Skulls in the Stars

Since this is supposed to be in large part a science-focused blog, I wanted to get started with some serious posts about scientific topics. Like most of the established science bloggers, I’ll be mixing up posts which are on basic scientific concepts and posts which are on specific, technical, topics. This post will be one of the former.

My physics specialization and area of research is optical science. Though most people associate the word ‘optics’ with the engineering of lenses for eyeglasses, telescopes, and microscopes, in physics the term more broadly refers to the study of the behavior of light and its interactions with matter. The connection to eyeglasses and the like is not accidental, however: the development of various optical tools led scientists to study more closely the behavior of the light that those tools channeled.

Today, we may roughly group the study of optics into three broad subfields of study:

1. Geometrical optics, the study of light as rays
2. Physical optics, the study of light as waves
3. Quantum optics, the study of light as particles

Let’s look at each of these subfields in turn, both historically and scientifically.

1. Geometrical optics. Our day to day experience with light suggests that it travels, for the most part, in straight lines. When the sun’s rays peek through a gap in a cloud or through a gap in some dark foliage, we see continuous ‘line’ or ‘stream’ of light emerging from that gap. If we make the gap smaller (within limits, discussed below), the stream gets narrower, but remains a stream of light.

Early optics researchers used geometry to model this view of light. Light is postulated to travel along rays – line segments which are straight in free space but may change direction, or even curve, when encountering matter.

Two laws dictate what happens when light encounters a material surface. The law of reflection, evidently first stated by Euclid around 300 BC, states that when light encounters a flat reflecting surface the angle of incidence of a ray is equal to the angle of reflection. The law of refraction, experimentally determined by Willebrord Snell in 1621, explains the manner in which a light ray changes direction when it passes across a planar boundary from one material to another. A direct consequence of this ‘bending’ of light rays is that an object half submerged in a glass of water will appear to be bent.

From the laws of reflection and refraction, one can determine the behavior of optical devices such as telescopes and microscopes. One can trace the paths of different rays (known as ‘ray tracing’) through the optical system and see how images can be formed, their relative orientation, and their magnification. This is in fact the most important use of geometrical optics to this day: the behavior of complicated optical systems can, to a first approximation, be determined by studying the paths of all rays through the system.

A simple illustration of this is the action of a clear glass lens on a collection of parallel rays, shown in the figure below. A collection of rays incoming from the left are refracted twice by the lens, once on entry and once on exit, and the net result is the accumulation of all rays at a focal point on the right.

In principle, there are an infinite number of parallel rays in the picture; we obviously draw only a few of these. The brightness of the light field at any particular point in space is proportional to the density of rays (how closely spaced they are) at that point. The focusing action of the lens therefore results in a bright spot at the focal point.

2. Physical optics. Looking again at the ray picture of focusing above, we run into a problem: at the focal point, the rays all intersect. The density of rays at this point is therefore infinite, which according to geometrical optics implies an infinitely bright focal spot. Obviously, this cannot be true.

If we put a black screen in the plane of the focal point and look closely at the structure of the focal spot projected on the plane, experimentally we would see an image as simulated below:

There is a very small central bright spot, but also much fainter (augmented in this image) rings surrounding the central spot. These rings cannot be explained by the use of geometrical optics alone, and result from the wave nature of light.

Though people had long suggested that light has wavelike properties, direct evidence was lacking (note the size of the focal spot in the picture above: the rings are quite difficult to see with the naked eye) until the early 1800s. A number of scientists provided the theoretical and experimental framework to demonstrate that light has wavelike properties, notable among them Thomas Young, Josef Fraunhofer and Augustin Fresnel. From this work, the field of physical optics was born.

Physical optics is the study of the wave properties of light, which may be roughly grouped into three categories: interference, diffraction, and polarization. Interference is the ability of a wave to interfere with itself, creating localized regions where the field is alternately extremely bright and extremely dark. Diffraction is the ability of waves to ‘bend’ around corners and spread after passing through an aperture. Polarization refers to properties of light related to its transverse nature. We will cover all these terms in more detail in subsequent posts.

The wave nature of sound can be readily determined by anyone even without special scientific apparatus. For instance, if you stand on the opposite side of a building from a friend, out of direct line of sight, your friend’s shouts will still be audible to you. The sound waves from your friend partially wrap around the corners of the building, allowing you to hear him or her. This may be considered an example of diffraction. The wave nature of light is not as readily apparent. The reason for this discrepancy has to do with the wavelength of the waves in each case. For our purposes, the wavelength may be considered a distance over which wave effects are typically apparent. For audible sound, wavelengths range from millimeters to 20 meters, while for visible light the wavelength is on the order of 0.0000005 meters, much smaller than can be observed with the human eye.

3. Quantum optics. We return to the picture of the focal spot illustrated above and now imagine that the light source which produces the focal spot is on a very precise dimmer switch. What happens as we slowly turn the dimmer switch down to the off position?

Physical optics predicts that the shape of the focal spot will remain unchanged; it will just grow less bright. When the dimmer switch is turned below some critical threshold, however, something different and rather unexpected happens: we detect light in little localized ‘squirts’ of energy, and do not see our ring pattern at all.

A few of these squirts are illustrated in part (a) of the (very rough artist’s impression) figure below. If we keep a running tally of how many squirts hit at each location, we can slowly build up an average picture of where light energy is being deposited; this is illustrated in parts (b) and (c) of the figure below.

Remarkably, we find that the average spatial distribution of squirts results in exactly the ring pattern predicted by the wave theory of light! The squirts of energy are now known in fact to be individual particles of light, called photons.

The recognition of this particle behavior of light evolved over a number of discoveries in the late 1800s and early 1900s, culminating in Einstein’s 1905 explanation of the photoelectric effect using the concept of a photon. The photoelectric effect is a phenomenon in which electrons can be ejected from a metal surface by shining a beam of light upon the surface. The effect had a number of curious features which Einstein demonstrated were most readily explainable by considering light as a stream of particles.

The reality is that light has both wavelike and particlelike properties, depending on the circumstances of measurement. This is what is known as wave-particle duality, and is one of the cornerstones of modern physics. It is illustrated by the curious progression of squirts mentioned above: individual particles (photons) eventually build up a wavelike pattern – each particle of light evidently ‘carries’ with it the wave information required to build up the diffraction pattern.

The field of quantum optics involves the study of this particle (quantum) nature of light.

***

The three branches of optical science therefore involve the study of light on progressively smaller and finer measurement scales.

All three branches are still actively being researched. Geometrical optics is commonly used in the design of complicated optical systems, and researchers are studying ways to ‘improve’ the geometric models to provide better overlap with the wave theory of light. Physical optics lies on the boundary of engineering and pure science, as new physical consequences of the wave nature of light are still being uncovered and optical devices are being built which take advantage of this wave nature. Quantum optics is used as a tool to better understand the theory of quantum mechanics, though a number of highly speculative applications, such as quantum computing and quantum cryptography, are being explored.

As this blog continues, we’ll be exploring each of the branches in more detail, and also discussing some of the applications.