Ebook: Frontiers in Modern Optics

The year 2015 has been designated by the United Nations General Assembly as the International Year of Light and Light-based Technologies. An extensive series of events involving many thousands of academic institutions and private sector partners around the world has celebrated the importance of light in our everyday lives, in modern technology and for future and emerging technologies. The year 2015 is also the anniversary of a number of significant historical events, some of which literally changed the world in which we live. In 1015 Ibn Al-Haytham published his Book of Optics, which is now recognised to have had major influence on the development of optics in Europe over the following 400 years. In 1815, Fresnel first proposed the notion that light is actually a wave. This concept was then firmly established 150 years ago by Maxwell and his electromagnetic theory of light propagation. In the words of Einstein, “one scientific epoch ended and another began with James Clerk Maxwell”. Not many years followed and Einstein published in 1905, another anniversary, his discovery of the photoelectric effect demonstrating that light is made of photons. In 1915 Einstein then published his general theory of relativity, possibly the most celebrated and grand theory in physics in which light plays a central role. In this School we attempted to give a broad and modern overview of the field of optics in a series of lectures that address ongoing topics of research. Nonlinear optics has played a central role in science since the invention of the laser in 1960 that gave us access for the first time to intense and coherent light that could excite the nonlinear response of various materials. The range and breadth of applications of nonlinear optics is staggering, ranging from simple green laser pointers to highly advanced, new-generation X-ray lasers and particle accelerators. In these lectures a number of topics are covered including long-range propagation of extreme intensity light pulses in air, supercontinuum generation with applications for example in the understanding oceanic rogue wave events, and photon-pair creation on micro-photonic chips for the next generation of quantum communication devices. Light is also a unique investigation tool that can provide insight into some of the deeper questions of modern physics, such as the role of symmetries in the universe. It can also be used to study peculiar solutions to the equations of quantum mechanics and this gave rise to the fertile field of Airy beams that propagate along curved trajectories. Optical beams can carry not only spin but also orbital angular momentum. The discovery of this remarkable additional degree of freedom is changing the way in which we think, for example, about optical communication systems, particle trapping or manipulation and quantum information encoding.

Finally, light is of course all about our ability to see the world. Detection and imaging are therefore at the forefront of modern optics and in our lectures we saw talks on fascinating and remarkable topics such as cloaking, weak measurements whereby photons are measured without actually perturbing their state, high resolution 3D imaging that is performed using a camera made from only one single pixel and new developments in “ghost” imaging that allows us to see even if the light never actually interacts with the object that we want to image.

A unique feature of this volume is that each chapter has been prepared as a collaboration between students at the school and the lecturers. We feel that this approach to prepare proceedings from schools such as this one has been very successful and a model for the future. We must thank all authors and lecturers for the effort devoted to the careful preparation of the individual chapters.

Acknowledgements go also to the local organisers, Barbara Alzani and Marta Pigazzini who, through their enthusiasm make the Enrico Fermi Summer Schools such unique events and to Monica Bonetti and Marcella Missiroli from the editorial/production office of the Italian Physical Society. Finally, we thank the Italian Physical Society for making this event possible.

D. Faccio, J.Dudley and M. Clerici

Throughout human history, people have used sight to learn about the world, but only in relatively recent times the science of light has been developed. Egyptians and Mesopotamians made the first known lenses out of quartz, giving birth to what was later known as optics. On the other hand, geometry is a branch of mathematics that was born from practical studies concerning lengths, areas and volumes in the early cultures, although it was not put into axiomatic form until the 3rd century BC. In this work, we will discuss the connection between these two timeless topics and show some “new things in old things”. There have been several works in this direction, but taking into account the didactic approach of the “Enrico Fermi” Summer School, we would like to address the subject and our audience in a new light.

Nonlinear optics deals with phenomena that occur when a very intense light interacts with a material medium, modifying its optical properties. Shortly after the demonstration of first working laser in 1960 by Maiman (Nature, 187 (1960) 493), the field of nonlinear optics began with the observation of second harmonic by Franken et al. in 1961 (Phys. Rev. Lett., 7 (1961) 118). Since then, the interest in this field has grown and various nonlinear optical effects are utilized for purposes such as nonlinear microscopy, switching, harmonic generation, parametric downconversion, filamentation, etc. We present here a brief overview of the various aspects on nonlinear optics and some of the recent advances in the field.

The ability to manipulate light has allowed scientists to verify fundamental theories of physics and to develop a new generation of technologies that use photons as a primary resource. Recent developments in quantum measurement theory have offered new alternatives to approach some of the most remarkable problems in quantum physics. Consequently, the principles of quantum mechanics have been exploited in the development of quantum technologies such as optical metrology, quantum communication, and quantum information. In recent years, weak measurements and two of its most remarkable variants: weak value amplification and direct measurement, have been developed and are considered important resources for quantum applications. In this paper, we discuss weak measurements and some significant applications of weak values. We elaborate on how distinct forms of weak values are used to observe and amplify small effects or to directly measure the quantum wave function of photons, a crucial task for schemes for quantum communication and quantum information. We also review some of the most recent methods for weak value amplification and direct measurement that our group has developed.

The common intuition of light propagating along a straight path was challenged by the discovery of the Airy beam. Optical beams with an Airy profile undergo self-bending and propagate along parabolic trajectories. Airy wavepackets, on the other hand, can self-accelerate during propagation. Due to their unusual and unique properties, Airy beams and pulses have been used in several applications such as microparticle manipulation, micromachining, and curved plasma channel generation. The future prospects of such beams are vast and they can be extended to other areas including plasmonics, microwaves and acoustics.

Two important classes of symmetries are investigated within the framework of optics; parity-time (PT) symmetry and supersymmetry (SUSY). It is shown that PT-symmetric optical structures can exhibit interesting properties which are otherwise unattainable in Hermitean systems. Floquet-Bloch analysis of periodic PT-symmetric potentials is presented and mode selection property of PT-symmetric laser systems is discussed. Additionally, notions from supersymmetry are applied to one- and two-dimensional optical structures in order to explore novel applications based on the design of systems that exhibit similar guided mode and scattering characteristics. Such devices can be exploited for selective mode filtering applications.

In this paper we review some of the main features and working principles of computational ghost imaging that requires only a single-pixel detector and illumination with structured light.

In this paper we give a review of orbital angular momentum in the context of light beams. A brief description is given of how orbital angular momentum can be introduced into an optical beam and some of the resulting applications.

We give an overview of the quantum theory of interference and show that this has important practical implications. We discuss an imaging technique that was designed and based on the principles of quantum mechanics.

The following paper reports the lecture delivered by Prof. Alexander Gaeta, from the School of Applied and Engineering Physics, Cornell University, Ithaca, USA, and describes recent developments in the field of nonlinear photonics in chip-based structures, focusing on silicon-based nanowaveguides and resonators. At first we describe the main physical effects underpinning nonlinear optics in integrated structure, arising from the third-order (Kerr) nonlinearity, such as self-phase modulation, four-wave mixing, and parametric oscillation. We show that, after suitably engineering the waveguide dispersion, silicon-based devices can produce supercontinuum light spanning more than an octave, frequency combs of more than 100 THz bandwidth, pulses of nearly 100 femtosecond duration, and photon pairs for quantum optics applications.

This paper reports the lecture delivered by Prof. Michal Lipson, from the School of Electrical and Computer Engineering, Cornell University, Ithaca, USA, and is an introduction to the field of silicon photonics, an area of research that has become increasingly important over the past 15 years due to its particularly great potential for replacing electrical by optical data communication in a CMOS-compatible fashion. The basic concepts of waveguide fabrication will be discussed as well as a selection of devices relevant to optical signal transmission such as resonators, electro-optics modulators and isolators. Moreover, other applications of silicon photonic devices e.g. for optofluidics and optomechanics will be presented.

In this paper we discuss the most prominent and widely used pulse characterization techniques, capable of measuring the electric field amplitude and phase of laser pulses of only few optical cycles in length. The measurement and stabilization of the carrier envelope phase, paramount in a range of applications, is also treated in some detail.

This paper reviews the basics of supercontinuum generation in optical fibers. After a brief introduction on pulse propagation in optical fibers, we provide an overview of the different nonlinear mechanisms that lead to the generation of broadband supercontinuum spectra with emphasis on the anomalous dispersion regime. Coherence and statistical aspects are also reviewed.

In this paper we give an overview of the propagation of ultra-intense laser pulses. Due to the intrinsic nonlinearity present even in air, these pulses will reshape, collapse and eventually form long-range filaments that have some very peculiar and unique properties that can be harnessed for applications such as long-distance energy transfer or electrical discharge control.