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A nonempty graph G is called generalized 3-distance-balanced, (3-GDB) whenever for every edge ab, |Wab|=3|Wba| or conversely. As well as a graph G is called generalized 3-nicely distance-balanced (3-GNDB) whenever for every edge ab of G, there exists a positive integer g, such that: |Wba|=gG. In this paper, we classify 3-GNDB graphs with, gG \in{1,2}., Comment: 9pages

In this paper, we design a dielectric-to-plasmonic slot waveguide mode converter based on the hybrid silicon-gold taper. The effects of mode matching, the effective index matching, and the metallic absorption loss on the conversion efficiency are studied. Consequently, a metallic taper-funnel coupler with an overall length of 1.7um is designed to achieve a very high conversion efficiency of 93.3% at 1550 nm. The configuration limitations for not allowing this mode converter to achieve a 100% conversion efficiency are also investigated. Such a high-efficiency converter can provide practical routes to realize ultracompact integrated circuits., Comment: 6 pages, 7 figures

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 V{\pi}*L=0.282Vmm 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., Comment: 12 pages, 4 figures, SPIE Photonics West Conference 2015

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., Comment: 13 pages, 7 figures, SPIE Photonics West Conference 2014

In this work, we design, fabricate and characterize a compact, broadband and highly sensitive integrated photonic electromagnetic field sensor based on a silicon-organic hybrid modulator driven by a bowtie antenna. The large electro-optic (EO) coefficient of organic polymer, the slow-light effects in the silicon slot photonic crystal waveguide (PCW), and the broadband field enhancement provided by the bowtie antenna, are all combined to enhance the interaction of microwaves and optical waves, enabling a high EO modulation efficiency and thus a high sensitivity. The modulator is experimentally demonstrated with a record-high effective in-device EO modulation efficiency of r33=1230pm/V. Modulation response up to 40GHz is measured, with a 3-dB bandwidth of 11GHz. The slot PCW has an interaction length of 300um, and the bowtie antenna has an area smaller than 1cm2. The bowtie antenna in the device is experimentally demonstrated to have a broadband characteristics with a central resonance frequency of 10GHz, as well as a large beam width which enables the detection of electromagnetic waves from a large range of incident angles. The sensor is experimentally demonstrated with a minimum detectable electromagnetic power density of 8.4mW/m2 at 8.4GHz, corresponding to a minimum detectable electric field of 2.5V/m and an ultra-high sensitivity of 0.000027V/m Hz^-1/2 ever demonstrated. To the best of our knowledge, this is the first silicon-organic hybrid device and also the first PCW device used for the photonic detection of electromagnetic waves. Finally, we propose some future work, including a Teraherz wave sensor based on antenna-coupled electro-optic polymer filled plasmonic slot waveguide, as well as a fully packaged and tailgated device., Comment: 20 pages, 16 figures

We design and demonstrate a compact, low-power, low-dispersion and broadband optical modulator based on electro-optic (EO) polymer refilled silicon slot photonic crystal waveguide (PCW). The EO polymer is engineered for large EO activity and near-infrared transparency. The half-wave switching-voltage is measured to be V{\pi}=0.97V over optical spectrum range of 8nm, corresponding to a record-high effective in-device r33 of 1190pm/V and V{\pi} L of 0.291Vmm in a push-pull configuration. Excluding the slow-light effect, we estimate the EO polymer is poled with an ultra-high efficiency of 89pm/V in the slot. In addition, to achieve high-speed modulation, silicon PCW is selectively doped to reduce RC time delay. The 3-dB RF bandwidth of the modulator is measured to be 11GHz, and a modulation response up to 40GHz is observed., Comment: 8 pages, 5 pages

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., Comment: 13 pages, 7 figures

Polymer based electro-optic modulators have shown great potentials in high frequency analog optical links. Existing commercial LiNibO3 Mach-Zehnder modulators have intrinsic drawbacks in linearity to provide high fidelity communication. In this paper, we present the design, fabrication and characterization of a traveling wave directional coupler modulator based on electro-optic polymer, which is able to provide high linearity, high speed, and low optical insertion loss. A silver ground electrode is used to reduce waveguide sidewall roughness due to the scattering of UV light in photolithography process in addition to suppressing the RF loss. A 1-to-2 multi-mode interference 3dB-splitter, a photobleached refractive index taper and a quasi-vertical taper are used to reduce the optical insertion loss of the device. The symmetric waveguide structure of the MMI-fed directional coupler is intrinsically bias-free, and the modulation is obtained at the 3-dB point regardless of the ambient temperature. By achieving low RF loss, characteristic impedance matching with 50{\Omega} load, and excellent velocity matching between the RF wave and the optical wave, a travelling wave electrode is designed to function up to 62.5GHz. Domain-inversion poling with push-pull configuration is applied using alternating pulses on a 2-section directional-coupler to achieve a spurious free dynamic range of 110dB/Hz2/3. The 3-dB electrical bandwidth of device is measured to be 10GHz., Comment: 11 pages, 12 figures, conference. "Improved performance of traveling wave directional coupler modulator based on electro-optic polymer," SPIE Photonics West, Proc. SPIE 8267, 82671B, 2012. arXiv admin note: text overlap with arXiv:1403.0134

The accelerating increase in information traffic demands the expansion of optical access network systems that require cost reduction of optical and photonic components. Low cost, ease of fabrication, and integration capabilities of low optical-loss polymers make them attractive for photonic applications. In addition to passive wave-guiding components, electro-optic (EO) polymers consisting of a polymeric matrix doped with organic nonlinear chromophores have enabled wide-RF-bandwidth and low-power optical modulators. Beside board level passive and active optical components, compact on-chip modulators (a few 100 micronmeters to a few millimeters) have been made possible by hybrid integration of EO polymers onto the silicon platform. This paper summarizes some of the recent progress in polymer based optical modulators and interconnects. A highly linear, broadband directional coupler modulator for use in analog optical links and compact, and low-power silicon/polymer hybrid slot photonic crystal waveguide modulators for on chip applications are presented. Recently, cost-effective roll-to-roll fabrication of electronic and photonic systems on flexible substrates has been gaining interest. A low-cost imprinted/ink-jet-printed Mach-Zehnder modulator and board-to-board optical interconnects using microlens integrated 45-degree mirror couplers compatible with the roll-to-roll fabrication platforms are also presented., Comment: 15 pages, 17 figures. arXiv admin note: text overlap with arXiv:1403.0134

In this paper, we present the design, fabrication and characterization of a traveling wave directional coupler modulator based on electro-optic polymer, which is able to provide both high linearity and broad bandwidth. The high linearity is realized by introducing domain-inversion technique in the two-domain directional coupler. A travelling wave electrode is designed to function with bandwidth-length product of 302GHz cm, by achieving low microwave loss, excellent impedance matching and velocity matching, as well as smooth electric field profile transformation. The 3-dB bandwidth of the device is measured to be 10GHz. The spurious free dynamic range of about 110dB Hz^(2/3) is measured over the modulation frequency range 2-8GHz. To the best of our knowledge, such high linearity is first measured at the frequency up to 8GHz. In addition, a 1-to-2 multi-mode interference 3dB-splitter, a photobleached refractive index taper and a quasi-vertical taper are used to reduce the optical insertion loss of the device., Comment: 18 pages, 12 figures

We present the design of a compact and highly sensitive electric field sensor based on a bowtie antenna-coupled slot photonic crystal waveguide (PCW). An electro-optic (EO) polymer with a large EO coefficient, r33=100pm/V, is used to refill the PCW slot and air holes. Bowtie-shaped electrodes are used as both poling electrodes and as receiving antenna. The slow-light effect in the PCW is used to increase the effective in-device r33>1000pm/V. The slot PCW is designed for low-dispersion slow light propagation, maximum poling efficiency as well as optical mode confinement inside the EO polymer. The antenna is designed for operation at 10GHz., Comment: 7 pages, 5 figures, conference. "Electric field sensor based on electro-optic polymer refilled silicon slot photonic crystal waveguide coupled with bowtie antenna," Proc. SPIE 8624, 862418 (2013)

We design and demonstrate a compact and low-power band-engineered electro-optic (EO) polymer refilled silicon slot photonic crystal waveguide (PCW) modulator. The EO polymer is engineered for large EO activity and near-infrared transparency. A PCW step coupler is used for optimum coupling to the slow-light mode of the band-engineered PCW. The half-wave switching-voltage is measured to be V{\pi}=0.97+-0.02V over optical spectrum range of 8nm, corresponding to the effective in-device r33 of 1190pm/V and V{\pi} L of 0.291+-0.006V mm in a push-pull configuration. Excluding the slow-light effect, we estimate the EO polymer is poled with an efficiency of 89pm/V in the slot., Comment: 4 pages, 4 figures