Microwave cavities Physics 401, Fall 2015 Eugene V. Colla Agenda

• Waves in waveguides • Standing waves and resonance • Setup • Experiment with microwave cavity • Comments on Bragg diffraction experiment

11/2/2015 2 Maxwell’s uniform plane wave traveling wave equation Equations in z-direction  H ┴ E 22 Exx1 E D 0 2 2 2 X zvt B 0 general form of solution Ex B z zz    Ez (,) z t f t    g  t    E   Hy vv t     Y propagation speed D 1  H  v    Z  t  E vs H

 i() t kz H  E E  ZH Ex  E0 e y  x x y

11/2/2015 3 Ey=Ey(x) at Z Y i Y

X

Y Ey=Ey(z) at xi v b X Z Zi Xi a

Z

i() t kz Eyx E0 sin k x e

11/2/2015 4 i() t kz Eyx E0 sin k x e + i() t kz Eyx E0 sin k x e

= L

L=n*l/2

11/2/2015 5 X X Ey=Ey(z) Y Y

Z Z

X Ey=Ey(x or z)

Ey

Z H-field

11/2/2015 6 2 2 2 22m   n    p   mnp v0         a   b   c 

2 v0 -phase velocity

TE101 mode: m=1, n=0, p=1

22 2 2 2 11    101v 0     c ac    b 

a

11/2/2015 7 cavity coaxial wave guide Y I coupling loop outer H conductor X

Z inner conductor R R M C C line L0 L Z0 Impedance of L wave guide

11/2/2015 8 coaxial wave guide cavity L QL  RZ 0 coupling loop Y outer conductor X L Q0 Z QL  , inner conductor R 1    Z0 1  Z0 : coupling coefficient

Maximum power transfer: Z 0 Z1R   Impedance of 0 wave guide 1 QQ , L 2 0 quality factor without external load

9 11/2/2015 Resonance Cavity

Gunn diode 11/2/2015 MW oscillator 10 A

11/2/2015 11 Tuner detector Open Slotted line end

Use detector to find distance between minimums in the slotted line (wave guide)

11/2/2015 12 50

40

30

20

E (mV) 10 l/2

0 0 2 4 6 8 10 12 14 16 18 x (cm)

Use detector to find distance between minimums in the slotted line (wave guide). Distance between consequent minima correspond l/2

11/2/2015 13 cavity

Movable plunger (c direction)

Use plunger to change the dimension of the cavity in z-direction and search for maxima in power stored using the cavity detector. Identify

TE101 and TE102.

11/2/2015 14 22 22 2 2 2 12    v0 12    v f102  102 0     2 ac    ac       

f Q  0 ~ 450 Df Df

f0

11/2/2015 15 By moving the plunger we changing the resonance 1st position of the frequency of the cavity plunger

2nd position of the plunger

Frequency of the oscillator

11/2/2015 16 11/2/2015 17 1. Oscilloscope should run in X-Y mode 2. To plot the I(f) dependence you have to download both Ch1 and Ch2 data 3. Use triangular waveform as a voltage applied to modulation input of the oscillator 4. Use a proper time scale setting on the scope which could estimated from scanning frequency 5. Apply the calibration equation to calculate the frequency of the oscillator from the modulation voltage

G

fV0.03706mod 2.9349

11/2/2015 18 Voltage tunable oscillator ZX95-3250a- S+ from

11/2/2015 19 FM Calibration for microwave oscillator

11/2/2015 20 11/2/2015 21 By changing of the coupling between oscillator and cavity we can control the quality factor of the cavity resonance but in the same time we changing the power delivered to the cavity

11/2/2015 22 Detector B field

While in resonance: turn orientation of the o input loop from the vertical direction in 10 o steps to 360 . Read cavity detector.

11/2/2015 23 12

10

8 Experimental result. 6 Fitted to 풏 푨 (cos(  + )) + 푨ퟎ I (mA) 4

2

0

0 50 100 150 200 250 300 350 grad)

11/2/2015 24 Presence of dielectric reduces length of cavity at a given resonance

frequency ω0. This effect grows with the electric field strength Ey.

(0) Without dielectric the cavity length at resonace is c0. (1) Place dielectric into cavity and move in 0.5cm steps, li. (2) At each place tune plunger to resonance and record ci. (3) Plot ∆ci=|c0-ci| versus li : this measures now Ey vs l!

11/2/2015 25 TE102 X

Y

Z

Courtesy of P. Debevec

11/2/2015 26 Quality factor (TE101 mode) of unloaded cavity can be calculated as: abc a22 c  Q  0 3 3 2 2  2b a c  ac a  c 

 is the skin depth at frequency 0  2/  

 – resistivity of the cavity material 7 c r0≈04x10 b

a

11/2/2015 27 For red brass  =6x10-8m  2/   ≈4x107

-6 2.25x10 m a=7.22cm, b=3.42 cm, c=6.91cm (TE101)

abc a22 c  Q  0 3 3 2 2  2b a c  ac a  c 

c Q0~7700 b

a

11/2/2015 28 q’=900-q

11/2/2015 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)

11/2/2015 30 Second order reflection ?

Lloyd’s mirror effect

11/2/2015 31