7 research outputs found
Geometric manipulation of light : from nonlinear optics to invisibility cloaks
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 189-203).In this work, we study two different manipulations of electromagnetic waves governed by macroscopic Maxwell's equations. One is frequency conversion of such waves using small intrinsic material nonlinearities. We study conversion of an input signal at frequency w1 to frequency Wk due to second or third harmonic generation or four-wave mixing using coupled-mode theory. Using this framework, we show there is a critical input power at which maximum frequency conversion is possible. We study in depth the case of third harmonic generation, its solutions, and their stability analysis. Based on the dynamics of the system, we propose a regime of parameters that 100%- efficient frequency conversion is possible and propose a way of exciting this solution. We also look at same analysis for the case of degenerate four-wave mixing and come up with 2d and 3d designs of a device that exhibits high-efficiency second-harmonic generation. Second, we consider proposals for invisibility cloaks to change the path of electromagnetic waves in a certain way so that the object appears invisible at a certain frequency or a range of frequencies. Transformation-based invisibility cloaks make use of the coordinate invariance of Maxwell's Equations and require complex material configuration e and p in the cloak. We study the practical limitations of cloaking as a function of the size of the object being cloaked. Specifically, we study the bandwidth, loss, and scattering limitations of cloaking as the object gets larger and show that cloaking of objects many times larger than the wavelength in size becomes practically impossible.by Hila Hashemi.Ph.D
Degenerate four-wave mixing in triply-resonant Kerr cavities
We demonstrate theoretical conditions for highly-efficient degenerate
four-wave mixing in triply-resonant nonlinear (Kerr) cavities. We employ a
general and accurate temporal coupled-mode analysis in which the interaction of
light in arbitrary microcavities is expressed in terms a set of coupling
coefficients that we rigorously derive from the full Maxwell equations. Using
the coupled-mode theory, we show that light consisting of an input signal of
frequency can, in the presence of pump light at
, be converted with quantum-limited efficiency into an output shifted
signal of frequency , and we derive expressions for
the critical input powers at which this occurs. We find that critical powers in
the order of 10mW assuming very conservative cavity parameters (modal volumes
cubic wavelengths and quality factors . The standard
Manley-Rowe efficiency limits are obtained from the solution of the classical
coupled-mode equations, although we also derive them from simple
photon-counting "quantum" arguments. Finally, using a linear stability
analysis, we demonstrate that maximal conversion efficiency can be retained
even in the presence of self- and cross-phase modulation effects that generally
act to disrupt the resonance condition.Comment: 13 pages, 8 figures. To appear in Physical Review
Delay-bandwidth and delay-loss limitations for cloaking of large objects
Based on a simple model of ground-plane cloaking, we argue that the diffculty
of cloaking is fundamentally limited by delay-loss and delaylbandwidth/size
limitations that worsen as the size of the object to be cloaked increases
relative to the wavelength. These considerations must be taken into account
when scaling experimental cloaking demonstrations from wavelength-scale objects
towards larger sizes, and suggest quantitative material/loss challenges in
cloaking human-scale objects.Comment: 4 pages, 2 figure
General scaling limitations of ground-plane and isolated-object cloaks
We prove that, for arbitrary three-dimensional transformation-based
invisibility cloaking of an object above a ground plane or of isolated object,
there are practical constraints that increase with the object size. In
particular, we show that the cloak thickness must scale proportional to the
thickness of the object being cloaked, assuming bounded refractive indices, and
that absorption discrepancies and other imperfections must scale inversely with
the object thickness. For isolated objects, we also show that bounded
refractive indices imply a lower bound on the effective cross-section.Comment: 7 pages, 3 figure
Nonlinear harmonic generation and devices in doubly-resonant Kerr cavities
We describea theoretical analysis of the nonlinear dynamics of third-harmonic
generation () via Kerr (\chithree) nonlinearities in a
resonant cavity with resonances at both and . Such a doubly
resonant cavity greatly reduces the required power for efficient harmonic
generation, by a factor of where is the modal volume and
is the lifetime, and can even exhibit 100% harmonic conversion efficiency at a
critical input power. However, we show that it also exhibits a rich variety of
nonlinear dynamics, such as multistable solutions and long-period limit
cycles.We describe how to compensate for self/cross-phase modulation (which
otherwise shifts the cavity frequencies out of resonance), and how to excite
the different stable solutions (and especially the high-efficiency solutions)
by specially modulated input pulses.Comment: 12 pages, 12 figure
Diameter-bandwidth product limitation of isolated-object cloaking
We show that cloaking of isolated objects using transformation-based cloaks is subject to a diameter-bandwidth product limitation: as the size of the object increases, the bandwidth of good (small-cross-section) cloaking decreases inversely with the diameter, as a consequence of causality constraints even for perfect fabrication and materials with negligible absorption. This generalizes a previous result that perfect cloaking of isolated objects over a nonzero bandwidth violates causality. Furthermore, we demonstrate broader causality-based scaling limitations on any bandwidth-averaged cloaking cross section, using complex analysis and the optical theorem to transform the frequency-averaged problem into a single-scattering problem with transformed materials.United States. Army Research Office. Institute for Soldier Nanotechnologies (contract no. W911NF-07-D-0004)United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (grant no. FA9550-09-1-0704
High-efficiency second-harmonic generation in doubly-resonant χ[superscript (2)] microring resonators
By directly simulating Maxwell’s equations via the finite-difference time-domain (FDTD) method, we numerically demonstrate the possibility of achieving high-efficiency second harmonic generation (SHG) in a structure consisting of a microscale doubly-resonant ring resonator side-coupled to two adjacent waveguides. We find that ≳ 94% conversion efficiency can be attained at telecom wavelengths, for incident powers in the milliwatts, and for reasonably large bandwidths (Q ~ 1000s). We demonstrate that in this high efficiency regime, the system also exhibits limit-cycle or bistable behavior for light incident above a threshold power. Our numerical results agree to within a few percent with the predictions of a simple but rigorous coupled-mode theory framework.National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (Award DMR-0819762)Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies (Contract W911NF-07-D-0004)United States. Defense Advanced Research Projects Agency (Contract N66001-09-1-2070-DOD