Introduction: Why Nonlinear Optics?

Nonlinear Optics Is the Child of Lasers: Lasers were born in May, 1960, as flashes of red light that dazzled observers and awed the inventors! Light unlike any created before! So powerful that it drilled holes in razor blades and ionized the air! The first time since the creation of earth had such dazzling light been seen!

Laser light’s dazzle comes from the fact it emits coherent light. How can we imagine coherent light? Why does coherent light dazzle? Coherence means that all parts of a light beam have a phase relation with every other part of the beam that is fixed for all time. The fixed phase controls exactly what is happening to the beam. It can now be focused to an extraordinarily small point – bright enough that laser light alone can break down air, creating a startling (and dangerous) spark!

• We explain the difference between ordinary incoherent light and coherent light this way: Think of ordinary incoherent light as a cloud of photons, each traveling in a different direction; like a crowd of individual people on New Year’s Eve, milling around in Times Square. These “photons” move randomly in many directions, individually or as small groups. Such crowds may be uncomfortable; motion is blocked by innumerable collisions and it is difficult to get out of the high density.
• Coherent light is comparable to a parade of well‐trained soldiers, marching in rows with synchronous steps and swinging arms. Their periodic motion mimics photons in a coherent wave. Each has the same periodic arm‐swing (frequency) and phase‐fronts (defining lines of identical physical motion). All individuals, identically marching can be impressively powerful. No wonder militaristic countries advertise their strength with vast fields of marching soldiers. Want to be powerful? Be coherent, not incoherent. What hopes for the future reside in coherent waves!

In 1961 lasers were the only source of powerful coherent optical waves. The laser revolution opened up opportunities for nonlinear optics (NLO), which requires powerful, coherent light beams. This book describes how this new field developed, from its original concepts through its developing technology to its wide application today. We learn how powerful coherent light interacts nonlinearly with transparent materials. We also present some of the fascinating science and engineering that resulted from applying the tools of nonlinear optics.

Why Is Nonlinear Optics Important? Lasers were the first technology that provided the coherent optical waves that enable NLO. From some primitive early experiments until today, laser technology has expanded into vastly new realms never before reached by human technology. New realms in time‐, frequency‐, and intensity‐scales that cannot be reached by any other means. Advanced NLO technologies have replaced traditional optical systems and offered numerous opportunities for technology development. Through NLO, coherent laser light has been transformed to new wavelengths (throughout the visible and extending to extreme UV, to IR, and further to terahertz radiation); light pulses have been shortened to femtoseconds (10−15 s) and NLO provides the only way to measure such short pulses. Nonlinear optics is behind several Nobel prizes: observing gravity waves for the first time required NLO to “squeeze” noise out of laser light to well below quantum predictions.

Important commercial applications such as optical fiber telecommunication systems were originally limited by optical nonlinearities in fibers, but NLO technology overcame all those impediments. Now, after 50 years of research, state‐of‐the‐art NLO devices and systems form the basis of ultrahigh‐speed data switching. World‐record laser intensities (W/cm2) are generated by NLO amplifiers in ultrahigh power laser facilities around the world. Practically anywhere lasers are used, NLO can make them better: physics, chemistry, biology, medicine; with commercial, industrial, and basic scientific applications.

Author’s Intent: Nonlinear optics requires coherent light. From a classical point of view, coherence means the light from lasers is truly “wavelike.” Even today, lasers remain the only direct sources of coherent light. Fortunately, nonlinear optics provides a lossless means to transform one form of coherent light into another while conserving energy and momentum. Read how this book extends traditional “linear optics” (low‐power, weak light) into the realm of “nonlinear optics” (high‐power, coherent) in dielectric nonlinear materials. Our approach includes both science and engineering viewpoints.

Readers will learn about the “magic” of NLO when powerful, coherent light travels through certain nonlinear transparent materials that transform coherent light in ways that appear magic! Each of the major NLO technologies is explained here, from beginning concept through analysis to final demonstration.

The book title says “from the beginning,” a phase that has several meanings; one means beginning from 1962. The second means beginning with the physics of light interacting with atoms and molecules in materials, describing technical challenges that were overcome, and ending with examples of today’s technology.

Yet a third meaning for “from the beginning” describes the author’s personal involvement in the exciting state of nonlinear optics from its beginning. I was fortunate enough to be a part of the first five years of nonlinear optics, as an MIT graduate student and post‐doc from 1961 to 1966. My PhD research pioneered stimulated Raman and Brillion scattering, and my post‐doc investigated nonlinear refractive index that introduced spatial solitons and four‐photon‐mixing.

This book is designed to be understandable by all interested users, no matter their technical field. No complex variables are introduced so the mathematics is straightforward. All concepts needed to understand nonlinear optical interactions are explained using classical concepts. Since NLO technology is rapidly evolving into new technical areas, I foresee numerous scientists and engineers having questions about NLO. This book is for those who may be curious about how NLO technology has changed the world.

The technical level is assumed to be science/engineering seniors or first‐year graduate students. Design issues are emphasized, particularly in problem assignments, offering possibilities of credit for engineering design.

Finally, it is planned that readers can teach themselves the material (along with access to the internet). Most topics have considerable supplemental information in Wikipedia, and other similar resources. I envisage some readers to have moved into this field later in life and are looking for a source “from the beginning.” Alternatively, this book offers key words that can lead readers to additional open sources on the internet to find much greater detail. Wikipedia is often a good source.

Textbook Contents: The purpose of studying NLO is to investigate how coherent light can interact with nonlinear dielectric materials and their technological implications. The background of the field includes understanding: (i) properties of coherent light; (ii) properties of dielectric materials; (iii) characteristics of the light–material interaction; (iv) practical applications.

Typical NLO textbooks assume the reader already understands these basic concepts in the linear regime and then emphasize the nonlinear interactions. As this book is designed for beginners whose background might be in fields broader than physics or engineering (chemistry and biology), we provide self‐contained appendices introducing necessary basic concepts.

My approach is to simplify concepts down to their basics, most of which were discovered in the 1960s. Students will come to understand how the earliest experiments opened up this entirely new field. This will be the basis for understanding how advancements in laser technology have led to revolutions in NLO. Femtosecond pulses have enabled reaching instantaneous nonlinearities at modest power levels. Lasers that include nonlinear optical fibers have offered exciting new commercial applications. Nonlinear optics in photonic crystals, in quantum, and in 2D materials is becoming practical, and nonlinearities are even finding opportunities in nanomaterials. This book provides the basics, but details are beyond this course level.

Three Branches of Nonlinear Optics: Nonlinear optics technology, as a whole, neatly divides into three branches, each of which is treated separately. While the underlying principles are the same for all three, their differences diverge immediately into three separate branches. The technical chapters are separated by branch, each containing three to four chapters.

Branch #1 is second‐order nonlinearities that can change the frequency of monochromatic coherent light using specific nonlinear crystals;

Branch #2 is third‐order nonlinearities that occur in all media, creating an intensity‐dependent refractive index (as well as third harmonic);

Branch #3 is optical‐loss nonlinearities. These are: inelastic scattering of coherent light from molecular vibrations (stimulated Raman scattering); similar scattering from acoustic waves (stimulated Brillouin...