Arbitrary Phase Responses Research Articles

Compact Multiway Plasmonic-Power-Splitters with Arbitrary Phase Responses

Compact Multiway Plasmonic-Power-Splitters with Arbitrary Phase Responses

On the Existence and Uniqueness of the Eigenvalue Decomposition of a Parahermitian Matrix

This paper addresses the extension of the factorization of a Hermitian matrix by an eigenvalue decomposition (EVD) to the case of a parahermitian matrix that is analytic at least on an annulus containing the unit circle. Such parahermitian matrices contain polynomials or rational functions in the complex variable $z$ and arise, e.g., as cross spectral density matrices in broadband array problems. Specifically, conditions for the existence and uniqueness of eigenvalues and eigenvectors of a parahermitian matrix EVD are given, such that these can be represented by a power or Laurent series that is absolutely convergent, at least on the unit circle, permitting a direct realization in the time domain. Based on an analysis of the unit circle, we prove that eigenvalues exist as unique and convergent but likely infinite-length Laurent series. The eigenvectors can have an arbitrary phase response and are shown to exist as convergent Laurent series if eigenvalues are selected as analytic functions on the unit circle, and if the phase response is selected such that the eigenvectors are Holder continuous with $\alpha >\frac{1}{2}$ on the unit circle. In the case of a discontinuous phase response or if spectral majorisation is enforced for intersecting eigenvalues, an absolutely convergent Laurent series solution for the eigenvectors of a parahermitian EVD does not exist. We provide some examples, comment on the approximation of a parahermitian matrix EVD by Laurent polynomial factors, and compare our findings to the solutions provided by polynomial matrix EVD algorithms.

Dielectric nanoresonator based lossless optical perfect magnetic mirror with near-zero reflection phase

We report an all-dielectric lossless optical mirror for the realization of controllable reflection phase based on an array of isolated dielectric nanoresonators. This dielectric mirror is comprised of a cross-shaped amorphous silicon nanoresonator array that has been designed to achieve a 99.8% reflectivity and zero reflection phase at the wavelength of 0.99 μm. The measured results from the fabricated sample match the theoretical predictions with 99.5% reflectivity and near-zero degree reflection phase at 1 μm, which is very close to the targeted wavelength. This concept and approach pave the way for synthesizing lossless artificial reflecting electromagnetic boundaries with arbitrary phase response and hold great promise in applications ranging from nanocavities to nanowaveguides and nanoantennas.

Compression of ultra-long microwave pulses using programmable microwave photonic phase filtering with > 100 complex-coefficient taps

Microwave photonic filters with arbitrary phase response can be achieved by merging high-repetition-rate electro-optic frequency comb technology with line-by-line pulse shaping. When arranged in an interferometric configuration, the filter features a number of programmable complex-coefficient taps equal to the number of available comb lines. In this work, we use an ultrabroadband comb generator resulting in a microwave photonic phase filter with >100 complex-coefficient taps. We demonstrate the potential of this filter by performing programmable chirp control of ultrawideband waveforms that extend over long (>10 ns) temporal apertures. This work opens new possibilities for compensating realistic linear distortion impairments on ultrabroadband wireless signals spanning over dozens of nanosecond temporal apertures.

Multitap microwave photonic filters with programmable phase response via optical frequency comb shaping

We present a programmable multitap microwave photonic filter with an arbitrary phase response operating over a broad bandwidth. Complex coefficient taps are achieved by optical line-by-line pulse shaping on a 10 GHz flat optical frequency comb using a novel interferometric scheme. Through high-speed real-time measurements, we demonstrate programmable chirp control of a waveform via phase filtering. This achievement enables us to compress broadband microwave signals to their corresponding bandwidth-limited pulse duration.

Finite impulse response utilizing the principle of superposition

A critical parameter in any finite impulse response (FIR) design is the impulse response length, which must be optimized for the given design specifications in order to reduce the size of the filter. To this end, many design algorithms have been introduced, such as Remez exchange, linear programming, and least mean squares. A new algorithm has been derived that is simple, efficient, and accurate for the design of arbitrary filter specifications and requires fewer computations than many other FIR approaches. This paper provides the definition of the basic functions used for the design process. An overview of the design process is given and the design technique used to design filters with tailored passband and stopband responses to yield a near-optimum time length is presented. This design can be very useful when compensating for the effects of a second transducer or other second order effects in surface acoustic wave (SAW) devices. The effects of monotonically increasing sidelobes on the impulse response length are discussed and illustrated. The addition of arbitrary phase response to the filter design process is discussed. The results of the current FIR approach are discussed and compared with other design techniques.

Weighted least-squares design and characterization of complex FIR filters

The paper presents two novel weighted least-squares methods for the design of complex coefficient finite impulse response (FIR) filters to attain specified arbitrary multiband magnitude and linear or arbitrary phase responses. These methods are computationally efficient, requiring only the solution of a Toeplitz system of N linear equations for an N-length filter that can be obtained in o(N/sup 2/) operations. Illustrative filter design examples are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Performance comparisons for nonrecursive digital filters with nonlinear phase characteristics

This letter presents a comparison between the performance, in terms of ripple and transition bandwidth, of nonrecursive digital filters with arbitrary phase characteristics and those with a linear phase response. Results are given which show that filters can be designed to have an arbitrary phase response, yet give as good a gain response as filters with linear phase.