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 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 xyz 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) zvt222 zvt222 1 Ex where v   z H y Exx E0 cos( t kx )

HHtkxyy 0 cos(-) Y  Solution for (7) and (8) can found as HE yx or EZHxy  where Z  known as characteristic impedance of medium  2  k  or k  k is wave vector and is defined as  v  Zohms0 377 For free space (r=1 and r=1) fs  0

10/26/2015 Physics 401 7 EEtkxxx0 cos() X HHtkxyy 0 cos(-)

Ex z Hy

1  v  HE Y  yx

 2  Z  EZH k  or k   xy  v

0 Zohmsfs 377  0

For free space (r=1 and r=1)

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 II0[exp1] 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=V0sint 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 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 22sin x 2 q qss 0 cos (kd sin( / 2) x

where xkb sin(/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 2 22sin x 2 xkb sin(/q 2) qss 0 cos(sin(/ kd 2)  x

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 equation 0 -100 -50 0 50 100 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 2222 “red” and “blue” rays is: DS hdhd1 2 (d 12 d )

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 1890-1971 1862-1942 The 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  222 crystal 2dhkl 

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.

 0.0110nm

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