Transcript Thapa-SaturationSpectroscopy

Saturation Spectroscopy
-Inside Photonic Band Gap Fiber
Rajesh Thapa
Kevin Knabe, Ahmer Naweed, Aaron Pung
Larry Weaver, Brian Washburn, Kristan Corwin
Outline
An overview:- optical frequency references
IR wavelength standard
Pump probe spectroscopy
Observations of saturation spectra
Modeling of Light Inside Fiber
Conclusion and future direction
An Overview : Optical Frequency References
  nm 
CH4
C 2H 2
3390
1556
C2HD
1064
Rb
Ca
I2
778
657
532
H
486
Well studied optical frequency references
v1+v3 combination band of acetylene
Robust and stable frequency
1.
communication and navigation System
2.
- Frequency division multiplexing
3.
- Spectrum analyzer
4.
Relevance to telecommunication industry
Well separated transitions.
~ms long lifetime, ~kHz linewidth.
Lack of permanent dipole moment.
Relatively immune to external field and
shifts.
Sarah L. Gilbert, W.C.S., Acetylene 12C2H2 Absorption Reference for 1510 nm to 1540 nm Wavelength
Calibration-SRM 2517a. 2001
Higher-accuracy IR wavelength standard:
nonlinear spectroscopy
• Comité International des Poids et Measures, 2000
– 13C2H2 P(16) ± 100 kHz (2000)
– Comb-based meas. ±
2 kHz (2005)
• Great Britain, Japan, Canada, Japan
Existing portable wavelength
references for the telecom industry
Line centers:±130 MHz or ±13 MHz
Used to calibrate optical spectrum analyzers
(OSA’s)
pressure → broadening & shift
laser
or LED
C2H2
W.C. Swann and S.L. Gilbert. (NIST), Opt. Soc. Am. B, 17, 1263 (2000).
Spectroscopy Inside Power Build up cavity
Basis for Highest-accuracy measurements
Cavity:
Long Interaction length
High Intracavity Power
Cavity and laser locked to resonance independently
Not Portable, Fragile
Figure from:
K. Nakagawa, M. de Labachelerie, Y. Awaji, and M. Kourogi, JOSAB 13, 2708 (1996)
Hollow Core Photonic Band Gap Fiber
Blaze Photonics
(www.blazephotonics.com)
J. C. Knight et al., Science, 282, 1476, 1998
photonic band gap fiber.
Advantages:
Long interaction length
High laser intensities
More portable
Proximity of fiber surfaces to the molecules
Small beam size inside the fiber (~15µm)as compared to cavities (500µm
Predicted loss from the fundamental mode in
ordinary hollow core fiber and PBG fiber
Knight, j.C., Photonic crystal fibers. nature, 2003. 424: p. 847.
How Popular is Acetylene in
PBG Hollow Core Fiber?
•Gas sensors (Helsinki U. of Tech., Crystal
Fiber 2004)
•Optical frequency standards (Bath, 2005)
•Sealed PBG fiber cells
•Saturated absorption in hollow-core
photonic bandgap fibers
(J. Henningsen et al., 2005)
Figure from F. Benabid et al., Nature (2005).
Recent Paper
Saturated absorption in acetylene and hydrogen cyanide
in hollow-core photonic bandgap fibers
Jes Henningsen, Jan Hald, and Jan C. Peterson
Opt. Express 13, 10475-10482 (2005)
See background noise,
We have at least 40 times higher signal to noise ratio
Fiber Diameter :- 10 µm
Width :- 22.4 MHz
Psat :- 23 mW
The improved SNR makes overtone
transitions in the near-infrared
region accessible to frequency
metrology.
Application and Motivation
• Basis of international frequency reference in
near-IR region with accuracy in KHz limit .
• Basis of portable frequency reference for
telecom industry .
Splice
Splice
Step Index,
Single
Mode Fiber
(SMF)
PBG Fiber
Fiber Cell
Step Index,
Single
Mode Fiber
(SMF)
LUMOS Spliced Fiber (2005)
74% coupling efficiency
First Fiber Cell
SMF Fiber
1550 nm
Diode
Laser
Electrodes
Gap
PBG
PBG Fiber
Optical
Power
Meter
SMF
Fiber Splicer
(a)
splice loss - 1.6 dB
(b)
Splice Loss ~ 1.3 dB
mechanical strength of the splices
Evacuated up to the pressure
[ 80 bar -1 µbar ]
of ~10 mT for ~14 hours
“Compact, stable and efficient all-fibre gas cells using
hollow-core photonic crystal fibres”
Benabid et al., Nature (2005).
Splicing hollow-core photonic bandgap fibers for gas-filled
optical frequency references to solid core fiber using an arc fusion splicer
R. Thapa, K. L. Corwin, and B. R. Washburn, Submitted in CLEO 2006
Theoretical Approach
Pump Probe Spectroscopy
Absorption Of Light
(Beer’s law)
∆I
= -() ∆z
I
‘ ‘is the absorption coefficient
Ne2
 / 2

4 o mc (o   )2  ( / 2)2
 ( ) z
I  Ioe
True basically If, ∆z
Or, I
0
0
This leaves most of population in Ground state
∆z
IO
I
∆I
Laser
Molecules
Fiber
Normalized Transmission
Absorption
1.0
0.8
0.6
0.4
0.2
0.0
-1000 -500
0
500
1000
Frequency in MHz
What if laser light is Intense
It Significantly begin to Deplete the Population of Ground State
N 0 (v z )
N (v z ) 
1  S0 (, v z )
N2(v)
v
 S ( ) 
 ( )
0
1  S0
P
S0 
Ps
N1(v)
Doppler Broadened
Profile, ~ 500 MHz Wide
v
Pump Probe Spectroscopy
•Pump burns hole in velocity distribution,
•probe samples different velocity class,
except when on resonance.
Schematic
Of Experimental
Experimental
Set-Up Set up
Pump
Probe
Probe
Pump
L
L
Photo Diode
BS
70%
L
Photo Diode
/4
30%
BS(30/70)
70%
L
30%
AOM
AOM
EDFA
400 mW
BS
90%
L
Glass Cell
5 mW
squeezer
Diode
Laser
Isolator
BS
Diode
Laser
Squeezer
EDFA
BS
(10/90)
Squeezer
Squeezer
L
/2
BS
Isolator
Photo Diode
//42
Vacuum Chamber
BS
L
Photo Diode
/4
L
Squeezer
BS
L
PBG Fiber
PBG Fiber
Vacuum Chamber
Michelson
Interferometer
Photo Diode
Photo Diode
P (13) line, 10µm diameter fiber
P (11) line, 20µm diameter fiber
1.0
i
ii
0.8
iii
0.6
iv
v
0.4
0.2
i
ii
iii
iv
v
145 mT
260 mT
530 mT
715 mT
2250mT
0.0
-600 -400 -200
0
200
400
600
800
Fractional Transmission
Fractional Transmission
1.0
0.8
0.6
138 mT
219 mT
317 mT
435 mT
540 mT
0.4
0.2
0.0
-1000
Frequency(MHz)
Saturated absorption spectra as a
function of 5 different pressures
-500
0
500
1000
Frequency (MHz)
More Background Noise
Surface mode?
Transmission of light through glass
We need some equation to fit this profile. SEARCH!!!
Our Fitting Equation
 2(  0 ) 
Y  Y0  Ag exp 




g
2
Fitting Parameters


l2
1  Al
2
2
4(



)



0
l 

Ag
Al
g
l
Ag * Al
Y   S ()* l
Ag
l
g

2

 S / 2

S0
0

 S ( )   ( ) 1 

2 (   ) 2  * / 2
0
S


 S   1  S0
 
*
S
 s
2



2



1/ 2
 1  1  S0  
2

See Our Fit
0.48
Absorbance,s
1.6
1.2
Data
0.45
2250 mT
715 mT
530 mT
260 mT
145 mT
0.42
0.39
0.36
0
30
60
90
0.8
0.4
0.0
-750
-500
-250
0
250
500
750
Frequency (MHz)
It Seems Our Equation Works!!!
Width (MHz)
Pressure-Broadening measurement of the different lines.
40
30
P (11) 10 m
P (11) 20 m
P (13) 20 m
P (16) 20 m
20
0.0
0.5
1.0
1.5
Pressure (T)
2.0
2.5
10µm diameter fiber , Width varies from 35 to 45 MHz
20µm diameter fiber , Width varies from 20 to 35 MHz
~10 MHz/Torr of Pressure Broadening
What determines width?? Perhaps other broadening mechanism ???
Broadening Mechanism
•Transit time broadenings
-Interaction time of the molecule with laser beam
In terms of frequency,
V, most probable velocity of molecule
v  0.75v / D
 v  25MHz
For 20µm diameter fiber
 v  46.5MHz
• Power broadenings
N 0 (v z )
N (v z ) 
1  S (, v z )
 S ( ) 
For 10µm diameter fiber
   N1  N2 
 ( )
0
1 S

s
 0  
 S  

See some Power broadening effect!!!
Optimum Signal Size
-1
Disc. (kHz )
3
P (11) 10 m
P (11) 20 m
P (13) 20m
P (16) 20 m
2
1
0
0.0
0.5
1.0
1.5
2.0
2.5
Pressure (T)
Discrimination = change in fractional transmission due to pump
signal width
Fractional Transmission
Power broadening effect on the lineshape for P (11) lines
8 mW (no offset)
16 mW (no offset)
32 mW (no offset)
64mW (offset 0.1)
100mW (offset 0.2)
1.2
1.0
0.8
0.6
0.4
0.2
-600
-400
-200
0
200
400
600
Frequency (MHz)
Higher the power – bigger the amplitude of narrow feature- good for freq. reference
Higher the power – wider the width of narrow feature- bad for freq. reference
Power-Broadening measurements
Fit *S 
Width (MHz)
50
P
S0 
Ps

1/ 2
1  1  S0  
2

Ps ~ 20mW
Ps ~ 45mW
40
P (11) 20m
P (13) 20 m
P (11) 10 m
30
0
25
50
75
100
125
Incident Pump Power (mW)
Why Psat different ??? A big question!!!
Theoretical Approach and Numerical Analysis
Calculation of Saturation Parameter
Remember:- Demtroder eq. is valid only for S<<1
But Psat is small so S is large !!!
The total absorption coefficient
 ( )   N (v z ) 12 ( , v z ) dv z
Absorption cross-section of
probe in presence of pump.
Population change
is due to Pump only
2


 / 2

 (, vz )   0 ( ) 

2
2
 (  0  k v z )   / 2  


S0   / 2 
N (v z )  N (v z ) 1 

2
2
 (  0  kv z )   s / 2  
2
0
Integration over entire velocity spectrum gives,
2
      2  

/
2


(   S )
S
0
1  S0
 S ( )   0 (0 ) exp  

 
0.6

2(1  S0 ) 2 S (   )2  * / 2
D

 

0
S


This is true for any S0
Usual linear attenuation
of the Weak probe beam
When S<<1,  S



2


Change in signal induced by the
Intense field, a Lorentzian of width w
  , above eq reduces to,
2


/
2
 S 
S
 S ( )   0 ( ) 1  0

2 (   ) 2  * / 2
0
S





2


Now, we have our
Own Equation!!!
Numerical Calculation of Psat Using Pump Propagation into account
Fiber
Pump
 Pn  Pn1  S ()z
 0 ( )
 S ( ) 
1  P / PS
P0 P1 P2
Pump Power
Pn
Small Finite Segment
We Know P0 and Pn, vary Ps until we get
measured pump output power.
Recent Paper
Saturated absorption in acetylene and hydrogen cyanide
in hollow-core photonic bandgap fibers.
Jes Henningsen, Jan Hald, and Jan C. Peterson
Opt. Express 13, 10475-10482 (2005)
Pump Power (mW)
Psat~ 23 mW
20
Psat ~ 20 mW
18
16
0.25 0.5 0.75 1 1.25 1.5 1.75
Distance along fiber
Modeling Of Light inside the fiber
Fiber
Pump
P0 P1 P2
Small Finite Segment
P’n
Pump Power
Probe Power
Pn
P’1 P’2P’0
Probe
From Beer’s Law (For Probe laser)
∆P’
= -S() ∆z
P’
 P 'n  P 'n1   S ()z
P
S0 
Ps
2
      2  
 S / 2 
S0
(   S )
0

 S ( )   0 (0 ) exp  
1

 
2
*
  0.6D    2(1  S0 ) 2 S (  0 )   S / 2

This Way we can find out Probe transmission
in presence of pump for entire frequency spectrum



2


Transmission effect along the fiber
Alpha Effective
22
20
Pump Power
18
Power (mW)
0.3
0.2
0.1
16
14
12
10
8
6
4
600 400 200
200 400 600
detuning MHz
Probe Power
2
0
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Distance along the fiber (in meter)
Vary Ps , Calculate Signal height (Al), Compared to Experiment ,
Repeat
We can find different S0 at each different
segment along the fiber and thus Psat.
Psat vs. Pressure
70
65
60
P11 line, 10 micron, 0.9 m Fiber at 31 mW
Psat (mW)
55
P13 line, 20 micron, 0.8 m Fiber at 14 mW
50
P13 line, 10 micron, 1.9 m fiber at 60mW
45
P13 line, 10 micron, 1.9 m fiber at 20mW
40
35
30
25
20
0
200
400
600
800
1000
Pressure (mT)
We can not say anything about dependence of Psat on Pressure
Psat varies from 25 mW to 60 mW!!!
Psat vs. Power
70
65
60
Psat(mW)
55
P-11, 20 um, 1T,0.8m
50
P-13, 20 um, 1T,0.8m
P-13, 10 um, 430 mT,1.92m
P-11, 10 um, 500 mT, 0.9m
45
40
35
30
-20
0
20
40
60
80
100 120 140 160
Pump Power(mW)
It seems there is linear dependence of Psat on Power.
We don’t believe it, Should not Psat be constant?
An Open question!!!
Conclusions
• Saturated absorption is readily achievable in photonic
bandgap fibers with power <10 mW.
• We have characterized linewidth in terms of pressure and
power.
• Linewidth dominated by transit-time broadening.
– larger-core photonic bandgap fibers desirable.
• Counter-propagation prone to noise- careful polarization
control required
• We have got Satuation Power to be somewhere between
25 to 50 mW.
• We have also spliced the fiber outside the vacuum
chamber and got very good splice.
Future:
• We are on the process of making splice with CO2
Laser to splice fiber inside the vacuum chamber.
• We are in final stage of generating frequency comb.
- Measure frequency shift and stability of those narrow feature using
frequency comb.
•
•
•
We are also in the final stage to peak-lock these
narrow feature.
To Narrow the line (Target ~1 MHz)
larger core size, coated cell?
To make fiber cell for portable frequency references.
• Funding generously provided by:
– AFOSR
– NSF CAREER
– Kansas NSF EPSCoR program
– Kansas Technology Enterprise Corporation
– Kansas State University
• Thanks to:
– Sarah Gilbert
– Mohammad Faheem
– Dirk Müller
– Bill Swann
– Kurt Vogel
– Mikes Wells and JRM staff
Ferrule
Steel tube
End of the fiber
(stripped and cleaved)
Rubber gasket
PBG Fiber
Collar
Torr sealed
region
Mode of vibration of acetylene
ν1(cm-1) ν3(cm-1)
3373.7
3278
ν1+ν3=6651.7(cm-1)
Wavelength=1.5  m
υ1 mode alone is dipole-forbidden,
it can be excited in combination with
the dipole-allowed υ3 mode excitation
V1 and v3 are doubly
degenerate (equal energy)
bending vibration.
Photonic Band-gap (PBG) Fiber
10µm
5µm
[ R. F. Cregan et al., Science 285, 1537 (1999) ]
Guidance of light
PBG Fiber
SMF Fiber
Total Internal Reflection
multiple Interference and scattering
at Bragg’s condition
Calculation Of Saturation Power
S0
Al 
1  S0 *(1  1  S0 )
Al
Psat(mW)
0.7
0.6
0.5
0.4
It Gives Sat. Power on resonance with out 0.3
taking Propagation effect into account.
0.2
0.1
Psat Calculation
Psat( mathematica)
105
100
95
90
85
80
75
70
65
60
55
50
45
40
35
2
4
6
8
10
S
Psat (from) calculation
Comparing Al vs. S
P13 line, 20 micron, 0.8 m long Fiber.
0
20
40
60
80
100
Input Pump Power
120
Psat (from) mathematica
by taking pump and probe
attenuation into account.
140
 ( )   N (v z ) 12 ( , v z ) dv z

 S / 2

S0

 S ( )   ( ) 1 

2 (   ) 2  * / 2
0
S

2
0

 2( X  X cg ) 
Y  Y0  Ag exp 




g
2

Demtroder eq.


2


*S 
 s


l2
1  Al
2
2
4(
X

X
)



cl
l 

2


1/ 2
1  1  S0  
2

Fitting eq in origin
My Calculation
2
      2  
 S / 2 
S0
(   S )
0

 S ( )   0 (0 ) exp  
1

 
2
*
  0.6D    2(1  S0 ) 2 S (  0 )   S / 2

     
0
0
 S ( )   (0 ) exp  

0.6

D 
 
Al 
Larry’s Calculation
2
2
   (   )
(



)
S
0
 
 S (   )2  * / 2
   S
0
S
2 s
s
1
s
1
Our calculation

1 s
Or,
1
1 s
1 s ^2
Demtroder Calculation



2


1
Al  1 
1 S



2


Effect of Probe saturation upon Saturation Power
When Probe saturation is taken into account, the total absorption must incorporate two different
Saturation Parameter due to both pump and probe.
2



/
2


(



)
S
S
S
0
S
1
2

 S ( )   ( ) 1 

2
 8(1  S1  1  S1 ) 2(1  S2 ) 2 S (   )2   * / 2  
0
S


S1=Saturation Parameter due to probe
S2=Saturation Parameter due to pump
There is almost no effect on Psat due to probe power
Psat (mW)
20 mW of pump Input
power
60 mW of Pump
power
Without probe
saturation
33.9
40.6
Probe saturation into
consideration
33.5
40
Transit time broadenings: a dominant factor in small core fiber
2

2 w 
I  I 0 exp  (  0 )
2
2v


FWHM   2 2ln 2(v / w)
Laser
Fiber
Molecules
In terms of the beam diameter,
D=2w,
  2 2ln 2(2v / D)  4.71v/D
In terms of frequency,
v  0.75v / D
 v  25MHz
for 13x10-6m mode field diameter
most probable velocity
2 RT
vp 
M
For acetylene, M=26.016 g/mole;
Room Temp, T=2950K
Vp  434m / s
Pump
Probe
Isolator
Squeezer
L
70%
Squeezer
/4
AOM
BS(30/70)
30%
Squeezer
Photo Diode
L
BS
BS
(10/90)
EDFA
/2
BS
L
Squeezer
Isolator
90%
BS
Diode
Laser
/4
Vacuum Chamber
BS
Photo Diode
L
PBG Fiber
L
L
Photo Diode
Glass Cell
Michelson
Interferometer
squeezer
Photo Diode
Mode of vibration of acetylene
ν1(cm-1) ν3(cm-1)
3373.7
3278
ν1+ν3=6651.7(cm-1)
Wavelength=1.5  m
υ1 mode alone is dipole-forbidden,
it can be excited in combination with
the dipole-allowed υ3 mode excitation
V1 and v3 are doubly
degenerate (equal energy)
bending vibration.