In Fig. 2 the sinusoidal curve having a period of Ad/2no depicts the intensity of the anding E-field, with the origin of the coordinate system chosen to coincide with one of its nulls. The standing H-field profile(not shown) is similar to that of the E-field, but shifted along the z-axis by 104no. The energy densities of the E-and H-fields, while stationary in space, oscillate in quadrature in time, so that the total optical energy swings back and forth between its electric and magnetic components n=n Hyd=x k2=士nok 6n=1 ↓个k2=士k E-field n/2no Intensity = k=士nk standing wave inside a dielectric medium of refractive index no. The field amplitudes for each lane-wave are(En H)=(Eo, o EZ.). The sinusoidal curve having a period of //2n, depicts he intensity of the standing E-field, with the origin of the coordinate system chosen to oincide with one of its nulls; the standing H-field profile(not shown)is similar but shifted ong the z-axis by 14n, Inside the narrow gap(width 8<<1)located at ===o, the field An extremely narrow gap of width &<<no is opened at ===o to pierce into the medium in in attempt to discern the nature of the local E-and H-fields at that particular location within the standing wave. While the gap is too narrow to affect in any significant way the standing wave profiles, the E- and H-fields inside the gap differ substantially from those within the dielectric host. We denote by Eg the E-field amplitude for each of the two counter propagating plane-waves inside the gap; the corresponding H-field amplitude is then Hy=Eg/Zo. The standing fields inside the gap are thus given by Ex=, 1)=2Eg sin(ko=+y)sin(@n) HE, 1)=2(ENZO)cos(ko =+y)cos(@n), where y is an as-yet-undetermined phase angle. The gap is sufficiently narrow that its upper and lower boundaries may be assumed to be effectively at the same location along the z-axis, namely, at ===0. Comparing Eqs. 3)and (4) shows that the continuity of(Ex H,)at the ga boundaries requires the following identities Eo sin(noko=0)= Eg sin(k。二0+v), #79094$1500USD Received 17 January 2007; accepted 22 February 2007 (C)2007OSA 5 March 2007/ VoL 15. No 5/ OPTICS EXPRESS 2680In Fig. 2 the sinusoidal curve having a period of λo/2no depicts the intensity of the standing E-field, with the origin of the coordinate system chosen to coincide with one of its nulls. The standing H-field profile (not shown) is similar to that of the E-field, but shifted along the z-axis by λo/4no. The energy densities of the E- and H-fields, while stationary in space, oscillate in quadrature in time, so that the total optical energy swings back and forth between its electric and magnetic components. Fig. 2. Two identical plane-waves propagate in opposite directions (along ± z) to create a standing wave inside a dielectric medium of refractive index no. The field amplitudes for each plane-wave are (Ex, Hy) = (Eo, no Eo/Zo). The sinusoidal curve having a period of λo/2no depicts the intensity of the standing E-field, with the origin of the coordinate system chosen to coincide with one of its nulls; the standing H-field profile (not shown) is similar but shifted along the z-axis by λo/4no. Inside the narrow gap (width δ << λo) located at z = zo, the field amplitudes for each of the two counter-propagating plane-waves are (Ex, Hy) = (Eg, Eg /Zo). An extremely narrow gap of width δ << λo is opened at z = zo to pierce into the medium in an attempt to discern the nature of the local E- and H-fields at that particular location within the standing wave. While the gap is too narrow to affect in any significant way the standing wave profiles, the E- and H-fields inside the gap differ substantially from those within the dielectric host. We denote by Eg the E-field amplitude for each of the two counter￾propagating plane-waves inside the gap; the corresponding H-field amplitude is then Hy = Eg/Zo. The standing fields inside the gap are thus given by Ex(z, t) = 2Eg sin(ko z + ψ ) sin(ω t), (4a) Hy(z, t) = 2(Eg/Zo)cos(ko z + ψ ) cos(ω t), (4b) where ψ is an as-yet-undetermined phase angle. The gap is sufficiently narrow that its upper and lower boundaries may be assumed to be effectively at the same location along the z-axis, namely, at z = zo. Comparing Eqs. (3) and (4) shows that the continuity of (Ex, Hy) at the gap boundaries requires the following identities: Eo sin(no ko zo) = Eg sin(ko zo + ψ ), (5a) n = no z x H Ex y kz = ± no ko × n = no δ n = 1 kz = ± no ko kz = ± ko zo Ex Hy E-field Intensity λo/2no #79094 - $15.00 USD Received 17 January 2007; accepted 22 February 2007 (C) 2007 OSA 5 March 2007 / Vol. 15, No. 5 / OPTICS EXPRESS 2680