Y. ZHENG ET AL.107

for approximating the exact wave equation for mono-

chromatic waves and solving the resulting equation nu-

merically. For the monochromatic type of waves, such as

,, exp

yzi t

, in a three-dimensional waveguide,

the beam propagation method satisfies the scalar equa-

tion as follows [6,7]:

222 2

2

2222 ,, 0nxyz

xyzc

(1)

where is the propagation direction of waves,

z

is

the angular frequency, is the refractive index

of the incident medium, 0 is in-

troduced for the spatially-dependent wave number, and

is the wave number in free space. If

,,nxyz

,,kxy

exp n

,,z knxyz

0

k

,,

,,

yz uxyzikz

, then is the con-

stant number to be chosen to make , where

is slowly varying.

n

k

,,uxyz z

22

dudz can then be neglected with

respect to ddku z. With this assumption and after a

slight rearrangement, the above equation is reduced to

the following:

22

22

22

2n

n

uiu u

kku

zkxy

(2)

The three propagation media in the coupling interface

between the planar optical waveguide chip and optical

fibers are the core of the optical fiber, adhesive, and core

of the planar optical waveguide chip. To facilitate calcu-

lation, only the electric field E is considered. The mag-

netic field H can be calculated in the same way as the

electric field E. The propagation field may be discon-

tinuous in the coupling interface. The boundary can be

given by:

12

12

EnEn

Dn Dn

(3)

where is the normal direction of input light, 1 and

2 are the electric field of the first and second media,

respectively, and 1 and 2 are the electric flux den-

sity of the first and the second media, respectively.

nE

ED D

3. Results and Discussion

The light coupling between a planar optical waveguide

chip and an optical fiber can be calculated by the overlap

integral of the optical field distributions in a reference

plane. As the goal of the present study is to understand

the properties of the coupling interface for planar optical

waveguide packaging, a sample model, as shown in Fig-

ure 2, is used to investigate them. The proposed model

presents the majority case in planar optical waveguide

packaging. It consists of a single mode fiber, a regular

square-type planar optical waveguide cross-section, and

an adhesive with the thickness of d in between. The re-

Fiber Core AdhesiveIntegrated Photonic Chip Core

d

Figure 2. Model for the optical fiber-planar optical wave-

guide coupling simulation.

fractive index of the fiber core and cladding is 1.4494

and 1.445, respectively, at a wavelength of 1.31 μm (Δ =

0.3%). The refractive index of the planar optical wave-

guide core and cladding is 1.4486 and 1.445, respectively,

(Δ = 0.25%) [2,8]. The diameter of the fiber core is 8.2

μm, and the planar optical waveguide core dimension is

8 × 8 μm. The adhesive has excellent transmittance at a

wavelength of 1.26 - 1.65 μm, which is the optical com-

munication wavelength.

The coupling loss at the coupling interface is calcu-

lated using the scalar BPM algorithm. The coupling loss

in optical power through a connection is defined simi-

larly to that of signal attenuation through a waveguide.

Coupling loss is also a log relationship. The coupling

loss (C.L.) in optical power through a connection is de-

fined as:

10

.. 10i

o

P

CLLog P

(4)

Po is the power emitted from the source optical

waveguide in a connection. Pi is the power accepted by

the connected optical waveguide. In any fiber optic con-

nection, Po and Pi are the optical power levels measured

before and after the joint, respectively.

3.1. Refractive Index and Thickness of Adhesive

Figure 3 shows the coupling loss of an optical fiber and

a planar optical waveguide chip with respect to the re-

fraction index of the adhesive for different adhesive

thicknesses. The present study assumes that no lateral

misalignment and angular misalignment exist between

the optical fiber and the planar optical waveguide chip.

Moreover, the propagation wavelength is considered

1.31 and 1.55 μm (optical communication wavelength).

In Figure 3(a), at a wavelength of 1.31 μm, the coupling

loss is less than 0.12 dB for the adhesive thickness of

less than 9 μm. When the adhesive thickness is greater

than 9 μm, the slope of the variation is large. In Figure

3(b), at a wavelength of 1.55 μm, the coupling loss is

less than 0.01 dB for various adhesive thicknesses, and

the slope of the variation is small.

As shown in Figure 3(a) and (b), a large adhesive

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