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  • Received: Apr. 10, 2019

    Accepted: Jun. 20, 2019

    Posted: Sep. 6, 2019

    Published Online: Sep. 6, 2019

    The Author Email: Xiaona Yan (xnyan@staff.shu.edu.cn)

    DOI: 10.3788/COL201917.113201

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    Xiaoyan Wang, Xiaona Yan, Kailong Jin, Ye Dai, Zuanming Jin, Xihua Yang, Guohong Ma. Generation of femtosecond dual pulses by a transverse standing wave in a volume holographic grating[J]. Chinese Optics Letters, 2019, 17(11): 113201

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n=n0+Δncos(Kx),(1)
er0(t)=exp(jω0tt2T2),(2)
Er0(ω)=12πer0(t)exp(jωt)dt=T2πexp[T2(ωω0)24].(3)
E(ω,z,x)=Er(ω,z,x)+Es(ω,z,x)=Er(ω,z)exp(jρ·r)+Es(ω,z)exp(jσ·r),(4)
dEr(ω,z)dz=jκEs(ω,z)cosθ,dEs(ω,z)dz+jδEs(ω,z)cosθ=jκEr(ω,z)cosθ,(5)
Er(ω,z)=r1exp(jγ1z)+r2exp(jγ2z),Es(ω,z)=s1exp(jγ1z)+s2exp(jγ2z),(6)
γ1,2=δ2cosθs±12(δcosθs)2+4κ2cosθscosθ,(7)
r1=1r2=γ2γ2γ1Er0(ω),s1=s2=κ(γ2γ1)cosθEr0(ω),(8)
Er(ω,z,x)=[r1exp(jq0z(1)z)+r2exp(jq0z(2)z)]exp(jq0xx)=Er1+Er2,Es(ω,z,x)=[s1exp(jq0z(1)z)+s2exp(jq0z(2)z)]exp[j(q0xK)x]=Es1+Es2,(9)
Ii(t,z,x)=|12π+Ei(ω,z,x)exp(jωt)dω|2,i=r,s,(10)
Ers1(ω,z,x)=Er1+Es1={r1exp(jq0xx)+s1exp[j(q0xK)x]}exp(jq0z(1)z),Ers2(ω,z,x)=Er2+Es2={r2exp(jq0xx)+s2exp[j(q0xK)x]}exp(jq0z(2)z).(11)
I(t,z,x)=|12π[Ers1(ω,z,x)+Ers2(ω,z,x)]exp(jωt)dω|2.(12)
Ers1j2sin(12Kx)exp(jq0z(1)z),Ers22cos(12Kx)exp(jq0z(2)z).(13)
Irs11cos(Kx),Irs21+cos(Kx).(14)
vgz(1,2)=ωq0z(1,2)|ω=ω0=2c·cosθ2n(cosθ)2Δn,(15)
Δt=dvgz(2)dvgz(1)=d·Δnccosθ.(16)