Abstract
We note that the self-similar waves recently reported, in a tapered graded-index waveguide, severely suffer from extreme increase in the amplitude, after traversing a finite distance. In this work, we theoretically described that by adding a suitable homogeneous background in the expression for widths of the self-similar solutions which is achievable through the modulation of tapering profile, we could avert this situation. We further find that the self-similar waves propagate in the nonlinear waveguide, quite a distance stably, albeit they undergo self-compression.
Highlights
Inspiralling compact binaries containing spinning black holes (BHs) are plausible sources for the network of second generation gravitational wave (GW) detectors like the advanced LIGO, advanced Virgo, KAGRA, GEO-HF and the planned LIGO-India [1]
GW frequency and associated phase evolution, crucial inputs to compute h×,+(t), are known to 3.5PN order for non-spinning compact binaries [3] whereas the amplitudes are available to 3PN order [4]
GW frequency evolution and amplitudes of h×,+(t) for maximally spinning BH binaries are fully determined to 2.5PN and 2PN orders, respectively, while incorporating all the relevant spin induced effects [6, 8]
Summary
Inspiralling compact binaries containing spinning black holes (BHs) are plausible sources for the network of second generation gravitational wave (GW) detectors like the advanced LIGO (aLIGO), advanced Virgo, KAGRA, GEO-HF and the planned LIGO-India [1]. An attractive feature of this convention is its ability to remove all the spin precession induced modulations from the orbital phase evolution. This allows one to express the orbital phase Φp(t) as an integral of the orbital frequency ω(t), namely Φp(t) = ω(t) dt. In this convention, the inspiral waveform from precessing binaries can be written as the product of a non-precessing carrier waveform and a modulation term that contains all the precessional effects. We present our L-based precessing convention and explore its data analysis implications in the later section
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