Measurement of spontaneous emission phase fluctation in helium, neon laser

Arrathoon, R.

Siegman, A. E.

English

NASA Technical Reports Server

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FITRT€ER MEASWMENTS OF QUANTUM PHASE NOISE I N  A He-Ne LASER 
by 
R .  Arrathoon and A. E .  Siegtnan 
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https://ntrs.nasa.gov/search.jsp?R=19680028337 2020-03-12T05:40:46+00:00Z
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N O I S  IN A He-Ne USE$ 
Siegmn 
Department of E l e c t r i c a l  Engineerlng 
Stanford University 
Stanford, Cal i forn ia  
ABSTR4CT 
Extended measwements of l a s e r  frequency f luc tua t ions ,  using 
improved instrumentation, have provided f u r t h e r  v e r i f i c a t i o n  of t h e  
Schawlow-Tomes r e l a t i o n  for  t h e  spontaneous-emission-lhdted l i n e -  
width of a l a s e r  o s c i l l a t o r .  
I 
FLIRTHER EEk3JEEMEW;ilS OF QUA;V;rUr;r ?X.ASE NOISE 7N A He-Ne LEER* 
R. -4rrathoon and A.  E. Siegman 
Department of E l e c t r i c a l  Engineering 
Stanford University 
Stanford, Cal i forn ia  
We recen t ly  reported t h e  observation of spontaneous-emiss ion- 
induced phase f luc tua t ions ,  or "quantum phase noise", i n  8 He-Ne 
6328 1 l a s e r  operating at  power l e v e l s  i n  the low nicrowatt  range. 
Using s l i g h t l y  modified instrumentation, we have now extended these 
quantum phase f l u c t u a t i o n  measurements over a wider range of l a s e r  
povers, and have used'amplitude f luc tua t ion  measurements t o  d-  termlne 
t h e  excess noise f a c t o r  appropriate t o  our l a s e r s .  
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i 
Our new r e s u l t s  
i n  general  va l ida t e  our e a r l i e r  measuremnts, and give f u r t h e r  support 
t o  t h e  Schawlow-Tovnes r e l a t i o n  f o r  t h e  spontaneous emission contrl.- 
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but ion  t o  t h e  l inewidth of a l a s e r  o s c i l l a t o r .  
The Schawlow-Tomes formula pred ic t s  t h a t  t h e  quantum phase 
noise contr ibut ion t o  the o s c i l l a t i o n  l inewidth of a l a s e r  5s 
where LY i s  the  f u l l  lorenizian l inewidth cont r ibu t ion  due t o  
9 
t h i s  noise source; N2 and N1 a r e  the  upper and lover l a s e r  l e v e l  
populat-.ions; P i s  t h e  l a se r  power levz l ;  f is  t h e  o s c i l l a t i o n  
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frequency; and ef i s  the  "cold" laser c a v i t y  bandwidth. The 
excess noise f ac to r  CY = Ne/lN2-(g2/gl)N1] my be determined 5y 
measuring the  amnlitude f luc tua t ions  i n  t h e  same l a se r ,  as shown 
by Freed and Haus . 3  The audio-frequency ar;lDlitude f l u c t u a t i o n  
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spectrum of t h e  laser ,  measured using a photomultiplier with an 
appropriate  load r e s i s t m c e  R L 
shot-noise term and an excess or quantum amplitude noise term 
, may be wr i t t en  as t h e  sum of a 
S(f) = s f S e ( f )  
G 
2 = RL 
In  t h i s  expression 
r l  
RL ( i n  V O ~ . ~ ~ / H Z ) ;  
S i s  the  s p e c t r a l  dens i ty  of the  vol tage across  
bI i s  the photomultiplier yower gain; Ia i s  
the  Anode dc current;  q i s  t h e  Fhotocathode quantum ef f lc icncy;  
r' i s  t h e  shot  noise enhancement f ac to r ;  and LY (= 10 t o  30 kHz) 
i s  t h e  bandwidth of the  amplitude f l u c t u a t i o n  spectrum. For lasers 
operating st low o s c i l l a t i o n  power leve ls ,  t h e  excess amplitude noise 
term Se ( f )  
frequencies l e s s  than Af . 
i s  s u b s t a n t i a l l y  l a rge r  t han  t h e  sho t  noise term f o r  
The escess m u l i t u d e  noise saectrum Se(f)  was  measured for 
our l asers ,  using an audio wave analyzer, a t  f requencies  up t o  approxi- 
mately 1 MHz . 
Freed and Haus, 
tude f luc tua t ions  a t  very low frequencies (5 3 kHz), which w e  t e n t a t i v e l y  
The r e s f i t s  were i n  general  agreement wi th  those of 
3 except f o r  a small a d d i t i o n a l  increase  I t !  t h e  ampli- 
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' a t t r i bu te  t o  plasm disturbances. The  mean-square voltage readings 
v = SeB , where B is  t h e  analyzer bandwidth, were mul t ip l ied  by 
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tremely simple form 
t h e  appropriate  correct ion factor  of .1.13 z to account fo r  gaussian 
noise  i n  a s inusoida l ly  ca l ibra ted  average-reading voltmeter.  The 
value of the  excess noise spectrum for frequencies l e s s  than 
toge thsr  with the  measured bandwidth kit? of the  excess noise 
f luc tua t ions ,  i n  essence measures the  excess noise  f a c t o r  Q . 
A€ , 
I n  facf;, if t h e  measured dc voltage V, across  the  anode r e s i s -  
tance R 
a t ions ,  ther? t h e  Schawlov-Townes formula may be c a s t  i n t o  t h e  ex- 
is 'measured a t  t h e  same time as the  excess noise  f l u c t u -  L 
i n  which a l l  quan t i t i e s  a re  d i r e c t l y  measurable. The measured value 
of t h i s  expression was used t o  provide the  t h e o r e t i c a l  value of 
aga ins t  which t o  compare OUT frequency f l u c t u a t i o n  measurements. 
Using t h i s  approach, it i s  not necessary t o  make separa te  determina- 
t i o n s  of t h e  photocathode qumtum e f f i c i ency  o r  the  photomultiplier 
gain.  
Af 
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However, these quapt i t ies  were a l s o  independently iwilcured t o  
guarantee t h a t  a l l  aspse ts  of the experiment were under proper czn t ro l .  
The p r inc ipa l  change i n  t h e  ;OA-ecjLlency f luc tua t ion  instrumentation 
W a s  t h e  replaseizent of the previous c o m c r c i a l l y  ava i l ab le  30 bXz FM 
discr imina tor  (WIG Elect.ron?'_-s Inc .  bIode1 IE 3006) with a quacbatwe 
de tec to r  discr iminator  centered a t  4.5 MHz . 4 The 4.5 Mkiz amplif ier ,  
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l imi te r ,  and discr iminator  were assembled from Fa i r ch i ld  and RCA in tegra ted  
c i r c u i t s .  
from RCA CA-3013  in tegra ted  c i r c u i t s .  A subsequent s tage  cons is t ing  of a 
s ing le  Fa i r ch i ld  pA71r(E in tegra ted  c i r c u i t  suppl ied f u r t h e r  ampl i f ica t ion  
and l imi t ing .  T h i s  stage,  i n  conjunction with an ex terna l  quadrature 
tank, a l so  provided t h e  frequency discr iminat ion.  The narrower bandwidth 
Two stages of  preamplif icat ion and l i q i t i n g  were constructed 
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and somewhat b e t t e r  s e n s i t i v i t y  of t h i s  system permitted quantuq phase 
f luc tua t ion  measurements a t  higher l a s e r  power l e v e l s  (lower frequency 
f luc tua t ion  l eve l s )  than previously possible .  
Our. t o t a l  experimental r e su l t s ,  together  with the  Schawlow-Townes 
predic t ion  as ca l ib ra t ed  from t h e  amplitude f l u c t u a t i o n  measurements, 
a r e  presented i n  Fig.  1. The t r i angu la r  da t a  po in t s  i nd ica t e  r e s u l t s  
obtained e a r l i e r  by a phase j i t t e r  technique a t  a s p e c i f i c  delay time 
T = 167 nsec. 
obtajned with the new 4.5 MHz discr iminator  and i , f .  system. 
these  r e s u l t s  d i f f e r  by approximately a f a c t o r  of two from the  e a r l i e r  
The square d a t a  poin ts  i nd ica t e  quantum noise  r e s u l t s  
Both of 
measurements made with the  30 MHz discr imina tor  system. The d i f fe rence  
may be due t o  d i f f e ren t  lirni-ting c h a r a c t e r i s t i c s  i n  the  two discr imi-  
na tors .  The Schawlow-Townes predic t ions ,  t ak ing  i n t o  account uncer- 
t a i n t i e s  i n  the  evaluation, seem t o  be i n  good agreement with our 
o v e r a l l  r e s u l t s .  
- 7 The apparent sharp increase i n  quantum noise  below P = 2 X 10 
watts  should probably, as  before,  be discounted. I n  t h i s  region the  
.. . 
signal--to-noise de tec t ion  r a t i o  has decreased below 20 dB; hence, 
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T '  
a l l  of the  FM measurement techniqws begin t o  d e t e r i o r a t e  rapidly,  In  
accordance with the  well-known threshold proper t ies  of FM rece ivers .  
Also, due t o  the  
expect t h a t  small f luc tua t ions  i n  the  power s t a b i l i z a t i o n  loop at  
these  low l eve l s  could result i n  an augmented noise output. 
1/P power dependence of quantum noise, we might 
Progress i s  cur ren t ly  being made on a high-gain He-Xe 3 .31~  
laser system with which we hope t o  observe quantum phase fluctu- 
a t ions  i n  grea te r  d e t a i l  and with irnproved accuracy. 
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Cambridge, Massachusetts. 
A.  E. Siegman and R. Arrathoon, "Observation of Quantum Phase Noise 
i n  a Laser Osci l la tor ,"  Phys. Rev. Le t t e r s  20, 901 (22 A p r i l  1968); 
see also, A .  E. S i cgun ,  5. Daino, and K. R. Ykines, "Beliminary 
Measurement of Laser Short-Term Frequency Fluctuat ions,  " D3EE J. 
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This  study was supported by t h e  N4SA Elec t ronics  Research Center, 
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&ant. E lec t .  - QE-3, 180 (May 1967). 
A. L. Schawlov and C. H. Townes, Phys. Rev. - 112, 1940 (1958); for 
B more recent  discussion,  c f .  M. Lax, i n  Physics of Quantum Elec-  
tronics, edi ted by P. L. Xelley, B. Lax, and P. 8. Tannenwald 
(McGra,w-Hill~ Book Company, Inc., New York, 1966), p. 733. 
R. Freed and H. A.  Haus, "Neasurem~nt or Amplitucie Noise i n  
Optical  Cevity Ihsers," Appl. Pnys. Le t t e r s  - 6, 83 (Vmch 1,065). 
2. 
3.  
4. James N. Giles, ed., F a i r c h i l d  Semiconductor Lfnear - In tegra ted  
C i rcu i t s  Applications - Handbook, Fa i r ch i ld  Semiconductors, Mountain 
View, California  (Library of Congress No. 67-27446). 
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1. Q u a r t u m  phase noise measurements as obtained with the 30 bNz 
discr in ina tor ,  the 4.3 MHz discriminator,  and the phase jitter 
ins t rmen ta t ion .  The shaded area represents  t h e  t h e o r e t i c a l l y  
expected values based on the evaluation of Eq. ( 3 ) .  
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PHASE JITTER = * 
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Further Measurement of Quantum Phase Noise in a He-ne Laser

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