Fano resonance based on 3x3 multimode interference structures for fast and slow light applications

Fano Resonance Based on 3x3 Multimode Interference Structures for Fast and Slow Light Applications Trung-Thanh Le* * International School VNU-IS Vietnam National University VNU, Hanoi,

Fano Resonance Based on 3x3 Multimode Interference

Structures for Fast and Slow Light Applications

Trung-Thanh Le*

*

International School (VNU-IS) Vietnam National University (VNU), Hanoi, Vietnam

E-mail: thanh.le@isvnu.vn

Abstract- We present for the first time a new method

for creating Fano resonance by using only one 3x3

multimode interference (MMI) coupler with a

feedback waveguide We use the silicon waveguide for

the whole design, so it is compatible with CMOS

technology The device is compact and has a large

tolerance fabrication In addition, many useful optical

functions such as all-optical switches, filters and

single-mode lasers can be realized using Fano-type

transmission device The transfer matrix method

(TMM) and beam propagation method (BPM) are

used to optimally design the structure We show that

by using the proposed structure, fast and slow light

can be obtained.

Index Terms- Multimode interference, Fano resonance,

microring resonator, Electromagnetically induced

transparency (EIT), optical signal processing, signal

processing, fast light and slow light

I INTRODUCTION Devices based on optical microring resonators have

attracted considerable attention recently, both as

compact and highly sensitive sensors and for optical

signal processing applications [1-3] In the literature,

the coupling element in microring resonator is to use

co-directional evanescent coupling between the ring

and an adjacent bus waveguide The transmission

spectrum of the bus waveguide with a single ring

resonator will show dips around the ring resonances

A single microring resonator behaves as a spectral

filter and notch filter, which can be used for

applications in optical communication, especially

wavelength division multiplexing (WDM) The

resonance line shape of a conventional microring

resonator is symmetrical with respect to its resonant

wavelength However, microring resonator coupled

Mach Zehnder interferometers can produce a very

sharp asymmetric Fano line shape that are used for

improving optical switching and add-drop filtering [4, 5]

It is shown that for functional devices based on one-ring resonator such as optical modulators and switches, it is not possible to achieve simultaneously high extinction ratio and large modulation depth [6, 7] To maximize the extinction ratio and modulation depth, we can use an asymmetric resonance such as the Fano resonance

Fano resonance is a result of interference between two pathways One of the conventional way to generate a Fano resonance is by the use of a ring resonator coupled to one arm of a Mach-Zehnder interferometer, with a static bias in the other arm [8-10] The strong sensitivity of Fano resonance to local media brings about a high figure of merit, which promises extensive applications in optical devices such as optical switches [10] Fano resonances have long been recognized in grating diffraction and dielectric particles elastic scattering phenomena The physics of the Fano resonance is explained by an interference between a continuum and discrete state [9] The simplest realization is a one dimensional discrete array with a side coupled defect In such a system scattering waves can either bypass the defect

or interact with it

It has been suggested that optical Fano resonances have many applications in resonance line shape sensitive bio-sensing, optical channel switching and filtering [11, 12] Recently, optical Fano resonances have also been reported in various optical micro-cavities including integrated waveguide-coupled microcavities [13], prism-coupled square micro-pillar resonators, multimode tapered fiber coupled micro-spheres and Mach Zehnder interferometer

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(MZI) coupled micro-cavities [14], plasmonic

waveguide structure [8, 15]

In this study, we propose a new structure based on

only one 3x3 multimode interference coupler based

microring resonator to produce Fano resonance line

shape The proposed device is analyzed and

optimized using the transfer matrix method (TMM),

the beam propagation method (BPM) and finite

difference time domain (FDTD) method [16] A

description of the theory behind the use of

multimode structures to achieve the Fano effect

presented in Section II Simulation results of MMI

based structures for components in the device

structure are covered in Section III A brief summary

of the results of this research is given in Section IV

II PRINCIPLE OF OPERATION

Microring structures based on a 3x3 MMI coupler

for optical filtering, modulating and switching

applications have been proposed in the literature

[17-19] The aim of this study is to show that this

structure can create the Fano line shape The phase

and group delay of the transmissions of the structure

are analysed It is shown that the fast and slow light

can be induced The schematic of a microring

resonator based on a 3x3 MMI coupler is shown in

Fig 1

The 3x3 MMI coupler can be described by a transfer

matrix M which describes the relationships between

the input and output complex amplitudes of the

coupler [20] Recently, we proposed a microring

resonator based on 3x3 MMI coupler for the first

time [21] In order for this microring resonator to

operate correctly, the width, length and access

waveguide positions need to be chosen carefully It

is assumed that the access waveguides are located at

the positionsy1W / 6e ,y2W / 2e ,y35W / 6e ,

whereWMMI, We are the width and effective width

of the MMI coupler [20]

The length of the MMI coupler is to be LMMI L,

where L is the beat length of the MMI coupler The 

relationship between the output complex amplitudes

j

b (j=1,2,3) and the input complex amplitudes

i

a (i=1,2,3) of the coupler can be expressed by



where a  [a a a ]1 2 3 T, b  [b b b ]1 2 3 T and

ij 3x3

[m ] (i, j=1, 2, 3)



MMI

W

1 y

2 y

3

y 0

y

z

Fig 1 Microring resonators based on a 3x3 MMI coupler

Equation (1) can be rewritten as

j2 /3 j2 /3

j2 /3 j2 /3

1

3

   

(2)

where

j2 /3 j2 /3

j2 /3 j2 /3

1

3

   





L

24

   

, a3 [ exp(j )]b 3, and

0

   is the transmission loss along the ring waveguide, where L2 R LMMI and 0 (dB/cm) is the loss coefficient in the core of the optical waveguide;   0Lis the phase accumulated over the racetrack waveguide, where   0 2 neff /, and neff is the effective refractive index

In our design, we use silicon waveguide, where 2

SiO (

2

SiO

n =1.46) is used as the upper cladding material An upper cladding region is needed for devices using the thermo-optic effect in order to reduce loss due to metal electrodes Also, the upper cladding region is used to avoid the influence of

VOL.12, NO.5, SEPTEMBER 2017

moisture and environmental temperature [22] The

parameters used in the designs are as follows: the

waveguide has a standard silicon thickness of

co

h 220nm and access waveguide widths are

a

W 0.5 m for single mode operation It is

assumed that the designs are for the transverse

electric (TE) polarization at a central optical

wavelength  1550nm For the first order design,

the TMM is used, then we use the three dimensional

beam propagation method (3D-BPM) and FDTD to

design finally the whole structure [2]

Fig 2 Output powers at port 1, 2, 3 at different MMI length

when input at port 1

Fig 3 Insertion loss at different MMI length when input at port 1

Here we show the optimized design of 3x3 GI MMI

coupler used for our proposed microring resonator

structure Fig 2 shows the BPM simulation results for output powers at output port 1, 2 and 3 at different MMI lengths when input is at port 1 For a compact device, the width of the MMI coupler is to

be WMMI 6 m The simulations show that the optimized length of the MMI is to be MMI

L 99.8 m The insertion loss of the device at this optimized length is -0.96dB Fig.3 shows the insertion loss at different lengths The field transmitting through the 3x3 MMI coupler at the length of LMMI 99.8 m is shown in Fig 4

Fig 4 Optical field through the 3x3 MMI coupler at optimized

length when input is at port 1

Fig 5 shows the simulation results for output powers

at output ports 1, 2, 3 when input signal is at port 1 The insertion loss in this case is about -0.45dB Our simulations show that the fabrication tolerance in MMI length of 30nm causes the fluctuation in output power of 0.05 For the existing CMOS fabrication technology with fabrication error of 5nm

 [3], the microring resonator based on 3x3 GI MMI coupler has an extremely large tolerance fabrication

The complex amplitudes at output ports 1 and 2 are given by

j

m13 31m e

33

j

m13 32m e

33









(4)

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j

23 31

j

23 32









(5)

(a) Insertion loss, input port 2

(b) Field at the optimized length, input port 2

Fig 5 Output powers at port 1, 2, 3 at different MMI length

when input at port 2

As a result, the transmissions at these output ports

are given by:

For the input signal presented at input port 1

(a2 0):

and

For the input signal presented at input port 2 (a10):

2

and

1

From the above equations, the transmissions are calculated

DISCUSSIONS Without loss of generality, we choose silicon waveguide with the width of 500nm and height of 220nm for our design The effective refractive index calculated by the FDM method is to be eff

n 2.416299 for the TE polarization [20] It assumed that the loss coefficient of the silicon waveguide is  0 0.98 [23], the length of ring waveguide is LR 700 m , the transmissions at output ports 1 and port 2 when input signal is at port

1 and port 2 are shown in Fig 6 and Fig.7, respectively

Next we investigate the effect of loss coefficients of the silicon waveguide on the transmissions The transmissions at output port 1 when input signal is at port 1 with different loss coefficients are shown in Fig.8 We see that the resonance wavelength of the structure is still not changed when the loss coefficient is changed These simulation result has a good agreement with theoretical analysis of microring resonator based on a 4-port device [24]

In recent years, the group delay and transmission characteristics of microring resonators used for optical filters and dispersion compensators have been studied [25, 26] However, these structures provide positive group delay and mainly designed for pulse delay applications While slow and fast light generation are emerging as a very attractive research topic Various techniques have been developed to realize fast light and slow light in atomic vapors and solid-state materials [27] One application among these techniques is to control the group velocity

VOL.12, NO.5, SEPTEMBER 2017

v of light pulses to make them propagate either

very slow (vg< c) or very fast (vg > c or vgis

negative), where c is the velocity of light

Fig 6 Transmissions at output port 1 and port 2 when input

signal at port 1

Fig 7 Transmissions at output port 1 and port 2 when input

signal at port 2

In our recent results, we have shown a new structure

by cascading microring resonators based on

directional couplers for fast and slow light

applications [28] Here, we show that by using only

one microring resonator based on a 3x3 MMI

coupler, the fast and slow light can be achieved very

effectively The group delay can be positive (slow

light) or negative (fast light) as shown in Fig.9

In order to verify our proposed analytical theory, we use the FDTD for accurate predictions of device’s working principle Fig.10(a) shows the comparison the TMM and FDTD simulations for the 3x3 MMI based microring resonator, where a Gaussian light pulse of 15fs pulse width is launched from the input

to investigate the transmission characteristics of the device The grid sizes    x y 0.02nm and

  are chosen in our simulations It is shown that the FDTD simulation has a good agreement with our theoretical analysis

Fig.10(b) and (c) show the field propagation via the device and the mask design of the whole device fabricated on an silicon on insulator (SOI) platform using CMOS technology

Fig 8 Transmissions at output port 1 and port 2 when input signal at port 1 at different loss coefficients

Fig 9 Group delay of the transmissions at port 1 and 2 when

signal at port 1

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(a) Transmissions by using TMM and FDTD simulations

(b) FDTD simulation

(c) Mask design Fig 10 (a) Transmissions by using TMM and FDTD, (b) field

propagation by using FDTD simulation of the microring

resonator based on 3x3 MMI for input port 1 and (c) mask

design of the whole device on an SOI platform

Next, we compare our analysis with the Fano

resonance in the literature In general, Fano

resonance profile can be expressed by the universal

formula for a scattering cross section [10]:

2

2

1

 

 

Where q is the shape parameter,  is the reduced

energy The proposed structure can produce the Fano

profile (transmission input port 1, output port 1)

compared with the Fano resonance profile for q=1 as

shown in Fig 11 The simulation shows that the

Fano resonance profile produced by our structure has

a good agreement with the conventional Fano resonance profile The shape of the proposed Fano resonance profile has a steeper slope compared with the original profile As a result, our structure can be applied to potential applications such as low power optical switching and high sensitive optical sensors

Fig 11 Comparison of Fano resonance profiles

IV CONCLUSIONS This paper has presented a new way of creating Fano resonance based on only one 3x3 general interference multimode interference coupler The 3x3 MMI coupler has been designed and optimized

by using the TMM and BPM It is shown that the FDTD simulation of the whole device has a good agreement with the theoretical analysis Effect of loss coefficients is also analyzed Our structure can created a sharp Fano resonance and the device has a large fabrication tolerance In addition, it is shown that the fast and slow light can be achieved from our structure This property is useful for high performance optical switches, optical buffers and high sensitive optical biosensors

ACKNOWLEDGEMENTS This research is funded by Vietnam National University, Hanoi (VNU) under project number QG.15.30

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