Weiss, M. Hentschel, and H. Wu, Y. Avitzour, and G. Lin, R. Chern, and H. Express 19 2 , — Alici and E. SPIE , B Avitzour, Y. Urzhumov, and G.
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Click here to see a list of articles that cite this paper. Table 2 Favorite values of h 1 , h 2 when strong resonant absorption occurs for each SRR. Equations on this page are rendered with MathJax. Learn more. Allow All Cookies. Optics Express Vol. Open Access. Express 19 , More Like This Reflection-less frequency-selective microwave metamaterial absorber.
Ultrathin multi-band planar metamaterial absorber based on standing wave resonances. Interference theory of metamaterial perfect absorbers. The topics in this list come from the Optics and Photonics Topics applied to this article.
Introduction 2. Theory 3. Design 4. Simulation results and discussion 5. Conclusion References and links. Abstract We propose a design of an extremely broad frequency band absorber based on destructive interference mechanism. If we look back at the first two figures in this section, we see that the waves are shifted by half of a wavelength. So, in the example with the speakers, we must move the speaker back by one half of a wavelength. What happens if we keep moving the speaker back?
At some point the peaks of the two waves will again line up:. At this position, we will again have constructive interference! As the speaker is moved back the waves alternate between constructive and destructive interference. What the example of the speakers shows is that it is the separation of the two speakers that determines whether there will be constructive or destructive interference. If the speakers are at the same position, there will be constructive interference at all points directly in front of the speaker.
If the speakers are separated by half a wavelength, then there is destructive interference, regardless of how far or close you are to the speakers. However, it already has become apparent that this is not the whole story, because if you keep moving the speaker you again can achieve constructive interference. This can be fairly easily incorporated into our picture by saying that if the separation of the speakers in a multiple of a wavelength then there will be constructive interference.
Note that zero separation can always be considered a multiple of a wavelength. What about destructive interference? We know that if the speakers are separated by half a wavelength there is destructive interference. However, if we move an additional full wavelength, we will still have destructive interference. So, this case is a bit hard to state, but if the separation is equal to half a wavelength plus a multiple of a wavelength, there will be destructive interference.
Thus, we have described the conditions under which we will have constructive and destructive interference for two waves with the same frequency traveling in the same direction. Unfortunately, the conditions have been expressed in a cumbersome way that is not easily applied to more complex situations.
So, before going on to other examples, we need a more mathematically concise way of stating the conditions for constructive and destructive interference. The proper way to define the conditions for having constructive or destructive interference requires knowing the distance from the observation point to the source of each of the two waves. Since there must be two waves for interference to occur, there are also two distances involved, R 1 and R 2.
For two waves traveling in the same direction, these two distances are as follows:. When we discussed interference above, it became apparent that it was the separation between the two speakers that determined whether the interference was constructive or destructive.
From this diagram, we see that the separation is given by R 1 — R 2. So, really, it is the difference in path length from each source to the observer that determines whether the interference is constructive or destructive. I emphasize this point, because it is true in all situations involving interference. The only difficulty lies in properly applying this concept.
With this more rigorous statement about interference, we can now right down mathematically the conditions for interference:. To illustrate the effect, consider a pair of light waves from the same source that are coherent having an identical phase relationship and traveling together in parallel presented on the left-hand side of Figure 4. If the vibrations produced by the electric field vectors which are perpendicular to the propagation direction from each wave are parallel to each other in effect, the vectors vibrate in the same plane , then the light waves may combine and undergo interference.
If the vectors do not lie in the same plane, and are vibrating at some angle between 90 and degrees with respect to each other, then the waves cannot interfere with one another. The light waves illustrated in Figure 4 are all considered to have electric field vectors vibrating in the plane of the page. In addition, the waves all have the same wavelength, and are coherent, but vary with respect to amplitude. The waves on the right-hand side of Figure 4 have a phase displacement of degrees with respect to each other.
Assuming all of the criteria listed above are met, then the waves can interfere either constructively or destructively to produce a resultant wave that has either increased or decreased amplitude. If the crests of one of the waves coincide with the crests of the other, the amplitudes are determined by the arithmetic sum of the amplitudes from the two original waves.
For example, if the amplitudes of both waves are equal, the resultant amplitude is doubled. In Figure 4 , light wave A can interfere constructively with light wave B , because the two coherent waves are in the same phase, differing only in relative amplitudes.
Bear in mind that light intensity varies directly as the square of the amplitude. Thus, if the amplitude is doubled, intensity is quadrupled. Such additive interference is called constructive interference and results in a new wave having increased amplitude.
If the crests of one wave coincide with the troughs of the other wave in effect, the waves are degrees, or half a wavelength, out of phase with each other , the resultant amplitude is decreased or may even be completely canceled, as illustrated for wave A and wave C on the right-hand side of Figure 4. This is termed destructive interference , and generally results in a decrease of amplitude or intensity.
In cases where the amplitudes are equal, but degrees out of phase, the waves eliminate each other to produce a total lack of color, or complete blackness. All of the examples presented in Figure 4 portray waves propagating in the same direction, but in many cases, light waves traveling in different directions can briefly meet and undergo interference. After the waves have passed each other, however, they will resume their original course, having the same amplitude, wavelength, and phase that they had before meeting.
Real-world interference phenomena are not as clearly defined as the simple case depicted in Figure 4. For example, the large spectrum of color exhibited by a soap bubble results from both constructive and destructive interference of light waves that vary in amplitude, wavelength, and relative phase displacement.
A combination of waves having amplitudes that are approximately equal, but with differing wavelengths and phases, can produce a wide spectrum of resultant colors and amplitudes. In addition, when two waves of equal amplitude and wavelength that are degrees half a wavelength out of phase with each other meet, they are not actually destroyed, as suggested in Figure 4.
All of the photon energy present in these waves must somehow be recovered or redistributed in a new direction, according to the law of energy conservation photons are not capable of self-annihilation. Instead, upon meeting, the photons are redistributed to regions that permit constructive interference, so the effect should be considered as a redistribution of light waves and photon energy rather than the spontaneous construction or destruction of light.
Therefore, simple diagrams, such as the one illustrated in Figure 4 , should only be considered as tools that assist with the calculation of light energy traveling in a specific direction. Among the pioneers in early physics was a nineteenth century English scientist named Thomas Young, who convincingly demonstrated the wave-like character of light through the phenomenon of interference using diffraction techniques.
Young's experiments provided evidence in contrast to the popular scientific opinion of the period, which was based on Newton's corpuscular particle theory for the nature of light.
In addition, he is also responsible for concluding that different colors of light are made from waves having different lengths, and that any color can be obtained by mixing together various quantities of light from only three primary colors: red, green, and blue.
In , Young conducted a classical and often-cited double-slit experiment providing important evidence that visible light has wave-like properties. His experiment was based on the hypothesis that if light were wave-like in nature, then it should behave in a manner similar to ripples or waves on a pond of water.
Where two opposing water waves meet, they should react in a specific manner to either reinforce or destroy each other. If the two waves are in step the crests meet , then they should combine to make a larger wave. In contrast, when two waves meet that are out of step the crest of one meets the trough of another , the waves should cancel and produce a flat surface in that area. In order to test his hypothesis, Young devised an ingenious experiment. Using sunlight diffracted through a small slit as a source of semi-coherent illumination, he projected the light rays emanating from the slit onto another screen containing two slits placed side by side.
Light passing through the slits was then allowed to fall onto a third screen the detector. Young observed that when the slits were large, spaced far apart and close to the detection screen, then two overlapping patches of light formed on the screen.
However, when he reduced the size of the slits and brought them closer together, the light passing through the slits and onto the screen produced distinct bands of color separated by dark regions in a serial order. Young coined the term interference fringes to describe the bands and realized that these colored bands could only be produced if light were acting like a wave. The basic setup of the double slit experiment is illustrated in Figure 5. Red filtered light derived from sunlight is first passed through a slit to achieve a semi-coherent state.
Light waves exiting the first slit are then made incident on a pair of slits positioned close together on a second barrier. A detector screen is placed in the region behind the slits to capture overlapped light rays that have passed through the twin slits, and a pattern of bright red and dark interference bands becomes visible on the screen.
The key to this type of experiment is the mutual coherence of the light diffracted from the two slits at the barrier. An example of constructive interference may be seen in. Constructive Interference : Pure constructive interference of two identical waves produces one with twice the amplitude, but the same wavelength.
Destructive interference is when two waves add together and the result is a smaller displacement than would have been the case. An example of destructive interference can be seen in. When the waves have opposite amplitudes at the point they meet they can destructively interfere, resulting in no amplitude at that point. For example, this is how noise cancelling headphones work.
By playing a sound with the opposite amplitude as the incoming sound, the two sound waves destructively interfere and this cancel each other out. The superposition of two waves of similar but not identical frequencies produces a pulsing known as a beat. Striking two adjacent keys on a piano produces a warbling combination usually considered unpleasant to the ear.
The culprit is the superposition of two waves of similar but not identical frequencies. When two waves of similar frequency arrive at the same point and superimpose, they alternately constructively and destructively interfere. This alternating is known as a beat because it produces an unpleasant pulsing sound.
Another example is often noticeable in a taxiing jet aircraft particularly the two-engine variety. The loudness of the combined sound of the engines increases and decreases.
This varying loudness occurs because the sound waves have similar but not identical frequencies. The discordant warbling of the piano and the fluctuating loudness of the jet engine noise are both due to alternately constructive and destructive interference as the two waves go in and out of phase. Beat Frequency : Beats are produced by the superposition of two waves of slightly different frequencies but identical amplitudes. The waves alternate in time between constructive interference and destructive interference, giving the resulting wave a time-varying amplitude.
The wave resulting from the superposition of two similar-frequency waves has a frequency that is the average of the two. This wave fluctuates in amplitude, or beats, with a frequency called the beat frequency. We can determine the beat frequency mathematically by adding two waves together.
One can also measure the beat frequency directly. When you hear a beat coming from two discordant sounds say, two notes on a piano you can count the number of beats per second. The number of beats per second, or the beat frequency, shows the difference in frequency between the two notes. Musicians often use this phenomena to ensure that two notes are in tune if they are in tune then there are no beats.
The ear is the sensory organ that picks up sound waves from the air and turns them into nerve impulses that can be sent to the brain. Sound waves are vibrations in the air. The ear is the sensory organ that picks up sound waves from the surrounding air and turns them into nerve impulses, which are then sent to the brain.
The sound waves carry a lot of information — language, music, and noise — all mixed together. The task of the ear is to turn the signals in these waves of bouncing air molecules into electrical nerve signals while keeping as much of the information in the signal as possible. Anatomy of the Human Ear : Anatomy of the human ear; the length of the auditory canal is exaggerated for viewing purposes.
Air surrounds the head and fills the ear canal and middle ear.
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