, c : λ µ c + µ D = c = ρ ρ Th Youg modulu, E, ad h Poio coffici, σ: 3λ + µ λ E = µ σ = λ + µ λ + µ Fud ilica: λ = g/m µ = g/m ρ =. 1 3 g/m 3 c D = 5975 m/ c = 3764 m/ E = g/m σ =.17

3 I. Opical ad acouic mod i a opical fib I.1. Th fudamal acouic mod Th oluio fo a cicula olid cylid [ ]. J B J A i W J C J B J A V J C J B J A U d d d d = + + = + + = Ω = Ω = d d c c I. Opical ad acouic mod i a opical fib I.1. Th fudamal acouic mod Th logiudial acouic mod Bouday codiio h ou ufac a = a f of acio: T = T = T φ = Logiudial mod copod o = ad u φ = c l = c/c x, c = Ω/, c x = E/ρ 1/ f = 1 MH, a = 15 µm.17

4 I. Opical ad acouic mod i a opical fib I.1. Th fudamal acouic mod Th fudamal logiudial acouic mod fa/c Cocluio: Fo a opical fib, a ~ 15 µm, ad a f < 1 MH, h fudamal logiudial mod will hav coa vlociy c = E/ρ 1/ = 576 m/, ad h ai will b appoximaly axial u ad u Λ I. Opical ad acouic mod i a opical fib I.1. Th fudamal acouic mod Th flxual acouic mod Bouday codiio h ou ufac a = a f of acio: T = T = T φ = Flxual mod copod o > Οly fo = 1 h i o mod wih o cuoff = 1 c l = c/c x, c = Ω/, c x = E/ρ 1/ c l c = π c x f a c.3 f = MH, a = 15 µm

5 xy I. Opical ad acouic mod i a opical fib I.1. Th fudamal acouic mod Th fudamal flxual acouic mod Si fa / c << 1: u A φ φ { i u coφ u } xp i Ω [ ] = Au xp[ i Ω ] y π/ pha diffc fa/c I. Opical ad acouic mod i a opical fib I.1. Th fudamal acouic mod Th fudamal flxual acouic mod Cocluio: Fo a opical fib, a ~ 15 µm, ad a f < MH, h fudamal flxual mod will hav a vlociy: cx f a cl c c ad h diplacm will b appoximaly aval: u xp i Ω = π [ ] A y

6 Co I-fib acouo-opic iacio I. Opical ad acouic mod guidd by a opical fib I.1. Th fudamal acouic mod I.. Co ad claddig opical mod II. Acouo-opic iacio: coupld mod hoy II.1. Th faciv idx pubaio gad by a acouic wav II.. Coupld wav hoy II.3. Flxual wav: Couplig coffici ad baic dvic II.4. Logiudial wav: Couplig coffici ad baic dvic III. Applicaio III.1. Dyamic add & dop muliplx III.. Wavlgh-wichabl all-fib la III.3. Q-wichd fib la III.4. Tuabl ad cofiguabl micowav opical fil IV. Cocluio Covioal opical fib I. Opical ad acouic mod i a opical fib I.. Co ad claddig opical mod Th fudamal opical co mod Hx,y,, = h x, y jβ jω E a.u. 9 µm co G-dopd ilica 15 µm claddig ilica h = h x, h y 1 + = m, m = β = ε h h j H ρ, φ,, = J ρ j H ρ, φ,, = K h ρ h = co = β β clad β β jω jω u u y y c v f ρ < a ρ > a co

7 I. Opical ad acouic mod i a opical fib I.. Co ad claddig opical mod Th fudamal opical co mod Gauia appoximaio E a.u. 4Z P x + y E = xp πw w w = a 3 / 6 V V u x co V = a co claddig jβ jω Ex,y,, = E ; co > β > clad β co β = mod co Covioal opical fib I. Opical ad acouic mod i a opical fib I.. Co ad claddig opical mod Th claddig mod 15 µm claddig ilica Th fild compo Φ Φ Φ h clad m ai m ' ' J ρ co φ K = ' ' h clad = β ρ co φ β lm jβ jβ jω jω ρ < a ρ > a clad clad clad > β > β ai clad β = mod clad

8 Co I-fib acouo-opic iacio I. Opical ad acouic mod guidd by a opical fib I.1. Th fudamal acouic mod I.. Co ad claddig opical mod II. Acouo-opic iacio: coupld mod hoy II.1. Th faciv idx pubaio gad by a acouic wav II.. Coupld wav hoy II.3. Flxual wav: Couplig coffici ad baic dvic II.4. Logiudial wav: Couplig coffici ad baic dvic III. Applicaio III.1. Dyamic add & dop muliplx III.. Wavlgh-wichabl all-fib la III.3. Q-wichd fib la III.4. Tuabl ad cofiguabl micowav opical fil IV. Cocluio II. Acouo-opic iacio: coupld mod hoy II.1. Th faciv idx pubaio Effc of ai o h popagaio of h opical mod Covioal opical fib Hx,y,, = h x, y jβ jω 9 µm co G-dopd ilica 15 µm claddig ilica β = Φ = β mod Φ = mod L ε = = E L d d mod F S co dφ = = co p ε Effciv faciv idx d + d ad mod mod d = ε dφ = Φ[ 1 p ]ε dff dff dφ = dff = [ 1 p ]ε dφ = mod dff = [ 1 p ]ε ff ff : Effciv lgh ff : ff

9 II. Acouo-opic iacio: coupld mod hoy II.1. Th faciv idx pubaio Effc of ai o h popagaio of h opical mod Flxual wav Logiudial wav Piolcic di Opical fib Ho RF gao u, = u co Ω δ =δ co Ω f δ = 1 p u f y ε, =ε co Ω =δ co Ω δ f δ = f 1 p ε Co I-fib acouo-opic iacio I. Opical ad acouic mod guidd by a opical fib I.1. Th fudamal acouic mod I.. Co ad claddig opical mod II. Acouo-opic iacio: coupld mod hoy II.1. Th faciv idx pubaio gad by a acouic wav II.. Coupld wav hoy II.3. Flxual wav: Couplig coffici ad baic dvic II.4. Logiudial wav: Couplig coffici ad baic dvic III. Applicaio III.1. Dyamic add & dop muliplx III.. Wavlgh-wichabl all-fib la III.3. Q-wichd fib la III.4. Tuabl ad cofiguabl micowav opical fil IV. Cocluio

10 II. Acouo-opic iacio: coupld mod hoy II.. Coupld wav hoy Bai popi of h mod of a wavguid Wavguid: Hx,y,, = h x, y ε x,y h = h + h y h = h, h jβ x jω y, Th i o af of pow bw mod popagaig alog a wavguid H = jβ H 1 H = 1 + = m, m = β = ε h h S * j * Hi P = h ds = P1 + i= 1 i h ds = Pδ i P ij c v f Couplig bw wo mod by ioducig a pubaio Oigial wavguid ~ ~ H1 ~ ~ H ~ ~ ~ = jβ1h1 = jβ H x, y ~ H ~ ε Ioducig a pubaio II. Acouo-opic iacio: coupld mod hoy II.. Coupld wav hoy ~ x, y ε x, y 1 ~ ~ ~ ~ = jβ1h1 + j1h = jβ H + j 1H1 ~ ~ jβ1 H 1 x,y,, = h1 x, y ~ ~ jβ H x,y,, = h x, y jω jω Taf of pow bw h oigial mod of h wavguid ε ~ H ~ h ~ h ~ ~ ~ ~ j β1 β = j 1h 1 ~ ~ ~ j β β = j 1h1 1

11 II. Acouo-opic iacio: coupld mod hoy II.. Coupld wav hoy Qualiaiv divaio of h couplig coffici 1 B D E = H = Ioducig a pubaio ε ε + δε D J D = = jωε E δj D = jω δε E 1 * Poyig Thom: P = J E dv 4 δε δ V * P1 δj1 E dv δε E1E V δ E * 1 1E V dv V * dv Co I-fib acouo-opic iacio I. Opical ad acouic mod guidd by a opical fib I.1. Th fudamal acouic mod I.. Co ad claddig opical mod II. Acouo-opic iacio: coupld mod hoy II.1. Th faciv idx pubaio gad by a acouic wav II.. Coupld wav hoy II.3. Flxual wav: Couplig coffici ad baic dvic II.4. Logiudial wav: Couplig coffici ad baic dvic III. Applicaio III.1. Dyamic add & dop muliplx III.. Wavlgh-wichabl all-fib la III.3. Q-wichd fib la III.4. Tuabl ad cofiguabl micowav opical fil IV. Cocluio

12 Flxual wav: Couplig coffici co ff Ω =δ δ j j j j j j j j y x y x Ω Ω + = Ω = = 1 co,, ω β ω β E E + Ω S V d dxdy dv * 1 * 1 1 co E E E E δ δ II. Acouo-opic iacio: coupld mod hoy II.3. Flxual wav Flxual wav: Couplig coffici [ ] + + Ω + +Ω + dxdy y x d j j j j * 1 1, δ ω ω β β ω ω β β Bagg codiio pha machig: Covaio of gy: ± β 1 β ±Ω ω 1 ω II. Acouo-opic iacio: coupld mod hoy II.3. Flxual wav + dxdy y x * 1 1, δ

13 II. Acouo-opic iacio: coupld mod hoy II.3. Flxual wav Flxual wav: Couplig coffici ad baic popi Bagg codiio pha machig: β 1 β ± Covaio of gy: ω 1 ω ±Ω δ f =δ co Ω δ = 1 p u f y LP 1, co + 1 δ x, y 1 * LP 11, claddig dxdy II. Acouo-opic iacio: coupld mod hoy II.3. Flxual wav Flxual wav: Opimiaio Dco RF gao Ho Piolcic + 1 δ x, y 1 * dxdy

14 II. Acouo-opic iacio: coupld mod hoy II.3. Flxual wav Tapig a opical fib 7.5/15 µm, NA=.13 Faco duco d.5 II. Acouo-opic iacio: coupld mod hoy II.3. Flxual wav Flxual wav: Baic popi Pha machig: β 1 β ±

15 II. Acouo-opic iacio: coupld mod hoy II.3. Flxual wav Flxual wav: Baic popi 85 µm ap Co I-fib acouo-opic iacio I. Opical ad acouic mod guidd by a opical fib I.1. Th fudamal acouic mod I.. Co ad claddig opical mod II. Acouo-opic iacio: coupld mod hoy II.1. Th faciv idx pubaio gad by a acouic wav II.. Coupld wav hoy II.3. Flxual wav: Couplig coffici ad baic dvic II.4. Logiudial wav: Couplig coffici ad baic dvic III. Applicaio III.1. Dyamic add & dop muliplx III.. Wavlgh-wichabl all-fib la III.3. Q-wichd fib la III.4. Tuabl ad cofiguabl micowav opical fil IV. Cocluio

16 II. Acouo-opic iacio: coupld mod hoy II.4. Logiudial wav Logiudial wav + fib Bagg gaig II. Acouo-opic iacio: coupld mod hoy II.4. Logiudial wav Fib Bagg gaig δ = δ co K + φ K ; π = Λ j β β1 j β β1+ [ + ] d δε x, y * 1 dxdy Bagg codiio: β 1 β ± If β 1 = β = π/λ mod Λ= λ/ mod λ Β = mod Λ

17 II. Acouo-opic iacio: coupld mod hoy II.4. Logiudial wav Fib Bagg gaig P P i P Couplig o h flcd fudamal mod: Λ = λ mod o Rflciviy: 9% Epcal widh: 4 pm Rflciviy > 99.9 % Epcal widh:.1 m II. Acouo-opic iacio: coupld mod hoy II.4. Logiudial wav Logiudial wav + fib Bagg gaig ε [ P ] 1/ EAv = / g

18 Bagg gaig: δ = δ co{ K+ φ} Bagg gaig pubad by a logiudial wav: δ = δ co{ K + δ + φ} P II. Acouo-opic iacio: coupld mod hoy II.4. Logiudial wav Logiudial wav + fib Bagg gaig δ = { Ω } d= { Ω } ε co ε Kε δ = δ co K Ω Λ λbm = λb m 1± y ωm = ω m mω λ δ E * 1 1E V dv 1..8 II. Acouo-opic iacio: coupld mod hoy II.4. Logiudial wav Logiudial wav + fib Bagg gaig λ Β R λ m λ m λ B λ B = f v

19 R L λ B ε λb m = ah J m 1,,8,6 ε II. Acouo-opic iacio: coupld mod hoy II.4. Logiudial wav Logiudial wav + fib Bagg gaig [ P ] 1/ EAv = / g R R1 R 1,,8,6,4,,,,5 1, 1,5 A p V pp f = 1 MH R,4, A p,4 V pp A p,75 V pp A p 1,4 V pp, λ m λ m λ m Co I-fib acouo-opic iacio I. Opical ad acouic mod guidd by a opical fib I.1. Th fudamal acouic mod I.. Co ad claddig opical mod II. Acouo-opic iacio: coupld mod hoy II.1. Th faciv idx pubaio gad by a acouic wav II.. Coupld wav hoy II.3. Flxual wav: Couplig coffici ad baic dvic II.4. Logiudial wav: Couplig coffici ad baic dvic III. Applicaio III.1. Dyamic add & dop muliplx III.. Wavlgh-wichabl all-fib la III.3. Q-wichd fib la III.4. Tuabl ad cofiguabl micowav opical fil IV. Cocluio

20 III. Applicaio III.1. Dyamic add & dop muliplx Objciv OFF ON III. Applicaio III.1. Dyamic add & dop muliplx Piodic af of pow wih flxual wav P P i P i i 4 V 1 V V P P P i 4 V, ii 1 V ad iii V

21 P i V III. Applicaio III.1. Dyamic add & dop muliplx Piodic af of pow wih flxual wav P V Dyamic add & dop a OUT wih acouic wav off b OUT wih acouic wav o c ADD/DROP wih acouic wav off d ADD/DROP wih acouic wav o III. Applicaio III.1. Dyamic add & dop muliplx

22 I-fib acouo-opic iacio I. Opical ad acouic mod guidd by a opical fib I.1. Th fudamal acouic mod I.. Co ad claddig opical mod II. Acouo-opic iacio: coupld mod hoy II.1. Th faciv idx pubaio gad by a acouic wav II.. Coupld wav hoy II.3. Flxual wav: Couplig coffici ad baic dvic II.4. Logiudial wav: Couplig coffici ad baic dvic III. Applicaio III.1. Dyamic add & dop muliplx III.. Swichabl-wavlgh all-fib la III.3. Q-wichd fib la III.4. Tuabl ad cofiguabl micowav opical fil IV. Cocluio Co III. Applicaio III.. Wavlgh-wichabl all-fib la Objciv λ 1, λ, λ 3...

23 III. Applicaio III.. Wavlgh-wichabl all-fib la Emiio a a fucio of acouic ampliud III. Applicaio III.. Wavlgh-wichabl all-fib la Emiio a a fucio of acouic ampliud

24 III. Applicaio III.. Wavlgh-wichabl all-fib la Emiio a a fucio of acouic ampliud Swichig fom od o od 1 Swichig fom od o od I-fib acouo-opic iacio I. Opical ad acouic mod guidd by a opical fib I.1. Th fudamal acouic mod I.. Co ad claddig opical mod II. Acouo-opic iacio: coupld mod hoy II.1. Th faciv idx pubaio gad by a acouic wav II.. Coupld wav hoy II.3. Flxual wav: Couplig coffici ad baic dvic II.4. Logiudial wav: Couplig coffici ad baic dvic III. Applicaio III.1. Dyamic add & dop muliplx III.. Wavlgh-wichabl all-fib la III.3. Q-wichd fib la 4 diff ca III.4. Tuabl ad cofiguabl micowav opical fil IV. Cocluio Co

25 III. Applicaio III.3. Q-wichd fib la Flxual wav: Vaiabl ad uabl auao E: 3 ppm, L ~1.4 m FBG1: 6%,.15 m FBG: 99%,.5 m LP 1 -LP 3 Vpp, 1. MH III. Applicaio III.3. Q-wichd fib la Flxual wav: Vaiabl ad uabl auao E: 3 ppm, L ~1.4 m FBG1: 6%,.15 m FBG: 99%,.5 m Coiuou CW wav opaio CW

26 III. Applicaio III.3. Q-wichd fib la Flxual wav: Vaiabl ad uabl auao E: 3 ppm, L ~1.4 m FBG1: 6%,.15 m FBG: 99%,.5 m III. Applicaio III.3. Q-wichd fib la Flxual wav: Vaiabl ad uabl auao 1 H 6 H P p = 9 mw

27 III. Applicaio III.3. Q-wichd fib la Logiudial wav: uplaic modulao E fib : 3 ppm, L ~1 m, FBG: 6%,.5 m, FBG1: 99%,.5 m III. Applicaio III.3. Q-wichd fib la Logiudial wav: uplaic modulao P p = 18 mw

28 III. Applicaio III.3. Q-wichd fib la Logiudial wav + fib Bagg gaig: Λ > L FBG ε [ P ] 1/ EAv = / g III. Applicaio III.3. Q-wichd fib la Logiudial wav + fib Bagg gaig: Λ > L FBG δf = 14 H, Q mchaical = 13 olid li 14 V pp, dahd li 4. V pp

29 III. Applicaio III.3. Q-wichd fib la Logiudial wav + fib Bagg gaig: Λ > L FBG III. Applicaio III.3. Q-wichd fib la Logiudial wav + fib Bagg gaig: Λ > L FBG

30 III. Applicaio III.3. Q-wichd fib la Logiudial wav + fib Bagg gaig: Λ > L FBG Tim µ III. Applicaio III.3. Q-wichd fib la Diibud fdbac DFB fib la coiuou wav Pump Emiio Aciv fib Bagg gaig wih a aic dfc Emiio Siglmod la wih vy aow pcal liwidh Gaio of dfc i uifom fib Bagg gaig Ioducig a dic pha hif i h modulaio pa Gaig local mpau o ai pubaio Focuig a UV bam o h fib

31 III. Applicaio III.3. Q-wichd fib la Dyamic dfc gad by a logiudial acouic pul ha popaga guidd by h opical fib ad iac wih a FBG P i P P Compio.8 cm v Poiio Uifom Bagg gaig of 1 cm log, λ B = m ad a auaio of 3 db 3 pm badwidh Acouic pul of 5 µ, popagaig a v = 576 m/, paial widh of.8 cm Th logiudial acouic wav ga a chag of λ B = Λ, ha ca b modld a a ffciv pubaio of h pich Λ III. Applicaio III.3. Q-wichd fib la Dfc locad a h middl of h gaig = 6 cm, wih diff ampliud δλ = 5, 1 y 15 pm

32 III. Applicaio III.3. Q-wichd fib la Dfc wih coa ampliud δλ = 1 pm locad a diff poiio =, 4 y 6 cm III. Applicaio III.3. Q-wichd fib la Spcal poiio ad amiac of h oac gad by a dfc of coa ampliud, δλ = 1 pm, a a fucio of i poiio alog h gaig

33 La chm: III. Applicaio III.3. Q-wichd fib la Bagg gaig: 1 cm-log, λ B = m, 3 pm badwidh ad auaio > 3 db Aciv fib: 1 ppm 15 cm, λ c = 919 m, NA =. y α 98 = 11.4 db/m Pump: 98 m Piolcic xciaio: 5 µ pul pubaio lgh: 8 mm, aiio im: 1 µ, bu oly 13 µ complly wihi h gaig La chaaciic: III. Applicaio III.3. Q-wichd fib la lf pul a 1 H, V PZ =.8 V, pump 35 mw igh dail of o pul a H, pump 1.6 mw

34 III. Applicaio III.3. Q-wichd fib la La chaaciic: igh liwidh <.8 pm, maud a 1 H ad 3 mw pump blow pa pow ad mpoal widh a a fucio of pump pow, fo diff piio fquci La chaaciic : igh pa pow a a fucio of volag ampliud a 1 H ad 33 mw pump pow III. Applicaio III.3. Q-wichd fib la B C Q A < Q B < Q C ba > bb > bc b : build-up im A A P B P C P

35 I-fib acouo-opic iacio I. Opical ad acouic mod guidd by a opical fib I.1. Th fudamal acouic mod I.. Co ad claddig opical mod II. Acouo-opic iacio: coupld mod hoy II.1. Th faciv idx pubaio gad by a acouic wav II.. Coupld wav hoy II.3. Flxual wav: Couplig coffici ad baic dvic II.4. Logiudial wav: Couplig coffici ad baic dvic III. Applicaio III.1. Dyamic add & dop muliplx III.. Wavlgh-wichabl all-fib la III.3. Q-wichd fib la 4 diff ca III.4. Tuabl ad cofiguabl micowav opical fil IV. Cocluio Co IV. Cocluio A opical fib guid h acouic wav fficily ad pmi lag iacio lgh wih h opical wav Th iacio ca b opimid by apig h opical fib uig a fuio ad pullig chiqu Th flxual wav pmi o obai vaiabl ad wavlgh uabl auao wih a im po h od of 1 µ Th logiudial wav pmi h modulaio of i-fib Bagg gaig: Suplaic modulao: gaio of a comb of flcio fquci Dic compio/xpaio of ho gaig Gaio of dyamic dfc i log fib gaig by ma of ho acouic pul Applicaio: Dyamic add & dop, wavlgh-wichabl fib la ad Q-wichd fib la