1. Optical Parametric Devices
David Hanna
Optoelectronics Research Centre
University of Southampton
Lectures at Friedrich Schiller University, Jena
July/August 2006

2. Outline of lecture series: Optical parametric Devices
Lecture1: Optical parametric devices: an overview
Lecture2: Optical parametric amplification and oscillation:
Basic principles
Lecture3: Ultra-short pulse parametric devices
Lecture4: The role of Quasi-Phase Matching in parametric devices, PLUS Brightness enhancement via parametric amplification

3. Lecture 1 Optical Parametric Devices: an overview
David Hanna
Optoelectronics Research Centre
University of Southampton
Lectures at Friedrich Schiller University, Jena
July/August 2006

4. Peter Alden Franken

5. Optical parametric amplification
3 – wave interactions
SFG
Energy conservation, ћω1, ћω2 annihilated, ћω3 created
DFG
ћω3 annihilated, ћω2, ћω1 created
input ω2, wave is amplified (parametric amplification)

6. 10-8 photon conversion efficiency, 10-6 % , 3x10-10 %/W
2006 Capability: ~1000%/W→13 orders in 45 years

7. Parametric gain: key information needed
Magnitude of gain, and its dependence on crystal length,
pump intensity, crystal nonlinearity
Gain bandwidth, ie range of signal wavelengths that
experience amplification
For significant gain, need phase-matching
k3 = k1 + k2
n3ω3 = n1ω1+n2ω2 (co-linear)

9. Parametric amplification and parametric noiseω3 ω1
Pump
>
>
Idler (generated) ω2 ω2
Signal
>
>
Signal (amplified)
Transparent nonlinear
(χ(2)) dielectric ω3
Pump
>
> ω1
>
Amplified noise
> ω2
>
Input pump spontaneously generates pairs of photons ћω1, ћω2 (parametric noise) which are then amplified.

11. Optical parametric oscillation
Pump
Signal
Idler
Doubly-resonant oscillator (DRO)
Pump
Signal
Idler
Singly-resonant oscillator (SRO)

12. Parametric gain vs laser gain
Gain peak can be tuned, by tuning the phase-match condition (change tilt of crystal, or temperature, or QPM grating period). Very wide signal-idler tuning is possible.
Gain is produced at two wavelengths – two outputs.
Choice of resonator (DRO or SRO).
Coherent relation between interacting waves;
restriction on relative direction of the waves.
No analogue of side-pumped laser.
Finite range of allowed pump wave directions can amplify single signal wave. Multimode pump can be used.
 brightness enhancement

13. Parametric gain vs laser gain
Gain only present while pump is present.
No storage of gain/energy
No equivalent of Q-switching.
Few OPO round trips if nsec Q-switched
pump pulses are used.
Gain is determined by peak pump intensity:
very high gain with intense ultrashort pump pulses.
No energy exchange with nonlinear medium – only exchange between the interacting waves.
No heat input to the medium

14. Parametric devices Pump > Signal > > Idler
Oscillators: SRO or DRO,
pump: single-pass, double-pass or resonated,
cw or pulsed.
long pulse (many round trips),
or train of short pulses,
SPOPO (synchronously pumped OPO)
OP Amplifier: input signal provided
OP Generator: no input signal, output generated by amplification from parametric noise

15. Synchronously-pumped OPO
>
>
Signal and idler
output pulse train
Mode-locked pump: pulse separation matches round trip of OPO
N.L.Xtal
>
>
>
OPO gain corresponds to the peak power of the pump pulse
Crystal length must be short enough so that group velocity
dispersion does not separate pump, signal and idler pulses in the crystal.

16. Attractions of SPOPO Low threshold average power
Synchronised outputs at two wavelengths
(e.g. for CARS)
Very high gain possible, can oscillate even with
very high idler loss
Very high efficiency,
e.g. makes the tandem OPO practical

17. Quasi-Phase-Matching Proposed
Armstrong, Bloembergen, Ducuing, Pershan, Phys Rev 27,1918,(1962)

18. Periodic-poling scheme (e.g. as in PPLN)
4lc
Period = 2lc
1st order
phase-matching
ESH
Phase-matched
3lc
c -c c -c c -c
Quasi-
phase-
matched
2lc lc lc
2lc period lc
2lc
3lc
4lc
ESH after each lc is p/2 smaller than for perfect phase-matching over the same length of medium.
So, effective nonlinear coefficient reduced by p/2.

19. Some benefits of QPM
Access materials having too low a birefringence for
phase-matching, e.g. LiTaO3, GaAs
Ability to phase-match any frequencies in the transparency range,
freedom to choose ideal pump for an OPO
Non-critical (90°) phase-matching,
allows tight (confocal) focussing
Access to largest nonlinear coefficient,
e.g. d33 in LiNbO3

20. Periodically Poled Lithium Niobate Crystal
Acknowledgements to Peter Smith, Corin Gawith and Lu Ming
ORC, University of Southampton

21. Frequency-conversion efficiency and parametric gain in PPLN
SHG conversion efficiency, confocal focus (l = b = 2π wo2n1/λ)
(ω1→ 2ω1)
~ 16π2P(ω1)d2eff l/cє0n1n2 λ13
SHG, 1064nm → 532nm or
Parametric gain 532nm → 1064nm
~2%/ Wcm
(deff = 17pm/V)
(Waveguide enhancement by lλ/2nw2 ~ ; >1000%/ Wcm2)
Parametric gain, 1µm → 2µm, ~0.25% / Wcm (PPLN)
2µm → 4µm, ~0.5% / Wcm (GaAs)

22. Minimum pump power/energy for 1µm – pumped PPLN parametric devices
cw SRO ~1-3W
Nanosecond-pumped OPO ~5 µJ
Synchronously-pumped OPO ~100pJ
(~ MHz)
Optical parametric generator ~100nJ (fs/ps)
~100µJ (1 nsec)
130 dB
gain
All power/energy values scale as (d2/n2λ3)-1

23. CW singly-resonant OPOs in PPLN
First cw SRO: Bosenberg et al. O.L., 21, 713 (1996)
13w NdYAG pumped 50mm XL, ~3w threshold, 3.3µm
Cw single-frequency: van Herpen et al. O.L., 28, 2497 (2003)
Single-frequency idler, 3.7 → 4.7 µm, ~1w → 0.1w
Direct diode-pumped: Klein et al. O.L., 24, 1142 (1999)
925nm MOPA diode, 1.5w thresh., 2.1µm (2.5w pump)
Fibre-laser-pumped: Gross et al. O.L., 27, 418 (2002)
1.9w 3.2µm for 8.3w pump

24. Some results from PPLN ps/fs parametric devices
Low threshold SPOPO;
7.5 mW (av), 1047nm pump, MHz
21mW, pumped by Yb fibre laser
High gain devices (at mode-locked rep. rate)
Widely-tuned SPOPO, idler >7µm
OPCPA, 40 dB gain, mJ output
OPG operated at 35 MHz, ~0.5W signal
High average power femtosecond SPOPO
19W (av) 1.45 µm, 3.57 µm

25. SPOPO facts and figures
Average output power > 20 W
Shortest pulses 13 fs
Tuning range – 9.7 micron
Efficiency
(diode  laser  OPO) 25%
Slope efficiency >100% (170% observed)

26. PPLN Waveguide Optical Parametric Generator
~2ps, 200pJ, (100W) 780nm gives ~100dB gain @1550nm
10dB needs a pump
Power of 1W
Xie
Xie et al JOSA B, 21, 1397, (2004)

27. Two spatial-mode waveguide parametric amplifier
OPG threshold: 300pJ , 780nm
Xie & Fejer, Optics Letters, 31, 799, (2006)

28. OPCPA Optical Parametric Chirped Pulse Amplification
Butkus et al Applied Physics B, 79, 693 (2004)

29. The OPCPA march towards Petawatts
Dubietis et al IEEE J Sel Topics in QE,12, 163, (2006)

30. Brightness Enhancement via Parametric Amplification
Although parametric amplification requires a high-brightness pump, this does not imply a perfect, diffraction-limited pump.
A range of pump wave angles (modes) can effectively pump a SINGLE signal wave (mode).
So the amplified signal wave can be brighter than the input pump. ▼
Brightness Enhancement
(and no heat input)

31. Angular acceptance of pump I
Angular acceptance: determined by the phase-mismatch, Δk,
that can be tolerated Δk kp ki θ ks ki kp
ΔkL = π sets limit to θ
Next: relate Δk to θ Δk

32. Concluding remarks Χ(2) Parametric processes now have the pump sources
they need and deserve.
Χ(2) Parametric devices are very versatile cw to femtosecond
UV to TeraHertz
mW→TW→PW
Absence(?) of heat generation in active medium is of growing interest.
Caveat: There is not an abundance of suitable χ(2) nonlinear media.