Optics, Light and Lasers
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Written for newcomers to the topic who will benefit from the author's ability to explain difficult theories and effects in a straightforward and readily comprehensible way.
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Content
1.1 Light rays in human experience.
1.2 Ray optics.
1.3 Reflection.
1.4 Refraction.
1.5 Fermat's principle: the optical path length.
1.6 Prisms.
1.7 Light rays in wave guides.
1.8 Lenses and curved mirrors.
*1.9. Autofocus
1.10 Matrix optics.
1.11 Ray optics and particle optics.
Problems for chapter 1.
2 Wave optics.
2.1 Electromagnetic radiation fields.
2.2 Wave types.
2.3 Gaussian beams.
Add: Collins integral
*2.3. Beyond Gaussian Beams
2.4 Polarization.
2.5 Diffraction.
Problems for chapter 2.
3 Light propagation in matter.
3.1 Dielectric interfaces.
3.2 Complex refractive index.
3.3 Optical wave guides and fibres.
3.4 Functional types and applications of optical fibres.
3.6 Photonic materials.
*NEW: Nano-Optis and Plasmonics
3.7 Light pulses in dispersive materials.
3.8 Anisotropic optical materials.
3.9 Optical modulators.
Problems for chapter 3.
4 Optical images.
4.1 The human eye.
4.2 Magnifying glass and eyepiece.
4.3 Microscopes.
4.4 Telescopes.
4.5 Lenses: designs and aberrations.
*4.6. Aspherical lenses
Problems for chapter 4.
5 Coherence and interferometry.
5.1 Young's double slit.
5.2 Coherence and correlation.
5.3 The double-slit experiment.
5.4 Michelson interferometer: longitudinal coherence.
5.5 Fabry-Perot interferometer.
5.6 Optical cavities.
*update: Microresonators
5.7 Thin optical films.
5.8 Holography.
5.9 Laser speckle (laser granulation).
Problems for chapter 5.
6 Light and matter.
6.1 Classical radiation interaction.
6.2 Two-level atoms.
6.3 Stimulated and spontaneous radiation processes.
6.4 Inversion and amplification.
Problems for chapter 6.
7 The laser.
7.1 The classic system: the He-Ne laser.
7.2 Mode selection in the He-Ne laser.
7.3 Spectral properties of the He-Ne laser.
7.4 Applications of the He-Ne laser.
7.5 Other gas lasers.
7.6 Molecular gas lasers.
7.7 The workhorses: solid-state lasers.
7.8 Selected solid-state lasers.
7.9 Tunable lasers with vibronic states.
7.10 Tunable ring lasers.
Problems for chapter 7.
8 Laser dynamics.
8.1 Basic laser theory.
8.2 Laser rate equations.
8.3 Threshold-less lasers and micro-lasers.
8.4 Laser noise.
8.5 Pulsed lasers.
*8.6. Femtocombs
Problems for chapter 8.
9 Semiconductor lasers.
9.1 Semiconductors.
9.2 Optical properties of semiconductors.
9.3 The heterostructure laser.
9.4 Dynamic properties of semiconductor lasers.
9.5 Laser diodes, diode lasers, laser systems.
9.6 High-power laser diodes.
*9.7 Quantum Cascade lasers + update
Problems for chapter 9.
10 Sensors for light.
10.1 Characteristics of optical detectors.
10.2 Fluctuating opto-electronic quantities.
10.3 Photon noise and detectivity limits.
10.4 Thermal detectors.
10.5 Quantum sensors I: photomultiplier tubes.
10.6 Quantum sensors II: semiconductor sensors.
10.7 Position and image sensors.
10.8. Superconducting detectors
Problems for chapter 10.
11 Laser spectroscopy.
11.1 Laser-induced fluorescence (LIF).
11.2 Absorption and dispersion.
11.3 The width of spectral lines.
11.4 Doppler-free spectroscopy.
11.5 Transient phenomena.
11.6 Light forces.
11.7. Remote Sensing, Trace gases, etc.
Problems for chapter 11.
12 Photons - an introduction to quantum optics.
12.1 Does light exhibit quantum character?
12.2 Quantization of the electromagnetic field.
12.3 Spontaneous emission.
12.4 Weak coupling and strong coupling.
12.5 Resonance fluorescence.
12.6 Light fields in quantum optics.
12.7 Two-photon optics.
12.8 Entangled photons.
*12.9 Quantum Communication
Problems for chapter 12.
13 Nonlinear optics I: optical mixing processes.
13.1 Charged anharmonic oscillators.
13.2 Second-order nonlinear susceptibility.
13.3 Wave propagation in nonlinear media.
13.4 Frequency doubling.
13.5 Sum and difference frequency.
13.6 Optical parametric oscillators.
Problems for chapter 13.
14 Nonlinear optics II: four-wave mixing.
14.1 Frequency tripling in gases.
14.2 Nonlinear refrac
Chapter 1
Light Rays
1.1 Light Rays in Human Experience
The formation of an image is one of our most fascinating emotional experiences (Figure 1.1). Even in ancient times it was realized that our "vision" is the result of rectilinearly propagating light rays, because everybody was aware of the sharp shadows of illuminated objects. Indeed, rectilinear propagation may be influenced by certain optical instruments, for example, by mirrors or lenses. Following the successes of Tycho Brahe (1546-1601), knowledge about geometrical optics led to the consequential design and construction of magnifiers, microscopes, and telescopes. All these instruments serve as aids to vision. Through their assistance, "insights" have been gained that added to our world picture of natural science, because they enabled observations of the world of both micro- and macro-cosmos.
Figure 1.1 Light rays.
Thus it is not surprising that the terms and concepts of optics had tremendous impact on many areas of natural science. Even such a giant instrument as the Large Hadron Collider (LHC) particle accelerator in Geneva is basically nothing other than an admittedly very elaborate microscope, with which we are able to observe the world of elementary particles on a subnuclear length scale. Perhaps as important for the humanities is the wave theoretical description of optics, which spun off the development of quantum mechanics.
In our human experience, rectilinear propagation of light rays - in a homogeneous medium - stands in the foreground. But it is a rather newer understanding that our ability to see pictures is caused by an optical image in the eye. Nevertheless, we can understand the formation of an image with the fundamentals of ray optics. That is why this textbook starts with a chapter on ray optics.
1.2 Ray Optics
When light rays spread spherically into all regions of a homogeneous medium, in general we think of an idealized, point-like, and isotropic luminous source at their origin. Usually light sources do not fulfill any of these criteria. Not until we reach a large distance from the observer, may we cut out a nearly parallel beam of rays with an aperture. Therefore, with an ordinary light source, we have to make a compromise between intensity and parallelism to achieve a beam with small divergence. Nowadays optical demonstration experiments are nearly always performed with laser light sources, which offer a nearly perfectly parallel, intense optical beam to the experimenter.
When the rays of a beam are confined within only a small angle with a common optical axis, then the mathematical treatment of the propagation of the beam of rays may be greatly simplified by linearization within the so-called paraxial approximation. This situation is met so often in optics that properties such as those of a thin lens, which go beyond that situation, are called "aberrations."
The direction of propagation of light rays is changed by refraction and reflection. These are caused by metallic and dielectric interfaces. Ray optics describes their effect through simple phenomenological rules.
1.3 Reflection
We observe reflection of, or mirroring of, light rays not only on smooth metallic surfaces but also on glass plates and other dielectric interfaces. Modern mirrors may have many designs. In everyday life they mostly consist of a glass plate coated with a thin layer of evaporated aluminum. But if the application involves laser light, more often dielectric multilayer mirrors are used; we will discuss these in more detail in the chapter on interferometry (Chapter 6). For ray optics, the type of design does not play any role.
1.3.1 Planar Mirrors
We know intuitively that at a planar mirror like in Figure 1.2, the angle of incidence is identical with the angle of reflection of the reflected beam,
1.1and that incident and reflected beams lie within a plane together with the surface normal. Wave optics finally gives us a more rigid reason for the laws of reflection. Therefore also details, for example, the intensity ratios for dielectric reflection (Figure 1.3), are explained, which cannot be derived by means of ray optics.
Figure 1.2 Reflection at a planar mirror.
Figure 1.3 Refraction and reflection at a dielectric surface.
1.4 Refraction
At a planar dielectric surface, for example, a glass plate, reflection and transmission occur concurrently. Therefore the transmitted part of the incident beam is "refracted." Its change of direction can be described by a single physical quantity, the "index of refraction" (also refractive index). It is higher in an optically "dense" medium than in a "thinner" one.
In ray optics a general description in terms of these quantities is sufficient to understand the action of important optical components. But the refractive index plays a key role in the context of the macroscopic physical properties of dielectric matter and their influence on the propagation of macroscopic optical waves as well. This interaction is discussed in more detail in Chapter 7.
1.4.1 Law of Refraction
At the interface between an optical medium "1" with refractive index and a medium "2" with index (Figure 1.3), Snell's law of refraction (Willebrord Snell, 1580-1626) is valid,
1.2where and are called the angle of incidence and angle of emergence at the interface. It is a bit artificial to define two absolute, material-specific refractive indices, because according to Eq. (1.2) only their ratio is determined at first. But considering the transition from medium "1" into a third material "3" with , we realize that, since , we also know the properties of refraction at the transition from "2" to "3." We can prove this relation, for example, by inserting a thin sheet of material "3" between "1" and "2." Finally, fixing the refractive index of vacuum to - which is argued within the context of wave optics - the specific and absolute values for all dielectric media are determined.
In Table 1.1 we collect some physical properties of selected glasses. The refractive index of most glasses is close to . Under usual atmospheric conditions, the refractive index in air varies between 1.00002 and 1.00005. Therefore, using , the refraction properties of the most important optical interface, that is, the glass-air interface, may be described adequately in terms of ray optics. Nevertheless, small deviations and variations of the refractive index may play an important role in everyday optical phenomena in the atmosphere (e.g., a mirage; p. 7).
Table 1.1 Optical properties of selected glasses
Name Boron crown Heavy flint glass Barium crown Flint glass Abbreviation BK7 SF11 LaSF N9 BaK 1 F 2 Abbe number 64.17 25.76 32.17 57.55 36.37 Refractive index n for selected wavelengths nm 1.5224 1.8065 1.8690 1.5794 1.6321 nm 1.5168 1.7847 1.8503 1.5725 1.6200 nm 1.5143 1.7760 1.8426 1.5695 1.6150 Dispersion constants of refractive index (see Eq. (1.6)) Density (g cm) 2.51 4.74 4.44 3.19 3.61 Expansion coefficient (30 to +70 C) 7.1 6.1 7.4 7.6 8.2Strain birefringence: typically 10 nm cm. Homogeneity of the refractive index from melt to melt: .
1.4.2 Total Internal Reflection
According to Snell's law, at the interface between a dense medium "1" and a thinner medium "2" (), the condition (1.2) can only be fulfilled for angles smaller than the critical angle :
1.3For the incident intensity is totally reflected at the interface. We will see in the chapter on wave optics that light penetrates into the thinner medium for a distance of about one wavelength with the so-called "evanescent" wave and that the point of reflection does not lie exactly at the interface (Figure 1.4). The existence of the evanescent wave enables the application of the so-called "frustrated" total internal reflection, for example, for the design of polarizers (Section 3.4.4).
Figure 1.4 Total internal reflection at a dielectric surface occurs for angles . The point of reflection of the rays does not lie exactly within the interface, but slightly beyond...
