Physics
Monochromatic Wave
A monochromatic wave refers to a wave that consists of a single frequency or wavelength. In other words, all the wave components have the same frequency and phase. This uniformity gives monochromatic waves a distinct and consistent appearance, making them useful for studying wave behavior and interference phenomena.
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4 Key excerpts on "Monochromatic Wave"
eBook - PDFOptics
Principles and Applications
- Kailash K. Sharma(Author)
- 2006(Publication Date)
- Academic Press(Publisher)
C H A P T E R 2 Coherence of Light Waves 2.1 POLYCHROMATIC LIGHT A number of Monochromatic Wave solutions of the wave equation were consid-ered in Chapter 1. A Monochromatic Wave must exist for all times. Such a wave, if it does exist, must have seen the big-bang if it ever occurred and should see the doom’s day if it comes! There are other unreal features of the Monochromatic Wave solutions. To establish even a small amplitude directed Monochromatic Wave, an infinite amount of energy must be expended. Needless to say that no source exists which gives strictly monochromatic light. Nevertheless, the Monochromatic Wave solutions of the wave equation are extremely useful to describe real light, which is polychromatic. A Monochromatic Wave has perfect coherence because its phase is completely defined at each and every point in space for all times. If the phase of a Monochromatic Wave at a space-time point r 1 t 1 is known, then its phase at any arbitrary space-time point r 2 t 2 can be precisely determined – in other words, the phases of a Monochromatic Wave are perfectly correlated. In the same spirit, the amplitude of a Monochromatic Wave is perfectly correlated. The extent to which the phase and amplitude correlations in time and space exist, determines the coherence properties of a light wave. A monochromatic plane wave E r t = E 0 e i k · r − t + 0 (2.1) has amplitude E 0 and phase constant 0 which are strictly independent of time and position. Monochromatic Waves are ideal single frequency waves and hence unrealiz-able. Practical light sources have spectral bandwidths varying from a fraction of a kHz for a good single mode laser to the broad spectrum of a black body radia-tor. All light fields are therefore polychromatic. This has to do with the inherent process of light emission. Thermal light is generated as a result of spontaneous emission from excited atoms and molecules radiating independently. Fourier 77
eBook - PDFWaves and Oscillations in Nature
An Introduction
- A Satya Narayanan, Swapan K Saha(Authors)
- 2015(Publication Date)
- CRC Press(Publisher)
Owing to the finite length of these wave-trains, the radiation forms a fre-quency spectrum. For a Monochromatic Wave field, the amplitude of vibration at any point is constant and the phase varies linearly with time. Conversely, the amplitude and phase in the case of a quasi-Monochromatic Wave field un-dergo irregular fluctuations[105]. The fluctuations arise since the real valued wave field U ( r ) consists of a large number of contributions that are indepen-dent of each other, the superposition of which gives rise to a fluctuating field. The rapidity of fluctuations depends on the light crossing time of the emit-ting region. The realistic light beam, U ( r ) , that is regarded as a member of an ensemble consisting of all realizations of the field, fluctuates as a function of time. At optical frequencies, the fluctuating field components are not ob-servable quantities, but are quadratic averages of them. Since, as a rule, the stochastic field is treated as ergodic, the ensemble average can be replaced by a time average. Let us consider that the waves (see equation 1.16), propagate in space where no sources and boundaries are present. There is a continuous multitude of such plane waves indexed by the continuous vector κ . We have seen in Section 1.4.2 that any superposition of solutions of an equation is also a solution of the wave equation. 360 Waves and Oscillations in Nature — An Introduction 8.2.1 Complex Representation A nonMonochromatic Wave can be expanded as a sum of Monochromatic Waves by using conventional Fourier analysis. An arbitrary function of time, such as the wave function, U ( r , t ), at a fixed position r , may be represented in the form of superposition of a large number of sinusoidal components of Monochromatic Waves of different frequencies, each component having a steady amplitude and phase over the period of observation, but both the amplitude and phase being random with respect to each other component.
eBook - PDFIntroduction to Optics I
Interaction of Light with Matter
- Ksenia Dolgaleva(Author)
- 2022(Publication Date)
- Springer(Publisher)
16 1. LIGHT Figure 1.12: (a) Monochromatic light wave and (b) its spectral representation showing an iso- lated frequency peak that can be represented as a delta-function. V.!/ is a spectral representation of the electric field, obtained by taking a Fourier transform of its temporal counterpart U.r; t/. The optical field of a Monochromatic Wave is given by the equation U.r; t/ D U.r/ e i!t ; (1.24) where ! represents the frequency (color) of the wave. The requirements of an infinitely thin spectral line and infinite time duration cannot be met in reality. That is why monochromatic light is an idealistic model of light that still can be used as an approximation in many physical situations. One example where light can be treated as monochromatic is quasi-monochromatic light emitted by a continuous-wave laser source. It has a very narrow (delta-like) spectral function, and it lasts for a relatively long time, limited by the atomic processes in the active medium of the laser. Different continuous laser sources have different coherence lengths, a parameter characterizing the quality of the emitted light. The larger the coherence lengths, the higher the spectral purity (narrower spectral line) of the laser radiation. Some examples of coherence length values are 10–30 cm for helium-neon gas laser- emitting red light with 0 D 632:8 nm and > 1 m for argon gas laser-emitting green light with 0 D 514:5 nm. We will discuss more related to this matter when studying laser sources. Polychromatic light is comprised of multiple spectral components or waves of a different wavelength. It can represent a set of discrete spectral components with different colors or a con- tinuum of colors. An example of polychromatic light comprised of multiple discrete frequency components is shown in Fig. 1.13a, and its spectral representation is shown in Fig.
- Wolfe, William L.(Authors)
- 2006(Publication Date)
Figure 7 The electromagnetic spectrum on a wavelength scale. approximately to give an idea of the entire range of the electromagnetic spectrum. I have intentionally given frequencies in several different ways. Coherence Laser light is coherent, and the coherence is especially important in communication by light waves. The word coherence means “go together,” just as cooperate means “operate together.” It means that the waves continue to travel together. The two waves with the same frequency shown in Fig. 5 (the amplitude example), go to-gether. The peaks of both occur at the same place and so do the troughs and the ze-roes. The only difference is the height. There are two ways in which two or more waves do not go to-gether, that is, are not coherent. One is if the waves start at differ-ent times, and the other is if they are of different frequencies. Fig-ure 8 shows how the waves grad-ually get out of synchrony if they start at the same time, but are of slightly different frequencies. Notice that they start in synch, but in about five cycles the maximum of one is about where the mini-mum of the other occurs. They are out of synch. So one requirement for light to be coherent is that it must be essentially monochro-matic (the same color) and the same frequency. The distance over which they are still in reasonably good synchronization is called the coherence length. If the waves are monochromatic but do not all have the same time of gen-eration, their combination will not be coherent. Figure 9 shows how this is with a few waves. As more and more waves are added, starting at different times, there will be peaks at all points and troughs at all points, and the concept of a mono-chromatic wave is completely blurred. The waves do not become increasingly out of phase as they go to the right as do the waves that consist of several frequencies; they are incoherent from the beginning. Rays Rays are straight lines that represent the direction of waves.
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