Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Magnetic monopole wikipedia , lookup
Time in physics wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Electrostatics wikipedia , lookup
Maxwell's equations wikipedia , lookup
Electromagnetism wikipedia , lookup
Superconductivity wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Lorentz force wikipedia , lookup
Field (physics) wikipedia , lookup
Optical Resonators APPH E4901/3 Applied Physics Seminar 1 Assignment from Last Week • What are the resonant optical frequencies of a cube? Numbers please. • What are the resonant frequencies of an “optical fiber ring”? • What is a Fabry-Pérot interferometer? And other types of interferometers, … ? 2 http://www.rsoftdesign.com/aboutUs.php 3 http://www.feynmanlectures.info http://www.youtube.com/watch?v=j3mhkYbznBk http://www.youtube.com/watch?v=kd0xTfdt6qw&feature=relmfu Resonators • Richard Feynman’s “Cavity Resonators” lecture • Next week: “The Great Seal Bug Story” 4 omagnetic and V to f our ideal is that for ossible to containing blem now, feW cases. ll produce ce. Also, ges on the e changes, me capacishown in s Land C h less than glect them. ant, and a L c R Fig. 23-1. real resistor. Equivalent circvit of q 5 Fig. 23-3 (b) is better. In fac impedance of a real, physica use in the artificial model o Let's look a little more of an inductance goes as wL circuit": all we see is the res becomes much larger than tance. As we go'still highe impedance is proportional t (a) frequencies a condenser is a (b) Fig. 23-3. (c) The equivalent circuit of a real inductance at higher frequencies. thing else, it ·draws no curre into the capacitance betwee the current in the coil jump around and around where intended that the current sho path of least impedance. If the subject had been called "the high-frequency b happens in all subjects. In the speed of sound when th It doesn't mean that there i should be redesigned. So t going to work as a good ind frequencies. For high frequ 6 23-2 A capacitor at hi negative charge on the other; and there will be a uniform electric field between the plates. Now suppose that instead of DC, we put an AC of low frequency on the plates. (We will find out later what is "low" and what is "high".) Say we connect the capacitor to a lower-frequency generator. As the voltage alternates, the positive charge on the top plate is taken off and negative charge is put on. While that is happening, the electric field disappears and then builds up in the 9Pposite direction. 0 - , CURVE f, r- SURFACE S 0 0 0 0 <l9 t E h 1_ 0 0 B T l' CURVE f2 liNES OF B LINES OF E ( 0) . .Fig, 23-4. (b) The electric and magnetic fields between the plates of a capacitor. 23-2 7 the induced field tends to reduce the electric field farther out. The E = E, + E2 is then E = E, + E2 = (1 - w:n S (23.8) Eoe'·'. N ric field in the capacitor is no longer uniform; it has the parabolic by the broken line in Fig. 23-5. You see that our simple capacitor is y complicated. now use our results to calculate the impedance of the capacitor I' / r' ncies. Knowing the electric field, we could compute the charges on I I d find out how the current through the capacitor depends on the I but we are not interested in that problem for the moment.o We are 23-5. the The frequency electric field between d in seeing what happens as we continue to go upFig.with the capacitor plates at high frequency, are neglected.) happens at even higher frequencies. Aren't (Edge we effects already finished? we have corrected the electric field, which means that the magnetic calculated is no longer right. The magnetic field of Eq. (23.5) is right, but it is only a first approximation. So let's call it B,. We write Eq. (23.5) as E T / clw - iwr E i(>lt B 1-2c oe. 2 (23.9) a A c r 8 s g a t f m N f a s Th e fu in num Th e f Co mp zero a x ap p -0. Fig. 23 -6. The Bessel function Jo(xJ. We g more find t 9 rs as they are, taking into account all the fields in the spaces in tance, if we want a resonant circuit at high frequencies we will one using a coil and a parallel-plate capacitor. eady mentioned that the paralIel-plate capacitor we have been e of the aspects of both a capacitor and an indnctance. With the are charges on the surfaces of the plates, and with the magnetic ck emf's. Is it possible that we already have a resonant circuit? uppose we pick a frequency for which the electric field pattern me radius inside the edge of the disc; that is, we choose wal c . Everywhere on a circle c'oaxial with the plates the electric field w snppose we take a tbin metal sheet and cut a strip just wide ween the plates of the capacitor. Then we bend it into a cylinder nd at the radius where the electric field is zero. Since there are here, when we put this conducting cylinder in place, no currents d there will be no changes in the electric and magnetic fields. We put a direct short circUlt across the capacitor without changing ok wbat we have; we have a complete cylindrical can with elecic fields inside and no connection at all to the outside world. on't change even if we throwaway the edges of the plates outside the capacitor leads. All we have left is a closed can with electric ds inside, as shown in Fig. 23-7(a). The electric fields are osforth at the frequency w-which, don't forget, determined the n. The amplitude of the oscillating Efield varies with the distance he can, as shown in the graph of Fig. 23-7(b). This curve is just he Bessel function of zero order. There is also a magnetic field cles around the axis and oscillates in time 90° out of phase with write out a series for the magnetic field and plot it, as shown in 23-7(c). t we can have an electric and magnetic field inside a can with no ons? It is because the electric and magnetic fields maintain themng E makes a B and the changing B makes an E-all according f Maxwell. The magnetic field has an inductive aspect, and the ii LINES OF /' - - 0 0 0 ® ® it ti 0 ® 0 0 + + + + + ( 0) ® ® + LINES OF 1.0 (b) 2.405-clw r cBe 1.0 (c) r Fig. 23-7. The electric and magnetic fields in an enclosed cylindrical can. 10 OUTPUT INPUT LOOP LOOP at the top must be p shown in also, so t of the can We can a what hap magnetic in the ma is what gi can. Fig. 23-8. Coupling into and out of a resonant cavity. R·F SIGNAL GENERATOR Fig. 23-9. A setup for observing the cavity resonance. >- ...crz You the can. W introduce member, bottom p on the ou capacitor insides of Altho gradually if we mak up the los and fasten If we now current w keep the o driving so frequency can will b The the can an The chan motive fo cr :0 U .5 >:0 >- llw = wo/Q Wo Frequency Fig. 23-10. The frequency response curve of a resonant cavity. circuit, th Suppose w as shown whose fre Then we c ment that portional the freque The outpu Wo, which 11 those like however, an da as can hen y it ent ted ons use ver, not the not 3050 3300 "" '"'' ,= QJ I Fig. 23-11. Z1T (M"IIac)",l.. per HCOnd} Observed resonant fre- quencies of a cylindrical cavity. 12 tric field should meet the wa11 at right angles. We have considered the case in ch the top and the bottom of the can are flat, but things would not be completely h anif the top and bottom were curved. In fact, how is the can supposed to mode, the electric and magnetic fields are as shown in Fig. 23-14. The electric erent a is its top and bottom, and which are its sides? It is, in fact, possible field does not bother to go all the way across the cavity. It goes from the sides to wnd which (b) how p, asthat there is a mode of osci11ation of the fields inside the can in which the the ends, as shown. Fig, 23-12. A higher-frequencyAs mode. fields go more or3050 less across the diameter ofthe can, as shown in Fig. 23-13. you will probably now believe, if we go higher and higher in frequency we striccan 3300 It is not too hard to understand why the natural frequency of this mode should expect to find more and more resonances. There are many different modes, When uld be not very different from the natural frequency of the first mode we have each of which will have a different resonant frequency corresponding to some parary it Suppose that instead of our cylindrical cavity we had taken a cavity B idered. mode,of thethese electric a ticular complicated arrangement of the electric and magnetic fields. Each rrent ch was a cnbe 3 inches on a side. It is clear that this cavity would haveEthree doesmode not bother field arrangements i. called a resonant mode. The resonance frequency field of each erent A mode with the electric field ictedmodes, but a11 with the same frequency. the ends, as shown. ,= can be calculated by solving Maxwell's equations for the electric and magnetic g more or less up and down would certainly have the same frequency as the QJ I Z1T (M"IIac)",l .. per HCOnd} As you will prob asons fields in the cavity. e in which the electric field was directed right and left. If we now distort thet should expect to find f cause When we have a resonance at some particular frequency, how each can we knowwill ha e into a cylinder, we will change these frequencies somewhat. We would stilI of which ---I J B a little wire into the Fig. 23-11. Observed resonant freever, which mode is being excited? One way is to poke cavity ect them not to be changed too mnch, provided we keep the dimensions of the ticular complicated a E of a So cylindrical cavity. nnot Fig. 23-14. the frequency of the mode of Fig. 23-13 shouldAnother mode of a cyty more or quencies less the same. through a small hole. If the electric field is along the wire, as in Fig. field 23-15(a), arrangements i. lindrical cavity. bethe too different from the mode of Fig. 23-8. We could make a detailed calcan be by of there will be relatively large currents in the wire, sapping energy from the calculated fields, tion of the naturalfrequency of the mode shown in Fig. 23-13, but we will not fields in the cavity. and the resonance will be suppressed. If tthe electric field is as shown in Fig. s not f we have hat now. When the calculations are carried through, it is found that, for the 23-15(b), the wire will have a much smaller effect. We could find whichWhen way the which mode is being ensions we have assumed, the resonant frequency comes out very close to the Fig. 23-13. A transverse mode of field points in this mode by bending the end of the wire, as shown in Fig. 23-15(c). cy ofresonance at 3300 megacycles. Fig. 23-14. Another mode of a cythrough a small hole erved the cylindrical cavity. Then, as we rotate the wire, there will be a big effect when the end of thewill wire lindrical cavity. that there be is relative By similar calculations it is possible to show that there should be still another parallel to E and a small effect when it is rotated so as to be at 90' to E. E and the resonance w de at the other resonant frequency we (ound near 3800 megacycles. For this nance 23-15(b), the wire w 23-9 ycles field points in this m might Then, as we rotate t ro of parallel to E and a s cond s one n out ating But over mode nd it have gnetic gnetic ments at the ase in letely ed to ssible h the 3-13. mode have cavity /------ "" '"'' /------ ----( 0) E (b) Fig. 23-15. ( c) A short metal wire inserted into a cavity will disturb the Ethan when it is at right ang.'es. ( resonance much more when it is parallel to Fig. 23-15. A short metal wire in resonance much more when it is paralle r 23-5 Cavities and resonant circuits Although the resonant cavity we have been describing seems to 23-5 be quite Cavities a different from the ordinary resonant circuit consisting of an inductance and a Although the re capacitor, the two resonant systems are, of course, closely related. They are both different from the o (b) Fig, 23-12. A higher-frequency mode. members of the same family; they are just two extreme cases of electromagnetic capacitor, the two re resonators-and there are many intermediate cases between these two extremes. members of the sam Suppose we start by considering the resonant circuit of a capacitor inresonators-and parallel with ther Suppose we start by an inductance, as shown in Fig. 23-16(a). This circuit will resonate althe frequency an inductance, Wo = I/VLC. If we want to raise the resonant frequency of this circuit, we can as sho Wo of = turns I/VLC. 13 do so by lowering the inductance L. One way is to decrease the number in If w do so by lowering the the coil. We can, however, go only so rar in this direction. Eventually we will get i r 1 8 h L ...-'liNES OF 8 fig. 23-16. L II I 0 ® ® ® ® ® ® "e" 0 0 0 0 - :'\ LINES OF E - (0) II I (c) Resonators of progressively higher resonant frequencies. object. Our inductance is now a cylindrical hollow can attached to the edges of the condenser plates. The electric and magnetic fields will be as shown in the figure. Such an object is, of conrse, a resonant cavity. It is called a "loaded" cavity. But we can still think of it as an L-C circuit in which the capacity section is the region where we find most of the electric field and the inductance section is that region where we find most of the magnetic field. 14 Next Week On May 26, 1960, U.S. Ambassador to the United Nations Henry Cabot Lodge, Jr. unveiled the Great Seal Bug before the UN Security Council to counter Soviet denunciations of American U-2 espionage. The Soviets had presented a replica of the Great Seal of the United States as a gift to Ambassador Averell Harriman in 1946. The gift hung in the U.S. Embassy for many years, until in 1952, during George F. Kennan's ambassadorship, U.S. security personnel discovered the listening device embedded inside the Great Seal. Lodge's unveiling of this Great Seal before the Security Council in 1960 provided proof that the Soviets also spied on the Americans, and undercut a Soviet resolution before the Security Council denouncing the United States for its U-2 espionage missions 15