The Domain Decomposition Method (DDM) for approximating the impact of 3DEMF effects was introduced nearly ten years ago as an approach to deliver good accuracy for rapid simulation of full-chip applications. This approximation, which treats mask edges as independent from one another, provided improved model accuracy over the traditional Kirchhoff thin mask model for the case of alternating aperture phase shift masks which featured severe mask topography. This aggressive PSM technology was not widely deployed in manufacturing, and with the advent of thinner absorbing layers, the impact of mask topography has been relatively well contained through the 32 nm technology node, where Kirchhoff mask models have proved effective. At 20 nm and below, however, the thin mask approximation leads to larger errors, and the DDM model is seen to be effective in providing a more accurate representation of the aerial image. The original DDM model assumes normal incidence, and a subsequent version incorporates signals from oblique angles. As mask dimensions become smaller, the assumption of non-interacting mask edges breaks down, and a further refinement of the model is required to account for edge to edge cross talk. In this study, we evaluate the progression of improvements in modeling mask 3DEMF effects by comparing to rigorous simulation results. It is shown that edge to edge interactions can be accurately accounted for in the modified DDM library. A methodology is presented for the generation of an accurate 3DEMF model library which can be used in full chip OPC correction.
It is noted that the fiber propagation loss is a random process
along the length of propagation. The stochastic nature of the loss
process induces a random fluctuation to the energy of the optical
signals, which, as an extra source of noise, could become
comparable to the amplified-spontaneous-emission noise of optical
amplifiers. The optical noise in random loss/gain has a quantum
origin, as a manifestation of the corpuscular nature of
electromagnetic radiation. This paper adopts the Schrodinger
representation, and uses a density matrix in the basis of photon
number states to describe the optical signals and their
interaction with the environment of loss/gain media. When the
environmental degrees of freedom are traced out, a reduced density
matrix is obtained in the diagonal form, which describes the total
energy of the optical signal evolving along the propagation
distance. Such formulism provides an intuitive interpretation of
the quantum-optical noise as the result of a classical Markov
process in the space of the photon number states. The formulism
would be more convenient for practical engineers, and should be
sufficient for fiber-optic systems with direct intensity
detection, because the quantity of concern is indeed the number of
photons contained in a signal pulse. Even better, the model admits
analytical solutions to the photon-number distribution of the
A set of nonlinear differential equations are derived from the
first principles, namely the Maxwell's equations and the material
responses to electromagnetic excitations. The derivation retains
the mathematical exactitude down to details. Still in compact and
convenient forms, the final equations include the effect of
group-velocity dispersion down to an arbitrary order, and take
into account the frequency variations of the optical loss as well
as the transverse modal function. Also established is a new
formulation of multi-component nonlinear differential equations,
which is especially suitable for the study of wide-band
wavelength-division multiplexed systems of optical communications.
The formulations are applied to discuss the problem of
compensating the optical nonlinearity of fiber transmission lines
using optical phase conjugation. Two system configurations are
identified suitable for nonlinearity compensation. One setup is
mirror-symmetric and the other translationally symmetric about the
optical phase conjugator, both being in a scaled sense.
When a Kerr medium is pumped by a strong laser beam, the nonlinear process of four-wave mixing (FWM) can mix the pump laser and a weak signal to generate a phase-conjugated version of the signal. Optical phase conjugation (OPC) may be employed to compensate the chromatic dispersion and nonlinearity of transmission fibers. It may even serve as a parametric amplifier when the pump is sufficiently intense. Furthermore, the FWM effect is capable of phase-conjugating or amplifying many wavelength-division multiplexed (WDM) signals simultaneously. However, the same FWM effect results in parasitic processes by generating inter-mixing terms among the WDM signals. The center frequency of such unwanted mixing terms may coincide with some of the original or conjugated WDM signals to cause significant interference. This paper studies such interference effect by means of theoretical calculation and computer simulation. It is shown that the coherent interference effect decreases as the pump-power to signal-power ratio (PSR) increases. Unfortunately, there could still be strong interference even with a PSR of 20dB. Some guard-band in the frequency domain is necessary to avoid such coherent interference: if the total bandwidth of the WDM signals is W, then the nearest signal should be more than W away from the pump frequency.
The optical add/drop multiplexer (OADM) is an important device in modern optical networks. Optical filters in OADMs often introduce group-velocity dispersion (GVD) and/or slope of GVD, the accumulation of which could distort the signals significantly. A computer model is built for commercial filters, accounting for the filtering gain and dispersion characteristics. When the model is incorporated into a network simulator, the filter dispersion is found to severely limit the number of OADMs that may be cascaded when transmitting 40Gb/s WDM signals with a channel spacing of 100GHz. As such high spectral efficiency difficult to achieve, the next considerations would be to transmit 40Gb/s over 200GHz channel spacing, or 10Gb/s over 50GHz channel spacing. The dispersion problem is mitigated, but still an un-negligible factor of limitation. For a large OADM network size, low-dispersion filters should be used, or a proper dispersion compensator is needed to offset the filter dispersion.
In this paper, a general model of wireless channels is established based on the physics of wave propagation. Then the problems of inverse scattering and channel prediction are formulated as nonlinear filtering problems. The solutions to the nonlinear filtering problems are given in the form of dynamic evolution equations of the estimated quantities. Finally, examples are provided to illustrate the practical applications of the proposed theory.