Physics 3232 Optics I: Introduction Prof. Rick Trebino Georgia Tech www.physics.gatech.edu/frog Light has always fascinated us! “Let there be light!” It’s how we understand the world. The great revolutions in physics and current tests of them. Two places at once! What is it? Particle? Wave? Telecom and imaging. Interactions with matter and itself. Why do things look the way they do? Windows/mirrors. Lasers/light bulbs. Rainbows, sunsets, sunglasses, cameras. Light is an amazing thing. And humankind has been fascinated by it from the time we became conscious: “Let there be light,” was the Judeo-Christian Deity’s first task. From the moment we awaken until the moment we fall asleep, it’s our main mechanism for understanding the world around us. It was responsible for the great revolutions in physics in the early 20th century, quantum mechanics and relativity. Even today, tests of the fundamental nature of quantum mechanics and general relativity involve light and are fascinating us. Indeed, I’ll show you an example of a photon being in two places at once. Light is also more practical: it’s also responsible for the great revolutions occurring now in telecommunications and medical imaging. In this course, we’ll talk about all aspects of light. What is it? Is it a particle or a wave, or both? How does it interact with matter? How does it interact (or interfere) with itself? And why do things look the way they do? We’ll discuss light’s fundamental and exotic properties, and we’ll show why windows look like mirrors at night. We’ll talk about lasers and why they’re different from light bulbs. And we’ll talk about rainbows, sunsets, polarized sunglasses, and cameras. And anything else that comes to mind—mine or yours. These Optics lectures were created by Rick Trebino and are intended to accompany a junior-level optics course taught using Hecht’s book, “Optics.” Many images have been scanned from this book and others; these contributions are noted where possible (if you see an improperly credited or uncredited image, please let me know). These lectures were originally intended mainly for my students at Georgia Tech. But if you’re a professor who is teaching such a course at another university, feel free to use them! My desire is to help to create a tradition of sharing of teaching materials, as espoused by the Digital Libraries initiative (e.g. MERLOT). And some day, no professor will ever have to endure the tedious task of lecture preparation, except to improve on existing lectures. If you use these lectures, please obey copyright laws (that is, reference Rick Trebino and also, if relevant, the original source of any figure or image). And if you improve on them, please be so kind as to contribute your improvements to the cause! Feedback is also welcome!

Michelson & Morley Michelson and Morley attempted to measure the earth's velocity with respect to the aether and found it to be zero, no matter the direction (despite the earth’s motion), effectively disproving the existence of the aether. Albert Michelson (1852-1931) Edward Morley (1838-1923) http://en.wikipedia.org

Albert Einstein Einstein showed that light: is a phenomenon of empty space; has a velocity that’s constant, independent of observer velocity; is both a wave and a particle; Albert Einstein (1879-1955) Excited medium and undergoes stimulated emission, the basis of the laser.

The interaction of light and matter Light excites atoms, which then emit more light. Electric field at atom Electron cloud Emitted electric field + = Incident light Emitted light Transmitted light On resonance (the light frequency is the same as that of the atom) The crucial issue is the relative phase of the incident light and this re-emitted light. If these two waves are ~180° out of phase, destructive interference occurs, and the beam will be attenuated—absorption. If they’re ~±90° out of phase: the speed of light changes—refraction.

Absorption of light varies massively. Visible spectrum Penetration depth into water Wavelength 1 km 1 m 1 mm 1 µm 1 nm UV X-ray Radio Microwave IR Penetration depth into water vs. wavelength Water is clear in the visible, but not in other spectral regions. Notice that the penetration depth varies by over ten orders of magnitude!

Variation of the refractive index with wavelength (dispersion) causes the beautiful prismatic effects we know and love. Prism Input white beam Dispersed beam Prisms disperse white light into its various colors.

Rainbows result from refraction and reflection of sunlight in water droplets. Note that there can be two rainbows, and the top one is inverted. There are many interesting optics effects in real life…

An interesting question is what happens to light when it encounters a surface. At an oblique angle, light can be completely transmitted or completely reflected (it depends on its polarization). Total internal reflection is the basis of optical fibers, a billion dollar industry.

Light beams can interfere with each other: Two point sources… Different separations. Note the different patterns. Constructive vs. destructive interference… The idea is central to many laser techniques, such as holography, ultrafast photography, and acousto-optic modulators. Tests of quantum mechanics also use it.

Light beams can be intentionally made to interfere with each other. Using a partially reflecting mirror, we can split a beam into two. Beam- splitter Input beam Mirror If we then combine the two beams, their relative phase matters. The above Sagnac Interferometer measures rotation.

Often, they do so by themselves.

Fourier decomposing functions plays a big role in optics. Here, we write a square wave as a sum of sine waves of different frequency.

The Fourier transform is perhaps the most important equation in science. It converts a function of time to one of frequency: and converting back uses almost the same formula: The spectrum of a light wave will be given by:

Diffraction Light bends around corners. This is called diffraction. The light pattern emerging from a single small rectangular opening The diffraction pattern far away is the (2D) Fourier transform of the slit transmission vs. position.

Light is not only a wave, but also a particle. Photographs taken in dimmer light look grainier. Very very dim Very dim Dim Bright Very bright Very very bright When we detect very weak light, we find that it’s made up of particles. We call them photons.

Electromagnetism is linear: The principle of Superposition holds. If E1(x,y,z,t) and E2(x,y,z,t) are solutions to Maxwell’s equations, then E1(x,y,z,t) + E2(x,y,z,t) is also a solution. This means that light beams pass through each other without affecting each other.

Nonlinear Optics produces many exotic effects. Sending high-intensity infrared laser light into a crystal yielded this display of green light: Nonlinear optics allows us to change the color of a light beam, to change its shape in space and time, and to test the fundamental principles of quantum mechanics.

Ultrashort laser pulses are the shortest events ever created. This pulse is only 4.5 x 10-15 seconds long, that is, 4.5 femtoseconds: How do we measure such a short event? We must use the event to measure itself.