Qualitative Studies with Microwaves Physics 401, Fall 2015 Eugene V. Colla The main goals of the Lab: Refreshing the memory about the electromagnetic waves propagation Microwaves. Generating and detecting of the microwaves Microwaves optic experiments This is two weeks Lab 10/26/2015 Physics 401 2 The microwave range includes ultra-high frequency (UHF) (0.3–3 GHz), super high frequency (SHF) (3–30 GHz), and extremely high frequency (EHF) (30–300 GHz) signals. Microwave Electromagnetic*by spectrum*courtesy Wikipedia 10/26/2015 Physics 401 3 Microwave oven (2.45GHz) Communication (0.8-2.69GHz) Satellite TV (4-18GHz) Radar Motion detector (10.4GHz) (up to 110GHz) Weather radar (8-12Ghz) *by courtesy Wikipedia 10/26/2015 Physics 401 4 B D (1) E (3) t D (2) HJ (4) B 0 t James Clerk Maxwell (1831–1879) If = 0 and J = 0 and taking in account that DE BH (1) and (4) can be rewritten as E Ex y Ez D D 0 H x y z t 10/26/2015 Physics 401 5 Now assuming that plane wave propagate in z direction and what leads to Ey=Ez=0 and Hx=Hz=0 Now (3) and (4) could be simplified as X H Ex y Ex (5) zt z Hy HE yy zt(6) Y where or or 0 is the free space permeability, 0 is the free space permittivity r is permeability of a specific medium , r is permittivity of a specific medium 10/26/2015 Physics 401 6 Combining (5) and (6) (see Lab write-up for more details) we finally can get the equations of propagation of the plane wave: 22 22 EExx1 HH1 X (7) yy (8) z2 v 2 t 2 z2 v 2 t 2 1 Ex where v z H y Exx E0 cos( t kx ) Hyy H0 cos( t - kx ) Y Solution for (7) and (8) can found as HE yx or Exy ZH where Z known as characteristic impedance of medium 2 k or k k is wave vector and is defined as v Z0 377 ohms For free space (r=1 and r=1) fs 0 10/26/2015 Physics 401 7 X Ex z 1 H v y Exx E0 cos( t kx ) Y Hyy H0 cos( t - kx ) HE yx Exy ZH or Z 2 k k v 0 Zfs 377 ohms For free space (r=1 and r=1) 0 10/26/2015 Physics 401 8 Vacuum tubes: klystron, magnetron, traveling wave tube Solid state devices: FET, tunneling diodes, Gunn diodes 426A Heated cathode as electron source Tunable frequency from 9 to 10GHz; Microwave oven magnetron; maximum output typical power 0.7-1.5kW power 20mW 10/26/2015 Physics 401 9 Russell Harrison Sigurd Fergus Varian (April 24, 1898 Varian (May 4, 1901 – July 28, 1959) – October 18, 1961) Varian Brothers...Klystron Tube (1940) 10/26/2015 Physics 401 10 Generating of the microwaves. Klystron. Single transit klystron Reflection klystron High power klystron Advantages: well defined used in Canberra Deep frequencies, Space Communications high power Complex (courtesy of output Wikipedia) 10/26/2015 Physics 401 11 Digital Volt Meter or Oscilloscope Digital Volt Meter or Oscilloscope attenuator horn horn frequency termination detector detector meter Klystron Microwave Transmitter Arm Microwave Receiver Arm 10/26/2015 Physics 401 12 Experimental setup. Main components. Attenuator Frequency meter detector Klystron 10/26/2015 Physics 401 13 Detector diode V out RF RF in choke Bypass capacitor eV Typical I-V dependence for p-n diode II0[exp 1] kT Taylor expansion for exp function will give: x2 x3 2 exp(x) 1 x ... I aV bV ... 2! 3! 0(DC) 2 If V=V0sint 2 V0 푉 0 푏 ∗ ퟏ − 풄풐풔ퟐ흎풕 IbDC ... And finally ퟐ 2 10/26/2015 Physics 401 14 fc ~ 200GHz 10/26/2015 Physics 401 15 Mirror A Mirror B LR Transmitter Albert Abraham Michelson Beam splitter (1852 - 1931) LB The Nobel Prize in Physics 1907 LR, LB optical paths (OP) for Condition for constructive interference “red” and “blue” rays Receiver OP = n*L G 2 LR LB n n – refraction index; LG – geometrical length 10/26/2015 Physics 401 16 Physics 403 Lab Michelson interferometer setup 10/26/2015 Physics 401 17 For constructive Interference r1 Dr=n or dsinq=n Thomas Young (1773 – 1829) r2 The measured envelope of the diffraction pattern can be defined as: 2 Dr=r1-r2=dsinq 22sin x 2 q ss 0 cos (kd sin( q / 2) x where x kbsin(q / 2) and d 2 k is wave vector of the plane wave b 10/26/2015 Physics 401 18 Transmitter Physics 403 Lab setup and example of the data 10/26/2015 Physics 401 19 x kbsin(q / 2) Model Two_slit (User) =3.141cm 200 Equation y=I0*(sin(K1*sin(pi*x/360+f))/(K1*sin(pi*x/360+f))) ^2 *(cos(K2*sin(pi*x/360+f)))^2+I00 Reduced Chi-Sqr 94.62111 Adj. R-Square 0.96659 Value Standard Error I0 190.6014 3.042882 K1 4.384042 0.074754 100 K2 13.51332 0.052244 I (nA) f -0.01525 7.19E-04 I00 9.572049 1.440409 Fitting equation2 22sin x 2 0 cos (kd sin( q / 2) -100 -50 0 50 100 ss 0 x o q Here in fitting expression: 흅풙 ퟐ 퐬퐢퐧(푲ퟏ 퐬퐢퐧 +풇 푰ퟎ = 흍ퟎ ; ퟑퟔퟎ 2 ퟐ 흅풙 풚 = 푰ퟎ ∙ 흅풙 퐜퐨퐬 푲ퟐ 퐬퐢퐧 + 풇 +I00 푲ퟏ 풔풊풏 +풇 ퟑퟔퟎ 푲ퟏ = 풌풃; ퟑퟔퟎ 푲ퟐ = 풌풅 10/26/2015 Physics 401 20 Mirror h Transmitter Receiver Humphry Lloyd 1802-1881 d1 d2 Difference of the wave paths of 2 2 2 2 “red” and “blue” rays is: DS h d1 h d2 (d 1 d 2) For constructive interference DS=n Lab setup picture 10/26/2015 Physics 401 21 n1sinq1=n2sinq2 Snell’s law Willebrord Snellius n1>n2 Claudius Ptolemaeus 1580-1626 q1 after AD 83–c.168) n1 n Equation for critical angle: 2 q2 o n1sinqc=n2sin90 -1 qc=sin (n2/n1) 10/26/2015 Physics 401 22 Transmitter n1(lucite) n2(air) Lucite prism 1.5 ) A ( 1.0 0.5 Signal intensity Experimental setup and the example of the data 0.0 0 20 40 60 80 100 0 Angle q 10/26/2015 Physics 401 23 Polarizer Transmitter Receiver Etienne-Louis Malus 1775 – 1812 Transmitter Malus law Metallic grid q E=E0cosq I∞E2 2 I=I0cos q 10/26/2015 Physics 401 24 Transmitter Rotatable receiver Polarizer 2 I=I0cos q Experimental data 10/26/2015 Physics 401 25 Interference of the EM waves reflected from the crystalline layers Sir William Henry Bragg William Lawrence Bragg 1890-1971 1862-1942 The Nobel Prize in Physics 1915 "for their services in the analysis of crystal structure by means of X-rays" 10/26/2015 Physics 401 26 (100) (110) (210) Different orientations of the crystal 10/26/2015 Physics 401 27 In our experiment ~3cm; For cubic symmetry the angles of Bragg peaks can be calculated from: n=2dsinq <2d 2 qsin2 2 2 2 crystal 2d h k l where h,k,l are the Miller Indices. For crystal with d=5cm and =3cm the 3 first Bragg peaks for (100) orientation can be found at Experimental setup angles: ~17.5o; 36.9o and 64.2o 10/26/2015 Physics 401 28 q q 10/26/2015 Physics 401 29 4 Matthew Stupca Longxiang Zhang ) A ( I 2 (100) (110)(111) (220) (200)(210) (211) (300) 0 0 10 20 30 40 50 60 70 80 90 (degree) *courtesy of Matthew Stupca 10/26/2015 Physics 401 30 Bragg diffraction. X-rays. 0.0110nm X-ray tube *courtesy of Wikipedia 10/26/2015 Physics 401 31 Bragg diffraction. X-rays. X-ray K-series spectral line wavelengths (nm) for some common target materials Target Kβ₁ Kβ₂ Kα₁ Kα₂ Fe 0.17566 0.17442 0.193604 0.193998 Co 0.162079 0.160891 0.178897 0.179285 Ni 0.15001 0.14886 0.165791 0.166175 Cu 0.139222 0.138109 0.154056 0.154439 Zr 0.70173 0.68993 0.78593 0.79015 Mo 0.63229 0.62099 0.70930 0.71359 David R. Lide, ed. (1994). CRC Handbook of Chemistry and Physics 75th edition. CRC Press. pp. 10–227 *courtesy of Matthew Stupca 10/26/2015 Physics 401 32 Bragg diffraction. X-rays. *courtesy of Matthew Stupca 10/26/2015 Physics 401 33 Comments and suggestions 1. Klystron is very hot and the high voltage (~300V) is applied to repeller. 2. You have to do 6 (!) experiment in one Lab session – take care about time management. The most time consuming experiment is the “Bragg diffraction”. 3. Do not put on the tables any extra stuff – this will cause extra reflections of microwaves and could result in smearing of the data. 4. This is two weeks experiment but the equipment for the week 2 will be different. Please finish all week 1 measurements until the end of this week Good luck ! 10/26/2015 Physics 401 34.