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  • Received: Feb. 11, 2015

    Accepted: Jun. 8, 2015

    Posted: Jan. 23, 2019

    Published Online: Sep. 14, 2018

    The Author Email: Abdul Ghaffar (aghaffar@ksu.edu.sa)

    DOI: 10.3788/COL201513.090801

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    Abdul Ghaffar, Majeed A. S. Alkanhal. High-frequency field intensity along focal point of a long metallic parabolic reflector coated by a magnetized plasma layer using oblique incidence[J]. Chinese Optics Letters, 2015, 13(9): 090801

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ζ=fξ2/4f,(1)

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ζ=fdξ2/4f,(2)

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ε¯¯==|ε1jε20jε2ε1000ε3|,(3)

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E0i=Ei(cosθ0e^xsinθ0e^z)exp[jki(xsinθ0+zcosθ0)].(4)

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pr=pi2(pi·N)N,(5)

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qr=pi+n21+(pi·N)2N(pi.N)N,(6)

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N=e^zcosα+e^xsinα.(7)

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p1=e^xsin(2αθ0)e^zcos(2αθ0),(8)

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q1=e^x(sinα(K1cos(αθ0))+sinθ0)e^z(cosα(K1cos(αθ0))+cosθ0).(9)

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p2=e^x(K2sinα+cosαsin(αθ0))e^z(K2cosα+sinαsin(αθ0)),(10a)

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q2=e^x(K3sinα+n1cosαsin(αθ))e^z(K3cosα+n1sinαsin(αθ)),(10b)

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K1=n12sin2(αθ0),K2=n12+cos(2α2θ0)1)/2,n1=(ε12ε22)/ε1,K3=(Γ+(cos(2α2θ0)1+2n12)n1)/2,Γ=2(ε1ε12ε22)/ε1.(11)

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E0i=Eie^yexp[jki(xsinθ0+zcosθ0)].(12)

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q3=e^x(sinα(sinθ0K4))(cosα(cosθ0K4))e^z,(13a)

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p3=e^x(K5sinα+cosαsin(αθ0))e^z(K5cosα+sinαsin(αθ0)),(13b)

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q4=e^x(K6sinα+ncosαsin(θα))e^z(K6cosα+nsinαsin(αθ)),(14)

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K4=cos(αθ0)n2sin2(αθ0),K5=(1+2n2+cos(2α2θ))/2,K6=(2n2n2+2n3+ncos(2α2θ))/2.(15)

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dx/dτ=px,dz/dτ=pz,dpx/dτ=0,dpz/dτ=0.(16)

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x=ξ0+p1xτ1,z=ζ0+p1zτ1,p1x=p1x0,p1z=p1z0,(17)

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x=ξ0+q1xτ1,z=ζ0+q1zτ1,q1x=q1x0,q1z=q1z0.(18)

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J1(τ1)=D1(τ1)D1(0)=1τ1cos3αfcos(αθ0),(19)

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J2(τ2)=D2(τ2)D2(0)=18fK22{8fK12+τ2cos3α[2K1(2K12+n2)n(4K12+n)cos(αθ0)+cos(3α3θ0)]}.(20)

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Er(x,z)=Ei[J1(τ1)]12exp[jk(Ψ0+τ1)],(21)

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Et(x,z)=Ei[J2(τ2)]12exp[jk(Ψ0+τ2+t)],(22)

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Er(r)=kj2πEt(x,z)[D(τ)D(0)(pz)(z)]12exp(jk(S0+τz(px,z)pz+pzz))dpz.(23)

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I1=D(τ1)D(0)(p1x)(x)=sin2(2αθ0)cos3αfcos(αθ0),(24)

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I2=D(τ2)D(0)(p3x)(x)=4K22sinα8fK22sec3α(K2sinα+n1cosαsin(αθ0))+4K22sinα+n1(sin(α2θ0)+sin(3α2θ0)+4K2sin2αθ0)8fK22sec3α(K2sinα+n1cosαsin(αθ0)).(25)

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S1=2rcos(αθ0)/cosα+cos(2αθ0θ),(26)

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S2=fK2secαK2rcos(α+θ)+acosα+t+f/2((2n1)cos(2αθ0)+n1cosθ0)sec2α+n1rsin(α+θ)sin(αθ0)).(27)

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Er(x,z)=Ei2(Ei·N)N.(28)

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Ex(x,z)Ei=2kfπil/2l/2cosθ0cos(αθ0)cos3αexp(jkS1)dα,(29)

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Ez(x,z)Ei=2kfπil/2l/2sinθ0cos(αθ0)cos3αexp(jkS1)dα.(30)

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Et(x,z)=T˜·Ei==[Titii+Titii]·Ei,(31)

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Ex(x,z)Ei=2kfπl/2l/2EtxK3cos3αq2xdq2αdαexp(jkS2)dα,(32a)

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Ez(x,z)Ei=2kfπl/2l/2EtzK3cos3αq2xdq2αdαexp(jkS2)dα,(32b)

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Etx=2n1cosαcos2θ0(K2cosα+n12sinαsin(αθ0)n1cosα+1n12sin2α,Etz=2n1cosαcos2θ0(K2cosα+n12cosαsin(αθ0)n1cosα+1n12sin2α.(33)

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E(x,z)/Ei=2kf/πil/2l/2cos(αθ0)/cos3αexp(jkS1)dα.(34)

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Ey(x,z)Ei=kaπl/2l/22ncosαncosα+1n2sin2α1q2xdq2zdαK2cos3αexp(jkS3)dα,(35)

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E(x,z)=kj2πejRRE0(ξ0,ζ0)exp(jkS0)dξ0,(36)

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