CLEO/QELS May 2008, San Jose
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1 CLEO/QELS May 2008, San Jose 1
2 2
3 crystal length l z y s s pump mode! i! s y p z p target modes E(r,t)= 1 2 [ ] E (+) (r,t)+e ( ) (r,t) g(r) =e ikz U(x, y) =e ikz e x2 +y 2 W 2 E p (r,t)= 1 [ E 0 2 p e p g p (r)e iωpt + c.c ] Ê s,i = i 2 ω s,i 2 n 2 s,i ɛ 0 k s,i α s,i L e s,i g s,i (r) e iω s,it â ks,i + h.c. y i z i 3
4 Ĥ I = 2ɛ 0χ (2) 8 dxdy l/2 l/2 dz E (+) p Ê ( ) s Ê ( ) i + h.c. = d dxdy l/2 l/2 dz k s,k i ω i ω s n s n i α s α i E 0 p L e i ωt g p (r)g s(r)g i (r)â k s (t)â k i (t)+ h.c. 2d = e p χ (2) : e s e i 4
5 Φ( k) = = dz dz dy dx g p (r)g s(r)g i (r) pump mode dy dx e i k r U p (r)u s (r)u i (r).! i crystal length l! s y p z p target modes y i z y s s z i Φ( k) = k x =0 k y =? π e k A C 4C 2 y dz e Hz2 +izk = Φ z A = C = 1 W 2 p 1 W 2 p D = sin 2θ s W 2 s F = sin2 θ s W 2 s + 1 W 2 s + cos2 θ s W 2 s + 1 W 2 i sin 2θ i W 2 i + sin2 θ i W 2 i H = F D2 4C K = k y D 2C + k z + cos2 θ i W 2 i 5
6 crystal length l z y s s Φ z = l 1 0 du e Ξ2 u 2 cos( ϕu) pump mode! i Ξ := Hl/2 ϕ := Kl/2! s y p z p target modes y i z i Ξ Ξ > 1 Ξ < 1 6
7 Ξ > 1 Ξ < 1 π Φ z l 2Ξ Erf(Ξ) Ξ π = H Erf(Ξ) θ i = θ s =0 K = k z Φ z = l sinc( ϕ) 7
8 %=0 %=1/2 %=1 " z /l %= ! -2! 0 2! 4! #$ 7
9 ρ( E) = m k i k i ( ω) = L 2π n i c m/ k i = L/2π R(k s )= 2π 2 f ĤI i ρ( E) = d αs α i EpΦ( k) 0 2 ω s ω i n 2 sn i cl dr(ω s ) dω s = [ dαs α i E 0 pφ( k) c ] 2 ω s ω i 2πn s n i 8
10 R T = [ dαs α i E 0 p c ] 2 ω s ω i 2πn s n i dω s Φ( k) 2 S! S! 2 Ξ = " 9
11 R T = 4d 2 Plω 2 p 9n s n i n p ɛ 0 πw 2 p (n i n s )c 2 10
12 R T = 4d 2 Plω 2 p 9n s n i n p ɛ 0 πw 2 p (n i n s )c 2 W p = W s = W i 10
13 R T 1 W 2 p W 2 s W 2 i (1/W 2 p +1/W 2 s +1/W 2 i ) R T R T 1 W 2 (1/ +2γ) 2 W p = γw W p = W s = W i R T (a.u.) γ 11
14 W p = W s = W i = 82µm Ξ =0.93 } mm mm 1 sr 1 } mm 1 sr 1 12
15 W p = W s = W i 13
16 Thanks! 14
17 crystal length l z y s s pump mode! i! s y p z p target modes α 2 dxdy U(x, y) 2 =1 y i z i 2 α p,s,i = πw 2 p,s,i E 0 2 p = α 2 p 2P ɛ 0 n p c 15
18 E p (r,t) = 1 2 = 1 2 [ E (+) p ] (r,t)+e ( ) p (r,t) [ E 0 p e p g p (r)e iω pt + c.c ] Ê s,i = 1 2 [Ê(+) s,i (r,t)+ê( ) s,i (r,t)] = i 2 ω s,i α 2 n 2 s,i ɛ s,i e s,i g s,i (r) e iω s,it â + h.c. 0 L ks,i k s,i 16
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