This book contains 500 problems that range over a wide spectrum of areas of high school mathematics and levels of difficulty. Some are simple mathematical puzzlers while others are serious problems ...at the Olympiad level. Students of all levels of interest and ability will be entertained and taught by the book. For many problems, more than one solution is supplied so that students can see how different approaches can be taken to a problem and compare the elegance and efficiency of different tools that might be applied.
The maximum photocurrent, power dissipation, and linearity of waveguide photodiodes are limited by the length over which the input optical power is absorbed. This absorption length is determined by ...the absorption coefficient of the absorbing layer material (α o ), the optical confinement factor (Γ), and the excess loss coefficient (α i ). In this paper, we analyze the fundamental limits to maximizing the absorption length and demonstrate a new waveguide photodiode structure that approaches these limits. The new structure is referred to as a slab-coupled optical waveguide photodiode (SCOWPD) and is realized in the InGaAsP/InP material system. Assuming 100% coupling efficiency, the SCOWPD has an ultralow optical confinement factor and a low excess loss coefficient, both calculated from measurements, of Γ = 0.069% and α i = 1.65 cm -1 , respectively. This results in a 1/ e absorption length of 2.1 mm. The SCOWPD exhibits an external responsivity of 0.8 A/W and a maximum photocurrent of 250 mA at a wavelength of 1.55 μm.
Chakerian and Klamkin present a mathematical theory regarding three-point characterization of central symmetry. They stress that if T is a triangle inscribed in a centrally symmetric curve C in ...Euclidean two-space E2, then there always exists some translate of the central reflection of T that is inscribed in C.
As datacenters continue to scale in size, energy efficiency for short reach (<; 2 km) links is a major factor for networks that may connect hundreds of thousands of servers. We demonstrate that links ...based on analog coherent detection (ACD) offer a promising path to simultaneously achieving significantly larger link budgets and improved link energy efficiency. A complete analysis is presented that considers the power consumption of all the photonic and electronic components necessary to realize an ACD link architecture based on 50 Gbaud (GBd) quadrature phase-shift keying (QPSK) signaling combined with polarization multiplexing to achieve 200 Gb/s/λ. These links utilize receivers that incorporate an optical phase-locked loop (OPLL) to frequency- and phase-lock the local oscillator (LO) laser to the incoming signal. QPSK modulation offers compelling advantages both in achievable link budget and in energy efficiency. Indeed, low-complexity electronics based on limiting amplifiers can be used as opposed to the linear front-ends, A/D converters, and digital signal processing (DSP) required for higher-order QAM or PAM formats. Our analysis indicates that links with 13 dB of unallocated budget operating at error rates of <; 10 -12 can be achieved and is compatible with higher error rates that require forward error correction (FEC). We present a comparison of silicon and InP platforms and evaluate both traveling-wave and segmented modulator designs, providing an illustration of the wide design space before converging on the most promising architectures that maximize energy efficiency and minimize laser power. We establish the theoretical potential to achieve picojoule-per-bit energy efficiency targets.
In this paper, we present a coherent receiver based on an optical phase-locked loop (PLL) for linear phase demodulation. The receiver concept is demonstrated at low frequency. For high-frequency ...operation, monolithic and hybrid integrated versions of the receiver have been developed and experimentally verified in an analog link. The receiver has a bandwidth of 1.45 GHz. At 300 MHz, a spurious free dynamic range (SFDR) of 125 dB ldr Hz 2/3 is measured.
Uni-traveling-carrier waveguide photodiodes (PDs) with variable optical confinement mode size transformers are demonstrated. For these waveguide PDs, the optical mode is large at the input for ...minimal front-end saturation. The mode transforms as the light propagates so that the absorption profile is optimized for both high-power and high-speed performance.
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