Modes generally provide an economical description of waves, reducing complicated wave functions to finite numbers of mode amplitudes, as in propagating fiber modes and ideal laser beams. But finding a corresponding mode description for counting the best orthogonal channels for communicating between surfaces or volumes, or for optimally describing the inputs and outputs of a complicated optical system or wave scatterer, requires a different approach. The singular-value decomposition approach we describe here gives the necessary optimal source and receiver "communication modes" pairs and device or scatterer input and output "mode-converter basis function" pairs. These define the best communication or input/output channels, allowing precise counting and straightforward calculations. Here we introduce all the mathematics and physics of this approach, which works for acoustic, radio-frequency and optical waves, including full vector electromagnetic behavior, and is valid from nanophotonic scales to large systems. We show several general behaviors of communications modes, including various heuristic results. We also establish a new "M-gauge" for electromagnetism that clarifies the number of vector wave channels and allows a simple and general quantization. This approach also gives a new modal "M-coefficient" version of Einstein's A and B coefficient argument and revised versions of Kirchhoff's radiation laws. The article is written in a tutorial style to introduce the approach and its consequences.

Optical or "orbital" angular momentum (OAM) beams offer one set of different spatial beam shapes that can be used for sending different channels of information. There has, however, been some confusion over these, especially whether they offer any advantage compared to other spatial beam shapes. One point that should be stated clearly is that they do not represent a new set of degrees of freedom in communication; they are just one possible set of basis functions for describing the spatial degrees of freedom of a beam. In fact, the process of choosing the best set of functions for communication, e.g., for maximum power coupling, has been well understood for some time, even though this may not be well known to some in the field. The mathematical process involves the singular value decomposition (SVD) of the coupling operator between the transmitting and receiving spaces. Other work has shown how the resulting orthogonal channels can even be determined automatically, without calculations. This recent short Letter discusses this point briefly, including an explicit example calculation and comparison of this SVD approach with a recent OAM approach, showing larger numbers of better coupled channels with less cross-talk and simpler transmitters and receivers.

Radiation laws must relate the fraction of incident radiation absorbed by an object and the amount of radiation emitted when it is hot so that objects can come to the same temperature just by exchanging electromagnetic radiation. Such laws are fundamentally important and set limits to practical applications such as in the conversion of light to electricity and in heat and thermal management generally. Kirchhoff’s classic results work well in many situations, but fail in others (specifically for “nonreciprocal” materials), and were derived using simplified models that do not apply to modern nanotechnology and light beams. We derive revised versions of laws that avoid these problems and discover additional and unexpected radiation laws that substantially expand the fundamental relations between optical absorption and emission.

This major review discusses the opportunities for the use of optics and optoelectronics to reduce the interconnect energies that dominate power dissipation in information processing and communications, showing how optics could make all interconnects inside even large machines behave like simple, low-energy local interconnects. It also summarizes the sources of energy dissipation inside machines, compares physical approaches to low-energy optoelectronic devices, and shows new opportunities for free-space optical systems to eliminate the electronic circuits responsible for most dissipation in interconnects.

**How to design any linear optical device ... and how to avoid it**

We can think of many different optical components we might like to make but that we have not known how to design. A good example is a mode-splitter that could separate multiple overlapping beams without loss. Up till now, we have had to use techiques such as "blind" design by optimization or exhaustive search, and it has not generally been obvious whether the device we wanted was even possible physically. Now we show how to design any linear optical component; the method always works and actually requires no calculations at all. This has now been demonstrated experimentally using a mesh of silicon photonics Mach-Zehnder interferometers that self-configures to undo the scattering of four arbitrarily mixed light beams.

**Are optical transistors the next logical step?**A transistor that operates with photons rather than electrons is often heralded as the next step in information processing, but optical technology must first prove itself to be a viable solution in many different respects. This article is a Commentary written for Nature Photonics, January 2010.

**Quantum Mechanics Book**

This introductory quantum mechanics text is published by Cambridge University Press. It is
intended both for physicists and for those from other
scientific and engineering disciplines, including electrical
and mechanical engineering, materials science, and
nanotechnology. The level of presentation is suitable for
junior undergraduates through graduate students to technical
professionals. Requirements for both physics and math are
minimized, and the necessary background in these areas is
summarized in appendices. Core topics are covered, the quantum
mechanics for key areas of application in electronic and
optical devices is explained, and advanced techniques and
areas, such as the quantum mechanics of light and quantum
information, are introduced.This is the textbook for both the EE222 and EE223 (Applied Quantum Mechanics I & II) classes at Stanford.

**Other highlights: **

*Device requirements for optical interconnects to chips*

This invited paper for the July 2009 Special Issue on Silicon Photonics in the Proceedings of the IEEE discusses the targets and requirements for optoelectronics and optical devices if they are to meet the needs of future interconnects to chips. Energy per bit is particularly important, with 10 fJ/bit being a key device benchmark. The various approaches to optical and optoelectronic devices and technology are summarized and compared.

**Fundamental limit to optical components **We have derived an upper bound to the
possible performance of linear optical components of given
sizes and maximum dielectric constants. (Most downloaded article from all OSA journals other than Optics
Express, October 2007)See
also the Physical Review Letter on a
general limit to one-dimensional slow light structures and
a brief summary in Optics and Photonics
News "Optics in 2007"

*Nanometallic-enhanced photodetectors*We have demonstrated that nanometallic structures can enhance photodetection, promising very low capacitance optoelectronic devices compatible in size with CMOS transistors. A nanoscale C-shaped aperture in a metal can enhance the photocurrent in the semiconductor beneath it, and recently an optical analog of a Hertz dipole antenna concentrates light to a ~ 100 nm sized germanium detector element on a silicon substrate.

*Quantum-confined Stark effect in germanium
quantum wells*A new modulation mechanism for
silicon-compatible optics, promising low energy devices for optical interconnects. See the Nature letter, a longer JSTQE paper on the original observations, the first modulator, a low-voltage C-band modulator, and a recent JSTQE paper on the detailed physics.

*And, for something different** How to become invisible!*See also a brief introduction to this
invisibility at http://newsroom.spie.org/x5923.xml?highlight=x535