Guiding And Confining Light In Nanostructures

2315 words - 10 pages

June 1, 2004 / Vol. 29, No. 11 / OPTICS LETTERS


Guiding and confining light in void nanostructure
Vilson R. Almeida, Qianfan Xu, Carlos A. Barrios, and Michal Lipson
School of Electrical and Computer Engineering, Cornell University, 411 Phillips Hall, Ithaca, New York 14853
Received January 20, 2004
We present a novel waveguide geometry for enhancing and confining light in a nanometer-wide low-index
material. Light enhancement and confinement is caused by large discontinuity of the electric field at highindex-contrast interfaces. We show that by use of such a structure the field can be confined in a 50-nm-wide
low-index region with a normalized intensity of 20 mm22 . This ...view middle of the document...

Unlike TIR, the external ref lection cannot be perfectly
unity; therefore the modes in these structures are inherently leaky modes. In addition, since interference
is involved, these structures are strongly wavelength
Here we show that the optical field can be enhanced
and conf ined in the low-index material even when light
is guided by TIR. For a high-index-contrast interface,
Maxwell’s equations state that, to satisfy the continuity of the normal component of electric f lux density D , the corresponding electric field (E-f ield) must
undergo a large discontinuity with much higher amplitude in the low-index side. We show that this discontinuity can be used to strongly enhance and confine
light in a nanometer-wide region of low-index material. The proposed structure presents an eigenmode,
and it is compatible with highly integrated photonics
The principle of operation of the novel structure can
be illustrated by analysis of the slab-based structure
shown in Fig. 1(a), where a low-index slot is embedded
between two high-index slabs (shaded regions). The
novel structure is hereafter referred to as a slot waveguide. The slot waveguide eigenmode can be seen as

where kH is the transverse wave number in the
high-index slabs, gC is the f ield decay coeff icient in
the cladding, gS is the field decay coeff icient in the
slot, and constant A is given by
k0 2 nH 2 2 kH 2 ,
A A0
where A0 is an arbitrary constant and k0
2p l0 is
the vacuum wave number. The transverse parameters kH , gS , and gC simultaneously obey the relations
k0 2 nC 2 1 gC 2
k0 2 nH 2 2 kH 2
k0 2 nS 2 1 gS 2
b2 ,
where b is the eigenmode propagation constant, which
can be calculated by solving the transcendental characteristic equation
tan kH b 2 a 2 F
where F

g S nH 2
tanh gS a ,
kH nS 2


arctan gC nH 2 kH nC 2 .

Fig. 1. Schematic of the slot waveguide structure (a) with
inf inite height and (b) with f inite height.
© 2004 Optical Society of America


OPTICS LETTERS / Vol. 29, No. 11 / June 1, 2004

From Eq. (1) the E-field immediately inside the slot
(jxj a2 ) is nH 2 nS 2 times higher than that immediately inside the high-index slabs (jxj a1 ). The ratio
nH 2 nS 2 equals 6 for a Si SiO2 interface and 12 for a
Si – air interface. When the width of the slot is much
smaller than the characteristic decay length inside the
slot (a , 1 gS ), the field remains high all across the
slot. By assuming that nH
3.48, nS
a 25 nm, and b 205 nm, we calculated the TM Ex
distribution at l0 1.55 mm. Figure 2 shows that the
Ex distribution, which evidences the large discontinuity and the high E-field confinement in the slot; in this
case a 25 nm , 1 gS
140 nm.
Hereafter we consider a three-dimensional (3D) slot
waveguide structure with f inite height [see Fig. 1(b)].
In this case the quasi-TE eigenmode presents the major E-field component...

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