1. Classical behaviour of CW Optical Parametric Oscillators T. Coudreau Laboratoire Kastler Brossel, UMR CNRS 8552 et Université Pierre et Marie Curie, PARIS, France also with Pôle Matériaux et Phénomènes Quantiques, Fédération de Recherche CNRS 2437 et Université Denis Diderot, PARIS, France

2. Introduction Basic principlesClassical operation Conclusion Definition Pump ( 0 ) Signal ( 1 ) Idler ( 2 ) Introduction An Optical Parametric Oscillator is a device that can generate two coherent waves (signal and idler) from a pump wave. It consists in : an active medium an optical cavity, Fabry Perot resonator, in which resonates one, two or three frequencies

3. Introduction Basic principlesClassical operation Conclusion History First realised in 1965 : Giordmaine & Miller, Phys. Rev. Lett 14, 973 (1965) Important development 1965 - 1975 as a tunable source of coherent radiation Outdated between 1975-1990 due to the occurrence of dye lasers Renewal since the 1990s due to improvements in laser sources and crystals quantum properties Introduction

4. Basic principlesClassical operation Conclusion Outline Introduction Definition History Basic principles Optical non linearities Second order non linearity Energy conservation and phase matching Classical Operation Singly resonant OPO Doubly resonant OPO Triply resonant OPO Conclusion Introduction

5. Basic principlesClassical operation Conclusion Optical nonlinearities An electric field applied to an atomic medium displaces the dipole : + - + - As the electric field becomes large, one gets : Basic Principles

6. Introduction Basic principlesClassical operation Conclusion Basic Principles Second order non linearity In a non centrosymetric medium, one can get a non zero O3O3 O3O3 O3O3 Nb Li Lithium Niobate Molecule AD

7. Introduction Basic principlesClassical operation Conclusion Basic Principles Second order non linearity With a pump wave at frequency 0, on can get two kinds of behaviour : Second Harmonic Generation (SHG) where a wave at frequency 2 0 is generated Parametric down-conversion where two waves at frequencies 1 and 2 are generated 0 0 2 0 0 1 2 1 2 1 + 2

8. Introduction Basic principlesClassical operation Conclusion Energy and momentum conservation Two conditions must be fulfilled : Energy conservation which must be always fulfilled exactly Momentum conservation which has to be fulfilled exactly only in the case of an infinite medium, the useful condition being Basic Principles

9. Introduction Basic principlesClassical operation Conclusion Momentum conservation is often called phase matching : the generated signal and idler remain in phase with the waves generated before in the crystal. If, the phase shift is after a length called the coherence length. Phase matching k 0 Crystals length Output power Basic Principles Pump signal, idler Signal, idler Pump

10. Introduction Basic principlesClassical operation Conclusion Realisation of phase matching The natural birefringence of the crystal is generally used to ensure phase matching Extraordinary axis Ordinary axis Input light Basic Principles Frequency Index of refraction

11. Introduction Basic principlesClassical operation Conclusion Influence of temperature The phase matching depends on the crystal temperature (and angle) T T min T T min Signal Idler Type II Signal Idler Type I Basic Principles

12. Introduction Basic principlesClassical operation Conclusion Basic Principles Quasi phase matching The previous solution is not always chosen : the most efficient nonlinear coefficient is not always used some wavelength regions are not reachable One can revert the sign of the non linearity after a length l c. Crystals length Single pass output power

13. Introduction Basic principlesClassical operation Conclusion Parametric down-conversion : basic eqns where | i | 2 is a number of photons and is a field envelope These equations can be solved analytically in terms of elliptic functions. Basic Principles

14. Introduction Basic principlesClassical operation Conclusion Notations For a weak efficiency, we have a linear variation of the amplitudes ! The variation depends on the relative phase ! Basic Principles

15. Introduction Basic principlesClassical operation Conclusion Pump Pump ( 0 ) Signal ( 1 ) Idler ( 2 ) Laser The pump creates a population inversion which generates gain through stimulated emission The system depends on the pump intensity OPO No population inversion, i.e. the medium is transparent The system depends on the pump amplitude Laser vs OPO Basic Principles

16. Introduction Basic principlesClassical operation Conclusion Singly resonant Doubly resonant Pump enhanced singly resonant Triply resonant Classical operation Different kind of cw OPOs Threshold Frequency tuning difficulty

17. Introduction Basic principlesClassical operation Conclusion Singly Resonant OPO Only the signal (or idler) wave resonates inside the cavity. Coupling mirror Usual assumptions : Good cavity : with close to resonance : with Finally, one gets : Classical operation is the free space round trip length is the crystal length is the amplitude reflection coefficient

18. Introduction Basic principlesClassical operation Conclusion SROPO - Basic properties Signal field at resonance Mean pump intensity constant which corresponds to optical powers on the order of 1W Pump threshold Behaviour above threshold Classical operation 4

19. Introduction Basic principlesClassical operation Conclusion SROPO - Output Power 100 % conversion efficiency at times above threshold The output power is given by the implicit equation E. Rosencher, C. Fabre JOSA B 19 1107 (2002) Classical operation

20. Introduction Basic principlesClassical operation Conclusion SROPO - Frequency tuning There is a linear variation of the frequency (for small variations of ).The SROPO is tunable like a standard laser has a bandwidth limited by phase-matching, and/or mirror bandwidth Classical operation

21. Introduction Basic principlesClassical operation Conclusion Doubly Resonant OPO Signal and idler Doubly resonant Signal and pump Doubly resonant : Pump enhanced singly resonant Similar to a SROPO Specific behaviour Classical operation

22. Introduction Basic principlesClassical operation Conclusion PESROPO - Basic Properties but the pump-cavity detuning, 0, must be taken into account. The output power is also modified : With (normalised detuning) The pump threshold power is diminished with respect to the SROPO case : Classical operation

23. Introduction Basic principlesClassical operation Conclusion PESROPO - Frequency tuning As in a SROPO, the frequency depends linearly on the cavity length. However, the cavity length region is limited by the pump resonance width. Classical operation

24. Introduction Basic principlesClassical operation Conclusion DROPO - Basic Properties The system forces the signal and idler detunings : 1 = 2 = with Output power : Classical operation

25. Introduction Basic principlesClassical operation Conclusion Since we have 1 = 2, the round trip phases are equal (modulo 2 ) : which gives for the signal frequency DROPO - Frequency tuning (1) As opposed to the previous case, the variation depends on the distance to frequency degeneracy Classical operation

26. Introduction Basic principlesClassical operation Conclusion DROPO - Frequency tuning (2) m m+1 The resonance width is the signal resonance width which is very narrow : it is almost impossible to tune by length without mode hops Classical operation

27. Introduction Basic principlesClassical operation Conclusion Triply Resonant OPO The output intensity now obeys a second degree equation : the system can be monostable, bistable or even chaotic... The threshold is again lower than for a DROPO : It can be below 1 mW ! Classical operation

28. Introduction Basic principlesClassical operation Conclusion TROPO - Stability Classical operation

29. Introduction Basic principlesClassical operation Conclusion TROPO - Frequency tuning The behaviour is similar to a DROPO with a limitation due to the pump resonance width. m m+1 m+2... Classical operation

30. Introduction Basic principlesClassical operation Conclusion Frequency of emission OPOs draw their advantage from their very broad tunability since it is not limited by the proximity of a resonance in the active medium. What then limits this tunability ? The nonlinear coefficient and the reflection coefficients of the mirrors Phase matching which can be varied using temperature (or orientation) Recycling of one or more waves inside the cavity The system oscillates on frequency corresponding to the lowest threshold and only on this frequency (in a cw laser) as an homogeneously broadened laser. Conclusion

31. Introduction Basic principlesClassical operation Conclusion Summary Singly resonantDoubly resonant Pump enhanced singly resonant Triply resonant Threshold ~ 10s mW Tuning by mode hops Threshold ~ 100s mW Tuning like a laser Threshold ~ 100s mW Tuning like a laser Threshold ~ 100s µW Tuning by mode hops Conclusion

32. Introduction Basic principlesClassical operation Conclusion The OPO is a coherent source of radiation can be tuned over large domains of wavelength can have a very low threshold can have a very small linewidth Conclusion