This Master thesis was accomplished within the Erasmus Mundus Joint Master Degree “Photonic Integrated Circuits, Sensors and NETworks (PIXNET)”.
Coordinating Institution: Scuola Superiore di Studi Universitari e di Perfezionamento Sant'anna Partners
Osaka University Aston University
Technische Universiteit Eindhoven
Project Data
Start: 01-09-2017 - End: 31-08-2022
Project Reference: 586665-EPP-1-2017-1-IT-EPPKA1-JMD-MOB EU Grant: 3.334.000 EUR
Website: http://pixnet.santannapisa.it
Programme: Erasmus+
Key Action: Learning Mobility of Individuals
Biochemical sensors
Kiranti Krishan
Masters in Photonic Integrated Circuits, Sensors and
NETworks
24
thAugust 2020
Summary
The project targets a very important application which has a significant impact on qual-ity of human life - Detection of contamination in drinking water. The idea of this project was to study integrated optical biochemical sensors built on Silicon on Insulator (SOI) platform. Mach-Zehnder Interferometer was used as a basic building block for bio chem-ical sensing. The project walks through different problems encountered in achieving a highly sensitive device on a compact platform with minimum losses. As MZI is highly sensitive to changes in refractive index due to environmental fluctuations, therefore, one of the part of this project was to detect different sources of noise responsible for the re-duction of sensitivity in MZI, and a significant limiting factor was thermal phase noise. Three different type of MZIs were characterized to analyze the performance of each type and different factors affecting the performance of each MZI. It was observed that thermal noise affected nearly all three types of MZI in a similar manner with a slight improvement of 20 dB in narrow MZI. Additionally, the sensitivity and dynamic range of MZI with nar-row free spectral range (FSR) was quite better than the other two. Another aspect of this project consist of designing a few passive components of MZI based biosensor at 1310 nm wavelength, which include Multi Mode Interference couplers and Grating couplers. This wavelength window was exploited to take advantage of lower water absorption in this wavelength range as compared to 1550 nm. It was observed that transmission of MMI coupler was ∼ 96-98% and in grating coupler it was ∼ 30-36 %. Higher loss was observed in grating couplers as compared to MMI couplers. Grating coupler with TM mode experienced ∼ 6.7% higher loss than the grating coupler with TE mode. These couplers have been sent for fabrication and can possibly be integrated with a MZI at 1310 nm wavelength in future.
Keywords: Silicon Photonics, Biochemical Sensor, Mach-Zehnder Interferometer, ther-mal phase noise
be possible. To my sister Neev and brother Sarosh, who helped me in the compilation of this thesis. Last but not the least, my husband-to-be Munaish, who had my back during the ups
I am highly grateful to my supervisor Dr. Philippe Velha who supported and guided me during the thesis period which enhanced my learning capabilities and made me competent enough to perform research in my future. I would like to thank Prof. Fabrizio Pasquale, Dr. Claudio Oton and Dr. Stefano Faralli who introduced me to the topic of photonic integrated sensing which motivated me to pursue my master’s thesis in this field, and managed the laboratory sessions in this difficult time of global pandemic due to Covid-19. I would also like to thank Yisbel Marin for helping me with experiments and Mahmoud Nasser for his help throughout the thesis period.
Last but not the least, i would like to show my gratitude to Dr. Piero Castoldi for his co-operation and support, Dr. Stylianos Sygletos and Dr. Sergey Sergeyev for helping remotely through emails and conference calls during the thesis time.
Summary 1 Acknowledgments 3 1 Introduction 11 1.1 Photonic Sensors . . . 11 1.2 Biosensors . . . 12 1.3 Optical Biosensors . . . 13
1.3.1 Integrated Photonic biochemical sensor . . . 14
1.4 Overview . . . 18
2 Background 19 2.1 Architecture . . . 19
2.2 Integrated devices used for sensing . . . 20
2.2.1 Photonic Crystal Sensors . . . 22
2.2.2 Ring Resonator Sensors . . . 24
2.2.3 Mach-Zehnder interferometer sensors . . . 27
2.3 Building Blocks and Design Parameters of MZI . . . 28
2.3.1 Principle of Optical interference . . . 28
2.3.2 Working Principle of MZI . . . 29
2.3.3 Challenges associated with MZI and their respective solutions . . . . 30
2.4 Passive Components of MZI at 1310 nm wavelength . . . 33
2.4.1 MMI couplers . . . 34
2.4.2 Grating couplers . . . 35
3 Designing of Passive components 37 3.1 Lumerical and its tools . . . 37
3.2 Designing of MMI couplers . . . 38
3.2.1 1x2 MMI Coupler . . . 38
3.2.2 2x2 MMI coupler . . . 48
3.3 Designing of Grating couplers . . . 52
3.3.2 3D grating coupler with fundamental TE mode . . . 58
3.3.3 3D grating coupler with fundamental TM mode . . . 60
4 Characterization of Integrated Biochemical sensor 64 4.1 Devices to be characterized . . . 66
4.2 Characterization of MZI . . . 66
4.2.1 Experimental Setup . . . 66
4.2.2 Results of Characterization . . . 69
4.2.3 Laser modulation . . . 72
4.2.4 Phase noise due to thermal changes . . . 77
4.2.5 Phase noise with varying modulation frequency . . . 81
4.2.6 Comparison of all three types of MZI . . . 82
5 Discussion/Analysis 85 5.1 Characterization Analysis . . . 85
5.2 Simulation analysis . . . 86
6 Conclusion and Future work 88
1.1 Top Impacting Factors of Photonic Sensor Market [1] . . . 12
1.2 Optical Biosensors[2] . . . 14
1.3 Schematic of an optical biosensor [3] . . . 15
1.4 Electric field intensity in a silicon waveguide 500 nm wide and 220 nm high for both the supported modes. In black are the structure limits [4] . 16 1.5 Scheme of biomolecular interaction taking place in an evanescent field at the surface of waveguide [5] . . . 17
2.1 General architecture of an integrated biosensor [5] . . . 20
2.2 Illustration of photonic crystals in: (a) 1D conformation; (b) 2D confor-mation; (c) 3D conforconfor-mation; (d) Measured transmission spectrum of a uniform photonic crystal (PhC) device after normalization [4] . . . 23
2.3 Structure of a micro ring resonator [4][17] . . . 25
2.4 Definition of the Q factor in terms of wavelength and linewidth . . . 26
2.5 Ring transmission before and after binding of analyte showing a clear shift in the resonance wavelength [4] . . . 26
2.6 Schematic of a Mach-Zehnder Interferometer [6]. . . 30
2.7 Intensity output of the MZI as a function of the bias voltage (V) . . . 31
2.8 Schematic of PGC technique on an unbalanced MZI . . . 32
2.9 Water absorption spectrum showing near-infrared wavelengths as a func-tion of absorpfunc-tion co-efficient (s.a.c) with red and black marks showing 1.3 micron and 1.5 micron window respectively. . . 33
2.10 Multimode waveguide showing the input field Ψ(y,0), a mirrored single image at (3Lπ), a direct single image at 2(3Lπ), and two-fold images at 1 2(3Lπ) and 3 2(3Lπ) [7] . . . 34
2.11 Schematic of a grating coupler [8] . . . 35
3.1 Structure of 1x2 MMI Coupler . . . 38
3.2 MMI structure with group spans of EME . . . 38
3.3 Material data base . . . 39
3.4 Object tree . . . 40
3.5 Cell group definition . . . 40
3.7 Transverse mesh settings of EME . . . 42
3.8 Propagation sweep of central waveguide . . . 42
3.9 Transmission as a function of Coupler length. . . 42
3.10 Parameters of taper length sweep . . . 43
3.11 Transmission as a function of Taper length . . . 43
3.12 Transmission as a function of taper width. . . 43
3.13 Field profile of 1x2 MMI Coupler . . . 44
3.14 S Matrix of 1x2 MMI Coupler. . . 44
3.15 Mode profiles of 1x2 MMI Coupler; a) Mode profile of input port (PORT 1); b) Mode profile of output 1(PORT 2); c) Mode profile of output 2 (PORT 3) 45 3.16 Histogram and Error distribution of coupler length and coupler width . . 45
3.17 Histogram and Box plot of deviation in coupler length and coupler width 46 3.18 Histogram and Box plot of deviation in 5 parameters . . . 47
3.19 Histogram and Noise distribution in 5 parameters . . . 48
3.20 Optimized structure of 2x2 MMI Coupler . . . 49
3.21 Cell group definition of 2x2 MMI Coupler. . . 49
3.22 Transmission as a function of Mesh cells . . . 49
3.23 Transmission as a function of Coupler length. . . 49
3.24 Transmission vs taper length . . . 50
3.25 Transmission vs taper width . . . 50
3.26 Field profiles of 2x2 MMI coupler . . . 51
3.27 S Matrix of 2x2 MMI coupler . . . 51
3.28 Mode profiles of 2x2 MMI coupler . . . 52
3.29 (a) 2-Dimensional view of grating coupler; (b) 3-Dimensional view of grat-ing coupler [9] . . . 53
3.30 Cross – section view of a 2- Dimensional grating coupler with fiber [9] . 53 3.31 Wavelength setting in FDTD . . . 54
3.32 Initial parameters of fiber and grating coupler . . . 55
3.33 Optimizing parameters through PSO . . . 56
3.34 Optimization results from PSO . . . 57
3.35 Transmission on port 2(waveguide) . . . 57
3.36 3D grating coupler. . . 58
3.37 Transmission on port 2 of TE grating coupler. . . 59
3.38 Mode profiles of input and output ports . . . 59
3.39 No. of modes calculated on port 2 . . . 60
3.40 TM mode selection on port 2 . . . 61
3.41 FOM of optimization . . . 61
3.42 Final properties of grating coupler with TM mode . . . 62
3.43 Transmission at port 2 . . . 62
4.1 Thermal phase noise [10] . . . 64
4.2 Schematic Athermal MZI . . . 65
4.3 Schematic of different types of MZI characterized . . . 66
4.4 Experimental setup . . . 67
4.5 Voltage sweep for classic MZI . . . 70
4.6 Notch count for classical MZI . . . 71
4.7 Voltage sweep for Athermal MZI. . . 71
4.8 Voltage sweep for Narrow FSR MZI . . . 72
4.9 Experimental Setup for Laser modulation . . . 73
4.10 Laser modulation of Classical MZI at 6 Hz . . . 74
4.11 Dynamic range of Classical MZI . . . 75
4.12 Dynamic range of Athermal . . . 76
4.13 Laser modulation on Narrow FSR MZI with 120 Hz . . . 76
4.14 Dynamic range of MZI with narrower FSR . . . 77
4.15 Behaviour of noise in MZI . . . 78
4.16 Behaviour of thermal noise with varying temperature . . . 79
4.17 Temperature fluctuation in Athermal MZI . . . 80
4.18 Temperature fluctuation in Athermal MZI . . . 80
4.19 Thermal noise in MZI with narrower FSR . . . 81
4.20 Effect of changing modulation frequency on classical MZI . . . 82
4.21 Comparison of slopes of 3 MZI . . . 83
2.1 Performance parameters comparison of different sensor types using
sev-eral strategies[4] . . . 21
3.1 Initial values of 1x2 MMI Coupler . . . 41
3.2 Optimum values of 1x2 MMI Coupler . . . 44
3.3 Optimum values of 2x2 MMI Coupler . . . 50
4.1 Comparison of MZIs in terms of sensitivity . . . 82
Abbreviations
DNA: DeoxyriboNucleic Acid RNA: Ribonucleic Acid RIU: Refractive Index Unit TIR: Total internal reflection SPR: Surface Plasmon Resonance PC: Personal Computer
FPGA: Field Programmable Gate Array PLC: Planar lightwave circuits
SOI: Silicon on Insulator Si: Silicon
SiO2: Silica
PD: Photodiode LOC: Lab on a chip
MZI: Mach-Zehnder Interferometer FOM: Figure of merit
LOD: limit of detection
NOSA: Nanoscale opto-fluidic sensor array PDMS: Polydimethylsiloxane
OSA: optical spectrum analyzer LIA: Lock in Amplifier
PSO: Particle Swarm Optimization Free spectral range (FSR)
One of the main motivations of the proposed Master’s thesis was to design and character-ize an integrated optical biosensor built on MZI to determine contamination in drinking water with an aim of achieving it at better sensitivity. The project targets a very important application i-e detection of contamination in drinking water which has a huge impact on the quality of human life and is hazardous for health. To enhance the learning experience, a two-stage thesis was proposed which includes designing as well as characterization of a biochemical sensor which led to familiarization of Lumerical suite software along with hands-on experience of handling various optical devices in the laboratory.
This chapter helps to build the fundamentals of the entire project by highlighting the growth trend of photonic sensors with a brief overview of biosensors, optical biosensors, procedures used to construct them and how they can be integrated on a small platform to achieve desired results.
1.1 Photonic Sensors
Over the last couple of decades, a lot of effort has been poured into the world of photonic technology. Initial designs prioritized enhancement in the telecommunication sector. However, the domain of photonics expanded with evolving technologies and was soon exploited for sensing applications. These sensors target numerous applications such as, biotechnology, monitoring pipelines and railway tracks, developing security appliances and many more. Optical sensors can either be used for distributed sensing, where the op-tical fiber itself acts as a sensing device or in discrete form where a black box contains the sensing fiber. As compared to electronic sensors, optical sensors have an added advantage of relatively smaller size, robustness in harsh environments, immunity to electromagnetic interference, portability, energy efficiency and cost effectiveness. These features has en-abled optical sensors to gain popularity in a short span of time and is progressive enough to attract more investments in near future. The international photonic sensors market
has experienced a drastic shift with the unfolding of innovative research experiments and by 2021 it is anticipated to grow at $18 billion [1] at a CAGR of 17.7%. A substantial transition was observed from 2014 to 2020 in the market trend of photonic sensing. It has evolved significantly and is still on an incline due to increased demand in safety and secu-rity appliances and improvement in sensing technologies as compared to the traditional ones. However, it is struggling in terms of standardization and demand for high initial investment as depicted in fig. 1.1. The area is quite vigorous in academic research but it still needs conviction in the market to overcome these hindrances. A sub class of photonic sensor that has recently gained importance is the biochemical sensor which plays a vital role in the health care sector and environmental industry to overcome hazardous health related issues. Specially in this era when one of the catastrophic virus such as Covid-19 has enhanced the demand for tele-medicine, research in photonic biosensors can assist in effective and rapid restorative measures to reach far and wide to minimize the impact of such pandemics.
Figure 1.1:Top Impacting Factors of Photonic Sensor Market [1]
1.2 Biosensors
A biosensor is an analytical device used to detect the presence or the quantity of a par-ticular biological entity called analytes in a matrix like water, saliva, urine, blood, ...etc. Those analytes can take different forms such as protein, antibody, DeoxyriboNucleic Acid
(DNA) or Ribonucleic Acid (RNA). The biosensor translates the presence or quantity into an electrical signal. It is further treated by signal processing to yield results useful for clinical diagnostics, environmental monitoring, detection of contamination in liquids and others [5]. These sensors can be designed using several techniques based on different types of transduction or bio recognition element including:
• Electrochemical biosensors- a technique in which electrodes convert the chemical signal into electrical signal.
• Thermal biosensors- measures thermal changes occurring in different biochemical recognitions.
• Piezo electric biosensors- give measurement of changes in mass due to biochemical recognition [11].
• Optical biosensors- a technique in which variation of optical properties (such as refractive index) are observed due to a biomolecular interaction between a bio re-ceptor and the chemical being tested [5].
Techniques based on bio recognition unit rely on biological process and chemical reac-tions [12] which can be categorized as enzymatic, nucleic – acid based, anti-body based and others [11].
1.3 Optical Biosensors
Optical biosensors are preferred over traditional analytical techniques due to its ability of direct detection in real time, miniaturized size, high sensitivity and selectivity towards targeted biological entity. Various types of optical sensors have been constructed de-pending on the type of targeted applications. Some of them include Bio-luminescent op-tical fiber sensors, Surface Plasmon Resonance (SPR) biosensors, Evanescent field based biosensors etc [2]. Typically an optical bio-sensing comprises of 4 steps that are illustrated in fig. 1.2. It elaborates each step from sample recognition to signal detection. Typically, each biological sample constitutes of biorecognition elements such as antibody, protein etc which is placed on the surface of biosensor. Light from Laser source interacts with these molecules on a waveguide, modulating properties of light through different opti-cal transduction mechanism such as interferometers, gratings, resonators etc that can be visualized using platforms such as PC or FPGA etc.
Figure 1.2:Optical Biosensors[2]
In the past years, many strides have been made towards the research in the field of optical biosensors to make them portable and user-friendly. In order to achieve it, a so-phisticated technology such as integrated optics is employed for further miniaturizing the devices so that real-time sensing is more efficient and require minimum quantity of sample[5]. There is still quite a room for augmenting reading units on the sensing plat-form to perplat-form post sensing operations such as signal detection, signal processing and manipulation of acquired data.
1.3.1 Integrated Photonic biochemical sensor
Introduction
Ideally, optical integration tends to combine light source, sensing mechanism, and de-tection capability on an individual platform [5]. Ideally, it comprises of the light source, sensing mechanism and detection capability on an individual photonic chip with robust, intelligent and user friendly mechanism as depicted in fig. 1.3. However, currently the research has not matured enough to obtain such a model. Yet, promising results with high precision and sensitivity has been obtained through fabrication of components on various photonic integrated platforms such as Lithium Niobate compounds, Planar lightwave cir-cuits (PLC) and semiconductors together with III-IV and silicon photonics platform [13]. Fabrication platforms
Each fabrication platform has its own benefits and constraints. PLC is favourable for de-signing passive devices as they can integrate large waveguides and makes fiber to chip
Figure 1.3:Schematic of an optical biosensor [3]
coupling easier. For applications requiring integration of active devices, PLC is not suit-able and an electronic compatible platform is needed which can integrate both optical and electronic components with minimum losses such as Silicon on Insulator. Particu-larly, Silicon on Insulator (SOI) is gaining high interest because of its ability to provide a complete package and large production volume applications, fostering as well Com-plementary Metal Oxide Semiconductor (CMOS) technology. Exploiting its advantage of high refractive index contrast in waveguides, dense structures can be fabricated on a sin-gle chip, thus making it a quite low-cost per device while sustaining its high-sensitivity performance [14].It has provided promising results in the field of photonic biosensors by integrating several optical components such as couplers, filters, modulators and detec-tors on a single substrate [3] aiming to enhance the DNA, RNA, proteins, etc. detection capability [14]. Typically, highly-sensitive and selective optical bio sensors are achieved through evanescent field detection principle [3], which rely on intermolecular interaction between the bio receptor layer and the analyte under test.
The SOI platform consist of a silicon (Si) substrate layer, followed by a silicon waveg-uide which is sandwiched between cladding of Silica (SiO2). The (Si) waveguide is then
known as a fully etched waveguide or a strip waveguide. Light travels in this waveg-uide through Total Internal Reflection (further explained is given in following section) and an evanescent wave will be generated at the interface of waveguide and cladding. As represented in fig. 1.4, light is not completely confined in the core of waveguide, rather spreads out a bit in horizontal/vertical direction, resulting in evanescent field area. When cladding of (SiO2) is removed from top and a sample of interest with a lower refractive
index is placed on the surface of a waveguide, the evanescent field will affect the proper-ties of light, thus producing a change in effective refractive index of the waveguide which can be translated into intensity or phase variation (∆φ).
Figure 1.4:Electric field intensity in a silicon waveguide 500 nm wide and 220 nm high for both the supported modes. In black are the structure limits [4]
Principle of Biochemical sensing
Snell’s law defines the propagation of light in a waveguide through total internal relection (TIR) represented by eq. 1.1
n1Sinθ1 = n2Sinθ2 (1.1)
Where θ1is the incident angle from air to the waveguide, n1 is the refractive index of
air ∼ 1. θ2is the reflected angle in the waveguide and n2is the refractive index of silicon
waveguide ∼ 3.4.
This phenomenon occurs when incident angle (θ1) is greater than the critical angle i-e
(θ1 > 90 °) and refractive index of second medium (silicon waveguide) should be greater
than first medium (Air) in order to guide the light. When these conditions are met and light is passed from this waveguide, an electromagnetic field known as evanescent field is formed around the waveguide interface and air. As the evanescent field deteriorates ex-ponentially into the external medium of lower refractive index (see fig.1.5), the biomolec-ular interaction occurs on the surface of the chip, where the detection of the analyte takes
place. This phenomenon can produce changes and affect the guiding properties of light such as refractive index, which offers a direct detection of the targeted analyte [5].
Figure 1.5:Scheme of biomolecular interaction taking place in an evanescent field at the surface of waveguide [5]
The evanescent field detection principle can be combined with a suitable signal detec-tion protocol to increase the selectivity of target molecules in real time. These protocols can be classified as label-based or label-free detection scheme [15]. Regardless of nu-merous applications of fluorescent- label- based sensors, they are time consuming and expensive, additionally, the conjugated fluorophore in the label also binds to the recep-tor layer with the target molecule thus decreasing the efficiency in terms of selectivity of the molecule of interest. On the other hand with label free detection protocol tests can be performed in real time without the need of fluorescent labels. Aptamers which are single strands nucleic acid fetched from combinatorial oligonucleotide sequences of DNA or RNA binds to a specific targeted small molecule [[16,17]. This can be achieved by synthesis of specific code out of several sequences to ensure proper affinity of required aptamers with the receptor layer thus enhancing the selection capabilities of the sensor towards specific antibodies [18].
Integrated optical sensors based on evanescent field detection principle with label free protocol can be used to detect changes in wave guiding properties of light such as refrac-tive index when a specific strand of DNA/RNA is captured by the receptor layer at the surface of sensing area of photonic chip through several photonic circuit based structures and different techniques to measure change in effective refractive index [5,3] such as photonic crystals [19,20], micro-ring resonators [21,22], MachZehnder interferometers (MZI) [6] which will be discussed in chapter 2.
1.4 Overview
Chapter 2 includes literature review of different photonic devices used for sensing, com-ponents used in sensor and design of few passive devices used in MZI based sensor is also explained.
Chapter 3 elaborates the procedure used for the design of couplers and experimental setup used for characterization of a photonic integrated chip.
Chapter 4 illustrates all the results acquired from the thesis. Simulation results are ex-plained followed by experimental results obtained in the laboratory.
Chapter 5 contains discussion and analysis of the obtained results from both simulation and experimental part.
Chapter 6 concludes the thesis along with providing future work which can be performed later to further enhance the project goals.
This chapter provide details about architecture of a biosensor, an overview of different optical biosensors characterized by variety of strategies utilized and their associated de-vices.It also discusses the problems encountered with each type and their possible so-lutions in integrated optics environment for achieving high sensitivity, high selectivity and robust performance in Lab on a chip (LOC) devices. Additionally , building blocks and design strategies for MZI based sensors and its components such as multiple type of couplers are also discussed in detail.
2.1 Architecture
An optical integrated biosensor is comprised of several components, which can be inte-grated on a single platform. Among those components there is
• a laser source - monochromatic or wide-band source
• a grating coupler - capable of coupling the light from fiber to integrated waveguides and vice versa.
• an MMI coupler - can integrate multiple inputs on a single chip which can be split and coupled back through them.
• a sensing device - for detection of biological entities in a sample and can take many forms such as ring resonator or MZI
• a photodiode (PD) - for converting the optical signal to electrical signal.
The signal from photodiode is post-processed by various digital signal processing tech-niques that amplifies and analyzes the signal from the photonic sensor. On top of the waveguide a microfluidic channel is built that brings the analyte to the sensing area, which optionally has been prepared to be sensitive to a specific target (many sensitive
areas can be prepared differently for different targets).
The commonly used fabrication platform for integrating all these components is known as SOI as it has the capability of supporting photonic components as well as electronics on the same chip. For a more comprehensive view fig. 2.1shows a general architecture of an integrated optical biosensor as mentioned above.
Figure 2.1:General architecture of an integrated biosensor [5]
2.2 Integrated devices used for sensing
Among many other techniques used for sensing in integrated photonics, one of the most promising is through variation in the surrounding medium through evanescent field de-tection principle.
This technique can be exploited with many structures such as photonic crystals, ring resonators, interferometric waveguides such as MZI [5], micro-disks [23] and still there is a lot of potential growing in this field and new structures are emerging to make the device highly sensitive (Large S, as figure of merit) with minimum limit of detection (LOD). These two figures of merit (FOM) are very important as they quantify the performance of the sensor and allow fair comparison between sensors of different type. Sensitivity is defined by the amount of signal change per unit quantity of analyte usually in (V/ng) but can also be quantified in (nm/RIU) if the sensor is based on the measurement of the refractive index.
S
¯ensor Type Suration¯ensor Config-S¯trategy OMode¯ptical QFactor¯ -(x103)
B¯ulk Sensitivity
(RIU−1) SLimit (RIU)¯ystem Detection
InterferometerMZI Vernier TE N/A 2.15 x 10ˆ4 nm N/A
Suspended TE N/A 740 nm N/A
Slot TE N/A 1730 x 2π rad 1.29x10ˆ-5
1.31 µ m Wvl TE N/A 540 x 2π rad N/A
N/A TM N/A 460 x 2π rad 3.3x10ˆ-5
N/A TE N/A 300 x 2π rad N/A
Microcavity Ring Vernier/SuspendedTM N/A 4.6 x 10ˆ5 nm N/A
Vernier TM 15 2.43x10ˆ4 nm N/A Vernier TE 20 1.3x10ˆ3 nm 5.05x10ˆ-4 Slot/critical cou-pling TE 6 1.3x10ˆ3 nm N/A Multi-box SWG TE 2.6 580 nm N/A SWG TE 7 490 nm 2x10ˆ-6 SWG TM 9.8 429 nm N/A Slot TE 0.33 298 nm 4.2x10ˆ-5 Suspended TM 12 290 nm N/A Thin WG TM 4.5 270 nm N/A N/A TM 10.1 200 nm N/A Thin WG TE 24 133 nm N/A 1.31 µ m Wvl TM 33.5 113 nm N/A 1.31 µ m Wvl TE 9.8 91 nm N/A N/A TE 15 38 nm N/A
Disk N/A TM 16 142 nm N/A
Suspended TM 0.1 130 nm 8x10ˆ-4 N/A TE 33 26 nm N/A Photonic Crystal 2D Slot TE 50 1.5 x 10ˆ3 nm 7.8 x 10ˆ-6 N/A TE 0.4 200 nm 2x10ˆ-3 Ring-slot TE 11.5 160 nm N/A 1D Slot TE 174 815 nm N/A N/A TE 3 130 nm 7x10ˆ-5
Bragg grating Phase-shifted Multi-box SWG TE 6.2 610 N/A
Slot TE 15 340 nm N/A
1.31 µ m Wvl TM 76 106 nm N/A
N/A TE 27.6 59 nm N/A
Uniform N/A TE N/A 182 nm N/A
Table 2.1: Performance parameters comparison of different sensor types using several strategies[4]
LOD is defined as minimum amount of sample required to give a minimum detectable amount of output signal usually in (pg/mm2). This parameter depends on the
interro-gation technique used (see table. 2.1as a reference) and the noise produced during the experiment [5] as it is often defined as three times the noise of the overall system.
Among many different physical mechanisms used for sensing, preferred approaches include using photonic crystals, micro ring resonators and Mach-Zehnder Interferometer due to their compact sizes, higher sensitivity and robust performance with minimum losses. These three techniques with their strengths and weaknesses are discussed below.
2.2.1 Photonic Crystal Sensors
Integrated biosensors based on Photonic crystals are an emerging technology in academic research mainly due to the fact that they can be easily integrated and researchers are trying to propose numerous arrangements of photonic crystals to be used in biosensors [24][25].
Photonic crystal is a systematized nanostructure with periodic dielectric arrangement de-signed to build an energy band assembly with periodically varying refractive index in 1D, 2D or 3D directions shown in fig. 2.2. The resultant lattice structure generates photonic bandgaps prohibiting light propagation in the crystal [26,5]. In order to exploit sens-ing capabilities, the width and position of photonic band gaps is optimized by varysens-ing refractive-index between dielectric substances or by introducing defects in lattice struc-ture [27]. The crystal defects enhance the sensitivity of photonic-crystal based sensors by generating cavities, confining light within a very small volume (fraction of a ) in the periodic lattice, which enables detection of nanometer scale chemical species.
Due to its sensitivity and miniaturized dimensions photonic-crystal based sensors found a wide range of applications in the realm of biochemical sensing such as virus and protein detection [28,29], measurement of small molecules for drug selection [30], identifying DNA [31,32].
A worth mentioning example is the SOI photonic-crystal waveguide designed and fab-ricated by Dofner et al. [33,34] consisting of hexagonal lattice with multiple arrange-ments of line and point defects which were evaluated using tapered fibers for coupling TE-polarized light in and out of the ridge waveguide along with placing a flow cell on
Figure 2.2:Illustration of photonic crystals in: (a) 1D conformation; (b) 2D conformation; (c) 3D conformation; (d) Measured transmission spectrum of a uniform photonic crystal (PhC) device after normalization [4]
top of the structure. Refractive-index sensing exhibited a bulk limit-of-detection (LOD) around 10−3RIU in its most optimum case (Q factor ∼ 3000) while sensitivity observed
was around 24.7 nm/pg. The negligible mass that can be detected using this waveguide was found to be 4 fg and its detection limit was around 500 pg/mm 2. A similar
struc-ture and test setup was employed for protein and DNA detection [31] and it was able to achieve LOD in the range of 6 x 10−4 RIU. Hybridization sensitivities of DNA strands
were supervised in the nM range [32]. In case of proteins, BSA-functionalized SOI planar photonic crystal waveguide was used to detect anti-BSA antibody and their mass detec-tion limit was found to be 2.1 pg/mm2(i.e mass detection limit ∼ 0.7 fg).
Another example of using a photonic-crystal sensor for DNA recognition was developed by Erickson’s group [35] known as nanoscale opto-fluidic sensor array (NOSA) that is based on parallel arrays of micro cavity structure (resonator) having different resonant wavelength tuned according to defect cavity spacing within the lattice, evanescently cou-pled to an neighboring single-mode silicon waveguide. The micro cavity structure is fab-ricated using X-ray lithography introducing defects in photonic-crystal by breaking the periodicity of the holes within the lattice structure. The test setup includes Nano tapers for light coupling and PDMS flow channel placed perpendicular to the array onto the chip for simultaneous detection. The experimental results of the sensor revealed a bulk
refrac-tive index LOD of 7 x 10−5 RIU. The sensor was also used to detect the stereotypes of
Dengue virus by immobilizing four different DNA probes in different resonators. These experiments were only a demonstration of proof-of-concept for nucleic acid interaction. A multichannel sensor based on 2D photonic crystal waveguides with a defect line gener-ated adjacent to the photonic micro cavities demonstrgener-ated Q factors around 400 and bulk LOD in the range of 10−2 RIU [36,37]. This sensor had its basics extracted from a 2D
photonic crystal structure developed by Lee and Fauchet [38] which exhibited minimum mass coverage of ∼ 2.5 fg for Biotin-streptavidin interaction and covalent immobilization of BSA.
Zlatanovic et al. [39] demonstrated real-time bio sensing capabilities of his design based on photonic crystal structure by immobilizing biotin-BSA and detecting distinct antibod-ies against biotin. Experimental results of the design were able to achieve a limit of de-tection of 20 pM for anti-biotin, corresponding to the bound material mass of 4.5 fg on the sensor surface as the consideration of affinity of the antibody/antigen was taken into account. Despite the low resolution of the device due to its low Q factor the design was capable of adequate bio functionalization of the sensor’s surface resulting in acceptable sensitivities for bio sensing purposes.
By close analyses of the proposed photonic crystal structures based bio sensing devices it can be concluded that photonic crystals are characterized as an intriguing solution for high performance sensors and are capable of achieving moderate sensitivities as com-pared to other label-free photonic sensors. Further optimization of the crystal and defect dimensions along with appropriate positioning of bio receptors in the holes by controlled immobilization, can result in enhanced resonant shifts and better sensing features. How-ever, they require expensive instruments for interrogation due to their reliance on trans-mission spectrum for changes to be detected and given the ultra-small size of photonic crystals, alignment issues during fabrication are inevitable, which makes its design quite challenging.
2.2.2 Ring Resonator Sensors
Owing to the compact footprint of sensors based on ring resonators and their high sensi-tivity, visible efforts on enhancement of this technology can be observed in literature. A
micro ring resonator consists of a straight waveguide coupled with a closely placed circu-lar waveguide. The straight waveguide serves as a path for input (f1, f2, f3) and output
as (f1and f2) as seen in fig.2.3. Optical coupling takes place by evanescent field principle
between input waveguide and the ring (see Fig. 1.5). Light at a frequency equivalent to the resonant mode constructively resonates in the core of the closed loop, denoted by f3
in fig.2.3, which has higher refractive index.
Figure 2.3:Structure of a micro ring resonator [4][17]
This resonance condition produces an effective length much larger than the physi-cal length of the ring, thus enhancing the sensitivity [40]. Condition for resonant mode achieved at the output is given by eq.2.1:
λ = 2π ∗ nef f ∗ r
m (2.1)
Where λ is the resonant wavelength, nef f is the effective refractive index of waveguide
material, r is the radius of the ring and m is the mode number of ring resonator. In optical biosensors, with the occurrence of biomolecular interaction, a drift in resonance spec-trum is observed which can be interrogated through optical specspec-trum analyzer (OSA) by scanning spectrum around the resonant wavelength or measuring power at a particular wavelength. Number of revolutions in the ring governs the interaction between waveg-uide and analyte, given by a quality factor, Q, calculated using eq.2.2:
Q = wo δw ≈
λo
δλ (2.2)
between wavelength and the linewidth as denoted in fig2.4.
Figure 2.4: Definition of the Q factor in terms of wavelength and linewidth
Figure 2.5:Ring transmission before and after binding of analyte showing a clear shift in the resonance wave-length [4]
As illustrated in fig2.5, sensing mechanism in a ring resonator can be achieved by ob-serving the change in resonance wavelength given by δλ. Since the light-analyte inter-action depends on revolutions in the ring rather than length of the waveguide, a higher Q factor of around 106 can be attained with 50 to 200 µm of ring radius, which shows that comparatively higher sensitives can be achieved with micro ring resonators covering smaller surface area as compared to straight waveguides. With their high level of integra-tion capability, a complex structure with multiple ring resonators can also be incorporated on a silicon circuit [5]. Devices with a number of materials such as glass [41,42], polymers [43] or SixNy-SiO2 [44] are also utilized to create ring resonators based sensors on SOI
platform to sense proteins, bacteria and other nucleic-acid sequences [42,45]. In the past few years, ring resonators with 5 µm radius were exploited for bio sensing application of interaction between biotinylated surface and avidin protein and as a result, Q factor of 20,000 and 70nm/RIU of sensitivity was measured with LOD around 10ng/mL [46,47]. Alternatively, in the same year, another scheme was proposed with two concentric rings which verified increment of sensitivity and Q factor to 683 nm/RIU and 5.1x104,
respec-tively but this included a larger dimension of ring resonator with outer and inner ring radius of 21 µm and 20 µm respectively [48]. In 2010, M.Iqbal et al. [21] integrated 32 ring resonators and performed simultaneous interrogation of 24 out of them and reached 7.6x10−7 detection limit [21], and LOD on surface as 1.5 pg/mm2 [49]. With the aim
of verifying the multiplexed analysis in real-time, DNA hybridization was considered to demonstrate the credibility of the system [21]. Reliability of the sensor is increased by increasing number of ring in the structure, such configuration is required when there are
several target molecules and a number of rings are used for each antibody, in this way simultaneous recognition of multiple proteins from an unidentified protein combination is possible [50], although such complex schemes can yield profound peak resolution and narrow linewidths with minimum LOD but they require bulky and expensive equipment for interrogation to scan the transmission spectrum which is a limiting factor of this trans-ducer. This factor gives us the motivation to move towards a cheaper solution which is based on interferometric waveguide based sensors.
2.2.3 Mach-Zehnder interferometer sensors
There is a visible advancement in optical bio sensors based on MZI [51]. Fabrication on glass [52] or polymer with NOA81 [53] or SU-8 [54] resist have proved tremendous performance. Silicon has proved to be one of the cost effective and viable platform for in-tegrated photonics. Optimized design of MZI based on Silicon substrate can be optimized to achieve desirable sensitivities. Initially, maximum surface sensitivity was acquired by optimizing geometry of MZI with a core and cladding layer of 250 nm and 2 µm, respec-tively, width = 4 µm; with rib of 3 nm. The device was protected with a layer of SiO2
except the sensing part [55]. The resulting LOD was 8x10−6 RIU and surface
sensitiv-ity as 2x10−4nm−1. Later, this design was repeated for DNA hybridization in real-time
test and achieved high surface mass Limit of Detection as 0.06 pg/mm2 with accurate
specificity [33]. Another robust sensor was designed for real time analysis based on di-rect phase modulation in one arm of MZI through pseudo heterodyne detection, resulting with 4.1x10−6RIU of detection limit and decent amount of sensitivity. It is quite robust
and can perform real time analysis of samples since it is free from thermal and wavelength fluctuations of the source. However, it uses Lock in Amplifier (LIA) to boost the signal which can introduce additional noise in the system [14].
The proposed design in [14] was further optimized in [3] by removing LIA from the setup and using Phase Generated carrier (PGC) technique for demodulation. A simpler scheme was proposed which eliminated the use of LIA and required only a fixed wavelength (1550 nm) source and a photodiode, thus leading towards robust, cost effective solution with im-proved performance with minimum LOD measured as 4.88x10−7RIU. Considering this,
a more compact design is proposed in the next section to reduce the losses and make a device further compact in terms of components used while maintaining the sensitivity and LOD of the device.
2.3 Building Blocks and Design Parameters of MZI
2.3.1 Principle of Optical interference
Optical sensors based on interferometry have gained popularity due to their high resolu-tion and accurate measurement of different parameters such as wavelength drift, phase change and rotation etc. These sensors are built on the principle of interference between two or more light beams. For a monochromatic light traversing in z direction the electric field can be represented mathematically as eq.2.3:
E(x, y, z, t) = Eoexp(i(kz − ωt + φo)) (2.3)
where Eobeing the amplitude of electric field, ω is the angular frequency of light and
φis the phase.
If the two waves are interfering with a same frequency, the total electric field can be expressed as eq.2.4
ET otal= E1exp(i(kz − ωt + φ1)) + E2exp(i(kz − ωt + φ2)) (2.4)
where E1and E2 are the amplitudes of two electric fields, φ1and φ2 being the phases
of the waves respectively.
The interfering waves when detected by a photodiode, the resultant intensity is pro-portional to the square of the electric intensities (I ∝ E E∗) . Therefore, total intensity at
the photodiode can b expressed as eq.2.5:
IT otal = [(E1+ E2).(E1+ E2)∗]
= |E1|2+ |E2|2+ 2Re(E1E2∗)
= |E1|2+ |E2|2+ 2|E1||E2|cos(φ1− φ2)
(2.5)
Eq. 2.5 shows that individual intensities cannot be directly summed up but can be written as eq.2.6:
IT otal= I1+ I2+ 2
p
I1I2cos(φ1− φ2) (2.6)
The important part of eq. 2.6is the effective phase difference (∆φ = φ1− φ2)which
= 0, ± 1, ±2, ... the resultant wave will have higher intensity than the individual wave and when ∆φ = (2n − 1)π for n = 0, ±1, ±2, ..., the combined wave will have intensity lower than the individual ones, thus forming destructive interference. If two identical waves undergo interference but have same phase i-e (φ1= φ2)but different path lengths
z1and z2respectively then the phase difference between both of them can be denoted as
∆φ = k(z1− z2) = k∆z. With variation in the phase difference, interference fringes
will occur, resulting in intensities ranging from maxima of Imax = I1+ I2+ 2
√
I1I2to a
minima of Imin= I1+ I2− 2
√
I1I2. The constrast of fringe or fringe modulation depth
can be calculated from eq.2.7:
V = Imax− Imin Imax+ Imin = 2 √ I1I2 I1+ I2 (2.7)
2.3.2 Working Principle of MZI
Mach-Zehnder Interferometer (MZI) based sensors enjoy popularity among researchers due to its simple structure, stable output, broad wavelength range and high sensitivity [5]. However, sensors based on this technique suffer in terms of physical dimensions as compared to aforementioned transducers that is ring resonators and photonic crystals. In an integrated environment, MZI is used as a building block for biochemical sensing where the setup consists of an input waveguide, which splits in two arms and is recombined at the end after travelling a certain distance in terms of spirals as shown in fig. 2.6When light propagates in both the arms of MZI, one of them being a reference and the other one is exposed to the sample, a biomolecular interaction takes place in the evanescent region resulting in variation of refractive index of light in the sensing branch as shown in figure 2.7. At the output, the accumulated phase shift is obtained which can be described as eq.
2.8.
φ = nef fkL (2.8)
where nef f is the effective refractive index of the waveguide, k is the wave number →
k = 2 π/λ and L is the path length. The changes due to light-analyte interaction can be calculated by differentiating equation2.8which yields equation2.9:
δφ φ = δL L + δnef f nef f +δk k (2.9)
Figure 2.6:Schematic of a Mach-Zehnder Interferometer [6]
Due to the change of refractive index in sensing arm, a phase difference (∆φ) between both branches is observed at the output which can be calculated by eq.2.10:
δφ = 2πL
λ [nef f,S− nef f.R] (2.10)
Where L is the detection length, λ is the wavelength of light, nef f,S and nef f,R are the
effective refractive indices of sensing branch and reference branch respectively.
2.3.3 Challenges associated with MZI and their respective solutions
Limitation of phase extraction
From the concepts of interferometry, the intensity modulation at the output of the MZI device is described by eq.2.11:
I = Io
2[ES2 + ER2+ 2ESERcos ∆φ] (2.11) Here I and Io are output and input light intensities respectively, ES2and ER2are electric field of waveguide in sensing and reference branches respectively, ∆φ is the phase differ-ence calculated by eq2.10[5]. For simplicity let us consider A = I1+ I2and B = 2
√ I1I2
then eq.2.11can also be written as:
I = A + Bcos(∆φ(t)) (2.12)
where A is the DC component, B is related to the input intensity and is dependent on mixing efficiency of MZI. ∆φ is the phase difference between both arms of the MZI. The intensity measurement from eq. 2.12 cannot provide a univocal solution, as the cosine function in the equation has two solutions. The reliance of MZI based designs on cosine function result in a drawback that the sensitivity depends on the position of the intensity curve. Maximum responsivity of the MZI is achieved on the slope whereas minimum
sen-sitivity of the device is observed on the ends of the curve (Maximum and Minimum) [13] as interpreted from fig.2.7. This is known as sensitivity fading. Two other issues can arise with intensity related output such as directional ambiguity and fringe order ambiguity. Therefore, the phase information will contain several perturbations due to signal noise, temperature and wavelength fluctuations of the source, optical alignment etc. which can be controlled through more sophisticated phase extraction schemes explained below:
Figure 2.7:Intensity output of the MZI as a function of the bias voltage (V)
Passive Phase Extraction: This modulation does not require an external modulation; instead the optical paths can be recombined with hybrid demodulator at the output to fetch the phase univocally without diminishing sensitivity. A hybrid demodulator is a device in which the I (in-phase signal) and Q (quadrature signal at 90° from I) compo-nents of a phase can be fetched, which are proportional to cosine and sine of the phase information respectively. Since they are not speed limited (as it does not have external modulator), it can be helpful in applications where a high-speed modulation is required [56]. But then thermal drifts and device deficiencies have to be controlled through so-phisticated calibration process.
Active Phase Extraction: Using active phase modulation scheme, accurate values of phase can be determined. This can be performed by either modulating the light source or modulating the sensing branch of MZI with a sine wave called Phase Generated Carrier (PGC) [57], a triangular wave where phase will be measured depending on the trigger signal, or through a sawtooth function called pseudo-heterodyne demodulation [14]. To avoid speed disruption due to external modulation and obtain an optimum responsivity, a feedback loop can be formed to limit the quadrature point of cosine function to a desired
value [13]. By exploiting this technique, phase variations can be measured precisely by applying a phase modulation in one of the arms of MZI with much higher frequency than our desired signal with an amplitude C and frequency ωo. The output of MZI from eq.
2.12can now be written as:
I = A + Bcos(Ccos(ωot∆φ(t)) (2.13)
This equation can be expanded in terms of Bessel function as: I =A + B[[Jo(C) + 2 ∞ X k=1 −1kJ2k(C)cos2kωot]Xcos∆φ(t) − [2 ∞ X k=0 −1kJ2k+1(C)cos(2k + 1)ωot]xsin∆φ(t)] (2.14)
Figure 2.8:Schematic of PGC technique on an unbalanced MZI
By mixing this eq. 2.14 with f and 2f (multiples of modulating frequency) as shown in fig. 2.8, and filtering undesired spectral components from this mixed signal using low pass filter, S1 and S2 components of the signal are obtained. The ratio between these
signals can be written as:
S1
S2
= J1(C)sin∆φ(t)
J2(C)cos∆φ(t) (2.15)
Here J1(C)and J2(C)are the first and second order Bessesl functions respectively. To
normalize these terms, modulation is performed in such a way that C is taken as 0.84 π which makes J1(C)= J2(C). Now by using arctangent method ∆φ an be written as:
∆φ = tan−1(S1 S2
) (2.16)
determined with this arc tan method without issues such as sensitivity fading, directional ambiguity and fringe order ambiguity etc. Now eq. 2.10can be used to determine ∆φ when there is a change of effective refractive index in the sensing arm of MZI due to light water interaction.
2.4 Passive Components of MZI at 1310 nm wavelength
As we know from a thorough literature review that in sensors based on MZI, either the source or the signal can be directly modulated to observe the phase shift. It comprises of a simple interrogation scheme, which requires only a fixed wavelength laser and a photodiode to achieve monolithic integration on Silicon platform. However, there is a trade-off between the size of MZI and the sensitivity. One of the solutions is to include photonic crystals in the sensing arm of MZI which gives a five-fold enhancement in the sensitivity but then again a complex interrogation schemes are required to obtain accurate results, which creates a deviation from the goal of our project. Therefore, one of the solutions proposed is to change the fixed wavelength of source from 1.5 µ m to 1.3 µ m where there is a large reduction in losses due to water absorption as displayed in fig.2.9. Only by a slight change of wavelength from 1.5 µ m to 1.3 µ m we can observe the reduction of loss by a factor of 10.
Figure 2.9:Water absorption spectrum showing near-infrared wavelengths as a function of ab-sorption co-efficient (s.a.c) with red and black marks showing 1.3 micron and 1.5 micron window respectively.
Losses can further be reduced by operating in visible light region but since we are us-ing silicon photonics platform, which will absorb visible light because the transparency region of silicon ranges from 1.1 µ m to 4 µ m. Therefore, 1.3 µ m is a good compromise, which is a wavelength short enough to have low losses and suitable enough to be guided by silicon waveguides. This creates new avenues for enhancement in terms of sensitivity due to a possible increase in interaction length of light and analyte. At 1.5 µ m wave-length losses due to water absorption results in a limitation of the spiral wave-length of MZI, but with a slight change in wavelength window (1.3 µ m) significant reduction in losses provides flexibility of increasing the spiral length, thus increasing sensitivity.
One of the objectives of this master’s thesis is to simulate optical components for inte-grated bio sensors at 1310 nm wavelength, which include a grating coupler, the waveg-uides used for sensing and a 1x2 Multimode Interference (MMI) coupler using Finite Dif-ference Eigenmode (FDE) solver and Eigenmode expansion EME solver of Lumerical soft-ware.
2.4.1 MMI couplers
Figure 2.10:Multimode waveguide showing the input field Ψ(y,0), a mirrored single image at (3Lπ), a direct single image at 2(3Lπ), and two-fold images at12(3Lπ) and 32(3Lπ) [7]
The design of MMI coupler consist of a large waveguide where several modes can prop-agate in it and it supports NxM inputs and outputs where N and M are the number of inputs and outputs respectively. The operation of this device is based on self-imaging principle which is described by fig.3.1where input field is replicated at periodic intervals with single image at multiples of p(3Lπ) and multiple images of the input field profile at
p
Light enters the input waveguide with the help of a taper whose width is decreasing gradually until it reaches the larger waveguide. The central large waveguide has a uni-form shape in which self imaging takes place. Similarly the light is coupled back in the output waveguides through same trapezoidal structures. Design procedure of these de-vices is explained in detail in chapter 3.
2.4.2 Grating couplers
Grating couplers in comparison with edge couplers are easier to align with fiber during experiment, they require lesser fabrication cost as testing can be performed from top of the chip but in edge coupler the chip needs to be cleaved for testing. However, mode mismatch between a fiber and grating coupler is higher than the edge coupler and even the coupling efficiency of edge coupler is better than the grating couplers. Both of them are intensely used in integrated optics environment. Grating couplers are mostly used to couple light from fiber to the chip and vice versa and MMI couplers (edge couplers) are usually used to split and recombine the light between the waveguides on the chip.
Figure 2.11:Schematic of a grating coupler [8]
A grating coupler is a periodic structure which diffracts light in a certain direction. As illustrated in fig. 2.11when a light wave enters from waveguide having (Pwg) power, it
travels in the grating period, some of the light is transmitted upwards in the core of fiber with a power denoted as (Pup) and some of it is lost as (Pdown) [8]. Fiber is placed at some
similar manner if light is injected from the fiber core and received at the waveguide end. Further details of the design are illustrated in chapter 3.
This chapter outlines the designing work performed during the thesis period. As it is a two-stage project, its one aspect comprises of simulation and another one consists of experimental work performed at optical sensing laboratory. This chapter walks through the details regarding Lumerical software tools used for designing, the designing process, results achieved from the simulations and their analysis.
3.1 Lumerical and its tools
A Photonic simulation software named "Lumerical" was used for the designing of passive components at 1.31 µm wavelength. The water absorption losses at 1.31 µm wavelength are quite less as compared to 1.5 µm wavelength. The idea was to exploit Eigen mode expansion (EME) solver and Finite Difference Time Domain (FDTD) solver methods of Lumerical to design edge couplers and vertical/grating couplers.
Lumerical enables designers to simulate optical components according to their require-ments and predict behavior of light propagating through components, devices and sys-tems. It’s tools permit users to modify device parameters to obtain high performance and validate the design before manufacturing, thus encouraging designers to explore and experiment with new concepts and bringing innovations in the world of photonics.
In this project, a simulation suite named “DEVICE Suite” was used which contains sev-eral products and solvers. The components designed in this project utilized "MODE" and "FDTD" utilities of Lumerical. In MODE, the solver region called "Eigen Mode Expansion-EME" was used to design 1x2 and 2x2 MMI Couplers and FDTD was used to design grat-ing couplers both with fundamental Transverse Electric (TE) and Transverse Magnetic (TM) modes at 1.3 µm wavelength. In this project, such solver was used to design grating couplers at 1.3 µm wavelength.
3.2 Designing of MMI couplers
MMI coupler plays a vital role in combining and splitting signals coming from one or more devices. It couples light along the edge and is sometimes referred to as edge coupler. It is desired for the couplers to have large optical bandwidth, low losses, high coupling effi-ciency for maximum transfer of power from one device to another. Along with that, it is expected to design them with miniaturized dimensions in order to be integrated efficiently with fabrication tolerances.
3.2.1 1x2 MMI Coupler
This device was designed with a goal to split light equally from 1 input to both the outputs (∼50 % transmission in each output) with the help of EME solver of MODE in Lumerical as illustrated in fig.3.1.
Figure 3.1:Structure of 1x2 MMI Coupler
These optimum values of the structure were selected to maximize light recovered from output waveguides when light is launched from the input waveguide. Single mode is injected in the input waveguide and self-imaging occurs in the central structure of MMI as explained in chapter 2. At the output of the waveguide one or more modes are collected.
To achieve these results in Lumerical, the EME solver region was divided into three group spans for better calculation as depicted in fig. 3.2. As the central part of MMI was uniformly changing along the length, therefore, one cell was enough to solve this region while group span 1 and 3 were subdivided into 10 cells because they consisted of a taper made with trapezoidal structure. Trapezoid is a non uniform structure along the length and width, therefore, it is a good approach to solve this region in more number of cells to get accurate results. The first step of designing an MMI coupler was to add the material of the structure in "Material Database" as shown by fig. 3.3where ’Si (Silicon) - Dispersive & Lossless’ was selected. This material was created using Lorentz model explained in eq.3.1: n2(λ) = + Lorentzω 2 o ω2 o− 2iδo2πc/λ − (2πcλ )2 (3.1) where = 7.9874, Lorentz= 3.6880 and ω2o = 3.9328 x 1015. This model can be used for a
wavelength range of 1.15 to 1.8 µm in both MODE and FDTD solvers. It can be used in FDTD as it fulfills Kramers-Kronig relations and is lossless for δo→0 [58].
The next step was to add physical structures, simulation regions, sources and monitors in
Figure 3.3:Material data base
the model as depicted in fig.3.4. Here ’Construct’ is the structure group which contains central part of MMI known as MMI_core and three tapers; one for input and two for outputs. Mesh override region was set across all the tapers to improve accuracy of each taper. A monitor was placed from input waveguide to output waveguides in order to
visualize propagation of light in the structure. Finally, EME region was added on the surroundings of the whole structure in which source wavelength was set to be 1.31 µm and cells were defined as depicted in fig. 3.5. In the cell group definition, the number of group spans, number of cells in each group, the subcell etc are set according to the geometry of the structure. The CVCS method is selected in the taper regions to avoid stair casing effects. By default each port consists of source as well as monitor, and we can select any desired port as a source. In this design, port 1 with fundamental mode was selected as the source in EME analysis window whereas port 2 and 3 automatically acted as the outputs.
Figure 3.4:Object tree
Figure 3.5:Cell group definition
Mesh accuracy is one of the essential parameters to be considered in designing. The optimum number of mesh cells are the ones where mesh is independent of the results targeted. It plays a role similar to calibration in experimental work. In EME, sweeps can be run for each parameter to be optimized ranging from minimum to maximum value given by the user. Exploiting the ’Optimization and Sweeps’ window using EME model it
is easier to track desired result (S-Matrix in our case) with the range of parameter value as a function of output. This result can then be plotted to visualize it in graphical form. Before optimizing the geometry of the coupler, a sweep was run for number of mesh cells ranging from 20 to 600 to find optimum mesh cells. The initial geometric parameters for MMI coupler working at 1.5 µm were obtained from [59] as seen in table. 3.1and were optimized for 1.3 µm.
S.No Name Value (µm)
1 Coupler length 32 2 Coupler width 6 3 Separation 3.14 4 Taper Length 10 5 Taper Width 1.1 6 Total Length 75 7 Waveguide Width 0.4 8 Total span 0.22
Table 3.1:Initial values of 1x2 MMI Coupler
After the number of mesh cells reached 160, it becomes independent of the transmission as depicted in fig.3.6. After attaining optimum number of mesh cells where transmission was independent of mesh cells, this number was placed in the transverse mesh settings of EME which are visible in fig.3.7.
Figure 3.6:Transmission as a function of Mesh cells
of the parameters same as table. 3.1, optimization of MMI coupler begun by performing a sweep over propagation length of coupler (central waveguide of MMI) with start and stop length as 5 µm and 50 µm respectively as depicted in fig.3.8
Figure 3.7:Transverse mesh settings of EME
Figure 3.8:Propagation sweep of
central waveguide Figure 3.9:tion of Coupler lengthTransmission as a
func-After the EME propagation the result was visualized as illustrated in fig. 3.9. The optimum coupler length was found at 40.3 µm. Plugging the best possible coupler length value in the settings and keeping rest of the parameters same as table3.1, another sweep of taper length was created from 10 to 20 µm as shown in fig. 3.10to obtain maximum transmission. The best taper length was found at 15.52 µm as seen in fig.3.11. This taper length from the sweep result was placed in the ’variables’ tab of the group structure. Updating coupler length and taper length to the optimum values obtained and keeping rest of the variables same as table. 3.1, one more sweep of taper width was performed
from 0 to 5 µm in order to maximize the transmission from input to the outputs.
Figure 3.10:Parameters of taper length sweep
Figure 3.11: Transmission as a
function of Taper length Figure 3.12:function of taper widthTransmission as a
Taper width of around 2 µm was found to be the best one (see fig. 3.12). Finally, the values obtained from each sweep were placed in the variables tab of the setup and the updated values can be seen in table.3.2.
Results of 1x2 MMI coupler
After setting all the optimum parameters obtained from the sweeps, simulation was run and after EME propagation, following field profile was observed (see fig. 3.13) from field profile monitor. Through this monitor, propagation of light is visible, with red color being the highest intensity followed by yellow green and then blue. By looking at the maximum transmission from input to both the outputs, it can be verified that light was transmitted
S.No Name Value (µm) 1 Coupler length 40.4 2 Coupler width 6 3 Separation 3.14 4 Taper Length 15 5 Taper Width 1.25 6 Total Length 55 7 Waveguide Width 0.4 8 Total span 0.22
Table 3.2:Optimum values of 1x2 MMI Coupler
correctly as expected. This was further verified by looking at the S Matrix obtained (see fig. 3.14). S21(the forward transmission) was observed and we obtained transmission of
around 48 % in each output port (Port 2 and 3). Here it is important to note from the S-Matrix that the MMI coupler designed follows the law of conservation of energy. S31
is same as S13and S21is same as S12. Reflections shown in the table as S11, S22, S33, S23
are very small which verifies the good transmission of the design.
In order to verify that fundamental TE mode was properly transmitted and received from input and outputs respectively, mode profile was observed at all the three ports. Fig.
3.15(a) shows the mode profile transmitted from input port, fig.3.15(b) and (c) shows the mode profile at output 1 and 2 respectively. It should be noted that light is concentrated in the center with maximum intensity which proves that the device is simulated effectively and yielded results according to the expectation.
Figure 3.13: Field profile of 1x2 MMI Coupler
Figure 3.14:S Matrix of 1x2 MMI Coupler
Robustness of the device
To prove robustness of the device, calculations were performed to observe the deviation from the optimal value of S- parameters. This was done using Monte Carlo approach,
Figure 3.15:Mode profiles of 1x2 MMI Coupler; a) Mode profile of input port (PORT 1); b) Mode profile of output 1(PORT 2); c) Mode profile of output 2 (PORT 3)
where random errors were added to the parameters and the S-matrix of 1x2 MMI coupler was calculated. First, comparison was made between coupler length and coupler width.
Figure 3.16:Histogram and Error distribution of coupler length and coupler width
It can be observed from fig.3.16that random noise was added in both (coupler length and coupler width) and a histogram was plotted with normal Gaussian distribution shown by a red colored bell curve. It can be observed that even after adding around 100 errors, the histogram follows the behaviour nearly similar to the red curve. It can also be noted
that most of the error values lie in the range of 0.5 to 0.45, which means that the device is capable of sustaining its transmission accuracy and is very unlikely for the transmis-sion to drop below 40% even if there occurs slight fabrication defect in terms of coupler dimensions.
Figure 3.17:Histogram and Box plot of deviation in coupler length and coupler width
To visualize this in a better way, box plot was plotted for errors as illustrated in the right side of fig.3.17, where it can be seen that the mean value of errors lie ∼ 3% (shown by red line). The blue rectangle represents more than 80% of the distribution, so we can observe that most of the errors we got were around 3 to 6%. Then there are some extreme cases that goes up to 10% shown by black dotted lines and few red + signs which represent very unlikely occurrence of such values. From the histogram of deviation shown on left side of fig. 3.17, it can be observed that most of the deviation is well below 5% and authenticate the design of 1x2 MMI coupler. These calculations were repeated for all the five parameters of 1x2 MMI coupler i-e Coupler length, coupler width, taper length, taper width and separation between both tapers at the output. It was observed from fig. 3.18
that the mean error is slightly larger i.e ∼ 5% deviation of the mean. In this case there was more possibility of error due to increased number of parameters under consideration. The blue rectangle is well below 10% which indicates that we can expect most of the fabrication errors to be within 10% of what we have designed.
Figure 3.18:Histogram and Box plot of deviation in 5 parameters
3.19in which left side represents histogram for five parameters mentioned and right side shows the noise distribution of these parameters as a function of transmission. It can be observed that there is a strong co-relation in the separation values and S12. It looks
al-most as if they are following a line. There are some values below 0.4 which indicates the values when the separation is quite deviated from the optimal design. Similar behaviour is observed for coupler width where most of the distribution follows a line. These ob-servations indicates that special attention has to be given to these two parameters while fabricating because only with a slight deviation they can highly affect the transmission. Other three parameters follow a distributed behaviour rather than a line which gives a slight flexibility in fabrication.
We can conclude from these results that even by inclusion of some errors, the design is quite robust and most deviation errors are within 10% of the optimal value. Some unlikely deviation of errors can occur up to 25% but as it can be seen from the graphs they correspond to large variation from the design parameters. In this tolerance check, an error of (∼ ± 50 nm) was inserted which is generally a margin kept for fabrication errors. This value can vary from foundry to foundry. Therefore, it is always a good practice to do a tolerance check on the designed devices by adding an error of ∼ ±50nm to verify the robustness of the device with slight variation in the design.
Figure 3.19:Histogram and Noise distribution in 5 parameters
3.2.2 2x2 MMI coupler
2x2 MMI coupler was designed to be placed after the MZI, to combine both the outputs of MZI and split the light equally to two photodiodes. This coupler was designed by taking into account the optimized design of 1x2 MMI coupler which yielded maximum
transmis-sion from input port to output ports. Therefore, taking the design of fig. 3.1, the values of variables as table. 3.2and same silicon material used before, a taper was added at the left-bottom of the central waveguide. The already present taper on the input end was moved at the top to follow symmetry of the structure and was optimized to yield maxi-mum transmission. This optimized design is shown in fig. 3.20. Since 2x2 MMI coupler
Figure 3.20:Optimized structure of 2x2 MMI Coupler
was larger than 1x2 MMI coupler, therefore, the cell group definition was also changed accordingly as in fig. 3.21to improve accuracy of the design. Similar to the previous
de-Figure 3.21:Cell group definition of 2x2 MMI Coupler
sign, a sweep was run for the number of mesh cells to obtain stable values of output at optimum number of mesh cells in the structure. Although there is less stability in this
Figure 3.22: Transmission as a
function of Mesh cells Figure 3.23:function of Coupler lengthTransmission as a
design in terms of mesh cells but between 150 to 200 the graph tends to be stable, there-fore, 160 was taken as the optimum number of mesh cells. Following that, optimization
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