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This PDF file contains the front matter associated with SPIE Proceedings Volume 6476, including the Title Page, Copyright information, Table of Contents, Introduction (if any), and the Conference Committee listing.
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Silicon Photonics is experiencing a significant increase in interest due to emerging applications and several high profile
successes in device and technology development. One of the most prominent trends in silicon photonics recently has
been a trend towards miniaturising waveguides. The shrinking of the device dimensions provides advantages in terms of
cost and packing density, modulation bandwidth, improved performance in resonant structures, and an increase in
optical power density within the devices. In this paper we analyse several silicon photonics devices based on both small
rib and strip waveguides. We have previously reported on issues related to single mode propagation and polarisation
independence of silicon waveguides, and produced design rules for such small waveguides that are reviewed here. We
have previously reported a modulator based on a small rib waveguide with the height of < 500nm for high speed
operation. However, in this paper we consider slightly larger designs to accommodate polarisation independence.
Finally we discuss the characteristics of ring and racetrack resonators based on both rib and strip waveguides and
methods of improving free spectral range whilst considering polarization effects, and the difficulty in coupling to such
strip waveguide based devices. Both theoretical and experimental results are presented. The maximum free spectral
range that we have demonstrated experimentally is approximately 43nm.
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While silica waveguide PLC products have been deployed in various systems and applications, hybrid
integration of semiconductor opto-electronic devices on silica-based planar lightwave circuit (PLC) has become
the mainstream platform for small form factor, low-cost and high volume integrated transceiver modules. One
of the main benefits of hybrid integration is the wafer-scale process, which greatly reduces chip/module size
and assembly cost. This paper reviews the development of this technology, and as an example, presents a
hybrid integrated transmitter with four wavelengths on silica PLC chip for LX4 and 10GbE applications.
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We review the different optoelectronic component and module technologies that have been developed for use in ROADM subsystems, and describe their principles of operation, designs, features, advantages, and challenges. We also describe the various needs for reconfigurable optical add/drop switching in agile optical networks. For each network need, we present the different ROADM subsystem architecture options with their pros and cons, and describe the optoelectronic technologies supporting each architecture.
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We have experimentally studied the electrical and optical properties of a silicon microsphere with a radius of 500 microns and a refractive index of 3.48 in the near-infrared. The silicon microsphere shows an MSM Schottky diode behavior. The morphology dependent resonances are spaced by 0.2 nm, which correlates well with the estimated mode spacing. The silicon microsphere heralds the way for a novel family of active microphotonic devices.
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We report our latest experimental and numerical work on silicon microresonator passive and electro-optic active devices.
On the passive device front, we demonstrate an electrically tunable silicon microring notch filter for converting 3.6-Gbps
non-return-to-zero (NRZ) data format to return-to-zero (RZ)-like data format. We show that the converted RZ-like data
quality highly depends on the notch filter extinction ratios. On the active device front, we demonstrate a silicon
microring modulator using a double-coupled U-bend waveguide as a feedback and a pair of laterally integrated injectiontype
p-i-n diodes for bias/signal modulation. We show that the microring modulator extinction ratios are electrically
controlled by applying a DC-bias across either the feedback-waveguide or the microring while applying a modulation
signal across the other p-i-n diode. We also propose silicon microdisk modulators with selectively integrated depletiontype
Schottky diodes. Our numerical simulations suggest that the microdisk structures can be advantageous compared
with microring structures. We show that electrical rise time on the order of a few ps is feasible using microdisks. We
also allude to on-going work on extending the microresonator devices discussed here to building functional silicon
optoelectronics integrated circuits.
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Optical technology plays an increasingly important role in numerous applications areas, including communications, information processing, and data storage. However, as optical technology develops, it is evident that there is a growing need to develop reliable photonic integration technologies. This will include the development of passive as well as active optical components that can be integrated into functional optical circuits and systems, including filters, switching fabrics that can be controlled either electrically or optically, optical sources, detectors, amplifiers, etc. We explore the unique capabilities and advantages of nanotechnology in developing next generation integrated photonic chips. Our long-range goal is to develop a range of photonic nanostructures including artificially birefringent and resonant devices, photonic crystals, and photonic crystals with defects to tailor spectral filters, and nanostructures for spatial field localization to enhance optical nonlinearities, to facilitate on-chip system integration through compatible materials and fabrication processes. The design of artificial nanostructured materials, PCs and integrated photonic systems is one of the most challenging tasks as it not only involves the accurate solution of electromagnetic optics equations, but also the need to incorporate the material and quantum physics equations. Near-field interactions in artificial nanostructured materials provide a variety of functionalities useful for optical systems integration. Recently, the inclusion of surface plasmon photonics in this area has opened up a host of new possibilities Finally and most importantly, nanophotonics may enable easier integration with other nanotechnologies: electronics, magnetics, mechanics, chemistry, and biology. We will address some of these areas in this paper.
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We present an overview of our work on the design and fabrication of micro/nano-scale photonic circuits and
networks on what we call "optical printed circuit boards" (O-PCBs) and "VLSI photonic integrated circuit
chips"(VLSI-PICs) of generic and application-specific nature. The O-PCBs and photonic chips consist of
2-dimensional planar arrays of optical wires, circuits, and networks of micro/nano-scale to perform the functions
of sensing, storing, transporting, processing, switching, routing, and distributing optical signals on flat
boards or chips. We describe and discuss scientific and technological issues concerning the miniaturization,
interconnection and integration of micro/nano-scale photonic devices, circuits, and networks leading to small
and very large scale integration in terms of photonic scaling rules and discuss their use for the design and fabrication
of the photonic integrated circuits and networks. Design rules for the miniaturization and integration of
the micro/nano-photonic systems are discussed in comparison with those of the micro/nano-electronic systems.
Materials include polymer/organic materials and silicon materials. Structural bases include photonic crystals,
ring resonators, and plasmonic structures. Compatibility issues between diverse materials and devices are
discussed especially in regard to applications. Recent progresses and examples are presented.
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This paper would like to discuss a self-imaging phenomenon in a multimode interference (MMI) coupler. From experiment, different self-images, which are undefined in MMI theory, are observed. These undefined self-images are named 'extraneous self-images' (Ex_SI) out of convenience. In order to estimate the applicability of the Ex_SI, the characteristics of both the 0-dB self-images (SI), which is defined in MMI theory, and the Ex_SIs are compared and analyzed through simulation and experiment. The results show that the Ex_SI has an imaging period that is the same as the 0-dB SI and that the excess loss and the extinction ratio of the Ex_SI improve more than that of the 0-dB SI, as the imaging period increases. Also, this paper introduces the wavelength multiplexer (MUX) for the wavelengths of 1310 nm and 1550 nm using the Ex_SI phenomenon. The optimum length of the multimode waveguide, with a width of 18 microns, is confirmed as a 3670 um wavelength MUX. For wavelengths of 1310 nm and 1550 nm, the excess losses are measured as -0.4 dB and -0.45 dB, respectively, while the extinction ratios are measured as 16.9 dB and 19.7 dB, respectively.
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Broadband reflection mirror is an important optical device to make a wide resonance bandwidth of the multi-wavelength
fiber laser cavity including fiber Bragg grating mirrors. Though a chirped fiber Bragg grating has been used for
broadband reflection mirror device, it still requires more improvements in the control of reflection wavelength
bandwidth and reflection ratio, which are key design parameters of broadband reflection mirror. In this research, we
propose an integrated mirror circuit based on polarization-maintaining fiber Sagnac loop interferometer to utilize for
tunable resonance cavity of fiber laser with semiconductor optical amplifier. It is available to control both resonance
bandwidth by varying the length of polarization-maintaining fiber and reflection ratio by tuning the polarization state of
Sagnac loop. Broad resonance bandwidth of 40 nm could be obtained from Sagnac mirror with thes 0.15 m length of
polarization-maintaining fiber.
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This paper presents a transimpedance amplifier (TIA) with the logarithmic compression of the input current
signal. The presented TIA has two regions of operation: a linear one for small input current signals and a compression
one for high input currents, that could otherwise saturate the TIA. The measured -3dB bandwidth in
the linear region of operation is 102MHz. The measured maximum input current overdrive is 20.5mA. However,
the maximum of the monotonic compression is approx. 8mA. Using the compression technique we could achieve
low rms equivalent input noise current (~20.2nA) within the measured bandwidth and with approx. 2pF capacitance
at the input. Thus the dynamic range at the input of the TIA is approx. 120dB considering the maximal
current overdrive. The proposed TIA represents the input stage of a optical receiver with integrated differential
50&OHgr; output driver. The optical receiver occupies approx. 1.24mm2 in 0.35 &mgr;m SiGe BiCMOS technology and
consumes 78mA from 5V supply.
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We developed a CMOS-based trans-impedance amplifier (TIA) circuits for analog optical
communication systems. Our TIA structure is based on common-source configuration and a novel functional
active load (FAL). Proposed FAL structure is composed the two PMOSs that have the symmetric structure. In
those schemes, transfer curve of TIA can be tuned by the gate voltage of FAL in the way to improve linearity.
In analog optical transceiver, TIA employing the FAL can suppress the nonlinearity originated from various
sources. Because the nonlinearity deteriorate analog communication systems, enhancement of linearity is
crucial to improve the analog transceiver performances. In this work, we have designed the TIA with FAL in a
0.18 &mgr;m CMOS technology. The linearity of TIA is controlled by the variation of transfer curve with the
change of the FAL bias voltage. As of the simulation results, the IIP3 level of the TIA employing FAL is
enhanced by about 3.393 dB with the Vg variation in FAL.
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Quantum key distribution (QKD) can produce secure cryptographic key for use in symmetric cryptosystems. By adopting clock-recovery techniques from modern telecommunications practice we have demonstrated a free-space quantum key distribution system operating at a transmission rate of 625 MHz at 850 nm. The transmission rate of this system is ultimately limited by the timing resolution of the single-photon avalanche photodiodes (SPADs), and we present a solution to take advantage of SPADs with higher timing resolution that can enable repetition rates up to 2.5 GHz. We also show that with high-repetition-rate sub-clock gating these higher-resolution SPADs can reduce the system's exposure to solar background photons, thus reducing the quantum-bit error rate (QBER) and improving system performance.
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Quantum communications is fast becoming an important component of many applications in quantum information
science. Sharing quantum information over a distance among geographically separated nodes using photonic qubits
requires a reconfigurable transparent networking infrastructure that can support quantum information services. Using
quantum key distribution (QKD) as an example of a quantum communications service, we investigate the ability of fiber
networks to support both conventional optical traffic and single-photon quantum communications signals on a shared
infrastructure. The effect of Raman scattering from conventional channels on the quantum bit error rate (QBER) of a
QKD system is analyzed. Additionally, the potential impact and mitigation strategies of other transmission impairments
such as four-wave mixing, cross-phase modulation, and noise from mid-span optical amplifiers are discussed. We also
review recent trends toward the development of automated and integrated QKD systems which are important steps
toward reliable and manufacturable quantum communications systems.
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OEIC Integration, Packaging and Interconnects I - Joint Session with Conference 6478
One of the grand challenges in solving the interconnection bottlenecks at the Printed Circuit Board (PCB) and
Multi-Chip-Module (MCM) level, is to adequately replace the PCB and intra-MCM galvanic interconnects with
high-performance, low-cost, compact and reliable micro-photonic alternatives. Therefore we address the following
components in this paper: 1) out-of-plane couplers for optical waveguides embedded in PCB, 2) peripheral fiber
ribbons and two-dimensional single- and multimode fiber connectors for high-speed parallel optical connections,
and 3) intra-MCM level optical interconnections via free-space optical modules.
For the fabrication of these micro-optical interconnect modules, we are focusing at the Vrije Universiteit
Brussel on the continuous development of a rapid prototyping technology, which we call Deep Proton Writing
(DPW). The special feature of this prototyping technology is that it is compatible with commercial low-cost
mass replication techniques such as micro injection moulding and hot embossing. Laser ablation is used at
Ghent University for the fabrication of PCB-embedded waveguides and integrated micro-mirrors. The main
advantage of this technology is that it is compatible with present-day PCB manufacturing.
For the free-space MCM-level optical interconnect module, we furthermore give special attention to the
optical tolerancing and the opto-mechanical integration of the components. We use both a sensitivity analysis to
misalignment errors and Monte Carlo simulations. It is our aim to investigate the whole component integration
chain from the optoelectronic device to the micro-opto-mechanical components constituting the interconnect
module.
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We report on the fabrication of a flexible optical interconnection module that has been incorporated as a part
of an optical printed circuit board (O-PCB). Optical waveguide arrays are fabricated on flexible polyethylen
terephthalate (PET) substrate by UV embossing technology. Electrical layers carrying vertical cavity surface
emitted laserdiode (VCSEL) and photodiode (PD) array are attached to the optical layer. We measured optical
losses of the flexible waveguide arrays bent over various curvatures and characterized transmission
performances of the flexible optical PCB (FO-PCB) module. FO-PCB performed high speed optical
interconnection between chips over four waveguide channels up to 7.5Gbps on each.
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OEIC Integration, Packaging and Interconnects II - Joint Session with Conference 6478
Recently a number of successful freespace
chip-to-chip and board-to-board optical
interconnects have been demonstrated. Here we
present some of the results that can be derived as a
result of this work.
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The idea of applying the two-photon 3D lithography (2P-3DL) to an industrial printed wiring board (PWB) fabrication
process is quite pioneering. Taking advantage of the unique rapid prototyping properties of 2P-3DL--its particularly
inherent true 3D capability and its high flexibility in processing- this lithographic method can be adapted and optimized
concerning the direct laser-writing of integrated optical interconnects with tens of microns in diameter. This will push
the method forward towards industrial fabrication of next generation PWBs with integrated optical layers, and put it on
the leading edge of printed circuit board (PCB) technology.
In this context, the concept of a direct laser-written embedded waveguide is based on the local increase of the refractive
index of the exposed material, which is triggered by two-photon absorption (TPA) at the laser focus. The laser induced
refractive index difference forms the core of the waveguide, whereas the unexposed surrounding material forms the
cladding. Thus, only one optical material is required to form the waveguide using true 3D lithographic process
compared to other devices, which significantly simplifies processes. The material is subject to stringent requirements
concerning the PWB production process: beside its high refractive index change, a low optical loss of the fabricated
optical interconnect is required. The integration of the waveguide into the volume of the material also requires thick
films up to 500 microns on the PWB substrate, and the material has to withstand the complete PWB fabrication process,
where the board is chemically treated and exposed to high temperatures as well as high pressure during the lamination
processes of subsequent metal layers.
For this application, an inorganic-organic hybrid polymer (ORMOCER) film is applied, casted onto a PWB substrate,
and the two-photon 3D lithography system parameters and optics are tuned such that waveguides with a diameter of
approx. 30 microns can be inscribed. The board is equipped with laser- and photodiodes, which are totally covered by the
thick ORMOCER film. The integration of the waveguide in such a preconfigured board requires precise 3D
registration of the sample prior to the waveguide writing in order to align the waveguide relative to the optoelectronic
components. By means of the 3D registration, the waveguide alignment is an inherent part of the fabrication process.
The 3D capabilities of the 2P-3DL permit not only the fabrication of single embedded waveguides with a simple
geometry, but also more complex waveguide structure (e.g. bundles) with largely arbitrary waveguide configurations.
In this paper, we present the development and realization of the two-photon 3D lithography for the fabrication of
integrated optical interconnects on PWBs. The ultimate goal of this approach is the large-scale fabrication of leadingedge
PWBs with an integrated optical layer for additional functionality. The functioning of the fabricated and embedded
waveguides is demonstrated by measurements of the essential parameters of such an optoelectronic system
(photocurrent, optical loss, throughput, etc).
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Free-space optical communications has recently been touted as a solution to the "last mile" bottleneck of high speed data networks providing highly secure, short to long range, and high bandwidth connections. However, commercial near infrared systems experience atmospheric scattering losses and scintillation effects which can adversely affect a link's uptime. By moving the operating wavelength into the mid or long wavelength infrared enhanced link uptimes and increased range can be achieved due to less susceptibility atmospheric affects. The combination of room temperature, continuous wave' high power quantum cascade lasers and high operating temperature type II superlattice photodetectors offers the benefits of mid and long wavelength infrared systems as well as practical operating conditions.
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We report development activities towards realization of fully integrated 1×2, 2×2 and 4×4 cross-point optical switches
for WDM-packet based data networking. Two enabling technologies, quantum well intermixing and etched turning
mirrors, are developed and demonstrated in InGaAs/InAlGaAs InP-based material at a wavelength of 1.55 &mgr;m. We
describe the use of both technologies to fabricate switch chips with different port counts.
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A novel Q-modulation scheme for high-speed modulation of semiconductor laser is presented. The modulator
consists of an anti-resonant Fabry-Perot cavity acting as a rear reflector of the laser. The change of the absorption
coefficient in the modulator results in a change in the Q-factor of the laser, and consequently the lasing threshold and
output power. Static and small-signal dynamic simulation results are presented, demonstrating its operating principle
and distinct characteristics. The monolithically integrated Q-modulated laser (QML) has potential advantages of high
speed, high extinction ratio, low wavelength chirp and high power efficiency.
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Authors report the demonstration of the emission wavelength tuning of InAs quantum-dashes within InAlGaAs
quantum-wells grown on InP substrate, that gives the initial wavelength emission at ~1.65 &mgr;m. The impurity-free
dielectric cap annealing and the nitrogen ion-implantation induced intermixing techniques have been implemented to
spatially control the group-III intermixing in the structure, which produces differential bandgap shift of 80 nm and 112
nm, respectively. Transmission electron microscopy, optical and electrical characterizations have been performed to
evaluate the quality of the intermixed QD material and bandgap tuned devices. Compared to the control (nonintermixed)
lasers, the light-current characteristics for the over 125 nm wavelength shifted QD lasers are not
significantly changed suggesting that the quality of the intermixed material is well-preserved. The intermixed lasers
exhibit the narrow linewidth as compared to the as-grown due to the improved QD homogeneity. The integrity of the QD
material is retained after intermixing suggesting the potential application for the planar integration of multiple
active/passive QD-based devices on a single InP chip.
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This paper reports on a fabrication method of 45°-mirror-ended polymer waveguide using single-step UV embossing
technique. This technique allows us to fabricate an array of twelve channel multimode polymer waveguides having 45°-
mirrors during single-step UV embossing process. For the embossing process we have used a 45°-ended silicon
waveguide mold. The silicon waveguide mold has a 45° slope prefabricated at the end of each waveguide structure.
With this mold, UV embossing is performed to form undercladding and 45° mirror structures simultaneously. And a
metal film is coated on the surface of the 45° slope. And then, core polymer is filled and cured by UV irradiation. By
using this method, small size of micro mirror structures can be formed during waveguide fabrication process and
fabrication steps can be reduced.
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This paper introduces the novel 1 × 3 wavelength multiplexer (MUX) using the extraneous self-imaging (Ex_SI)
phenomenon, which is not mentioned in multimode interference (MMI) theory. The Ex_SI phenomenon in silica-based
multimode waveguides is experimentally studied, and then with data for the Ex_SI phenomenon, the wavelength MUX
for the wavelengths of 1310 nm, 1490 nm and 1550 nm is developed. The novel 1 × 3 wavelength MUX is consisted of
cascaded two multimode waveguides which have the same width of 18 &mgr;m. For wavelengths of 1310 nm, 1490 nm and
1550 nm, the excess losses are measured as -1.37 dB, -0.63 dB and -1.10 dB, respectively, while the extinction ratios are
measured as 15.93 dB, 24.28 dB and 15.66 dB, respectively.
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We have demonstrated a novel bio-signal processing technique with hybrid bio-systems using an optical microcavity
ring resonator. The intensity of the transmitted light through the ring resonator has a periodic and sensitive region
depending on the wavelength of the incident light into the ring resonator. It is possible to detect biomolecules with the
ring resonator, because the resonance profile is shifted by refractive index changes due to an amount of biomolecules on
the surface of sensing areas. Our processing technique is based on using dual-wavelength. In this scheme, high accuracy
can be achieved by comparing the intensity of two incident lights which has channel spacing of the half period of the
sensitive region. More detailed experimental results on a novel bio-signal processing technique will be presented.
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We fabricated an arrayed waveguide grating (AWG) demultiplexer for optical fiber communication systems and
photonic integrated circuits. We also used an embossing technique to fabricated the AWG instead of traditional
semiconductor technologies, such as photolithography and etch process. UV curable polymers (ZPU 12-47 and ZPU 12-
45) were used as the core and upper cladding layers. The polydimethylsiloxane (PDMS) mold used for the embossing
process is manufactured by a photoresist structure formed on a silicon wafer. We tried the embossing onto a fused silica
glass using the PDMS mold. After UV curing, the PDMS mold was peeled away carefully, and a pattern of the AWG
demultiplexer was left on the surface of that substrate. The upper cladding layer was coated over the patterned structure.
The fabrication of the AWG demultiplexer was completed by a cleaving process. The residual layer produced after an
embossing process was adjusted by the volume of polymer droplet. The embossing technique will have the potential for
broad applications in fabrication of photonic devices.
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Nanoporous polymer films were prepared by using surfactant as porogen in order to be used as optical waveguides. We
prepared porous polymer films by spin-coating of PMMA solutions containing surfactant (NaDDBS) at concentrations
higher than the critical micelle concentration (CMC). The pore structure of the films was affected by such factors as the
type of the pore generator (porogen) and solvent, the molecular weight of the polymer, and processing parameters. After
removal of NaDDBS, the nanoporous structure was observed via FE-SEM. Since the resulting pore size is much smaller
than the wavelength of the visible light, the nanoporous thin films were optically homogeneous. The refractive index was
given by an average over the film, and it was controlled by changing the amount of the surfactant in the film. The
refractive index of the nanoporous polymer film was found to decrease with the increase in the pore volume ratio.
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We propose and demonstrate a photonic crystal optical group delay device, in which two dimensional photonic crystal line
defect waveguide with chirped hole, induces sequential optical group delays for time-spreading/wavelength-hopping optical
code division multiple access (O-CDMA). The photonic crystal line defect waveguide allows ultrasmall size of device due to
its strong optical confinement by the photonic bandgap. And chirped photonic crystal waveguides, in which radius of holes are
gradually changed so that the photonic bands are smoothly shifted to the higher frequency side. When a short pulse signal with
a wide spectrum comes into this device, the guided light is localized at specific position depending on wavelength. This
concept is suitable to realize a pulse waveform synthesizer and an en/decoder for time-spreading/wavelength-hopping O-CDMA.
We have confirmed that this device has a chromatic temporal dispersion of ~ 33-fs/nm, corresponding to the repetition
rate of ~ 1-ps for pulses with wavelength-interval of 30-nm, by two dimensional finite difference time domain simulation.
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A polymer waveguide grating coupler to vertically couple light between planar waveguide and fiber is proposed and
designed. In order to estimate the coupling performance of the proposed coupler with curved and chirped grating, the
diffraction characteristics of the waveguide grating with a uniform period as an in/out out-of-plane coupler are
investigated. The coupling efficiency and coupling length exhibiting the diffraction characteristics of a uniform
waveguide grating with various structure parameters are calculated based on Bloch-wave analysis. With the optimized
structure parameters showing the high coupling performance, the overall coupling efficiency of the polymer waveguide
grating coupler is obtained by introducing 2D Bloch-wave analysis-based local linear grating model. The calculated
overall coupling efficiency of the coupler is determined to be approximately 30%.
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Nano-pattering process by low-voltage electron beam lithography based on microcolumn with beam energy of 500 eV
has been developed. Low kV exposure provides the advantages of high sensitivity, reduced charging, and a lack of
proximity and heating effects. However a low-voltage electron beam has very thin penetration range. At 500 V, the
penetration range is less than 20 nm, while typical resist thickness is > 200 nm. A resist process with bilayer scheme, 17
nm-thick PMMA resist on 100 nm-thick SiO2 layer, and wet etch method was demonstrated for 250 nm line patterns
transfer to Si substrate. The process was applied to fabricate periodic grating patterns on a silicon substrate. The results
of nano-pattern process by low energy microcolumn lithography will be discussed in detail.
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We report numerically analyzed results on various parameters of planar-type long period waveguide gratings
(LPWGs) for potential temperature-insensitive refractive index sensor applications. The LPWGs based on polymer
materials can be low cost mass-produceable devices because they can be fabricated in a wafer-level process with a
typical imprinting technology and can be integrated with other multi-functional photonic devices of planar type such as
optical printed circuit board (O-PCB). We have designed a temperature insensitive long-period waveguide grating by
using a 4-layer waveguide structure which consists of a silica substrate, polymer core and clad layers, and the upper clad
layer for materials or analytes to be tested. Our numerical calculation show that there are optimized conditions on the
thermo-optic coefficients of the core polymer materials for a temperature-independent LPWGs with given core and clad
polymer materials as well as with the given waveguide dimensions. The maximum temperature range and the refractive
index sensitivity of the temperature-independent LPWGs have been also calculated for several conditions of the
waveguide parameters.
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