1. 0 Frequency Gain 1/R 1 R 2 R 3 0 Frequency Intensity Longitudinal modes of the cavity c/L G 0 ( ) Case of homogeneous broadening R2R2 R3R3 R1R1 G 0 ( ) Frequency condition Gain condition

2. 0 0 G 0 ( ) Gain G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Intensity Case of homogeneous broadening Frequency

3. 0 0 Gain G 0 ( ) G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Intensity Case of homogeneous broadening Frequency

4. 0 0 Gain G 0 ( ) G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Intensity Case of homogeneous broadening Frequency

5. 0 0 Gain G 0 ( ) G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Intensity Case of homogeneous broadening Frequency

6. 0 0 Gain G 0 ( ) G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Intensity Case of homogeneous broadening Frequency

7. 0 0 Gain G 0 ( ) G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Intensity Case of homogeneous broadening Frequency

8. 0 0 Gain G 0 ( ) G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Intensity Case of homogeneous broadening Frequency

9. 0 0 Gain G 0 ( ) G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Intensity Case of homogeneous broadening Frequency

10. 0 0 Gain G 0 ( ) G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Intensity Case of homogeneous broadening Frequency

11. 0 0 Gain G 0 ( ) G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Frequency Intensity Case of homogeneous broadening

12. 0 0 Gain G 0 ( ) G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Intensity Case of homogeneous broadening Frequency

13. 0 0 Gain G 0 ( ) G( ) 1/R 1 R 2 R 3 Single frequency operation R1R1 R2R2 R3R3 G( ) Intensity Case of homogeneous broadening Frequency

14. 0 Gain 1/R 1 R 2 R 3 0 c/L G 0 ( ) Case of inhomogeneous broadening R1R1 R2R2 R3R3 G( ) Frequency Intensity Cavity modes

15. 0 0 Gain G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Case of inhomogeneous broadening Frequency Intensity

16. 0 0 Gain G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Case of inhomogeneous broadening Frequency Intensity

17. 0 0 Gain G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Case of inhomogeneous broadening Frequency Intensity

18. 0 0 Gain G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Case of inhomogeneous broadening Frequency Intensity

19. 0 0 Gain G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Case of inhomogeneous broadening Frequency Intensity

20. 0 0 Gain G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Case of inhomogeneous broadening Frequency Intensity

21. 0 0 Gain G( ) 1/R 1 R 2 R 3 R1R1 R2R2 R3R3 G( ) Case of inhomogeneous broadening Frequency Intensity Multi-mode operation

22. Active medium Standing wave related to longitudinal mode 1 1.0 0.8 0.6 0.4 0.2 0.0 Population inversion  n/  n 0 1 /20 1  1 /2  1  1  1 z Saturation effect of 1 over  n Abscissa in the gain medium Case of linear cavity Effect of spatial hole burning on the laser spectrum R1R1 R2R2

23. Active medium Standing wave related to longitudinal mode 1 Case of linear cavity Effect of spatial hole burning on the laser spectrum 1.0 0.8 0.6 0.4 0.2 0.0 Population inversion  n/  n 0 1 /20 Abscissa in the gain medium 1  1 /2  1  1  1 z Saturation effect of 1 over  n Population inversion available for 2 Standing wave related to longitudinal mode 2 The medium is spatially inhomogeneous : multimode operation R1R1 R2R2

24. Single frequency laser : ring cavity with one propagation direction R1R1 R2R2 R3R3 G( ) Optical diode Polarizer Faraday rotator  45° T diode =1 T diode Polarizer Faraday rotator  45° T diode =0

25. 0 Frequency Gain 1/R 1 R 2 k Frequency Intensity Longitudinal modes of the cavity c/2L G 2 0 ( ) Single frequency lasers : Case of short linear cavities R1R1 G 0 ( ) R2R2 Action on the frequency condition k =k c/2L L variation -> k variation L

26. 0 Frequency Gain 1/R 1 R 2 Frequency Intensity G 2 0 ( ) G 0 ( ) R1R1 R2R2 Single frequency lasers : Case of short linear cavities

27. 0 Frequency Gain 1/R 1 R 2 Frequency Intensity G 2 0 ( ) G 0 ( ) R1R1 R2R2 Single frequency lasers : Case of short linear cavities

28. 0 Frequency Gain 1/R 1 R 2 Frequency Intensity G 2 0 ( ) G 0 ( ) R1R1 R2R2 Single frequency lasers : Case of short linear cavities

29. 0 Frequency Gain 1/R 1 R 2 Frequency Intensity G 2 0 ( ) G 0 ( ) R1R1 R2R2 Single frequency lasers : Case of short linear cavities

30. 0 Frequency Gain 1/R 1 R 2 Frequency Intensity G 2 0 ( ) R1R1 G 0 ( ) R2R2 Single frequency operation Single frequency lasers : Case of short linear cavities

31. Case of short linear cavities Example 0 Frequency Gain 1/R 1 R 2 0 Frequency Intensity c/2L G 2 0 ( ) R1R1 G 0 ( ) R2R2 Single frequency operation Microchip laser (Mirrors directly coated on the crystal faces ) Input mirror Output mirror Laser beam at 1064 nm Volume <1mm 3 Nd:YAG L = 300 µm to 1 mm Pump beam at 808 nm

32. M1M1 M2M2 Gain medium G 0 ( ) Spectral filter T( ) R2R2 R1R1 Single frequency lasers : Insertion of a spectral filter Frequency 1/R 1 R 2 Gain G 0 2 ( ) G 0 2 ( )*T 2 ( )  1 Gain condition : G 0 2 ( ) T 2 ( ) R 1 R 2 >1 Single frequency operation Action on the gain condition

33. M1M1 M2M2 Fabry Perot Etalon T( ) R2R2 R1R1 Examples of spectral filters M1M1 M2M2 Prisme Laser diode Anti reflection coating Lens Output beam Grating Order 0 Order 1 Volume bragg grating M1M1 R1R1  n   Index modulation T( ) R 2 ( ) Transmission filtersReflection filters 0 10 20 30 40 50 60 70 80 90 100 85090095010001050110011501200 Wavelength (nm) Reflectivity (%) Typical reflectivity of mirrors

34. M1M1 M2M2 Thin glass plate T( ) R2R2 R1R1 Case of the Fabry Perot etalon Frequency 1/R 1 R 2 Gain G 0 2 ( ) G 0 2 ( )*T 2 ( )  Frequency T( ) Single frequency operation Bad finess coming from the face reflectivities (4%)

35. Frequency Gain c/2L G 2 0 ( ) Frequency tuning : action on the frequency condition G 0 ( ) R2R2 k =k c/2L L L variation -> k variation Maximum tuning range c/2L k+3 k+4 k+5 k-1 k-2 k-3 k-4 k-5 k k+1 k-+2 1/R 1 R 2 R1R1

36. Frequency Gain c/2L G 2 0 ( ) Frequency tuning : action on the frequency condition G 0 ( ) R2R2 k =k c/2L L L variation -> k variation Maximum tuning range c/2L k+3 k+4 k+5 k-1 k-2 k-3 k-4 k-5 k k+1 k-+2 1/R 1 R 2 R1R1

37. Frequency Gain c/2L G 2 0 ( ) Frequency tuning : action on the frequency condition G 0 ( ) R2R2 k =k c/2L L L variation -> k variation Maximum tuning range c/2L k+3 k+4 k+5 k-1 k-2 k-3 k-4 k-5 k k+1 k-+2 1/R 1 R 2 R1R1

38. Frequency Gain c/2L G 2 0 ( ) Frequency tuning : action on the frequency condition G 0 ( ) R2R2 k =k c/2L L L variation -> k variation Maximum tuning range c/2L k+3 k+4 k+5 k-1 k-2 k-3 k-4 k-5 k k+1 k-+2 1/R 1 R 2 R1R1

39. Frequency Gain c/2L G 2 0 ( ) Frequency tuning : action on the frequency condition G 0 ( ) R2R2 k =k c/2L L L variation -> k variation Maximum tuning range c/2L k+3 k+4 k+5 k-1 k-2 k-3 k-4 k-5 k k+1 k-+2 1/R 1 R 2 R1R1

40. Frequency Gain 1/R 1 R 2 c/2L G 2 0 ( ) Frequency tuning : action on the frequency condition R1R1 G 0 ( ) R2R2 k =k c/2L L L variation -> k variation Maximum tuning range c/2L k+3 k+4 k+5 k-1 k-2 k-3 k-4 k-5 k k+1 k-+2 Piezo-electric transducer

41. M1M1 M2M2 Gain medium G 0 ( ) Action on the spectral filter T( ) R2R2 R1R1 Frequency 1/R 1 R 2 Gain G 0 2 ( ) G 0 2 ( )*T 2 ( )  1 Gain condition : G 0 2 ( ) T 2 ( ) R 1 R 2 >1 Frequency tuning : action on the gain condition

42. M1M1 M2M2 Fabry Perot Etalon T( ) R2R2 R1R1 M1M1 M2M2 Prisme Laser diode Anti reflection coating Lens Output beam Grating Order 0 Order 1 Gratings Volume bragg grating M1M1 R1R1  n   Index modulation T( ) R 2 ( ) Transmission filtersReflection filters Temperature variation (dilatation) Examples of frequency tuning

43. Frequency Gain 1/R 1 R 2 c/2L G 2 0 ( ) Spectral width of single frequency laser R1R1 G 0 ( ) R2R2 k =k c/2L L L variation -> k variation k+3 k+4 k+5 k-1 k-2 k-3 k-4 k-5 k k+1 k-+2  =  L/L AN : L=30cm, =633 nm;  L=1 nm ->  =1,6 MHz

44. Frequency Gain 1/R 1 R 2 c/2L G 2 0 ( ) Spectral width of single frequency laser R1R1 G 0 ( ) R2R2 k =k c/2L L L variation -> k variation k+3 k+4 k+5 k-1 k-2 k-3 k-4 k-5 k k+1 k-+2  =  L/L AN : L=30cm, =633 nm;  L=1 nm ->  =1,6 MHz

45. Frequency Gain 1/R 1 R 2 c/2L G 2 0 ( ) Spectral width of single frequency laser R1R1 G 0 ( ) R2R2 k =k c/2L L L variation -> k variation k+3 k+4 k+5 k-1 k-2 k-3 k-4 k-5 k k+1 k-+2  =  L/L AN : L=30cm, =633 nm;  L=1 nm ->  =1,6 MHz

46. Frequency Gain 1/R 1 R 2 c/2L G 2 0 ( ) Spectral width of single frequency laser R1R1 G 0 ( ) R2R2 k =k c/2L L L variation -> k variation k+3 k+4 k+5 k-1 k-2 k-3 k-4 k-5 k k+1 k-+2  =  L/L AN : L=30cm, =633 nm;  L=1 nm ->  =1,6 MHz We see an average value of the frequency 