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This PDF file contains the front matter associated with SPIE Proceedings Volume 9368 including the Title Page, Copyright information, Table of Contents, Introduction, and Conference Committee listing.
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We introduce GI-core multimode polymer optical waveguides as a promising component triggering the migration of optical interconnects from inter-racks to PCBs in high performance computers and servers. In particular, we spotlight “the Mosquito method” we developed for simultaneous fabrication and integration for the GI-core polymer waveguides on-board. For high density channel alignment, small-core waveguides are desirable so that single-mode waveguides are regarded as an ideal component. In this paper, we show the Mosquito method is capable of fabricating single-mode polymer waveguides. Furthermore, we focus on polymer waveguide circuits on PCBs in which horizontally and vertically (three-dimensionally) curved cores are aligned.
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Optical interconnects on printed circuit board level are a promising choice to support high bandwidth for short distance interconnects. These interconnects consists of highly multimode step index waveguides with rectangular core cross sections. Therefore ray tracing is an excellent method to determine the optical path parameters, e.g. optical power, ray path lengths and local ray directions. Based on these parameters the step response, the transient transfer function and the coupling behavior can be calculated. Classical ray tracing methods calculates the optical path parameters of each ray by successively computing internal reflections until a termination condition is reached. Therefore the computing time depends on the number of internal reflections. If the optical waveguide consists of cascaded straight and curved segments, e. g. point-to-point interconnects, one can use the analytic ray tracing method to determine the optical path parameters. The whole path parameters of each ray are determined by one analytical computation. The computing time depends on the number of segments. The analytic ray tracing method is unusable to determine ray path parameters of segments with varying core cross sections, e.g. tapers, crossings, splitters and combiners.
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Multimode step index polymer waveguides achieve high-speed, (<10 Gb/s) low bit-error-rates for onboard and
embedded circuit applications. Using several multimode waveguides in parallel enables overall capacity to reach beyond
100 Gb/s, but the intrinsic bandwidth limitations due to intermodal dispersion limit the data transmission rates within
multimode waveguides. Single mode waveguides, where intermodal dispersion is not present, have the potential to
further improve data transmission rates. Single mode waveguide size is significantly less than their multimode
counterparts allowing for greater density of channels leading to higher bandwidth capacity per layer. Challenges in
implementation of embedded single mode waveguides within printed circuit boards involves mass production fabrication
techniques to create precision dimensional waveguides, precision alignment tolerances necessary to launch a mode, and
effective coupling between adjoining waveguides and devices. An emerging need in which single mode waveguides can
be utilized is providing low loss fan out techniques and coupling between on-chip transceiver devices containing Si
waveguide structures to traditional single mode optical fiber. A polymer waveguide bridge for Si to glass optical fibers
can be implemented using silicone polymers at 1310 nm. Fabricated and measured prototype devices with modeling and
simulation analysis are reported for a 12 member 1-D tapered PWG. Recommendations and designs are generated with
performance factors such as numerical aperture and alignment tolerances.
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We design, fabricate and experimentally demonstrate a highly efficient adiabatic mode converter for coupling light into a silicon slot waveguide with a slot width as large as 320nm. This strip-to-slot mode converter is optimized to provide a measured insertion loss as low as 0.08dB. Our mode converter provides 0.1dB lower loss compared to a conventional V-shape mode converter. This mode converter is used to couple light into and out of a 320nm slot photonic crystal waveguide, and it is experimentally shown to improve the coupling efficiency up to 3.5dB compared to the V-shape mode converter, over the slow-light wavelength region.
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Quasi-Vertical tapers are designed to enable high coupling efficiency from a conventional single mode fiber into a single mode polymer rib waveguide. A triangular region fabricated under the single mode waveguide is adopted to adiabatically transform the fiber mode into the polymer rib waveguide mode. This structure works as an optical mode transformer. Because the trenches are deeper at the facets than at the active regions of the waveguide, the waveguide mode size in vertical direction becomes larger at the facets and can better match the input and output fiber mode. A coupling efficiency of 82.95% is achievable with a tip width of 1 μm.
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high-efficiency silicon strip waveguide to plasmonic slot waveguide converter based on the hybrid silicon-gold taper
is proposed and optimized. Through investigating the mode matching, the effective index matching, and the metallic
absorption loss considerations, the hybrid silicon-gold taper with an overall length of 1.7 μm having a very high
conversion efficiency of 93.3% at 1550nm is achieved. Besides, the configuration limitations for restricting this mode
converter to achieve a 100 % conversion efficiency are also studied in this paper. Such a high efficiency converter will
be an essential component in ultra-compact integrated circuits.
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The capability of mounting a parallel-optical module onto a PCB through solder-reflow process contributes to reduce the
number of piece parts, simplify its assembly process, and minimize a foot print for both AOC and on-board applications.
We introduce solder-reflow-capable parallel-optical modules employing 1060-nm InGaAs/GaAs VCSEL which leads to
the advantages of realizing wider modulation bandwidth, longer transmission distance, and higher reliability. We
demonstrate 4-channel parallel optical link performance operated at a bit stream of 28 Gb/s 231-1 PRBS for each channel
and transmitted through a 50-m-core MMF beyond 500 m. We also introduce a new mounting technology of paralleloptical
module to realize maintaining good coupling and robust electrical connection during solder-reflow process
between an optical module and a polymer-waveguide-embedded PCB.
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We present a vision for transceiver integration on a 3 μm SOI waveguide platform for systems scalable to Pb/s. We also
present experimental results from the first building blocks developed in the EU-funded RAPIDO project. At 1.3 μm
wavelength 80 Gb/s per wavelength is to be achieved using hybrid integration of III-V optoelectronics on SOI. Goals
include athermal operation, low-loss I/O coupling, advanced modulation formats and packet switching. An example of
the design results is an interposer chip that consists of 12 μm thick SOI waveguides locally tapered down to 3 μm to
provide low-loss coupling between an optical single-mode fiber array and the 3 μm SOI chip. First example of
experimental results is a 4x4 cyclic AWGs with 5 nm channel spacing, 0.4 dB/facet fiber coupling loss, 3.5 dB center-tocenter
loss, and -23 dB adjacent channel crosstalk in 3.5x1.5 mm2 footprint. The second example result is a new VCSEL
design that was demonstrated to have up to 40 Gb/s operation at 1.55 μm.
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We report a 40 Gb/s photoreceiver based on vertical-illumination type Ge-on-Si photodetectors and a silica-based AWG
demultiplexer by employing 4-channel CWDM. The 60um-diameter Ge-on-Si photodetector arrays, grown on a bulk
silicon wafer by RPCVD and fabricated with CMOS-compatible process, have ~0.9 A/W responsivity with 13 GHz
bandwidth at λ ~ 1330nm. Ge-on-Si photodetector arrays are hybrid-integrated with TIA/LAs and directly-coupled to the
AWG. The low-cost FPCB-package based photoreceiver module shows 10.3 Gb/s × 4-channel interconnection with -11
~ -12.2 dBm sensitivity at a BER = 10-12.
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Hybrid polymers have been already widely applied in photonic applications to manufacture microlenses or 2D and 3D waveguides. Thus, they are promising candidates to manufacture optical systems down to the chip level. A brief review on hybrid polymers consisting of both inorganic and organic functional units and thus combine superior material properties in just one material class will be given in this report. The material properties, which can be adjusted to the application in wide ranges enable to fabricate micro-optical elements (e.g. microlenses) using replication techniques such as UV-assisted replication or nano-imprint lithography. Aside of their applicability in 2D, emphasis will be in particular on the evaluation of hybrid polymer materials for two-photon absorption lithography, which is employed to directly manufacture sophisticated 3D photonic structures impossible to be generated with conventional 2D techniques.
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In recent years there has been considerable progress in utilizing fully automated machines for the assembly of microoptical systems. Such systems integrate laser sources, optical elements and detectors into tight packages, and efficiently couple light to free space beams, waveguides in optical backplanes, or optical fibers for longer reach transmission. The required electrical-optical and optical components are placed and aligned actively in more than one respect. For one, all active components are actually operated in the alignment process, and, more importantly, the placing of all components is controlled actively by camera systems and power detectors with live feedback for an optimal coupling efficiency.
The total number of optical components typically is in the range of 5 to 50, whereas the number of actors with gripping tools for the actual handling and aligning is limited, with little flexibility in the gripping width. The assembly process therefore is strictly sequential and, given that an automated tool changing has not been established in this class of machines yet, there are either limitations in the geometries of components that may be used, or time-consuming interaction by human operators is needed.
As a solution we propose and present lasered glass building blocks with standardized gripping geometries that enclose optical elements of various shapes and functionalities. These are cut as free form geometries with green short pulse and CO2 lasers. What seems to add cost at first rather increases freedom of design and adds an economical flexibility to create very hybrid assemblies of various micro-optical assemblies also in small numbers.
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We report on the manufacturing, reliability, and optical functionality of multimode optical waveguide devices developed with a fast processable optical grade silicone. The materials show proven optical losses of <0.05 dB/cm @ 850 nm, surviving >2000 hours 85°C/85% relative humidity testing as well as >4 cycles of wave solder reflow. Fabrication speeds of <10 minutes are shown for a full waveguide stack. Step index 50×50 μm waveguides were fabricated and passively MT connectorized on rigid FR4 and flexible polyimide substrates with precise alignment features (cut by dicing saw or ablated by UV laser). Two out-of-plane coupling techniques were demonstrated in this paper, a MT connectorized sample with a 45° turning lens as well as 45° dielectric mirrors on waveguides by dicing saw. Multiple connections between fiber and polymer waveguides with MPO and two out-of-plane coupling techniques in a complete optical link are demonstrated @ 10 Gbps data rates with commercial transceiver modules. Also, complex waveguide geometries such as turnings and crossings are demonstrated by QSFP+ transceiver. The eye diagram analyses show comparable results in functionality between silicone waveguide and fiber formats.
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Polymer-based integrated optics is attractive for inter-chip optical interconnection applications, for instance, for coupling photonic devices to fibers in high density packaging. In such a hybrid integration scheme, a key challenge is to achieve efficient optical coupling between the photonic chips and waveguides. With the single-mode polymer waveguides, the alignment tolerances become especially critical as compared to the typical accuracies of the patterning processes. We study novel techniques for such coupling requirements. In this paper, we present a waveguide-embedded micro-mirror structure, which can be aligned with high precision, even active alignment method is possible. The structure enables 90 degree bend coupling between a single-mode waveguide and a vertical-emitting/detecting chip, such as, a VCSEL or photodiode, which is embedded under the waveguide layer. Both the mirror structure and low-loss polymer waveguides are fabricated in a process based mainly on the direct-pattern UV nanoimprinting technology and on the use of UVcurable polymeric materials. Fabrication results of the coupling structure with waveguides are presented, and the critical alignment tolerances and manufacturability issues are discussed.
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Silicon-organic hybrid integrated devices have emerging applications ranging from high-speed optical interconnects to photonic electromagnetic-field sensors. Silicon slot photonic crystal waveguides (PCWs) filled with electro-optic (EO) polymers combine the slow-light effect in PCWs with the high polarizability of EO polymers, which promises the realization of high-performance optical modulators. In this paper, a broadband, power-efficient, low-dispersion, and compact optical modulator based on an EO polymer filled silicon slot PCW is presented. A small voltage-length product of Vπ×L=0.282V×mm is achieved, corresponding to an unprecedented record-high effective in-device EO coefficient (r33) of 1230pm/V. Assisted by a backside gate voltage, the modulation response up to 50GHz is observed, with a 3-dB bandwidth of 15GHz, and the estimated energy consumption is 94.4fJ/bit at 10Gbit/s. Furthermore, lattice-shifted PCWs are utilized to enhance the optical bandwidth by a factor of ~10X over other modulators based on non-band-engineered PCWs and ring-resonators.
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We demonstrate wavelength domain multiplexed (WDM) data transmission with a data rate of 14 Gbps based on optical
carrier generation with a single-section semiconductor mode-locked laser (SS-MLL) and modulation with a Silicon
Photonics (SiP) resonant ring modulator (RRM). 18 channels are sequentially measured, whereas the best recorded eye
diagrams feature signal quality factors (Q-factors) above 7. While optical re-amplification was necessary to maintain the
link budgets and therefore system measurements were performed with an erbium doped fiber amplifier (EDFA),
preliminary characterization done with a semiconductor optical amplifier (SOA) indicates compatibility with the latter
pending the integration of an additional optical filter to select a subset of carriers and prevent SOA saturation. A
systematic analysis of the relative intensity noise (RIN) of isolated comb lines and of signal Q-factors indicates that the
link is primarily limited by amplified spontaneous emission (ASE) from the EDFA rather than laser RIN. Measured RIN
for single comb components is below -120 dBc/Hz in the range from 7 MHz to 4 GHz and drops to the shot noise level at
higher frequencies.
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A stable reproducible optical standard source for measuring multimode optical fiber attenuation is required as recent
round robin measurements of such fibers at several international companies and national standards organizations showed
significant variation when using a source having only the encircled flux in the near field emerging from it defined. The
paper presents and compares the far field modal power distributions for (i) 2 km and 3 km step-index multimode Hard
Plastic Cladding Fibers, HPCF, (SI-MMF) with 200 μm silica core diameter, 0.37 numerical aperture (NA) and polymer
cladding, (ii) a 10 m silica graded-index multimode fiber (GI-MMF) with 50 μm core diameter and 0.2 NA, and (ii) a
near field Encircled Flux Mode Convertor or “modcon”. A free space method for measuring the far field using a Lightemitting
diode (LED) centered at 850 nm wavelength with 40 nm 10 dB-bandwidth and a charge-coupled device (CCD)
camera is compared with a f-theta multi-element lens based far field pattern (FFP) system. Mandrels of different
diameter and different numbers of turns of the fiber around them were used to achieve an equilibrium mode distribution
(EMD) for the GI-MMF. The paper defines encircled angular flux (EAF) as the fraction of the total optical power
radiating from a multimode optical fiber core within a certain solid angle in the far field. The paper calculates the EAF
when the solid angle increases from the far field centroid.
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An updated version of the paper with revised references has been published
The review part of the paper addresses analytical (mathematical) modeling in structural analysis in fiber optics
engineering, mostly fiber optics interconnects, and deals with optical fibers subjected to thermal and/or mechanical
loading (stresses) in bending, tension, compression, or to the combinations of such loadings. Attributes and significance
of predictive modeling are indicated and discussed. The review is based mostly on the author’s research conducted at
Bell Laboratories, Physical Sciences and Engineering Research Division, Murray Hill, NJ, USA, during his tenure with
this company, and, to a lesser extent, on his recent work in the field. The addressed structures include, but are not
limited to, optical fibers of finite length: bare fibers; jacketed and dual-coated fibers; fibers experiencing thermal
loading; fibers soldered into ferrules or adhesively bonded into capillaries; as well as the roles of geometric and material
non-linearity; dynamic response to shocks and vibrations; and possible applications of nano-materials in new generations
of coating and cladding systems. The extension part is concerned with a novel, fruitful and challenging directionprobabilistic
design for reliability (PDfR) of opto-electronic and photonic products, including optical fibers and
interconnects. The rationale behind the PDfR concept is that there is no such thing as zero probability of failure, that the
difference between a highly reliable product and an insufficiently reliable product is “merely” in the level of the never
zero probability of its failure and that when the operational performance of the product is imperative, the ability to
predict, quantify, assure and, if possible and appropriate, even specify its reliability is highly desirable. Accordingly, the
objective of the PDfR effort is to quantify the likelihood of an operational failure of a material, device or a system,
including the field of fiber optics.
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As the implementation of parallel optics continues to evolve, development of a universal coupling interface between
VCSEL/PD arrays and the corresponding photonic turn connector is necessary.
A newly developed monolithic mechanical-optical interface efficiently couples optical transmit/receive arrays to the
accompanying fiber optic connector. This paper describes the optical model behind the coupling interface and validates
the model using empirical measurements. Optical modeling will address how the interface is adaptable to the broad
range of VCSEL/PD optical parameters from commercially available VCSEL hardware manufacturers; the optical model
will illustrate coupling efficiencies versus launch specifications. Theoretical modeling will examine system sensitivity
through Monte Carlo simulations and provide alignment tolerance requirements.
Empirical results will be presented to validate the optical model predictions and subsequent system performance.
Functionality will be demonstrated through optical loss and coupling efficiency measurements. System metrics will
include characterizations such as eye diagram results and link loss measurements.
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Data communication over Polymer Optical Fibers using Wavelength Division Multiplexing, offer high extension
capabilities for the overall data rates. Here, a de/multiplexer as a key component was developed im PMMAusing an
optical grating placed on an aspheric mirror by injection molding. A demonstrator is fabricated by directly machining it
in the PMMA material by means of diamond turning technique. The paper presents the results of the different
simulations followed by the development steps and the measurements done with the first demonstrator accompanied by
the first BER measurements using a 4 channel WDM transmission The record 8.26 Gb/s data transmission based on the
offline-processed discrete multitone modulation technique has been demonstrated over 100-m SI-POF at a bit-error ratio
of 10-3.
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A 4-channel planar concave grating device with a flattened spectral response based on SU-8 polymer is presented.
The flattened spectral response is accomplished by using an optimized multi-mode interference coupler as the input
aperture of the device for spectrally separated channels. The mode field distribution in the input plane is controlled
by adjusting the width of input taper coupled to the multi-mode interference coupler. The effects of the input taper
width on the flattened spectral response are demonstrated in detail through simulation results. The devices are
realized by using an SU-8 polymer strip waveguide with a UV lithography technology. Experimental results show
that the flattened spectral response can be easily controlled by adjusting the taper width.
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Silicon photonics have emerged as a promising solution to meet the growing demand for high-bandwidth, low-latency, and
energy-efficient on-chip and off-chip communication in many-core processors. However, current silicon-photonic interconnect
designs for many-core processors waste a significant amount of power because (a) lasers are always on, even during
periods of interconnect inactivity, and (b) microring resonators employ heaters which consume a significant amount of
power just to overcome thermal variations and maintain communication on the photonic links, especially in a 3D-stacked
design. The problem of high laser power consumption is particularly important as lasers typically have very low energy
efficiency, and photonic interconnects often remain underutilized both in scientific computing (compute-intensive execution
phases underutilize the interconnect), and in server computing (servers in Google-scale datacenters have a typical utilization
of less than 30%). We address the high laser power consumption by proposing EcoLaser+, which is a laser control
scheme that saves energy by predicting the interconnect activity and opportunistically turning the on-chip laser off when
possible, and also by scaling the width of the communication link based on a runtime prediction of the expected message
length. Our laser control scheme can save up to 62 - 92% of the laser energy, and improve the energy efficiency of a manycore
processor with negligible performance penalty. We address the high trimming (heating) power consumption of the
microrings by proposing insulation methods that reduce the impact of localized heating induced by highly-active components
on the 3D-stacked logic die.
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Optical interconnects for data transmission at board level offer increased energy efficiency, system density, and
bandwidth scalability compared to purely copper driven systems. We present recent results on manufacturing of electrooptical
printed circuit board (PCB) with integrated planar glass waveguides. The graded index multi-mode waveguides
are patterned inside commercially available thin-glass panels by performing a specific ion-exchange process. The glass
waveguide panel is embedded within the layer stack-up of a PCB using proven industrial processes. This paper describes
the design, manufacture, assembly and characterization of the first electro-optical backplane demonstrator based on
integrated planar glass waveguides. The electro-optical backplane in question is created by laminating the glass
waveguide panel into a conventional multi-layer electronic printed circuit board stack-up. High precision ferrule mounts
are automatically assembled, which will enable MT compliant connectors to be plugged accurately to the embedded
waveguide interfaces on the glass panel edges. The demonstration platform comprises a standardized sub-rack chassis
and five pluggable test cards each housing optical engines and pluggable optical connectors. The test cards support a
variety of different data interfaces and can support data rates of up to 32 Gb/s per channel.
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Widespread adoption of optical circuit boards will herald substantial performance, environmental and cost benefits for
the data communications industry. Though optical circuit board technology has advanced considerably over the past
decade, commercial maturity will be gated by the availability of conformity standards to forge future quality assurance
procedures. One important prerequisite to this is a reliable test and measurement definition system, which is agnostic to
the type of waveguide system under test and therefore can be applied to different optical circuit board technologies as
well as being adaptable to future variants. A serious and common problem with the measurement of optical waveguide
systems has been lack of proper definition of the measurement conditions for a given test regime, and consequently
strong inconsistencies ensue in the results of measurements by different parties on the same test sample. We report on the
development of a new measurement identification standard to force testers to capture sufficient information about the
measurement conditions for a given optical circuit board such as to ensure consistency of measurement results within an
acceptable margin. Furthermore we demonstrate how the application of the measurement identification system can bring
about a dramatic improvement in results consistency, by comparative evaluation of the results on multimode polymer
waveguide based optical circuit test boards from a large selection of testing organisations.
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PICs for Optical Interconnects: Joint Session with Conferences 9367 and 9368
In the Information and Communications Technology (ICT) sector, the demands on bandwidth continually grow due to
increased microprocessor performance and the need to access ever increasing amounts of stored data. The introduction of
optical data transmission (e.g. glass fiber) to replace electronic transmission (e.g. copper wire) has alleviated the
bandwidth issue for communications over distances greater than 10 meters, however, the need has arisen for optical data
transfer over shorter distances such as those found inside computers. A possible solution for this is the use of low–cost
single mode polymer based optical waveguides fabricated by direct patterning Nanoimprint Lithography (NIL). NIL has
emerged as a scalable manufacturing technology capable of producing features down to the hundred nanometer scale
with the potential for large scale (roll-to-roll) manufacturing.
In this paper, we present results on the modeling, fabrication and characterization of single mode waveguides and optical
components in low-loss ORMOCER™ materials. Single mode waveguides with a mode field diameter of 7 μm and
passive structures such as bends, directional couplers and multi-mode interferometers (MMIs) suitable for use in 1550
nm optical interconnects were fabricated using wafer scale NIL processes. Process issues arising from the nano-imprint
technique such as residual layers and angled sidewalls are modeled and investigated for excess loss and higher order
mode excitation. Conclusions are drawn on the applicability of nano-imprinting to the fabrication of circuits for intrachip/
board-level optical interconnect.
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Device Coupling Approaches for Silicon Photonics Chips: Joint Session with Conferences 9367 and 9368
Based on either a SOI wafer or a bulk-silicon wafer, we discuss silicon photonic devices and integrations for chip-level
optical interconnects. We present the low-voltage silicon PICs on a SOI wafer, where Si modulators and Ge-on-Si
photodetectors are monolithically-integrated for intra-chip or inter-chip interconnects over 40 Gb/s. For future chip-level
integration, the 50 Gb/s small-sized depletion-type MZ modulator with the vertically-dipped PN-depletion-junction
(VDJ) is also presented. We report vertical-illumination-type Ge photodetectors on bulk-silicon wafers, with high
performances up to 50 Gb/s. We present the bulk-silicon platform for practical implementation of chip-level
interconnects, and the performance of the photonic transceiver silicon chip.
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As parallel optics applications continue to expand, there remains a need for an effective coupling interface between the
board-level active components and the passive components of the network. While mid-board level photonic turn
connectors are available, coupling interfaces are generally not available outside of proprietary solutions. Development of
a general mechanical-optical coupling interface opens the door for broader parallel optics implementation.
An interface for use between the optical transmitter and the photonic turn connector is introduced. The interface is a
monolithic injection molded component with an array of collimating lenses to couple efficiently with common
VCSEL/PD designs. The component has precise epoxy control features to manage epoxy bond-line thickness and
strength. Suitable UV and thermal epoxies have been qualified for effective die bond placement of the component in the
VCSEL/PD environment.
Environmental and mechanical performance of the component to industry-standard qualification requirements are
reviewed, and tensile force testing and durability results validate the mechanical characteristics of the interface.
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In on-chip optical interconnect, dielectric waveguide arrays are usually designed with pitches of a few wavelengths to
avoid crosstalk, which greatly limits the integration density. In this paper, we for the first time propose to use multipleinput
multiple-output (MIMO), a well-known technique in wireless communication, to recover the data from entangled
signals and reduce the waveguide pitch to subwavelength range. In the proposed on-chip MIMO system, there is
significant coupling among the adjacent waveguides in the high density waveguide region. In order to recover signals,
the N×N transmission matrix of N high-density waveguides is calculated to describe the relation between each input
ports and output ports. In the receiving part, homodyne coherent receivers are used to receive the transmitted signals, and
obtain the signal in phase and /2 out of phase with local oscillator. In the electrical signal processing, the inverse
transmission matrix is utilized to recover the signals in the electronic domain. To verify the proposed on-chip MIMO, we
used the INTERCONNECT package in Lumerical software to simulate a 10x10 MIMO system. The cross section of
each waveguide is 500 nm x 220 nm. The spacing is 250 nm. The simulation verifies the possibility of recovering 10
Gbps data from the heavily coupled 10 waveguides with a BER better than 10−12. The minimum input optical power for
a BER of 10−12 is greater than -18.1 dBm, and the maximum phase shift between input laser and local oscillator can
reach to 73.5˚.
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