Investigation and modeling of Novel Silicon based
Integrated Optics
A thesis submitted for the degree of
Doctor of Philosophy
PhD candidate:
Costanza Lucia Manganelli
Supervisor:
Fabrizio Di Pasquale Tutor:
Phd Course
Emerging Digital Technologies
2016/2017
Investigation and Modeling of Novel
Silicon based Integrated Optics
Author
Costanza Lucia Manganelli
Supervisor
Fabrizio Di Pasquale
Tutor
To whom decided to stay by my side teaching me how to love the swell.
Dedicated to my sister Nunzia Pia and to the loving memory of my grandmother Costanza.
A quelli che hanno scelto di stare dalla mia parte insegnandomi ad amare il mare agitato.
Dedicata a mia sorella Nunzia Pia e all’adorabile memoria di mia nonna Costanza.
C O N T E N T S
1 i n t r o d u c t i o n 1
1.1 Modulators and switches in Si photonics . . . 1
1.2 Recent research activity . . . 7
1.3 Future perspectives . . . 11 1.4 This thesis . . . 14 i t h e r m a l t u n i n g r e s o nat o r f i lt e r s f o r w d m a p p l i c at i o n s 17 2 t h e r m a l t u n i n g r e s o nat o r f i lt e r s f o r w d m s w i t c h -i n g a p p l -i c at -i o n s 19 2.1 Introduction . . . 19
2.2 Final aim of this work: IRIS project . . . 20
2.3 Just a bit of definitions . . . 23
2.4 Model and design . . . 25
2.5 Fabrication and passive characterization . . . 28
2.5.1 Single rings . . . 28
2.5.2 Coupled rings . . . 32
2.5.3 Comparison between single and coupled rings 34 2.6 Thermal tuning . . . 35
2.6.1 Thermal Model . . . 36
2.6.2 Single rings . . . 37
2.6.3 Metal heater and comparison with temper-ature shift . . . 41
2.6.4 Coupled rings . . . 42
2.7 Wafer variability . . . 47
2.7.1 Effects of wafer variability on the performance of ring resonators . . . 50
2.8 Conclusions . . . 53
ii i n v e s t i g at i o n o f n ov e l m at e r i a l s 55 3 o p t i c a l n o n-linearities: novel approaches 57 3.1 Introduction . . . 57
3.2 Strained silicon: state of the art . . . 58
3.3 Symmetries in crystal . . . 61
3.3.1 Type I symmetry operation . . . 62
3.3.2 Type II symmetry operation . . . 62
3.3.3 The inversion symmetry operation . . . 63
3.3.4 Cubic lattice symmetries . . . 63
3.4 Nonlinear susceptibility, Electro-optic effect and Pock-els effect . . . 65
3.4.1 Strain simulation details . . . 67
3.5 The strain-induced Pockels effect . . . 70
3.6 The effective susceptibility . . . 73
3.7 Investigation of strain-induced susceptibility in fab-ricated devices . . . 74
3.7.1 Devices under investigation . . . 75
3.7.2 Results . . . 76
3.7.3 Comparison with experimental results . . . 78
3.7.4 Free carrier influence . . . 79
3.7.5 Presence of fabrication defects . . . 81
3.8 Recent theoretical results . . . 82
3.9 Future perspectives . . . 83
3.10 Limitations of strained silicon: introducing more stan-dard solutions . . . 83
3.11 Electro-optic effect in LiNbO3 . . . 84
3.12 How to construct an electro-optic modulator . . . . 86
3.13 Second harmonic generation from Lithium Niobate 88 3.14 Heterogeneous integration of lithium niobate and silicon nitride . . . 90
3.14.1 Damascene process . . . 91
3.15 The heterogeneous platform . . . 92
3.16 Conclusions . . . 94
4 c o n c l u s i o n s 97 a a p p e n d i x 103 a.1 Appendix to Chapter 3 . . . 103
a.1.1 Contracted index notation . . . 103
a.1.2 Symmetry analysis of the tensor T . . . 103
a.1.3 Explicit form of some relations for the octa-hedral lattice . . . 105
a.1.4 The variation of the refraction index . . . . 106
a.1.5 Extension for Secon Harmonic generation . 107 a.1.6 Electro-optic effect . . . 111
List of Publications 117
L I S T O F F I G U R E S
Figure 1 Switch unit cell with MEMS actuator and movable directional coupler ([32]). . . 3 Figure 2 Simplified scheme of a waveguide with a
heater. . . 4 Figure 3 Schematics of (a) a MZI modulator and (b)
a ring modulator. The silicon optical waveg-uide cross-section with the pn diode phase shifters are shown. . . 6 Figure 4 Typical pn-junctions in SOI waveguides:
lat-eral (a), vertical (b), interleaved (c). . . 6 Figure 5 Schematic and cross sectional views of GeSi
FK modulator. . . 8 Figure 6 (a) the silicon waveguide is connected to
the metal electrodes by thin silicon strip loads. The electro-optic polymer covers the waveguide and fills the slot. The silicon sub-strate is used as a gate. (b) the cross-section of the waveguide shows that the light is concentrated in the slot. (c) When a posi-tive gate voltage is applied across the sub-strate, a highly conductive electron accu-mulation layer forms in the strip-loads. . . 10 Figure 7 SOH MZM (a) Two 1-mm-long silicon
slot-waveguides act as phase modulators. (b) Cross section of the MZM where the or-ganic cladding is deposited into the slot region of the SOI waveguide. (c) Electrical field well confined in the slot waveguide. (d) chemical structure of the cladding ma-terial. . . 10 Figure 8 Three-dimensional schematic illustration of
the device; (a) monolayer graphene sheet is on top of a silicon bus waveguide, sepa-rated from it by a 7-nm-thick Al2O3 layer . The silicon waveguide is doped, and con-nected to the electrode (right, shown gold) through a thin layer of silicon defined by selective etching. (b), Left, cross-section of the device, with an overlay of the optical mode plot. The waveguide was carrying a single optical mode, and was designed in order to maximize the field at the interface between the waveguide and the graphene. 11
Figure 9 Schematic of the PPM. Continuous-wave (c.w.) infrared light guided by the upper-left silicon nanowire is coupled through a metal taper to the plasmonic slot waveg-uide. The slot in the metal sheets is filled with an electro-optic polymer. The phase of the surface plasmon polariton (SPP), which propagates in the slot, is changed by ap-plying a modulating voltage. A second ta-per transforms the SPP back to a photonic mode in the lower-right nanowire. . . 12 Figure 10 Colourized SEM image of the MZM
com-ponents. The suspended bridge enables elec-trical control of the device. . . 13 Figure 11 Conventional ROADM structure [74]. . . . 21 Figure 12 Colorless-directionless and contentionless
ROADM [94]. . . 22 Figure 13 Architecture of IRIS TPA . . . 22 Figure 14 Ring resonators in all-pass (a) and add and
drop configuration (b). Pictures from ref. [40] 24 Figure 15 Through and drop spectrum of an add and
drop ring resonator filters, with FSR and FWHM highlighted. . . 25 Figure 16 Schematic cross section of a coupled ring . 26 Figure 17 Insertion loss (a), 3 dB bandwidth (b),
pass-band ripple (c) and channel rejection (d) as functions of the bus-to-ring (K1) and
ring-to-ring coupling coefficients (K2). The line
corresponding to the impedance matching condition is shown in white. . . 27 Figure 18 Limitations of single and double rings in
terms of 20 dB (a) and 35 dB (b) half band-width versus the 1dB channel half-bandband-width. Definitions are shown in (c) where fRis the
resonance frequency. . . 28 Figure 19 Single ring schematic and relative optical
microscope pictures . . . 29 Figure 20 Through port of the single ring spectrum
(blue), individuation of the resonance po-sition (red circle), out-of-resonance shape of the single ring (green), fit of the out of resonance shape (red dashed) . . . 29 Figure 21 Single ring spectra (drop port) for different
values of the gap (175 nm (a) and 200 nm (b)) and different values of the coupling angle 30
List of Figures ix
Figure 22 Central wavelength (a), 3-dB bandwidth (b), maximum value of the transmission (c) and group index (d) for gaps of 175 nm or 200 nm . Measured and simulated coupling co-efficients for different values of coupling angles and gap equal to 175 nm (e). . . 31 Figure 23 Double ring schematic and relative optical
microscope pictures . . . 32 Figure 24 180o bend loss spectra for different
nor-malized node distances δnode fixing Reff
= 3 µm and for semicircular bend and rel-ative optical microscope pictures. . . 33 Figure 25 Measured double ring spectra for different
geometries of the Bezier bends.with waveg-uide width of 410 nm (a) and measured double ring spectra for the different values of the waveguide width (b). . . 34 Figure 26 Transmission response of single (blue) and
double micro-rings (red). Solid lines repre-sent the experiments, and dashed lines, the simulations. Zero frequency corresponds to ∼1555nm wavelength. . . 35 Figure 27 Basic switch cross section. . . 37 Figure 28 Basic switch cross section of a single ring
and variable quantities. . . 38 Figure 29 Profile of the fundamental mode. . . 38 Figure 30 Thermal simulation of one of the device
and relative temperature distribution. . . . 38 Figure 31 Basic heater thermal simulation (a) and
rel-ative mask layout (b); full heater thermal simulation (b) and relative mask layout (c); interdigitated heater thermal simulation (d) and relative mask layout (e) . . . 40 Figure 32 Basic heater tuned spectra (a) and relative
consumption as a function of the heater distance (b); full heater tuned spectra (c) and relative efficiency as a function of the heater distance (d); interdigitated heater tuned spectra (e) and relative efficiency as a func-tion of the heater distance (f) . . . 41 Figure 33 Rise and fall time measurements for a basic
heater . . . 42 Figure 34 Mask design for a metal heater . . . 43 Figure 35 Fall time measurements for a metal heater 43 Figure 36 PWM signal at 2 MHz duty cycle. . . 44 Figure 37 Ripples at 1 MHz and 2 MHz frequencies. 44 Figure 38 Coupled ring top view with different
heat-ing elements: doped silicon (a) and silicide (b). In (c) the optical microscope picture. . 45
Figure 39 Effect of thermal tuning on a doped heater with heater distance of 0.5 µm. . . 46 Figure 40 Coupled ring spectra with different
heat-ing elements: doped silicon (a) and silicide (b). Legend shows the voltages and electri-cal power sent to each ring. Blue dash-dot curves: cold. Green dashed curves: same voltage applied to both heaters. Red solid: improvement of the response by adjusting the voltage independently. . . 46 Figure 41 Coupled ring spectra with doped silicon
heaters for distances of 0.5 µm and 0.92 µm and waveguide width of 450 nm, in pres-ence or abspres-ence of thermal tuning. . . 48 Figure 42 Zoomed plot with the gradual improvement
in response when the asymmetry is elec-trically compensated for heater distance of 0.5 µm (a) and 0.92 µm (b).In the legend there are the voltages applied on each ring in thermal tuning process. . . 48 Figure 43 Consumption per FSR and per ring as a
function of the heater distance for p-type doped heater coupled rings. Different curves are for different geometries of the waveg-uide (450 nm and 410 nm). . . 49 Figure 44 Effective and group index as a function of
waveguide width (a); derivative of the same quantity versus with. . . 50 Figure 45 Schematic view of MZI pair used for the
experiment. The widened waveguide is in (a), the narrow is in (b). . . 51 Figure 46 From the estimation of the group index of
widened MZI, the SOI thickness was ex-tracted and in (a) there is its map along the wafer; the same map for the waveg-uide width extracted from narrow MZI (b); width deviation from nominal measurements with SEM (c) . . . 51 Figure 47 Map of the resonance position (a) and the
3-dB bandwidth (b) along the wafer sur-face. The device is a 480-nm wide single ring resonator with coupling coefficient. . 52 Figure 48 Layout of the unbalanced MZI (a) in
push-pull configuration, cross section of the MZI modulator (b) Measurements of the phase shift induced by the application of the elec-tric field (c), linear relation between the vari-ation of the refractive index and the ap-plied voltage [14]. . . 60
List of Figures xi
Figure 49 Strain profile of silicon waveguide used in Chmielak et al. [15]: (a) εxx, (b) εyy, (c) εzz,
(d) εxy. . . 70 Figure 50 Strain profile of silicon waveguide used in
Damas et al. [19]: (a) εxx, (b) εyy, (c) εzz,
(d) εxy. . . 71 Figure 51 Cross-section of the strained silicon based
MZI studied in [14, 15] and [19],
respec-tively. In (a) the slab waveguide cross-section described in [14, 15]. The cases of
waveg-uide width (wSi) equal to 300 nm, 350 nm,
400nm, 450 nm, and 500 nm have been in-vestigated. In (b) the channel waveguide cross-section described in [19]. The cases
of waveguide width (wSi) equal to 385 nm,
435nm, and 465 nm have been investigated. Pictures are not to scale. . . 75 Figure 52 Electric field components in the case of Chmielak et al. [15] . . . 76 Figure 53 Electric field components in the case of Damas
et al. [19] for an incident wavelength of
1550nm. . . 77 Figure 54 Behavior of the overlap functions for the
waveguides under investigation with respect to waveguide width for (a) the device used by Chmielak et al. [15] and (b) the device
used by Damas et al. [19]. In both cases
only the most significant overlaps are plot-ted at λ = 1550nm. . . 78 Figure 55 Behavior of the overlap functions for (a) the
waveguide used in Chmielak et al. [15] and
(b) the waveguide used in Damas et al. [19]
with respect to the wavelength for a waveg-uide width wSi = 385 nm. Only the most
significant overlaps are plotted. . . 79 Figure 56 Comparison of experimental data for χeffy
and the fit results. . . 80 Figure 57 Strain components profile εxx (a), εyy(b),
εzz(c) and εxy(d) in the strained silicon
waveg-uide [15] in presence of defect fabrication
in the Si3N4 slab. . . 81 Figure 58 Comparison between the overlap factors for
the case of Chmielak et al. [15] with and
without fabrication defect. . . 82 Figure 59 Description of the trigonal fundamental cell. 84 Figure 60 Description of symmetry elements for LiNbO3
Figure 61 The electro-optic effect for uniaxial crys-tals. (a)Principal axes in absence of an ap-plied field, (b) principal axes in presence of an applied field, (c) The intersection of the index ellipsoid with the plane x = X = 0 . 87 Figure 62 Construction of a voltage-controllable
in-tensity modulator. . . 88 Figure 63 Simple scheme of the setup for the
detec-tion of SHG. . . 89 Figure 64 Schematic representation of a gaussian beam. 89 Figure 65 Quadratic fit of the second harmonic
gen-eration from bulk Lithium Niobate. . . 90 Figure 66 Fabrication procedure for LN-Si3N4platform 92 Figure 67 Schematic structure of a tapered mode
con-verter connecting the two types of waveg-uides. The top and bottom areas show schemat-ics of the waveguide cross-sections and sim-ulated profiles of the fundamental TE modes at 1540 nm. Inset is the simulated confine-ment factor in the LN layer for LN − Si3N4
hybrid waveguides calculated as a function of the Si3N4 rib width. . . 93
Figure 68 Top view of integrated LN − Si3N4 chip
(a). B On the right part (b) spectra of total insertion loss for the reference waveguide (blue) and heterogeneous waveguide (red). 94 Figure 69 Transmission response of single (blue) and
double micro-rings (red). Solid lines repre-sent the experiments, and dashed lines, the simulations. Zero frequency corresponds to ∼1555nm wavelength. . . 98 Figure 70 Effect of thermal tuning on a doped heater
with heater distance of 0.5 µm. . . 98 Figure 71 Strain components profile εxx (a), εyy(b),
εzz(c) and εxy(d) in the strained silicon
waveg-uide [15] in presence of defect fabrication
in the Si3N4 slab. . . 100
Figure 72 Top view of integrated LN-Si3N4 chip. . . 101 Figure 73 Normal surfaces . . . 110 Figure 74 Intersection of the normal surface with the
xyplane for (a) biaxial crystals, (b) uniaxial crystals, (c) isotropic crystals . . . 111 Figure 75 Graphical representation of
L I S T O F TA B L E S
Table 1 Characteristics of the state-of-the-art car-rier depletion modulators . . . 7 Table 2 Summary list of Si MZI modulators with
different device configurations . . . 7 Table 3 Summary list of state-of-the-art optical switches 8 Table 4 Waveguide-integrated GeSi electro-absorption
modulator on Silicon. . . 9 Table 5 Applied tension and relative power in
ther-mal tuning activity for different heater dis-tances. . . 47 Table 6 Best fit coefficients. Error have been
1
I N T R O D U C T I O N
1.1 m o d u l at o r s a n d s w i t c h e s i n s i p h o t o n i c s
Silicon photonics is a wide-range discipline whose applications are quite diverse. The long list of applications includes high-speed optical communications, optical interconnects, microwave photon-ics, ultrafast signal processing, nonlinear optical effects, photonic crystals, group IV materials science, mid and long infrared wave devices-and-systems, infra-red fibers, quantum information, car-bon nanotube devices, nano- and micro-opto-electromechanical devices and more. This amazing scope mirrors the diversity of photonics itself. The myriad applications of silicon in photonics are analogous to the multiple roles that silicon plays in chemistry, physics materials science and, overall, micro-electronics [92].
One of the most important frontiers of silicon photonics is op-toelectronic integration. In the last years the Internet’s coming has permitted to transfer more data for larger transmission band-width.
The electronic device bandwidth has unfortunately been limited by metal connections, parasite capacitances and charge mobility in silicon, the most important material for the micro-electronic in-dustry. Moreover, the very high transistor density can cause chip overheating, affecting its performance. These limitations could be overcome employing photonic devices and optical interconnects. In addition, optical communications are not affected by electro-magnetic interference, as it happen in electronic circuits. Photonic integrated circuits (PICs) allow the development of more compact optical systems with higher performance and lower cost if com-pared with systems based on discrete optical components. Addi-tionally, they can also be integrated with the present electronics to provide increased functionality.
While electronics is dominated by silicon and the primary de-vice is the transistor, for what concerns photonics a variety of ma-terials are used and different functionalities are implemented by distinct kinds of devices such as low loss interconnect waveguides, filters, lasers, amplifiers and modulators.
In this framework indium phosphate-based is the more reli-able technology platform allowing for the integration on a sin-gle chip of hundreds of active and passive devices. However, the cost of fabrication for this technology is very high and, conse-quently, does not allow high production volumes. Alternatively silicon photonics, where PICs are fabricated by using silicon or sil-icon compatible materials and where the manufacturing is based on the available microelectronics manufacturing (CMOS
technol-ogy), is emerging as a cost effective platform capable of support-ing the high volumes required by the datacom market.
Although silicon is a good material for passive optical waveg-uides at around 1550nm, its indirect band-gap makes its use very challenging for achieving optical gain. Moreover, this material has no χ(2) nonlinearity, making it impossible to realize electro-optic modulators and integrated switches. On the one hand, several so-lutions have been proposed to realize light emitters on silicon compatible platform, like the use of porous silicon [43], silicon
nano-clusters [70], hybrid integration with III-V semiconductors
[24], rare earth-doped dielectric waveguides [34]. More recently,
the fabrication and lasing of germanium grown directly on silicon has been demonstrated [54] based on this non-linear effects. On
the other hand, few effective solutions have been explored in sili-con photonics to modulate the refractive index, i.e. thermal tuning and carrier injection. However, while the former approach is slow (on the order of milliseconds), the latter one is affected by higher loss. The solutions provided by both method are still far from the state of the art modulator manufactured on LiNbO3 and based on
electro-optical modulation.
The development of efficient solutions for modulators and switches in silicon-based technology is then needed considering the advan-tages of this technology, like low cost per device, compatibility with micro-electronics and easy integration with CMOS technol-ogy. This is the context where this thesis is collocated.
Optical modulators and switches are amongst the key-elements in integrated optics. An optical modulator is a device used to con-trol the amplitude, the phase, the frequency or the polarization of a light beam. Optical switches enable to be selectively the optical path of a light signal from one circuit to another.
Optical modulators and switches can be classified in terms of the origin of the optical refractive index modulation and this leads to the following list
• Micro-Electro-Mechanical system based switch/modulator • Thermo-optic based switch/modulator
• Acousto-optic based switch/modulator • Electro-optic-based switch/modulator.
For both switches and modulators, the response time is a critical parameters.
Micro-Electro-Mechanical system based switch/modulator
Micro-Electro-Mechanical systems (MEMS) have broad applica-tions and have been efficiently used for displays, optical com-munication, spectroscopy, and maskless lithography. In many of these applications (such as color displays and multicolor images),
1.1 modulators and switches in si photonics 3
it is desirable for the modulator to have wavelength selective or wavelength-tunable characteristics.
An interesting application of MEMS is their used for optical path switching in silicon photonics [32]. An example is shown in
Figure 1, where a MEMS-actuated directional coupler is used in an integrated crossbar network-on-chip. The measured switching time is 2.5 µs.
Figure 1: Switch unit cell with MEMS actuator and movable directional
coupler ([32]).
Thermo-optic based modulators
A typical and basic thermo-optic phase shifter consists of a waveg-uide, or a ring-resonator, and a heater. The refractive index of the core and the cladding are changed by heating the waveguide. The phase-shift is defined by the expansion:
∆φ = L2π λ0
∂n
∂T∆T (1)
where ∂n/∂T is the thermo-optic coefficient that depends on the material, ∆T is the variation of the temperature, L is the length of the waveguide and λ0 the modulated wavelength. Switching time
is of the order of 10 µs. Acousto-optic based modulators
Acousto-optic based modulators are typically used for Q-switching and spectroscopy and exploit the acousto-optic effect. This effect is represented by the change in the refractive index induced by a mechanical strain, induced by the excited acoustic waves. Those
Figure 2: Simplified scheme of a waveguide with a heater.
devices usually consist of a piezo-electric transducer which cre-ates sound waves in the material and the modulation of the optical beam happens because of the acoustic field. The order of magni-tude of the switching time is between 20 ns and 100 ns.
Electro-optic modulators
The electro-optic effect is the linear change of the refractive index and the absorption spectrum with applied electric field. In semi-conductors, several effects can originate it:
• Franz-Keldysh Effect (FK): variation of absorption in bulk semiconductors (neglect Coulomb interaction between elec-trons and holes);
• DC Stark Effect: Franz-Keldysh effect plus Coulomb interac-tion between electrons and holes (excitons) in bulk semicon-ductor;
• Quantum confined Stark effect (QCSE): DC Stark Effect in quantum wells;
• Pockels effect: variation of the refractive index caused by the fix charges in the crystal when the material lacks of a center of symmetry;
• Band filling: enlargement of the bandgap due to the carrier concentration;
• Band shrinking or Burstein Moss effect: effective squeezing of the band gap due to electron-electron interaction in heav-ily doped semiconductor;
• Free carrier plasma effect: variation of the refractive index/op-tical absorption due to free carriers.
Most electro-absorption modulators and switches are made in the form of a waveguide with electrodes in order to apply an elec-tric field in the perpendicular plane with respect to the modulated light beam. Quantum well structures, thanks to quantum confined Stark effect, are usually the best option in order to achieve high extinction ratio.
1.1 modulators and switches in si photonics 5
A field applied to an anisotropic electro-optic material modi-fies its refractive indices and thereby its effect on light travelling through it. Electro-optic effect is usually associated with anisotropic crystals that have different indices for different optical polariza-tions, and the displacement might not be parallel to the electric field for all orientations. The effect can also take place in materials that are isotropic but become anisotropic with the application of a field. Outside of the semiconductors, the most popular material for photonic integrated circuits is the lithium niobate (LiNbO3)
which is an anisotropic medium. In all cases, depending on the crystal orientation with respect to the applied electric field, the change in index is generally different for different polarizations of the optical field for a given applied dc field orientation. The switching time is of around 5-10 ns.
The most common method to realize electro-optic modulation in silicon is to exploit the plasma dispersion effect [91]. This
ap-proach does not need integration of any other materials like ger-manium or polymer, and thus it is intrinsically compatible with CMOS technology. To implement optical modulation by the plasma dispersion effect, the charge density inside an optical waveguide has to be manipulated by an electrical signal. Three working con-dition can be considered to design a plasma based modulator: carrier injection, accumulation, and depletion. Since the carrier-depletion-based modulator offers merits of processing simplicity and high operation speed, a lot of efforts have been devoted to improve its performance [91]. Different configuration have been
investigated to perform optical modulator in silicon such as Mach-Zehnder interferometer (MZI) [96], ring resonant [106], racetrack
resonator [82, 83] and microdisk resonator [102].
MZI and ring resonator modulators are schematically shown in Figure 3.
The cross section of the optical waveguides is a pn junctions for carrier injection or depletion. It plays a crucial role in the modu-lator performance. The modulation efficiency, which is the achiev-able modulation depth per volt, and the maximum modulation rate are both determined by the pn junction. The pn-junction ge-ometries in SOI waveguides can be lateral, vertical and interleaved as shown in figure4.
To be compatible with high-speed CMOS electronics, it is desir-able that the next generation optical modulator speed will exceed at 50 Gbit/s, consume less than 10 fJ of energy per bit, operate with drive voltages below 2V, with a footprint size smaller than 10 µm2[44,80]. Carrier injection through a pn junction is a slow
pro-cess, and can only reach modulation bandwidths of a few GHz at most [107]. Hence, carrier depletion in pn diodes is the common
method for light modulation in SOI waveguides [80].
The characteristics of state-of-the-art carrier depletion modula-tors are detailed in Table 1. Important performance metrics such as modulation speed, extinction ratio, energy consumption per bit,
Figure 3: Schematics of (a) a MZI modulator and (b) a ring modulator. The silicon optical waveguide cross-section with the pn diode phase shifters are shown.
Figure 4: Typical pn-junctions in SOI waveguides: lateral (a), vertical (b), interleaved (c).
peak-to-peak modulation voltage (Vpp), bias voltage (Vbias) and
the footprint size (area efficiency), have been summarized.
Some interesting results are summarized in table 2 where the comparison between carrier accumulation [52], injection [31],
de-pletion [95] is presented. The most important parameters of Mach
1.2 recent research activity 7
br(Gbits/s) E/bit(fj/bit) E.r (dB) Vpp(V) Vbias (V) f (µm2)
[2] 20 200 3.7 0.63 0 104 [99] 50 5.56 7 -5 104 [105] 40 4.1·103 7 7 -3.5 103 [48] 40 7 2 -1 50 [104] 44 300 3.45 3 -3 102 [103] 12.5 3 3.2 1 -3.5 10 [112] 56 4 4 103 [45] 20 1.8 4 103
Table 1: Characteristics of the state-of-the-art carrier depletion modula-tors
Device VπL (V-cm) α(dB/mm) Speed (Ghz) Mod. Depth (dB)
MOS [52] 8 1 16 lateral pin [31] 0.036 10 6-10 lateral pn [95] 0.036 10 6-10 pipin[113] 3.5 1 40 6.6 doping [98] 2.18 0.75 10 8 fringe filled [45] 1.8 1.3 11.8 8.1
Table 2: Summary list of Si MZI modulators with different device config-urations
compensation method [98] are also presented, together with the
more innovative fringe-field design [45].
In the following part of this introduction, I will report recent de-velopment and future perspectives of silicon modulators describ-ing their potentials and innovative characteristics.
1.2 r e c e n t r e s e a r c h a c t i v i t y
Since few years ago, optical modulators were mainly limited to III-V semiconductors [38] and Lithium niobate (LiNbO3). In those
materials, light modulation is obtained by inducing light absorp-tion properties or by changing the refractive index of the material due to an applied electric field.
Although those materials are very efficient, they cannot be eas-ily integrated on silicon, which provides a very reliable and low cost platform for integrated optics. As a result, the research inter-est on CMOS compatible integrated modulators and switches is constantly growing and is related to the extremely inefficiency of these devices on silicon platforms. While Silicon is transparent at
Ports Bandwidth (GHz) E.R. dB [89] 4x4 39 20 [51] 8x8 100 -[10] 1x2 102 -[76] 5x5 19 -[63] 1x2 13 14
Table 3: Summary list of state-of-the-art optical switches
the 1.55 µm, which is the wavelength used for optical communica-tion in fiber, it lacks of second order susceptibility that is required for electro-optic effects for switches and modulators [60].
Ge material systems
Germanium and Silicon-Germanium (SiGe) materials, which are CMOS compatible, are characterized by a strong electro-absorption effect which can be exploited for very high-speed modulation, in terms of both Franz-Keldish and quantum confined Stark effect. The electro-absorption in those materials is very large and it can be used for realizing compact devices with high speed, low power consumption and broad band operation.
Recently, Liu et al. [53] have demonstrated a GeSi FK modulator
integrated on a submicron silicon waveguide with 1.2 GHz mod-ulation speed. High speed Ge FK modulators working at around 1620nm have been demonstrated on 3 µm silicon waveguides [103].
A compact and energy efficient modulator, now representing a key building block for optical interconnection applications, has been investigated in Feng et al. [26]. In this work, the authors have
demonstrated a high speed GeSi electro-absorption (EA) modu-lator monolithically integrated on 3 µm silicon-on-insumodu-lator (SOI) waveguide. The proposed device has a compact active region of 1.0x55 µm2, an insertion loss of 5 dB and an extinction ratio of 6 dB at wavelength of 1550 nm [4] [41].
1.2 recent research activity 9
[53] [56] [26]
Energy per bit 50 50 50 Extinction ratio 10 10 10 Bandwidth (GHz) 1.2 1.2 40.7
Device footprint 30 30 55
Table 4: Waveguide-integrated GeSi electro-absorption modulator on Sil-icon.
Polymers
Polymers with nonlinear inclusions are considered as cheap alter-natives to the conventional modulator materials, especially for fill-ing nanoscaled gaps and slits in waveguides. Such small volumes intensify light-matter interactions due to the high-field confine-ment and allow fast operation speed, at least 100 GHz as recently reported by Alloatti et al. [1].
The device in ref. [1] is shown in figure6. In a Silicon Organic hybrid (SOH) modulator, the optical transverse electric (TE) field propagates in a silicon waveguide, while the electro-optic effect is provided by an organic cladding with a high Pockels effect. The optical nonlinear interaction occurs inside a nanoscale slot, taking advantage of the field enhancement caused by the lateral discon-tinuity of the refractive index. The external modulation voltage drops across the nanoscale slot because of the strip-load silicon electrodes, which must be both optically transparent and electri-cally highly conductive as seen in Figure 6.
The natural evolution of the device proposed in ref [1] is the
Sil-icon Organic Hybrid (SOH) Mach Zehnder modulator in ref [42]:
the 1-mm-long device consumes only 0.7 fJ/bit to generate a 12.5 Gbit/s signal. The structure is reported in Figure 7.
Graphene
Graphene is another cutting edge material, and its modulation efficiency is due to the changes in the Fermi level driven by an ap-plied voltage [56] (Figure8). A graphene-based integrated electro-absorption modulator has several distinctive advantages. In com-parison to QCSE in III-V semiconductors, a monolayer of graphene possesses a much stronger inter-band optical transition. It can be effectively exploited in novel optoelectronic devices such as photodetectors. Secondly, the optical absorption of graphene is in-dependent of wavelength, covering all telecommunications band-width and also the mid- and far- infrared because of the exploita-tion of the constant dynamic conductivity. Finally, with such a large carrier mobility, the Fermi level and hence the optical
ab-Figure 6: (a) the silicon waveguide is connected to the metal electrodes by thin silicon strip loads. The electro-optic polymer covers the waveguide and fills the slot. The silicon substrate is used as a gate. (b) the cross-section of the waveguide shows that the light is concentrated in the slot. (c) When a positive gate voltage is applied across the substrate, a highly conductive electron accumulation layer forms in the strip-loads.
Figure 7: SOH MZM (a) Two 1-mm-long silicon slot-waveguides act as phase modulators. (b) Cross section of the MZM where the organic cladding is deposited into the slot region of the SOI waveguide. (c) Electrical field well confined in the slot waveg-uide. (d) chemical structure of the cladding material.
sorption of graphene can be rapidly modulated through the band-filling effect. In addition, speed limiting processes in graphene
1.3 future perspectives 11
(such as photocarrier generation and relaxation) operate on the timescale of picoseconds, which implies that graphene-based elec-tronics can potentially operate at 500 GHz. Moreover, the athermal optoelectronic properties of graphene and its reliable integration processes at wafer scale make it a promising candidate for post-CMOS electronics also with a small footprint (∼ 25 µm2).
Figure 8: Three-dimensional schematic illustration of the device; (a) monolayer graphene sheet is on top of a silicon bus waveg-uide, separated from it by a 7-nm-thick Al2O3 layer . The sili-con waveguide is doped, and sili-connected to the electrode (right, shown gold) through a thin layer of silicon defined by selective etching. (b), Left, cross-section of the device, with an overlay of the optical mode plot. The waveguide was carrying a single optical mode, and was designed in order to maximize the field at the interface between the waveguide and the graphene. However, to compete with the compactness of conventional elec-tronic elements, photonic solutions have to overcome the diffrac-tion limit of light by implementing nanoscale optical components. 1.3 f u t u r e p e r s p e c t i v e s
One avenue that offers subwavelength light confinement is to em-ploy surface plasmon polaritons (SPPs). These are surface waves existing on metal-dielectric interfaces. SPPs are tightly confined to an interface and allow for the manipulation of light at the nanoscale, thus leading to a new generation of fast on-chip de-vices with excellent capabilities. In particular, they could offer a higher bandwidth and reduced power consumption [22].
The structure of the most compact high-speed plasmonic modu-lator demonstrated till now is reported in figure9. This new ultra-compact plasmonic phase modulator is based on Pockels effect in a non linear polymer. This Plasmonic phase modulator consists
of two metal tapers that perform the photonic-to-plasmonic mode conversion and a phase modulator section located between them. Light guided through the silicon nanowire efficiently excites the SPP via the metal taper. The SPP is then guided into the phase modulator section, which consists of two metal pads separated horizontally by a nanometre-scale vertical slot. The slot is filled with a nonlinear organic material, whose refractive index can be changed via the Pockels effect. By modulating the refractive in-dex of the polymer in the slot, the information is encoded in the phase of the SPP. At the end of the modulator section, the SPP is back-converted into a photonic mode.
Figure 9: Schematic of the PPM. Continuous-wave (c.w.) infrared light guided by the upper-left silicon nanowire is coupled through a metal taper to the plasmonic slot waveguide. The slot in the metal sheets is filled with an electro-optic polymer. The phase of the surface plasmon polariton (SPP), which propagates in the slot, is changed by applying a modulating voltage. A sec-ond taper transforms the SPP back to a photonic mode in the lower-right nanowire.
Another great success of plasmonic modulators have been re-ported in [57]. A 70 GHz all-plasmonic Mach-Zehnder modulator
that fits into a silicon waveguide of 10 µm length has been demon-strated. This dramatic reduction in size by more than two orders of magnitude compared with photonic Mach-Zehnder modulators results in a low energy consumption of 25 fJ per bit up to the high-est speeds.
The device consists of three sections. In a first photonic plas-monic interference (PPI) section, incident laser light from the sili-con waveguide is sili-converted into SPPs and split by the island tip. In the second section, the SPPs are guided along the two arms of
1.3 future perspectives 13
the plasmonic phase shifters. The phase shifters are designed as metal-insulator-metal plasmonic slot waveguides formed by gold contact pads and a gold island, with the island contacted through a suspended bridge. The slots are filled with DLD-164, a highly nonlinear χ(2) material. When a voltage is applied between the island and the outer electrodes, SPPs propagating in the slots change their phase due to the linear electro-optic effect. Finally, another PPI section transforms the relative phase relations of the SPPs in the two arms into an amplitude modulation. If the SPPs are in phase they will couple to the only guided mode of a sub-sequent silicon waveguide, and if they are out of phase they will couple to lossy evanescent modes (figure10).
Figure 10: Colourized SEM image of the MZM components. The sus-pended bridge enables electrical control of the device.
To provide the basic nanophotonic circuitry functionalities, ele-mentary circuit components such as waveguides, modulators, sources, amplifiers, and photodetectors are required. Among them, a waveg-uide is the key passive component connecting all elements in the circuit. Various designs of plasmonic waveguides have been proposed, aiming to achieve the highest mode localization while maintaining reasonable propagation losses. However, because of the high intrinsic losses of plasmonic materials, signal propaga-tion is highly damped even for the best (with the highest DC con-ductivity) metals such as silver and gold. Thus, the ultimate goal is to reduce material losses utilizing new plasmonic materials.
Recently, efforts have been directed towards developing new material platforms for integrated plasmonic devices. Transparent conducting oxides (TCOs), for instance, indium tin oxide (ITO) and aluminum-doped zinc oxide (AZO), are oxide semiconduc-tors conventionally used in optoelectronic devices such as flat panel displays and in photovoltaics. The optical response of TCOs is governed by free electrons, whose density is controlled through
the addition of n-type dopants. The free carrier concentration in TCOs can be high enough so that TCOs exhibit metal-like behav-ior in the near-infrared (NIR) and mid-infrared (MIR) ranges, and can be exploited for subwavelength light manipulation. Moreover, in contrast to the optical properties of noble metals, which cannot be tuned or changed, the permittivity of TCOs can be adjusted via doping and/or fabrication process, providing certain advantages for designing various plasmonic and nanophotonic devices. 1.4 t h i s t h e s i s
While the previous section may offer an interesting overview of recent research activities and technological processes, we should however point out that most of them present several limitations. Ge based modulators, indeed, suffer the indirect-gap nature of Ge especially for electro-absorption processes, SOH device perfor-mance can easily deteriorate due to their polymeric nature, plas-monic modulators present high losses and graphene fabrication process is not mature up to now.
In this thesis we have decided to study three different approaches for efficient modulators and switches in silicon platforms which are separately explained. In particular I will concentrate on:
• thermo-optic effect in Silicon due to its strong reliability for integration of several devices on the same chip;
• Strained silicon for its low power consumption, low cost and CMOS compatibility;
• possible integration on Silicon of Lithium Niobate represent nowadays the best source of non-linearities.
In chapter 2, I will present the framework of a scalable inte-grated switching matrix for telecom and datacom applications. The data reported in table 3 summarize some examples of the state-of-the-art optical switches and represent the buildin block of our analysis. The reported theoretical and experimental results will clearly point out that silicon photonic technology is highly promising for achieving very large integration and for being CMOS-compatible. In particular, I will present the design and experi-mental characterization of CMOS compatible electronic and pho-tonic integrated device for low cost, low power, transparent, mass-production optical switching developed within the IRIS European project; the final aim is the realization of a transponder aggrega-tor device which interconnect up to eight transponders to a four direction colorless-directionless-contentionless reconfigurable op-tical add and drop multiplexer (ROADM). In particular, the work will concentrate on the design, fabrication and characterization of micro-ring resonators, used for very compact and efficient switch-ing functionality. I will present the design procedure and exper-imental results of thermally tunable double ring resonators
to-1.4 this thesis 15
gether with a detailed analytical model specific for double rings and a modified racetrack geometry using Bezier bends. The exper-imental results of thermally tunable double ring resonators will also include the optimization of doped silicon and silicide inte-grated heaters, allowing the device to be used as a tunable filter or a switch.
In chapter3, I will focus on the strain-induced Pockels effect in silicon, which has attracted a lot of attention in Silicon Photonics after the first demonstration in [39]. Strained silicon based devices
are promising candidates for realizing very fast integrated opti-cal modulators and switches. I will show that the presence of a strain gradient can effectively induce second-order non-linearities in centro-symmetric crystals as silicon and I will derive a simple linear relation between the second order non-linearities in strained silicon and the strain gradient. Such a relation can be deduced by symmetry arguments, providing an easy framework for the opti-mization of optical devices based on this effect, and reducing the computational effort to a standard strain calculation and electro-magnetic mode analysis.
In the second part of the same chapter, I will give an overview of electro-optic effect in LiNbO3 presenting possible future
per-spectives of CMOS compatible integration, non-linear applications and low losses. In particular, I show a heterogeneous platform on which lithium niobate (LN) thin films are bonded on silicon ni-tride (Si3N4) waveguides. I will point out that large second and
third order nonlinear coefficients can be achieved ensuring at the same time very low propagation losses and high performance.
Part I
T H E R M A L T U N I N G R E S O N AT O R
F I LT E R S F O R W D M A P P L I C AT I O N S
2
T H E R M A L T U N I N G R E S O N AT O R F I LT E R S F O R W D M S W I T C H I N G A P P L I C AT I O N S
2.1 i n t r o d u c t i o n
CMOS compatibility and small footprint are two of the main rea-sons of success of Silicon photonic technology for switching ap-plications. Ring resonators have been widely used as filters and modulators providing very compact and efficient basic switching elements [6]. The performance of wavelength division
multiplex-ing (WDM) switchmultiplex-ing matrices based on a smultiplex-ingle rmultiplex-ing add/drop filter is fundamentally limited in terms of neighbor channel rejec-tion for a given channel bandwidth [21, 77], lacking in tolerance
to variations in fabrication and environmental changes (e. g. tem-perature). Therefore, a higher-order filter is better suited for this purpose, as it provides a more uniform pass band over a wider wavelength range, and at the same time has a larger extinction ratio outside the pass band improving the filter performance ([30, 50, 65]) in terms of pass-band flatness, filter roll-off and channel
rejection. However, these filters are more sensitive to fabrication inaccuracies, as typical designs require them to be identical. On the other hand, if tuning is needed, collective tuning of many res-onators consumes more power.
In a WDM system, the necessity of dropping only one channel from the WDM grid may require large free spectral ranges (FSRs). Since the FSR is inversely proportional to the length of the ring, very small resonators with low bend loss are required. On the other hand, the bandwidth constraint needs large coupling coeffi-cients.
In the following sections, we will describe the design procedure and the successful experimental demonstration of single and cou-pled rings for WDM application. We will exploit an original theo-retical model for second-order filters and a Bezier bend modified racetrack design procedure. We will compare first and second or-der filters and show that the filtering performance of double-ring switches in terms of propagation, insertion losses and channel re-jection is quite robust to fabrication deviations.
In the second part of his chapter we will explore the active tun-ing. WDM systems based on a large number of switches need a very efficient tuning process in order to reduce the power budget. The large thermo-optic response of silicon is the main reason why thermal tuning is one of the most widely used ways of active tun-ing. We will then investigate the thermal tuning approach both for single and coupled filters. From the formers, we will show an efficient integrated thermal heater, its optimization procedure
obtained varying the heater cross-section and the location of the electrical contacts.
We will conclude this chapter demonstrating the agreement be-tween theoretical and experimental results. For the latters, we will show their successful tuning capabilities and how small fab-rication deviations, which could generate slight asymmetries in the heating, can be fully compensated by individually addressing each ring. Finally, the variability of the filter response along the full wafer will be evaluated, together with its consequences on filter performance.
2.2 f i na l a i m o f t h i s w o r k: iris project
Reconfigurable optical add and drop multiplexer (ROADM) nodes have been historically implemented using broadcast and select architecture as the one shown in Fig. 11. In this case, the four-directional ROADM is based on an optical line switching section and a local add and drop section. The optical line switching is con-stituted by N node directions, Nx1 wavelength selective switching (WSS) and four power splitters. The power splitters distribute dif-ferent wavelengths that are selectively combined by the WSS and then sent to the output fibers. Local add and drop section includes arrayed waveguide gratings (AWG), receivers (Rx) and fixed wave-length trasponders (T x). The first AWG array demultiplexes the signals that are distributed by the power splitters and links them to the receivers Rx, the second multiplexes the signals coming from the WSS and links them to the fixed wavelength transpon-der. The limitations of this kind of structure are mainly due to the WDM array. Added and dropped signals are indeed assigned to fixed directions and fixed colors and possible changes in terms of wavelength require manual rewiring.
Next generation ROADMs should provide higher flexibility and in particular they should guarantee the following features: The requirements, for ROADM, are to operate in:
• directionless mode: the routing of added/dropped wave-length channels should be guaranteed without manual rewiring; • colorless mode: the routing should be independent from
the transponder wavelength;
• contentionless mode: multiple transponders may operate at the same wavelength in order to be handled by the same add and drop section.
An example of a four directional colorless, contentionless and di-rectionless CDC ROADM is shown in Fig. 12.
In order to satisfy these requirements, it is necessary to replace the fixed WDM multiplexer and demultiplexer with an additional block denoted as transponder aggregator (TPA). The TPA is a switching sub-system working in two directions: distribute selected
2.2 final aim of this work: iris project 21
Figure 11: Conventional ROADM structure [74].
combs of wavelengths from WSS to transponders (without limita-tions in terms of wavelength and direclimita-tions) and combine wave-lengths from transponders to WSS. In this framework, Silicon Pho-tonics plays an important role. CMOS compatibility, small foot-print and extremely low cost of the devices are some of the most important reasons why Silicon Photonics became so promising for scalable integrated switch matrices.
The FP7 IRIS project (Integrated Reconfigurable silicon photonic based optical Switch) proposes a new concept of integrated TPA device as shown in Fig.13. In that figure, the drop switching port is implemented, where four sets of 12 WDM channels, 200 GHZ spaced, are coupled to the chip by four single polarization grating couplers (SPGC). The input channels are splitted into even and odd by interleaver blocks to increase the wavelength spacing and the channel isolation. AWG demultiplexer blocks separate the sig-nals and send them to the switching matrix. This matrix is consti-tuted by micro-ring resonators thermally tuned in order to couple the input signal to to the corresponding drop coloumn. At that point two waveguides for odd and even wavelength channels are then recombined by an interleaver and coupled to an output op-tical fiber by a SPGC. If the input/output port of the photonic circuit in figure 13 are reversed, the same device operates as an add switch. In this operating mode, the signals coming from 8 tunable transmitters can be added and redirect to 4 directions.
The tunable resonators play a crucial role in this structure. They are all switched off with the exception of the ones in the directions to which the signal has to be dropped (or added). At this point, the
signal is deviated toward the multiplexer reaching an interleaver that combines odd and even wavelengths to the same output fiber.
Figure 12: Colorless-directionless and contentionless ROADM [94].
2.3 just a bit of definitions 23
2.3 j u s t a b i t o f d e f i n i t i o n s
The success of ring resonators in Silicon Photonics can be mainly attributed to their small footprint. A generic ring resonator is con-stituted by an optical waveguide looped back on itself. When the optical path length of the resonator equals a whole number of wavelengths, a resonance occurs. Ring resonators can support mul-tiple resonances and the spacing among them, which is called free spectral range, is determined by the ring radius.
The utility of ring resonators appears in presence of a coupling mechanism. One of the most common coupling is the codirec-tional evanescent coupling between a ring and an adjacent bus waveguide. In this contest ring resonators act like spectral filters.
The simplest form of a ring resonator is represented by the so called all-pass filter, also said notch-filter configuration. In this case, as shown in Fig.14(a), the light in the ring resonator can be built up by feeding one output of the directional coupler. When two waveguides are fabricated in the proximity of a ring resonator, the overall configuration acts as an add/drop filter. The light, at wavelength in resonance with the ring resonator, is coupled from one waveguide to the second one, performing optical path switch-ing, as shown in Fig.14(b).
The basic spectral characteristic of a ring resonator can be eas-ily derived by assuming continuous wave (CW) operations and matching fields as shown in [5]. The ring is on resonance when
the phase of the electric field after one trip, φ, is a multlple of 2π or, equivalently, when the wavelength of the electro-magnetic wave fits a whole number of times inside the optical length of the ring. As a result, the resonance wavelength can be defined as:
λres= neffL
m m = 1, 2, 3, ... (2)
where neff is the effective index and L is the cavity perimeter.
Within a first order dispersion, the wavelength range between two resonances is called free spectral range (FSR), it is shown in fig15 for an add and drop ring resonator filter and it equals:
FSR = λ
2 res
ngL. (3)
The term ngthat appears at the denominator is called group index
and is defined as: ng= neff− λ
dneff
dλ (4)
where λ is the optical wavelength.
In fig 15 the full width at half maximum is also shown. The FWHM. also known as 3 dB bandwidth, is the fraction of the spec-trum which is added/dropped by the filter. In literature, loss is basically included by insertion of the parameter α in the formu-las. Loss in ring resonator filters scales the spectral curves without
Figure 14: Ring resonators in all-pass (a) and add and drop
configura-tion (b). Pictures from ref. [40]
changing them significantly if the loss is not too large. Different types of losses have been considered and described in literature
2.4 model and design 25
to account for various fabrication methods and tolerance such as radiation loss in the curved section or surface roughness.
Figure 15: Through and drop spectrum of an add and drop ring res-onator filters, with FSR and FWHM highlighted.
2.4 m o d e l a n d d e s i g n
The input/output transfer function of a ring resonator filter (i.e. all-pass and add/drop filters) can be derived using the transfer matrix approach, as described in [6]. Using the same approach, in
this section I computed the transfer funtion of a double ring res-onator filter. The double ring configuration of the add/drop ring based filter structure under investigation is schematically shown in Fig. 16.
The matrix equation that links ingoing and outgoing fields in a double ring resonator is
Eth Edrop ! = t11 t12 t21 t22 ! Ein Eadd ! (5) where Ein and Eadd are the ingoing electric fields at the input
and add port, respectively, while Eth and Edrop are the
outgo-ing electric fields at the through and drop port, respectively. In this analysis, we assumed continuous wave operation, matching fields and negligible back reflections [6]. The t
ij elements have
been computed combining the transfer matrix of the couplers Mi = ti ki
k∗i t∗i !
i = 1, 2, 3 (6)
and the round trip transmission factor of the two rings ηj=exp
Figure 16: Schematic cross section of a coupled ring
where Lj are the resonator perimeters, while αj and βj are the
field attenuation and the phase constant of the circulating mode in each ring. In the more general case, we assumed that the coupler can be lossy (i.e., di = det(Mi) = |ti|2+|ki|2
< 1 for i=1,2,3). The final transfer functions are
t11 = t1− t ∗ 2η1d1− t∗3η2[t1t2− η1d1d2] ∆ (8) t12 = t∗21 = −k1k ∗ 2k∗3η 1/2 1 η 1/2 2 ∆ (9) t11 = t3− t ∗ 2η2d3− t∗1η1t∗2t3− η2d2d3 ∆ (10) where ∆ = (1 − t∗1t∗2η1) (1 − t2t∗3η2) +|k2|2t∗1t∗3η1η2 (11) The coefficient ∆ plays a key role because it defines the resonance of the device. Indeed, the resonances of the first ring are described by 1 − t∗1t∗2η1, the resonances of the second ring are defined by 1 − t2t∗3η2, while|k2|2t∗1t∗3η1η2takes into account the resonances
in the loop made of the two rings (figure-eight shape loop [74]).
The resonance wavelength split observable in double rings is due to the stronger influence of the figure-eight shape loop resonance over the single ring resonances. In the hypothesis of negligible losses (αj=0, for j=1,2), lossless coupler (di=0, for i=1,2,3),
identi-cal resonators and symmetric couplers (k1=k3), the drop response
is Tdrop = 1 − t21 1 − t22 1 + 4t21t22+ t41+ 2t21cos(2βL) − 4t1t2cos(βL)(1 + t21) . (12)
2.4 model and design 27
As we mentioned, a high-order filter shows benefits in terms of band sharpness and neighbor channel rejection. However, these filters can also show ripples which can be problematic. Using the maximally-flat criterion (Butterworth-type filter), we derived the impedance matching condition at the limit where ripples are not present. Such a condition fixes the relation between the bus-to-ring (K1) and the ring-to-ring (K2) power coupling coefficients
K2 = K
2 1
(2 − K1)2 (13)
The derived equation is valid also for large coupling coefficients, unlike the expressions reported in [50] that is an approximation
for low coupling values.
Our main simulation findings for the double ring are summarized in Fig.17. Considering T
drop in Eq.12 as a function of K1 and K2,
we have computed the insertion loss (IL), the 3 dB bandwidth (BW), the passband ripple and the channel rejection for a 200 GHz (1.6 nm) spaced channel. In the plots, the impedance matching condition is indicated with a white line.
Figure 17: Insertion loss (a), 3 dB bandwidth (b), passband ripple (c) and
channel rejection (d) as functions of the bus-to-ring (K1) and
ring-to-ring coupling coefficients (K2). The line corresponding
to the impedance matching condition is shown in white. At this point, it is worth making a comparison between single and double ring filters in terms of channel rejection and band-width. For a FSR of 2.4 THz (∼19 nm), we have first compared in Fig.18the 20 dB and 35 dB half-bandwidth ∆f−20 and ∆f−35 ver-sus the 1 dB half-bandwidth ∆f−1 for the first and second order
filters. From these results, it is clearly evident that the second or-der filter provides a significant improvement in terms of channel
rejection of neighbor WDM channels, when the same 1 dB band-width is considered.
(a)
(b)
Figure 18: Limitations of single and double rings in terms of 20 dB (a) and 35 dB (b) half bandwidth versus the 1dB channel
half-bandwidth. Definitions are shown in (c) where fRis the
reso-nance frequency.
2.5 f a b r i c at i o n a n d pa s s i v e c h a r a c t e r i z at i o n
The devices were fabricated at CEA-LETI on an 8” silicon-on-insulator (SOI) wafer with 2 µm buried oxide and 220 nm top c-Si layer [25]. The silicon layer was patterned by a
reactive-ion-etching (RIE) step after deep-UV 193 nm optical lithography print-ing. Waveguides are covered with SiO2 by chemical vapor
depo-sition (CVD). Single polarization grating couplers with a shallow-etch depth of 70 nm were used for optical access to the input, through, and drop ports of the ring filter. Grating coupling loss was∼5dB at λ=1550 nm from a reference sample. Grating coupler bandwidth was of around 45 nm (5.62 THz).
2.5.1 Single rings
The single-ring shown in 19 is a fully-etched circular ring with 5µm radius, 480 nm width and curved couplers. Two values of the gap distance between the bus waveguide and the ring were considered, 175 nm and 200 nm, and the angle (θ) of the bended coupler was set to 4, 8, 16, 20, 24, 28 or 32 degrees in order to provide increasing power coupling coefficient [75, 93]. The single
ring structure and the bend coupling are shown in Figure19. The single ring devices are characterized using an automated alignment procedure in a temperature-controlled environment. A tunable laser between 1520 nm and 1580 nm was swept with a wavelength spacing of 10 pm. The spectral responses are
normal-2.5 fabrication and passive characterization 29
Figure 19: Single ring schematic and relative optical microscope pictures
ized with the grating coupler spectrum extracted from the through port of each ring filter, after a fitting procedure, as shown in Fig.20.
Wavelength (nm) 1530 1535 1540 1545 1550 1555 1560 1565 1570 Transmission (dB) -60 -50 -40 -30 -20 -10 0 Through resonance position out-of-resonance through fit
Figure 20: Through port of the single ring spectrum (blue), individuation of the resonance position (red circle), out-of-resonance shape of the single ring (green), fit of the out of resonance shape (red dashed)
In Fig. 21, Tdrop is reported for the single ring filter assuming different coupling angles. In Fig. 21(a) the nominal gap distance between the waveguide and the ring is 175 nm, while in Fig.21(b) the gap is 200 nm. As we expected, the channel rejection increases for small coupling angles (i.e., small coupling coefficients). Figure 22 shows the resonance position, the 3-dB bandwidth, peak trans-mission (i.e., the maximum of Tdrop) and the group index versus
the coupling angle θ, for both gap values. The resonance posi-tion slightly drifts (<1 nm) with θ, which is much smaller than the wafer-scale drift, that reaches 8 nm. Such a resonant shift is mainly due to the different effective index in the coupling region. The larger θ is, the larger the coupling region and the stronger
Wavelength (nm) 1530 1535 1540 1545 1550 1555 1560 1565 Normalized Transmission (dB) -40 -30 -20 -10 0 10 θ=8o θ=12o θ=16o θ=20o θ=24o θ=28o θ=32o (a) Wavelength (nm) 1530 1535 1540 1545 1550 1555 1560 1565 Normalized Transmission (dB) -40 -30 -20 -10 0 10 θ=8o θ=12o θ=16o θ=20o θ=24o θ=28o θ=32o (b)
Figure 21: Single ring spectra (drop port) for different values of the gap (175 nm (a) and 200 nm (b)) and different values of the cou-pling angle
the resonance red-shift. The 3dB bandwidth increases with the an-gle, as expected because θ is proportional to the power coupling coefficient. Vice versa, the peak transmission decreases when the coupling angle is reduced because a lower K implies a higher Q-factor, which makes the ring more sensitive to the propagation loss. Finally, the group index is evaluated from the equation:
ng=
c
L∆νFSR (14)
where c is the speed of light in the vacuum, L is the ring length and ∆νFSR is the free spectral range (in Hz) extracted from the
spectra. The mismatch between the experimental ng value (∼ 4.29)
and the simulated one (4.235) are due to fabrication deviations. Metrology results from SEM, ellipsometry, and Mach-Zehnder in-terferometers in this fabrication run [69] show a fabrication
2.5 fabrication and passive characterization 31
218nm for the chips in the central part of the wafer. This geometry yields a simulated group index of∼4.29 which agrees with the ex-perimental value. In Fig.22the measured and simulated coupling
θ (o) 0 20 40 central λ (nm) 1554 1555 1556 θ (o) 0 20 40 BW (GHz) 50 100 150 200 θ (o) 0 20 40 T max (dB) -4 -2 0 2 θ (o) 0 20 40 n g 4.28 4.285 4.29 4.295 gap 175 nm gap 200 nm (a) (b) (c) (d) θ (o) 8 12 16 20 24 28 32 Coupling coefficient K (%) 4 9 14 19 24 measured simulated (nominal) simulated (fab. err.)
(e)
Figure 22: Central wavelength (a), 3-dB bandwidth (b), maximum value of the transmission (c) and group index (d) for gaps of 175 nm or 200 nm . Measured and simulated coupling coefficients for different values of coupling angles and gap equal to 175 nm (e).
coefficients are compared for the single ring device. The coupling coefficient has been estimated using the following equation [62]:
∆λ = λ 2 resK 2π2n gR √ 1 − K (15)
where ∆λ is the 3-dB bandwidth, λres the central wavelength,
ng the group index, R the radius of the ring resonator and K the
power coupling coefficient. As shown in Fig. 22(e), when fabri-cation errors are considered. Simulated and measured coupling coefficients show a good agreement.
2.5.2 Coupled rings
As we already mentioned, the constraints of bandwidth and chan-nel rejection for WDM switching matrices lead us to consider sec-ond order filters. In order to reach a maximum extinction ratio of 35dB and a 200-GHz channel rejection of 20dB, we have designed a double ring resonator with a bus-to-ring coupling coefficient K1
=20% and a ring-to-ring coupling coefficient K2=1.23 % that is
esti-mated from Eq.13, as shown in Fig.17. The values of K1and K2are considerably different and this happens because of the minimum impedance condition exracted in the model section. The transfer matrix method previously described can be considered valid not only for point coupling but also for extended coupling sections.
Figure 23: Double ring schematic and relative optical microscope pic-tures
Considering a circular shape and a fully-etched waveguide (to reduce the bending loss), it is difficult to reach large coupling values of 20%, even using curved couplers. For this reason, a racetrack-geometry is better suited, as the coupler is symmetric and can be extended. Despite this, a high FSR of 2.4 THz limits the perimeter to about 30µm, which means bend radius smaller than 4µm. In this case, using circular bends would yield too high loss in the transition between the straight and curved sections. For this reason, we designed bends with gradual curvature variation using Bezier-type bends, which have been used in the past to re-duce bend loss in silicon photonic circuits [3,5,16]. In our case, we
have used full cubic-splines 180o bends, which can be calculated using Casteljau algorithm [72] and 4 node positions, by using the
following equation:
R(ζ) = (1 − ζ)3P0+ 3 (1 − ζ)2ζP1+ 3 (1 − ζ) ζP2+ ζ3P3 (16) where Pi for i=1,2,3,4, are the node positions, ζ is a
dimension-less parameter which varies between 0 and 1, and R is the bend trajectory. The node positions P0 and P3 are the initial and final
2.5 fabrication and passive characterization 33
points of the bend (the white squares in Fig.23), while P1 and P2 (represented with black squares in the same figure) determine the sharpness of the bend. We define the node distance dnodeas the
distance between P0 and P1, which is the same as between P3
and P2. If we normalize that number with the effective radius, we
obtain a dimensionless parameter which we call normalized node distance δnode = dnode/Reff. This parameter is used to identify
the shape of the bend, considering that δnode = 1.3 corresponds
to a bend which resembles a circular bend whose curvature radius is of 3 µm in terms of footprint.
In order to evaluate the performance of the Bezier bends, a very high number of them have been fabricated (up to 480 bends in series), set at random distances to suppress periodic interference. The waveguide cross section was 220 nmx480 nm. Figure24shows the total loss per bend, including transition loss, bend loss due to radiation, and loss due to unavoidable sidewall roughness. An
Figure 24: 180o bend loss spectra for different normalized node
dis-tances δnode fixing Reff = 3 µm and for semicircular bend
and relative optical microscope pictures.
improvement by a factor 3 was measured for the loss between the circular and Bezier bends, for the 3 values of δnode parameter
under investigation (1.7, 2.0 and 2.4).
It is worth noting that the mode in a standard waveguide cross section (220 nmx480 nm) is strongly confined, so high coupling coefficients require long coupling lengths. To reach a power cou-pling ratio of 20% with a short coucou-pling length, the width was decreased. For this purpose, two waveguide widths have been considered: 450 nm and 410 nm. Therefore the coupling length of the couplers is fixed to 2.2 µm and the gap distances were calcu-lated for the two different waveguide widths. For a 410 nm wide waveguide, the gaps g1 = 208 nm and g2= 386 nm are
consid-ered for ring-to-waveguide and ring-to-ring coupler, respectively; while 450 nm-wide waveguides had g1= 158 nm and g2= 320 nm,
respectively.
Figure 25(a) shows spectra of double rings drawn with the three different values of δnode. The positions of the resonance peaks are
