Cavity quantum electrodynamics with three-dimensional photonic bandgap crystals

This paper gives an overview of recent work on three-dimensional (3D) photonic crystals with a "full and complete" 3D photonic band gap. We review five main aspects: 1) spontaneous emission inhibition, 2) spatial localization of light within a tiny nanoscale volume (aka "a nanobox for light"), 3) the introduction of a gain medium leading to thresholdless lasers, 4) breaking of the weak-coupling approximation of cavity QED, both in the frequency and in the time-domain, 5) decoherence, in particular the shielding of vacuum fluctuations by a 3D photonic bandgap. In addition, we list and evaluate all known photonic crystal structures with a demonstrated 3D band gap.Comment: 21 pages, 6 figures, 2 tables, Chapter 8 in "Light Localisation and Lasing: Random and Pseudorandom Photonic Structures", Eds. M. Ghulinyan and L. Pavesi (Cambridge University Press, Cambridge, 2015, ISBN 978-1-107-03877-6

Foerster resonance energy transfer rate and local density of optical states are uncorrelated in any dielectric nanophotonic medium

Motivated by the ongoing debate about nanophotonic control of Foerster resonance energy transfer (FRET), notably by the local density of optical states (LDOS), we study an analytic model system wherein a pair of ideal dipole emitters - donor and acceptor - exhibit energy transfer in the vicinity of an ideal mirror. The FRET rate is controlled by the mirror up to distances comparable to the donor-acceptor distance, that is, the few-nanometer range. For vanishing distance, we find a complete inhibition or a four-fold enhancement, depending on dipole orientation. For mirror distances on the wavelength scale, where the well-known `Drexhage' modification of the spontaneous-emission rate occurs, the FRET rate is constant. Hence there is no correlation between the Foerster (or total) energy transfer rate and the LDOS. At any distance to the mirror, the total energy transfer between a closely-spaced donor and acceptor is dominated by Foerster transfer, i.e., by the static dipole-dipole interaction that yields the characteristic inverse-sixth-power donor-acceptor distance dependence in homogeneous media. Generalizing to arbitrary inhomogeneous media with weak dispersion and weak absorption in the frequency overlap range of donor and acceptor, we derive two main theoretical results. Firstly, the spatially dependent Foerster energy transfer rate does not depend on frequency, hence not on the LDOS. Secondly the FRET rate is expressed as a frequency integral of the imaginary part of the Green function. This leads to an approximate FRET rate in terms of the LDOS integrated over a huge bandwidth from zero frequency to about 10 times the donor emission frequency, corresponding to the vacuum-ultraviolet. Even then, the broadband LDOS hardly contributes to the energy transfer rates. We discuss practical consequences including quantum information processing.Comment: 17 pages, 9 figure

Light propagation and emission in complex photonic media

We provide an introduction to complex photonic media, that is, composite materials with spatial inhomogeneities that are distributed over length scales comparable to or smaller than the wavelength of light. This blossoming field is firmly rooted in condensed matter physics, in optics, and in materials science. Many stimulating analogies exist with other wave phenomena such as sound and seismology, X-rays, neutrons. The field has a rich history, which has led to many applications in lighting, novel lasers, light harvesting, microscopy, and bio optics. We provide a brief overview of complex photonic media with different classes of spatial order, varying from completely random to long-periodically ordered structures, quasi crystalline and aperiodic structures, and arrays of cavities. In addition to shaping optical waves by suitable photonic nanostructures, the realization is quickly arising that the spatial shaping of optical wavefronts with spatial light modulators dramatically increases the number of control parameters. As a result, it is becoming possible for instance to literally see through completely opaque complex media. We discuss a unified view of complex photonic media by means of a photonic interaction strength parameter. This parameter gauges the interaction of light with any complex photonic medium, and allows to compare complex media from different classes for similar applications.Comment: 8 pages, 2 figures, Light Localisation and Lasing: Random and Quasi-Random Photonic Structures, Eds. M. Ghulinyan and L. Pavesi, (Cambridge Univ. Press, Cambridge, 2015) Ch. 1, p.

Optimal control of light propagation through multiple-scattering media in the presence of noise

We study the control of coherent light propagation through multiple-scattering media in the presence of measurement noise. In our experiments, we use a two-step optimization procedure to find the optimal incident wavefront. We conclude that the degree of optimal control of coherent light propagation through a multiple-scattering medium is only determined by the number of photoelectrons detected per single speckle spot. The prediction of our model agrees well with the experimental results. Our results offer opportunities for imaging applications through scattering media such as biological tissue in the shot noise limit

Design of a 3D photonic band gap cavity in a diamond-like inverse woodpile photonic crystal

We theoretically investigate the design of cavities in a three-dimensional (3D) inverse woodpile photonic crystal. This class of cubic diamond-like crystals has a very broad photonic band gap and consists of two perpendicular arrays of pores with a rectangular structure. The point defect that acts as a cavity is centred on the intersection of two intersecting perpendicular pores with a radius that differs from the ones in the bulk of the crystal. We have performed supercell bandstructure calculations with up to $5 \times 5 \times 5$ unit cells. We find that up to five isolated and dispersionless bands appear within the 3D photonic band gap. For each isolated band, the electric-field energy is localized in a volume centred on the point defect, hence the point defect acts as a 3D photonic band gap cavity. The mode volume of the cavities resonances is as small as 0.8 $\lambda^{3}$ (resonance wavelength cubed), indicating a strong confinement of the light. By varying the radius of the defect pores we found that only donor-like resonances appear for smaller defect radius, whereas no acceptor-like resonances appear for greater defect radius. From a 3D plot of the distribution of the electric-field energy density we conclude that peaks of energy found in sharp edges situated at the point defect, similar to how electrons collect at such features. This is different from what is observed for cavities in non-inverted woodpile structures. Since inverse woodpile crystals can be fabricated from silicon by CMOS-compatible means, we project that single cavities and even cavity arrays can be realized, for wavelength ranges compatible with telecommunication windows in the near infrared.Comment: 11 figure

Electro-Magnetic Bunch Length Measurement in LEP

Bunch lengths between 3 and 12 mm have been measured routinely in LEP in 1997 with a small (7 mm diameter) button electrode. The measurement method is based on the spectral analysis of the electrode signal and relies on the fact that the transfer function of the complete set-up, including the signal cable, can be computed rather exactly thus eliminating the need for external calibration. The information of beam intensity is recovered as a by-product. It provides an interesting internal validation of the measurement by comparison with the normal intensity measurement. The system has been used to detect subtle but real bunch length changes with bunch intensity which can be attributed to the inductive impedance in LEP. A value for the imaginary (inductive) longitudinal impedance is derived from the observations. An indication for the resistive part of the impedance is given as well

Signal processing for beam position measurement

The spectrum of the signals generated by beam position monitors can be very large. It is the convolution product of the bunch spectrum and the transfer function of the monitor including the transmission cable. The rate of information flow is proportional to the bandwidth and the maximum amplitude rating of monitor complex. Technology is progressing at a good pace and modern acquisition capabilities are such that nearly all the information contained in the spectrum can be acquired with a reasonable resolution [1]. However, the cost of such a system is enormous and a major part of the information is superfluous. The objective of a beam position measurement system is generally restricted to trajectory measurements of a portion of the beam that is much larger than the finer details that can be observed with the bare signal generated by the position monitor. Closed orbit measurements are a simple derivation product of the trajectory and will not be considered further. The smallest beam portion that is of practical interest is one bunch. Hence the maximum frequency is in the order of the bunch repetition rate. Lower frequencies than the bunching frequency may be chosen either to obtain better resolution, either because it is technically easier to accomplish. The sensitivity of beam position monitors degrades quickly at low frequencies. Therefore, signals are selected at some convenient multiple of the bunching frequency and are shifted to so called baseband to match the capabilities of the acquisition system. The task of signal processing is to make a selection among the many frequencies that are available and prepare the signals for acquisition. The signal selection is done by filtering, a vast subject but it will not be treated in this paper. Three signal processing techniques will be examined from the point of view of (amplitude) resolution of a single acquisition of the beam position, dynamic range and operational frequency. They are the following: the homodyne receiver, the phase processor and the logarithmic detector. Baseband techniques are also used in practice and will be briefly mentioned to start

Decoherence form space-charge

The theory of the Laslett direct space-charge effect is well established since many years. Nevertheless, the fact that transverse coherent tune shifts and decoherence of transverse oscillations have been attributed to direct space-charge, by lack of other explanations, is the origin of a lasting controversy. The observed decoherence in the CERN SPS and the expected decoherence in the CERN LHC have such profound consequences for the construction of transverse feedback systems that lifting the controversy has an interest that is more than purely academic. A collection of beam observations is presented concerning tune shifts and decoherence where the space-charge effect is eminent. A physical model is proposed from which tune shifts and decoherence can easily be derived. The computation can not only be applied to machines where the effect is modest but not negligible, as the SPS and the LHC, but also to the CERN PS and PSB where the effect is massive