# All Optical Integrated MOEMS Optical Coherence Tomography System

Ashish Singh Bais  Applied Photonics Laboratory, Department of Applied Physics
and Optoelectronics, Shri G. S. Institute of Technology and Science, 23 Park
Road Indore, MP 452003 India.  Lokendra Singh Chouhan  Applied Photonics
Laboratory, Department of Applied Physics and Optoelectronics, Shri G. S.
Institute of Technology and Science, 23 Park Road Indore, MP 452003 India.
Also at St. Paul HSS, Indore, MP 452001 India  Joseph Thomas Andrews
Corresponding author<EMAIL_ADDRESS>Applied Photonics Laboratory,
Department of Applied Physics and Optoelectronics, Shri G. S. Institute of
Technology and Science, 23 Park Road Indore, MP 452003 India.

###### Abstract

Integrating all optical components of an optical coherence tomography (OCT)
device into a single chip is a non-trivial and a challenging job. The design
and development of such a lab-on-a chip will be possible only via Micro-Opto-
Electro-Mechanical System (MOEMS) technology. The reproducible and integrated
optical device fabrication would reduce cost and size many fold as compared to
bulk or fiber optic OCT system. A miniaturized OCT of size less than 5mm2 area
is designed, simulated and optimized. The successful fabrication of this
device would help in point-of-contact devices as well as embedded biomedical
sensor applications. Also, the design promises the possibility of fabrication
of all optical components of OCT integrated into a single chip.

##  I Introduction

Significant advantage of integrated optical devices are its size, portability,
mobility, multi-functional measurement capabilities, etc., over the bulk
optical devices. Common methods adopted for the integration multiple optical
components into a single chip is e-beam methods, pulse laser deposition,
epitaxy methods, chemical vapor deposition or a cheaper photo-lithography. The
developed micro-opto-electro-mechanical systems (MOEMS), once optimized can be
used in industry, clinics, point-of-contact devices, mobile devices, etc. [1].

Figure 1:  Schematic of an optical coherence tomography setup. SLD-Light
source, D-Light detector, BS-Beam splitter, Sa-Sample, M-Scanning mirror.
A1-Source, A2-Detector, A3-Reference and A4-Sample arms of an Michelson
Interferometer.

Optical coherence tomography (OCT) systems have been implemented so far using
free-space or fiber optics components only. Although systems based on fiber
optics allow for the compact, inexpensive and portable instrumentation, the
final size and price of the devices are still not adequate for many
applications. OCT systems composed of many optical components, such as:
optical fibers, lenses beam splitters or directional coupler (DC), etc. These
components are necessary to relay the optical signal through the OCT system.
The combination of all these components makes OCT systems bulky, expensive and
complex.

To solve above problem we will fabricate OCT system by using MOEMS fabrication
technology. This technology has been proven that the low loss waveguide
structure can be easily fabricated with either silicon on insulator waveguide
technology or polymer (PMMA, SU8, S1813 etc) based waveguide. Before going for
any waveguide fabrication process we need to simulate the system. In this
article we simulate polymer based OCT system by using appropriate software
codes.

##  II Theory

Figure 1, shows schematic of a free space OCT system. The heart of the OCT
system is a Michelson Interferometer. The low coherence light beam entering at
one arm (A1) of OCT is directed to reference (A3) and sample (A4) arms by beam
splitter. The mirror in A3 is moved or scanned to induce a path difference
mechanically or optically. The light scattered from the stratified media of
the sample beam also return towards the detector. The back scattered light
from A4 interfere with the back reflected light from the A3, when the path
difference between them is within the coherence length of the light source [2,
3]. OCT measures the interference resulting from different axial locations
within the tissue by moving the mirror at the reference arm which generates
continuous interference signals along the depth. The depth-resolved sample
information from each column of data is appended together and visualized as a
2-D cross-sectional image after signal processing.

We are proposing a polymer based MOEMS OCT system, where Michelson
interferometer is fabricated using a waveguide bi-directional coupler. The
moving mirror is replaced with an optical delay line generator. The delay line
is integrated and replaced with the mirror component of the MI. The delay line
which can generate temporal bunches of waves delayed in time is equivalent to
the movement of a mirror.

Figure 2: Demonstration of frustrated total internal reflection. $P_{in}$ may
leak through the waveguide at bottom.

###  II.1 Bi-directional coupler

If two similar linear waveguides are parallel and sufficiently closely spaced
over a length $L$ (coupling length) the energy is transferred from one to
another due to the evanescent field between them. The fraction of the power
coupled is determined by the overlap of the modes in the separate channels. In
case of the synchronous co-directional coupler (both waveguide channels have
same phase velocity, ($\Delta k=0$) all the energy can theoretically be
transferred from one waveguide to another if $L=z$ is such that

$\kappa z=\frac{(2m+1)\pi}{2},$ (1)

with $\kappa$ as the coupling constant and $m=0,1,2...$, Shown in Figure 2.

Generally, $\kappa$ controls the ratio of power transferred between the
waveguides. The value of $\kappa$ depends on the percentage of overlap of the
mode profiles within the waveguides. The coupling constant is generally
defined as [Huns]

$\kappa=\frac{2k_{x}^{2}q_{x}\exp(-q_{x}c)}{k_{z}b(q_{x}^{2}+k_{x}^{2})}.$ (2)

Here, $b$ \- channel width, $c$ \- separation between the channels, $k_{x}$
and $k_{z}$ are the propagation constants along the two transverse direction
($x$ and $z$ axis) to propagation of wave (we suppose to direction of
propagation of wave along $y$ axis) and $q_{x}$ is the exponential falloff
along the direction of propagation of wave.

This principle is the basis for the operation of directional couplers, by
adjusting the suitable coupling length $L$, any desired portion of energy from
a waveguide can be transferred into adjacent waveguide. In our case both
waveguide channel have same phase velocity and we need to transfer same energy
between both sample and reference arm so, we need to choose the coupling
length such that 50% of light coupled from one waveguide to the adjacent one.
Accordingly, the condition for 50:50 splitting ratio is [4],

$\frac{L}{2}=\frac{(2m+1)\pi}{4\kappa}.$ (3)

###  II.2 Optical delay line

Optical delay line is another important functional component of OCT that
provides optical delay at the reference arm to get interference signal with
the back-scattered optical signals at sample arm and it also attends fast
scanning speed and scan depth. Fiber optic delay lines are already been
demonstrated [5]. Compact Silicon-Based Integrated Optic time delay line has
been fabricated [6, 7] and demonstrated optical time delay. The silicon-on-
insulator (SOI) technology is adopted with an incremental time delay of 12.3
ps. Guided- wave optical delay line provide the required precision and are
more compact than optical fibers [8].

##  III Design and Working

The proposed lab-on a chip device of optical coherence tomography is exhibited
in Figure 3. This design is divided into three sections: P1: Michelson
interferometer with a 3dB coupler, P2: Y coupler for connecting the delay line
with 3dB coupler and P3: Optical delay line.

Figure 3: Schematic diagram of all optical integrated time domain optical
coherence tomography using synchronous directional coupler. P1-Michelson
interferometer, P2-Y-channel light coupler and decoupler and P3- temporal
delay line mechanism. A1 - A4 : input-output arms of MI, YA1-YA2: Y-channel
couplers. Design of OCT system; Inset: magnification of particular part of
system.

Further a comparison of Figures 1 and 3, can be made to understand the arms of
A1-A4 of MI with the proposed design.

Figure 4:  Power distribution requirement for OCT design. The power
distribution is optimized for best visibility and good modulation index.

The power distribution as shown in Figure 4, is discussed below. As we
launched an optical power of $P_{in}$ from A1 arm of 3dB coupler, the light is
divided into two equal parts to the arms A3 and A4. The optical power expected
in the arms A3 and A4 is $P_{in}/2$. A4 is sample arm and the arm A3 is
connected to Y coupler. Further at P2 region the power is divided to
$P_{in}/4$ to each YA1 and YA2 arms. Delay line consist of 20 C-channels
separated at a pre-calculated distance. at YA1 arm, all C-channel is directly
connected while in YA2 all C-channels (except 20th C-channel) is separated by
a pre-calculated distances. Gap between lower YA2 arm and the C-channels are
calculated for a leakage of 5% of optical power only.

1st C-channel decouples nearly 5% of optical power to the YA2 arm,
corresponding to an optical power of $P_{in}/80$. The remaining optical power
is passed to 2nd and rest of the channels. The design ensure that all
C-channels decouples a only 5% $P_{in}$, and the remaining is passed on. While
the power is splitted, each bunch of $P_{in}/80$ optical power also generates
a path delay equivalent to 60$\mu$m with each other. The path difference
induces a temporal delay of about 0.6ps with next $P_{in}/80$ optical power.
This pulse delay is typically required resolution in a OCT system. In other
words the OCT system can resolve those two layers of samples whose optical
distance is nearly 30$\mu$m.

##  IV Results

We consider the fabrication of lab-on chip OCT system with following
parameters:
Design wavelength ($\lambda$) = 1.55 $\mu$m; $n_{core}=1.48$ (SU 8);
$n_{clad}=1$ (air);
Channel width = 1 $\mu$m; Radius of curvature of each C-channel = 6 $\mu$m;
The estimated values of coupling length of each C-channel for constant power
coupling of $P_{in}/80$ in Table 1.

Table 1: Estimated values of coupling length of each C-channel for constant power coupling of $P_{in}/80$. R: required percentage coupling for constant power coupling of $P_{in}/80$, $L_{c}$: coupling length of particular C channel. C-channel # | $R$ | $L_{c}$ | C-channel # | $R$ | $L_{c}$
---|---|---|---|---|---
1 | 5.00 | 4.0 $\mu$m | 11 | 10.00 | 8.60 $\mu$m
2 | 5.26 | 4.2 $\mu$m | 12 | 11.11 | 9.60 $\mu$m
3 | 5.56 | 4.5 $\mu$m | 13 | 12.50 | 11.2 $\mu$m
4 | 5.88 | 4.8 $\mu$m | 14 | 14.29 | 12.8 $\mu$m
5 | 6.25 | 5.2 $\mu$m | 15 | 16.67 | 15.0 $\mu$m
6 | 6.67 | 5.7 $\mu$m | 16 | 20.00 | 17.4 $\mu$m
7 | 7.14 | 6.2 $\mu$m | 17 | 25.00 | 20.0 $\mu$m
8 | 7.69 | 6.5 $\mu$m | 18 | 33.33 | 27.0 $\mu$m
9 | 8.33 | 7.0 $\mu$m | 19 | 50.00 | 45.0 $\mu$m
10 | 9.09 | 7.7 $\mu$m | 20 | 100.0 | Directly connected

Simulation is performed using appropriate software code, where the complete
structure as shown in Fig. 4 is used. All design parameters discussed above
are incorporated. About 20 grid points as shown (in dashed gray lines) the
figure are the places where measurements were made.

Figure 5:  Power output measured from the P1 as shown in Fig. 3. The optical
power is measured at three cross-sectional locations of the directional
coupler.

The Y-coupler as depicted as P1 in the design as simulated and studied first.
The results are shown in Fig. 5. The measurements made at grid points 1, 2 and
3 are exhibited. The inset shows the power profile. The optical power coupled
to the input port A2 is assumed as 100 % power. At grid point 3, the power is
divided to 50:50 and act as 3dB coupler.

Simulation of the complete design as given in Fig. 4 is performed. The results
obtained with optimized values are shown in Figure 6. The optical power
profile values obtained at the grid point locations are plotted. The light is
coupled at A2 port 18-19 $\mu$m, region, YA1 is located at a distance of 23-24
$\mu$m region while the C-channels ends at 25-26 $\mu$m region. YA1 can be
located at 31-32 $\mu$m region.

Figure 6a, clearly demonstrates the capability of all the components P1, P2
and P3. The expected 50:50 ratio may be noted at grid point 3. The power is
further makes round trips via YA1 to YA2 as well as through YA2 to YA1. Both
outputs reaches the directional coupler and A2 arm.

The magnified and enhanced view of YA2-C-channel region is depicted in Fig 6b.
The results shows light coupling between these channels. However, expected
values of 5% optical power from each channel could not be found. A exponential
decay of power reduction happens at channels 10 and beyond. Overall we could
see that required delay is generated, but with slight change in power ratio.
The change power ratio might change the visibility of the images only.

Figure 6:  Optical power output as measured from the complete design as shown
in Fig. 4. (a) Shows all measured locations marked as 1-20 in Fig. 4. (b)
Exhibits the optical power at small region where the light coupling between
the C-channel and YA2 is made.

##  V Conclusions

We proposed a design of all optical optical coherence tomography system using
SU-8 polymer. The simulated results shows the definite possibility of
miniaturized OCT. The lab-on-a-chip design dimensions are : length = 1.4mm and
width = 50 $\mu$m approx. The area of the chip after embedding the detector
and light source would be less than 2mm2. This promises the possibility of
fabrication of all optical OCT for point of contact devices as well as for
embedded OCT chip a reality.

## Acknowledgments

ASB and JTA acknowledge the financial support received from SERB, New Delhi
GoI, under the project number CRG/2018/003871.

## References

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