Proposal for 2-D High Precision Displacement Sensor Array ...

Proposal for 2-D High Precision Displacement Sensor Array

based on Micro-ring Resonators using Electromagnetically

Induced Transparency (Nanophotonic Device)

R. Yadipour [a], K. Abbasian [a], A. Rostami [a, b], Z. D. Koozehkanani [c] and R. Namdar [d]

a) Photonics and Nanocrystals Research Lab. (PNRL), Faculty of Electrical and Computer

Engineering, University of Tabriz, Tabriz 51664, Iran

b) School of Engineering Emerging technologies, University of Tabriz, Tabriz 51664, Iran

c) Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz 51664, Iran

d) Department of Physics, Azarbaijan University of Tarbiat-e-Moallem, Tabriz, Iran

Tel/Fax: +98 411 3393724

E-mail: [email protected]

Abstract- Array of ring resonators as a basic cell for detection of different physical quantities such as

displacement is used. Electromagnetically Induced Transparency (EIT) implemented by nanocrystals

doped in the ring resonators is used for enhancement of the capability of the ultra small displacement

detection. Different physical quantities such as temperature, mechanical strain, acoustic waves and

position of array of micro mirrors in the micro electromechanical systems can be measured using the

proposed basic cell too. We show that high precision measurement is available when EIT is used. Also,

using array of ring resonators, we show that the sensor array have high precision signal detection

capability compared single ring case. The proposed structure is investigated in detail and different

quantities for evaluation of the quality of the sensor are extracted. Finally we show that in the case of

nanocrystal doped ring resonators tolerances of the parameters in the proposed system have a little effect

on output quantities compared without nanocrystals.

Keywords- EIT, Displacement sensor, Ring resonator

1. Introduction

High-precision and integrated sensors have been studied recently generally in industry and biomedical

applications especially. Displacement sensing in Micro and Nano machines and also, ultrasound imaging

sensors for intravascular applications are two highly interested tasks for technology developers. Micro-

ring resonator is a suitable alternative for realization of different integrated tasks. Because of inherent

interesting properties of the ring resonators including high quality coefficient and easy to implement, it is

a good alternative for realization of sensor array especially in 2-D case. In this work we like present

framework of 2-D sensor array for detection of different physical quantities. For this purpose the transfer

function of the considered structure is studied and simulated results are discussed.

Combination of optical and mechanical systems named optomechatronics or optical micro

electromechanical systems (optical-MEMS) opened new insight to device design for making processing

blocks. Also, design strategy based on optical-MEMS is suitable approach for sensor design too. For

realization of ultra high precision systems in deep sub-micron or nano-scales one of important sensors is

displacement sensor. So, for realization of this sensor different methods have been used. Here, we are

going to review some of them and investigate advantages and disadvantages of the reported works. Some

of standard displacement sensing methods in technology community is used such as using variable

resistance as physical phenomenon for detection of the object displacement, using capacitance measuring,

using piezoelectric material, change of air gap in transformer which introduces variable induced voltage

and advanced version of this method for displacement measurement is linear variable differential

transformer (LVDT) [1]. This type of displacement sensors cover sub-micron to mm range of operation.

Ultrasound method is another interesting approach for displacement monitoring. In this method

ultrasound pulses applied to the object and backward wave is detected. Based on forward transmitting and

backward receiving waves the object displacement is calculated [1]. Since wavelength of the ultrasound

wave is high enough, so precision of the displacement measurement is low. Optical method is another

important technique for displacement measurement. This approach was discussed in [2-4]. In this method

two basic techniques are used. One of these methods based on the reflected back intensity. In this

technique variation of displacement converted to the level of intensity measured with high resolution

photodetectors. Interference of the forward and backward traveling waves and phase difference is another

criterion of the displacement measurement. In these methods displacement resolution can be increased to

near Pico meter ranges. In these sensors range of operation usually limited to micro meter range. Another

interesting method developed recently is based on ring resonators and used for high resolution

displacement measurement [5]. In this method usually a narrow gap is made on top part of the ring and

outgoing wave from this gap impact on object and reflected back to the ring. On the other hand object and

ring simultaneously introduce a resonant cavity. Displacement of object changes the oscillation and

resonance frequency of the complex system. So, measuring of output intensity for input light at given

wavelength is used for measurement of the displacement. Micro-ring resonator is a basic and important

device which is used recently more [6-14] as the building block for optical systems such as filters. So, in

this paper we have proposed array of nanocrystal doped micro resonators as an ultra-high precision

displacement sensor with equal spacing between adjacent resonators without coupling where each of them

are coupled to a waveguide. Thus the array is coupled to an input and output bus waveguides. There is a

basic problem with ring resonator. It is wide spectral shape which causes low precision in displacement

measurement. For this purpose in this paper, we present a new idea for improving this problem. Our

method is based on doping of ring resonator with 3-level atoms or nanocrystals. In this situation the

spectral profile of the ring resonators is decreased strongly and thus the precision of the sensor is

increased. For this proposal, we use quantum optical tools for description of optical properties of the

nanocrystals doped ring resonators [15]. In this proposal, we used 3-level atoms with given density. First,

we calculate the optical susceptibility and then using control field changing of the obtained susceptibility

is controlled. Obtained optical susceptibility is used for management of the guided wave and finally

optical output intensity is extracted. Since obtained optical susceptibility determine the resonance

frequency, so applied light in a given wavelength may have different output intensity in the output port.

So, ultra small narrowband spectral profile can be used for obtaining on-off behavior in the output for

small displacement. We show that our proposed method can measure well below nanometer and even

picometer range.

Also, in this work we consider 2-d array of ring resonators for developing imaging sensor especially in

intravascular applications for micro and nano machines. Our simulated results show that the proposed

idea works well.

Organization of the paper is as follows.

In section 2 mathematical backgrounds for theoretical description of the proposed system is presented.

Simulation results and discussion of the introduced structure are presented in section 3. Finally the paper

ends with a short conclusion.

2. Mathematical Background

In this section, mathematical background for description of the input-output relation of array of ring

resonators is presented. For doing this purpose, first, we consider a single ring resonator coupled to a

single mode optical waveguide which is illustrated in Fig. 1. This structure is used as a basic cell of

horizontal array.

Fig. 1. Schematic of the ring resonator as a basic cell of horizontal array

According to light propagation theory in linear and isotropic media the following relations are presented to describe

the input-output transfer function.

],1[1 2111 EjEE io κκγ −−−= (1)

],1[1 12114 iEjEE κκγ −−−= (2)

where γ1 and κ1 are coupler’s loss and the coupling coefficient respectively. By using the wave propagation inside

ring resonator and after some mathematical manipulation the following transfer function is obtained as follows.

Lj

L

Lj

L

i

o

ee

ee

E

E

βα

βα

κγ

κγγ

211

112

1

)1)(1(

)1)(1(1

−−−

−−−−= , (3)

where α and β are the ring (and fiber) loss coefficient and wave propagation vector respectively and L=2πr is the

total length of the ring. Now, we consider the following basic cell of vertical array as illustrated in Fig. 2.

Fig. 2. A single ring as basic cell of vertical array

Using mathematical manipulation, the transfer function of the ring resonator which is illustrated in Fig. 2 is obtained

as follows:

(3)

where γ1, γ2, κ 1 and κ 2 are coupler’s loss and coupling coefficients respectively. Also, α and β are loss coefficient

and propagating wave vector respectively.

Fig. 3. Two rings vertical array

Transfer function of two rings illustrated in Fig. 3 can be obtained similarly as follows.

, (4)

where , and are given with following relations.

(5)

(6)

(7)

Fig. 4. Three rings vertical array

Similarly the transfer function of three rings vertical array is obtained with following relation as well.

, (8)

where , , , and are given as follows respectively.

, (9)

(10)

(11)

(12)

(13)

Fig. 5. Two rings horizontal array

Now, we consider the horizontal case and the transfer function of two rings which is shown in Fig.4, is obtained

with some mathematical manipulations as follows as an example.

, (14)

where z1 is waveguide length between two couplers and α, β are loss and wave propagation vector of

propagating field in waveguide respectively. A1 and A2 are transfer functions of first and second rings

respectively which are given by following relations.

(14)

(15)

Fig. 6. Three rings horizontal array

Transfer function of three rings which is shown in Fig.5, is obtained with some mathematical

manipulations as well.

, (16)

where z1, z2, α and β are waveguide lengths between couplers, the loss coefficient and propagating wave

vector respectively. Also, A1, A2 and A3 are transfer functions of first, second and third ring resonator

respectively.

Finally the transfer function of considered 2-D matrix can be obtained with mathematical manipulation of

horizontal and vertical studied array relations.

Fig. 7. Two in two matrix array of rings

Transfer functions of the array of ring resonators illustrated in Fig. 7 are obtained with following relations.

(17)

, (18)

where , and are given by relations (5-7).

Fig. 8. Matrix array of rings

Transfer functions of three in three matrix array are obtained as follows.

(19)

(20)

, (21)

where , , , and are given by relations (9-13 ).

These ideas can be used in micro-ring arrays as illustrated in following Figure (micro ring with air gap,

see one basic block of Fig. 9), whose transfer function can be given as follows.

( )( )

( )( )

0 0

45

0 0

. . . .

. 2 .. 2 .4 2 4 21 1 1

.. ... 2 .. 2 .4 2 4 2

1 1

1 1 (1 ). .e .e .e .e .e .e .e .e

1 1 1 . .e .e .e .e .e .e .e .e

L j L L j L

x j xh j h

oi

j Lj L LL

i x j xh j h

K rE

EK r

α β α βα βα β

ββ ααα βα β

γ γ

γ

− − − −− ∆ − ∆− −

−− −−− ∆ − ∆− −

− − − −=

− − −

, (22)

where L, h, ∆x and r are ring length, fiber and free space lengths and the reflection coefficient of the

reflecting surface of the object, respectively. In the following an example is presented for monitoring of

position of array of micro-mirrors. In the following figure, we presented only four ring resonators as

displacement sensors. In the next section, we illustrate simulated result of each displacement ring

resonator. Also, the proposed structure can be used for high precision two-dimensional surface moving.

Fig. 9. Array of ring resonators for detection of position of array of Micro-mirrors

In this section array of ring resonators as building block of 2-D sensor matrix has been studied and analytical

transfer functions derived. In the next section simulation results are illustrated and discussed.

3. Simulation Results and Discussion

In this section, simulation results are divided into four cases as follows:

1. Normal case (ring resonator without 3-level doping)

2. Vertical arrays of ring resonators with EIT (ring resonator with 3-level doping)

3. Horizontal arrays of ring resonators with EIT (ring resonator with 3-level doping)

4. 2-D array of ring resonators with EIT (ring resonator with 3-level doping)

Also, in final part of this section effect of practical tolerances on output signals are investigated too.

1. Normal case (Without EIT) The following figure shows the transmission coefficient and phase of a single ring (basic cell of

horizontal array) without EIT versus differential wavelength. As we can see the transmission coefficient

sensitivity (wavelength displacement between minimum and maximum) is about 0.2 nm and phase

changes about 4π radians at resonance wavelength.

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

x 10-9

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Wavelength Shift (m)

Tra

nsm

issi

on

Co

ef.

Of

Sin

gle

Hori

z. B

asi

c C

ell

a

-2 -1.5 -1 -0.5 0 0.5 1 1.5

x 10-9

-3

-2

-1

0

1

2

3


Ph

ase

of

Sin

gle

Ho

riz.

Ba

sic

Cel

l

b

Fig. 10. Transmission coefficient of single horizontal ring without EIT vs. differential wavelength

(a) Magnitude (b) Phase

0.15, L=2πr=5e-4 m,

EIT Case: Now, we are going to review mathematical method to describe effect of 3-level dopants, on

characteristics of the proposed sensor. Using Λ type 3-level nanocrystals in ring resonator, we show that

the resolution of the proposed sensor can be increased and tuned optically. Fig. 11 shows Λ type 3-level

particle schematic including probe and control fields and decay rates. In the model the control and probe

fields applied between levels 2-3 and levels 1-2 respectively. Due to applied electric field the optical

characteristics is changed and in the following brief theoretical calculation for description of the system

performance is presented. With strong control and weak probe laser pulses, the time evolution of

coherences between atomic levels are described by following equation [2]:

[ ],d i

Hdt

ρ ρ ρ= − − Γ , (23)

where H, ρ and Γ are the system’s Hamiltonian, density and decay rate matrixes respectively.

Fig. 11. Schematic of 3-level particles

After some mathematical manipulation [1], the real and imaginary parts of optical susceptibility are given

as

( )

Ω−−∆++−=

4

2

31

2

313

0

2' µγγγγγ

ε

γχ

Z

N aba

, (24)

( )

Ω−−∆−+∆=

4"

2

31

2

331

2

0

2

µγγγγγε

γχ

Z

N aba

, (25)

where ( )2

21

2

22

21

2

4γγγγ µ +∆+

Ω−−∆=Z and υω −=∆ ab

, γ1 , γ2, γ3, µΩ and

aN are detuning of probe

frequency from resonance, decay rates of atomic levels population, Rabi frequency of control field and

density of doped nanocrystals. Based on basic and fundamental relations between optical susceptibility and

absorption coefficient and refractive index, we have the following relations.

"

2χ

κα = ,

2

'χδ nn = , (26)

Finally the propagating wave vector in ring resonator doped with 3-level particles is given in the following.

c

nυβ = , (27)

In the following illustrated simulation results, effect of the control field on performance of horizontal ring

arrangement is investigated. It is observed that, in wide frequency range of input signal, the considered

system is transparent and oscillatory nature of the transmission coefficient is increased [5]. In the

mentioned region the transmission coefficient sensitivity (wavelength displacement between minimum

and maximum) is modified to about 5 pm.

-5.5 -5 -4.5 -4 -3.5 -3 -2.5 -2

x 10-9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


Tra

nsm

issi

on

Co

effi

cien

t

Normal

EIT

a

-5 -4.5 -4 -3.5 -3 -2.5 -2

x 10-9

-3

-2

-1

0

1

2

3


Ph

ase

of

Tra

nsm

issi

on

Normal

EIT

b

-3.015 -3.01 -3.005 -3

x 10-9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Tra

nsm

issi

on

Coef

fici

ent

EIT

Normal

c

-3.015 -3.01 -3.005 -3

x 10-9

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5


Ph

ase

of

Tra

nsm

issi

on

EIT

Normal

d

Fig. 12. Transmission coefficient vs. differential wavelength for normal and EIT cases of single horizontal ring (a)

Magnitude (b) Phase (c) Zoom in on the transmission coefficient (d) Zoom in on the phase

0.15, L=2πr=5e-4 m,

The similar situation is for the basic cell of vertical arrays, where in normal case the transmission

coefficient sensitivity (wavelength displacement between minimum and maximum) is about 0.2 nm and

phase rotates about 2π radians at resonance. In EIT case transmission coefficient sensitivity is modified to

about 5 pm as so.

-8 -6 -4 -2 0 2 4 6 8 10

x 10-9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Tra

nsm

issi

on

Coef

f. o

f S

ingle

Ver

. B

asi

c C

ell

a

-8 -6 -4 -2 0 2 4 6 8 10

x 10-9

-3

-2

-1

0

1

2

3


Ph

ase

of

Sin

gle

Ver

. B

asi

c C

ell

b

Fig. 13. Transmission of single vertical ring without EIT vs. differential wavelength, a) Magnitude and b) Phase

0.15, L=2πr=5e-4 m,

-4 -3.8 -3.6 -3.4 -3.2 -3 -2.8

x 10-9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Tra

nsm

issi

on

Coef

fici

ent

Normal

EIT

a

-3.316 -3.314 -3.312 -3.31 -3.308 -3.306

x 10-9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


Tra

nsm

issi

on

Co

effi

cien

t

EIT

Normal

c

-4 -3.8 -3.6 -3.4 -3.2 -3 -2.8

x 10-9

-3

-2

-1

0

1

2

3


Ph

ase

of

Tra

nsm

issi

on

Normal

EIT

b

-3.34 -3.33 -3.32 -3.31 -3.3 -3.29 -3.28

x 10-9

-3

-2

-1

0

1

2

3


Ph

ase

of

Tra

nsm

issi

on

EIT

Normal

d

Fig. 14. Transmission coefficient vs. differential wavelength for normal and EIT cases of single vertical ring. (a)

Magnitude (b) Phase (c) Zoom in on the transmission coefficient (d) Zoom in on the phase

2. Vertical Array

In horizontal array our simulations show that by increasing the number of rings, the slope of transmission

coefficient increases. On the other hand in oscillatory region envelope of the transmission coefficient is

returned to minimum. Also, the phase variation increases to 4π times by increasing the number of rings at

resonance wavelength.

It is observed that sensitivity of the vertical arrays improves from 5 pm for single ring to 2 pm for three

rings where the transmission coefficient has one and three peaks for them respectively. Also, phase

rotation varies from 2π to 10π in same oscillation duration of wavelength.

-3.322 -3.32 -3.318 -3.316 -3.314 -3.312 -3.31 -3.308

x 10-9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


Tra

nsm

issi

on

Coef

fici

ent

Single

Two

Three

a

-3.322 -3.32 -3.318 -3.316 -3.314 -3.312 -3.31 -3.308

x 10-9

-3

-2

-1

0

1

2

3


Ph

ase

of

Tra

nsm

issi

on

Single

Two

Three

b

Fig. 15. Transmission of vertical array with fixed control field vs. differential wavelength. (a) Magnitude. (b) Phase

0.15, L1= L2= L3=5e-4 m,

Following figures show that oscillation wavelength varies with control field variation and oscillation wavelength

duration increases with increasing of control field.

-3.318 -3.316 -3.314 -3.312 -3.31 -3.308 -3.306 -3.304 -3.302 -3.3

x 10-9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


Tra

nsm

issi

on

Co

effi

cien

t

Single

Two

Three

a

-3.318 -3.316 -3.314 -3.312 -3.31 -3.308 -3.306 -3.304 -3.302

x 10-9

-3

-2

-1

0

1

2

3


Ph

ase

of

Tra

nsm

issi

on

Single

Two

Three

b

Fig. 16. Transmission of vertical arrays with fixed control field vs. differential wavelength


0.15, L1= L2= L3=5e-4 m,

3. Horizontal Array In following figures it is illustrated that increasing of the control field extends the oscillation region. Also,

in horizontal array it can be shown that by increasing the number of rings the transmission coefficient is

decreased and find the minimum value while it is at maximum for single ring in out of oscillation region.

On the other hand in oscillatory region the envelope of transmission coefficient is returned to minimum

value. Also, the phase rotation increases 2π times by increasing the number of rings at oscillation

wavelength.

-3.7 -3.6 -3.5 -3.4 -3.3 -3.2 -3.1 -3 -2.9

x 10-9

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


Tra

nsm

issi

on

Co

effi

cien

t

Single

Two

Three

a

-3.41 -3.4 -3.39 -3.38 -3.37 -3.36 -3.35 -3.34

x 10-9

-4

-3

-2

-1

0

1

2

3


Ph

ase

of

Tra

nsm

issi

on

Single

Two

Three

b

Fig. 17. Transmission of horizontal arrays with fixed control field vs. differential wavelength (a) Magnitude (b)

Phase

0.15, L1= L2= L3=5e-4 m,

-4 -3.5 -3 -2.5

x 10-9

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


Tra

nsm

issi

on

Coef

fici

ent

Single

Two

Three

a

-3.41 -3.4 -3.39 -3.38 -3.37 -3.36 -3.35 -3.34

x 10-9

-4

-3

-2

-1

0

1

2

3


Ph

ase

of

Tra

nsm

issi

on

Single

Two

Three

b

Fig. 18. Transmission of horizontal arrays with fixed control field vs. differential wavelength (a) Magnitude (b) Phase

0.15, L1= L2= L3=5e-4 m,

4. Matrix Array

In the following results it is shown that the transmission coefficient and phase of matrix arrays have

characteristics of both horizontal and vertical arrays except the first one which, in fact, is a vertical array.

-3.322 -3.32 -3.318 -3.316 -3.314 -3.312 -3.31 -3.308

x 10-9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


Tra

nsm

issi

on

Co

effi

cien

t

Single

2x2

3x3

-3.326 -3.324 -3.322 -3.32 -3.318 -3.316 -3.314 -3.312 -3.31 -3.308 -3.306

x 10-9

-3

-2

-1

0

1

2

3


Ph

ase

of

Tra

nsm

issi

on

Single

2x2

Three

a b

Fig. 19. First transmission of matrix arrays with fixed control field vs. differential wavelength a) Magnitude b)

Phase

0.15, L1= L2= L3=5e-4 m,

-3.32 -3.318 -3.316 -3.314 -3.312 -3.31 -3.308 -3.306 -3.304 -3.302 -3.3

x 10-9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


Tra

nsm

issi

on

Coef

fici

ent

Single

2x2

Three

a

-3.318 -3.316 -3.314 -3.312 -3.31 -3.308 -3.306 -3.304 -3.302

x 10-9

-3

-2

-1

0

1

2

3


Ph

ase

of

Tra

nsm

issi

on

Single

2x2

Three

b

Fig. 20. First transmission of matrix arrays with fixed control field vs. differential wavelength a) Magnitude b)

Phase

0.15, L1= L2= L3=5e-4 m,

Following figures show that the second transmission coefficient of matrix arrays varies between 0 and

about 0.23 and phase of transmission can’t complete its rotations as horizontal and vertical array cases.

-3.322 -3.32 -3.318 -3.316 -3.314 -3.312 -3.31 -3.308

x 10-9

0

0.05

0.1

0.15

0.2

Wavelength Shift

Tra

nsm

issi

on

Coef

fici

ent

2 x 2

3 x 3

a

-3.32 -3.315 -3.31 -3.305

x 10-9

-3

-2

-1

0

1

2

3

wavelength Shift (m)

Ph

ase

of

Tra

nsm

issi

on

2 x 2

3 x 3

b

Fig. 21. Second transmission of matrix arrays with fixed control field vs. differential wavelength


0.15, L1= L2= L3=5e-4 m,

-3.32 -3.315 -3.31 -3.305 -3.3

x 10-9

0

0.05

0.1

0.15

0.2


Tra

nsm

issi

on

Co

effi

cien

t

2 x 2

3 x 3

a

-3.32 -3.315 -3.31 -3.305 -3.3

x 10-9

-3

-2

-1

0

1

2

3


Ph

ase

of

Tra

nsm

issi

on

2 x 2

3 x 3

b

Fig. 22. Second transmission of matrix arrays with fixed control field vs. differential wavelength


0.15, L1= L2= L3=5e-4 m,

It is illustrated that the third transmission coefficient of matrix arrays has decreased to about 0.14. Also, it

can be seen that not only horizontal and vertical array specification contributions on third transmission

vary by magnitude of the control field but also oscillation wavelength position and duration varies too. It

can be seen that phase rotations aren’t complete as so.

-3.32 -3.315 -3.31 -3.305 -3.3

x 10-9

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14


Tra

nsm

issi

on

Coef

fici

ent

6.58 e7

16.45 e7

a

-3.32 -3.315 -3.31 -3.305 -3.3 -3.295

x 10-9

-3

-2

-1

0

1

2

3


Ph

ase

of

Tra

nsm

issi

on

6.58 e7

16.45 e7

b

Fig. 23. Third transmission of matrix arrays with variable control field vs. differential wavelength


(b) 0.15, L1= L2= L3=5e-4 m,

The effect of refractive index variation on transmission of basic cells in both normal and doped cases is

illustrated in Figs. 24-27.

In Figs. 24-26 it can be seen that resonance wavelength displacement is about 0.5 nm for 0.0005 change

of the refractive index in normal case of basic cells. On the other hand, in doped case, it is shown that

resonance wavelength displacement is about 4 pm for the same change of refraction index in Figs. 25-27.

-4 -3 -2 -1 0 1 2

x 10-9

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95


Tra

nsm

issi

on

Coef

fici

ent

1.5

1.5005

1.501

a

-4 -3 -2 -1 0 1 2

x 10-9

-3

-2

-1

0

1

2

3


Ph

ase

of

Tra

nsm

issi

on

1.5

1.5005

1.501

b

Fig. 24. Transmission of normal horizontal basic cell vs. differential wavelength for different refraction index


-3.08 -3.06 -3.04 -3.02 -3 -2.98 -2.96

x 10-9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


Tra

nsm

issi

on

Coef

fici

ent

1.5

1.5005

1.501

a

-3.32 -3.3 -3.28 -3.26 -3.24 -3.22 -3.2

x 10-9

-3

-2

-1

0

1

2

3


Ph

ase

of

Tra

nsm

issi

on

1.5

1.5005

1.501

b

Fig. 25. Transmission of doped horizontal basic cell vs. differential wavelength for different refraction index


-4 -3 -2 -1 0 1 2

x 10-9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Tra

nsm

issi

on

Coef

fici

ent

1.5

1.5005

1.501

a

-4 -3 -2 -1 0 1 2

x 10-9

-3

-2

-1

0

1

2

3


Ph

ase

of

Tra

nsm

issi

on

1.5

1.5005

1.501

b

Fig. 26. Transmission of normal vertical basic cell vs. differential wavelength for different refraction index


-3.4 -3.38 -3.36 -3.34 -3.32 -3.3 -3.28

x 10-9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


Tra

nsm

issi

on

Coef

fici

ent

1.5

1.5005

1.501

a

-3.4 -3.38 -3.36 -3.34 -3.32 -3.3 -3.28

x 10-9

-3

-2

-1

0

1

2

3


Ph

ase

of

Tra

nsm

issi

on

1.5

1.5005

1.501

b

Fig. 27. Transmission of doped vertical basic cell vs. differential wavelength for different refraction index (a)

Magnitude (b) Phase

Finally effect of displacement on the transmission coefficient for different displacement values in both normal and

EIT cases of micro-ring resonators are illustrated in Fig. 28. It is shown that the EIT case is so sensitive compared

normal case.

-2.91 -2.9 -2.89 -2.88 -2.87 -2.86 -2.85 -2.84 -2.83 -2.82 -2.81

x 10-9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Wavelength Shift [m]

Tra

nsm

issi

on

Coef

fici

ent

1pm

0.1nm

10nm

1nm

5nm

10nm,Normal

Fig. 28. Wavelength displacement vs. displacement in EIT and Normal Cases for different displacement values

In this section different aspect of the proposed structure for operation as displacement or sensing other

quantities were considered. It was shown that application of EIT in ring resonator has critical effect on

increasing the sensitivity of the proposed sensor.

4. Conclusion In this paper sensor matrix based on array of ring resonators has been presented. It has been shown that application

of nanocrystals such as 3-level atoms in ring resonator strongly improves displacement measurement even less than

5 pm. The proposed structure can be used to measure displacement of 2-D micro mirror array. The proposed

structure can be used as 2-D imaging sensor for ultrasound signals especially in intravascular case.

REFERENCES

[1] A. Rostami and K. Abbasian, "All-optical Filter Design: Electromagnetically Induced Transparency and Ring

Resonator," Proceeding of MICC-ICT’2007, Malaysia, 2007.

[2] Ka-Di Zhu, W. S. Li, "Electromagnetically induced transparency due to Exciton–phonon interaction in an

organic quantum well," J. Phys. B: At. Mol. Opt. Phys. 34, pp. L679–L686, (2001).

[3] S. E. Harris, L. V. Hau, "Nonlinear Optics at Low Light Levels," Phys. Rev. Lett., 82, 4611, (1999).

[4] S. E. Harris, "Electromagnetically induced Transparency," Physics Today, pp. 36-42, July 1994.

[5] R. Yadipour, K. Abbasian, A. Rostami, Z. D. Koozehkanani, "A novel proposal for ultra-high resolution and

compact optical displacement sensor based on Electromagnetically Induced Transparency in Ring

Resonator," Progress In Electromagnetics Research, PIER 77, 149–170, (2007).

[6] M. O. Scully, M. S. Zubairy, "Quantum Optics", Cambridge Uni. Press, ISBN: 0 521 43458 0, (2001).

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(2000).

[8] Govind P. Agrawal, "Nonlinear Fiber Optics," 0-12-045143-3, Academic Press, (2001).

[9] A. Kasapi, Maneesh Jain, G. Y. Yin, S. E. Harris, "Electromagnetically Induced Transparency: Propagation

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[10] F. Vollmer, P. Fisher, "Frequency-Domain Displacement Sensing with a Fiber Ring Resonator Containing a

Variable Gap," Sensors and actuators, Vol. 134, (2007).

[11] I. Kiyat, C. Kocabas, A. Aydinli, "Integrated Micro Ring Resonator Displacement Sensor for Scanning Probe

Microscopies," Journal of Micromechanics and Micro engineering, Vol.14, (2004).

[12] A. Rostami, M. Noshad, H. Hedayati, A. Ghanbari and F. Janabi-Sharifi, "A Novel and High-Precision

Optical Displacement Sensor," International Journal of Computer Science and Network Security, vol.7,

(2007).

[13] M. Noshad, H. Hedayati and A. Rostami, "A Proposal for High-Precision Fiber Optic Displacement Sensor,"

Proceedings of the Asian Pacific Microwave Conference, Yokohama, Japan, December 12-15, (2006).

[14] C. Y. Chao, S. Ashkenazi, S. W. Huang, "High-Frequency Ultrasound Sensors Using Polymer Microring

Resonators," IEEE, Trans. On Ultrasonics, Ferroelectrics and Freq. Control, Vol. 54, No. 5, (2007).

[15] A. Rostami and G. Rostami, "Linear and nonlinear Applications of Ring Resonators," Book Chapter, Nova

Publishers, USA 2007.

Proposal for 2-D High Precision Displacement Sensor Array ...

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