Case of homogeneous broadening R 2 Intensity Frequency
Case of homogeneous broadening R 2 Intensity Frequency condition R 3 G 0(n) c/L R 1 Longitudinal modes of the cavity n 0 Frequency n Gain G 0(n) Gain condition 1/R 1 R 2 R 3 n 0 Frequency n
Case of homogeneous broadening R 2 R 3 Intensity G(n) R 1 n 0 Frequency n Gain G 0(n) G(n) 1/R 1 R 2 R 3 n 0 Frequency n
Case of homogeneous broadening R 2 R 3 Intensity G(n) R 1 n 0 Frequency n Gain G 0(n) G(n) 1/R 1 R 2 R 3 n 0 Frequency n
Case of homogeneous broadening R 2 R 3 Intensity G(n) R 1 n 0 Frequency n Gain G 0(n) G(n) 1/R 1 R 2 R 3 n 0 Frequency n
Case of homogeneous broadening R 2 R 3 Intensity G(n) R 1 n 0 Frequency n Gain G 0(n) G(n) 1/R 1 R 2 R 3 n 0 Frequency n
Case of homogeneous broadening R 2 R 3 Intensity G(n) R 1 n 0 Frequency n Gain G 0(n) G(n) 1/R 1 R 2 R 3 n 0 Frequency n
Case of homogeneous broadening R 2 R 3 Intensity G(n) R 1 n 0 Frequency n Gain G 0(n) G(n) 1/R 1 R 2 R 3 n 0 Frequency n
Case of homogeneous broadening R 2 R 3 Intensity G(n) R 1 n 0 Frequency n Gain G 0(n) G(n) 1/R 1 R 2 R 3 n 0 Frequency n
Case of homogeneous broadening R 2 R 3 Intensity G(n) R 1 n 0 Frequency n Gain G 0(n) G(n) 1/R 1 R 2 R 3 n 0 Frequency n
Case of homogeneous broadening R 2 R 3 Intensity G(n) R 1 n 0 Frequency n Gain G 0(n) G(n) 1/R 1 R 2 R 3 n 0 Frequency n
Case of homogeneous broadening R 2 R 3 Intensity G(n) R 1 n 0 Frequency n Gain G 0(n) G(n) 1/R 1 R 2 R 3 n 0 Frequency n
Case of homogeneous broadening R 2 R 3 Intensity G(n) R 1 n 0 Frequency n Gain G 0(n) G(n) 1/R 1 R 2 R 3 n 0 Frequency n
Case of homogeneous broadening R 2 Intensity Single frequency operation R 3 G(n) R 1 n 0 Frequency n Gain G 0(n) G(n) 1/R 1 R 2 R 3 n 0 Frequency n
R 2 R 3 Case of inhomogeneous broadening Intensity G(n) c/L R 1 Cavity modes n 0 Frequency n Gain G 0(n) 1/R 1 R 2 R 3
R 2 R 3 Case of inhomogeneous broadening Intensity G(n) R 1 n 0 Frequency n Gain G(n) 1/R 1 R 2 R 3 n 0 Frequency n
R 2 R 3 Case of inhomogeneous broadening Intensity G(n) R 1 n 0 Frequency n Gain G(n) 1/R 1 R 2 R 3 n 0 Frequency n
R 2 R 3 Case of inhomogeneous broadening Intensity G(n) R 1 n 0 Frequency n Gain G(n) 1/R 1 R 2 R 3 n 0 Frequency n
R 2 R 3 Case of inhomogeneous broadening Intensity G(n) R 1 n 0 Frequency n Gain G(n) 1/R 1 R 2 R 3 n 0 Frequency n
R 2 R 3 Case of inhomogeneous broadening Intensity G(n) R 1 n 0 Frequency n Gain G(n) 1/R 1 R 2 R 3 n 0 Frequency n
R 2 R 3 Case of inhomogeneous broadening Intensity G(n) R 1 n 0 Frequency n Gain G(n) 1/R 1 R 2 R 3 n 0 Frequency n
R 2 Case of inhomogeneous broadening Intensity Multi-mode operation R 3 G(n) R 1 n 0 Frequency n Gain G(n) 1/R 1 R 2 R 3 n 0 Frequency n
Case of linear cavity Effect of spatial hole burning on the laser spectrum Active medium Standing wave related to longitudinal mode n 1 R 2 R 1 Population inversion Dn/Dn 0 Saturation effect of n 1 over Dn 1. 0 0. 8 0. 6 0. 4 0. 2 z 0. 0 0 l 1/2 l 1 3 l 1/2 2 l 1 5 l 1/2 3 l 1 Abscissa in the gain medium
Case of linear cavity Effect of spatial hole burning on the laser spectrum Active medium Standing wave related to longitudinal mode n 1 Population inversion Dn/Dn 0 Saturation effect of n 1 over Dn 1. 0 R 2 R 1 Standing wave related to longitudinal mode n 2 Population inversion available for n 2 0. 8 0. 6 0. 4 0. 2 z 0. 0 0 l 1/2 l 1 3 l 1/2 2 l 1 5 l 1/2 3 l 1 Abscissa in the gain medium The medium is spatially inhomogeneous : multimode operation
Single frequency laser : ring cavity with one propagation direction R 2 Optical diode Tdiode R 3 G(n) R 1 Polarizer 45° l/2 Tdiode=1 Faraday rotator Polarizer Tdiode=0 Faraday rotator 45° l/2
Single frequency lasers : Case of short linear cavities Intensity G 0(n) R 2 Action on the frequency condition R 1 L nk=k c/2 L L variation -> nkvariation c/2 L Longitudinal modes of the cavity nk Frequency n n 0 Frequency n Gain G 20(n) 1/R 1 R 2
Single frequency lasers : Case of short linear cavities Intensity G 0(n) R 2 R 1 Frequency n Gain G 20(n) 1/R 1 R 2 n 0 Frequency n
Single frequency lasers : Case of short linear cavities Intensity G 0(n) R 2 R 1 Frequency n Gain G 20(n) 1/R 1 R 2 n 0 Frequency n
Single frequency lasers : Case of short linear cavities Intensity G 0(n) R 2 R 1 Frequency n Gain G 20(n) 1/R 1 R 2 n 0 Frequency n
Single frequency lasers : Case of short linear cavities Intensity G 0(n) R 2 R 1 Frequency n Gain G 20(n) 1/R 1 R 2 n 0 Frequency n
Single frequency lasers : Case of short linear cavities Intensity G 0(n) R 2 R 1 Frequency n Gain G 20(n) Single frequency operation 1/R 1 R 2 n 0 Frequency n
Intensity Case of short linear cavities Example G 0(n) R 2 R 1 c/2 L n 0 Frequency n Gain G 20(n) Single frequency operation 1/R 1 R 2 n 0 Frequency n Microchip laser (Mirrors directly coated on the crystal faces) Volume <1 mm 3 Laser beam at Pump beam at 808 nm Input mirror 1064 nm Output mirror Nd: YAG L = 300 µm to 1 mm
Single frequency lasers : Insertion of a spectral filter Gain medium G 0(n) R 1 Spectral filter T(n) R 2 Action on the gain condition M 2 M 1 Gain condition : G 02(n) T 2(n) R 1 R 2 >1 Gain Single frequency operation G 02(n)*T 2(n) Dn G 02(n) 1/R 1 R 2 n 1 Frequency n
Examples of spectral filters Output beam R 1 Reflection filters Anti reflection coating Order 1 Grating Laser diode M 2 M 1 Or Fabry Perot Etalon T(n) R 2 de r 0 Transmission filters Lens R 2(n) Volume bragg grating R 2(n) R 1 Prisme l=2 n. L M 1 M 2 T(n) Index modulation Typical reflectivity of mirrors Reflectivity (%) M 1 100 90 80 70 60 50 40 30 20 10 0 850 900 950 1000 1050 1100 1150 1200 Wavelength (nm) L
Case of the Fabry Perot etalon Thin glass plate T(n) R 2 R 1 M 2 M 1 Bad finess coming from the face reflectivities (4%) T(n) Gain Frequency n Single frequency operation G 02(n)*T 2(n) 1/R 1 R 2 Dn G 02(n) Frequency n
Frequency tuning : action on the frequency condition nk=k c/2 L G 0(n) R 2 R 1 L L variation -> nkvariation Maximum tuning range c/2 L Gain 1/R 1 R 2 G 20(n) c/2 L nk-5 nk-4 nk-3 nk-2 nk-1 nk nk+1 nk-+2 nk+3 nk+4 nk+5 Frequency n
Frequency tuning : action on the frequency condition nk=k c/2 L G 0(n) R 2 R 1 L L variation -> nkvariation Maximum tuning range c/2 L Gain 1/R 1 R 2 G 20(n) c/2 L nk-5 nk-4 nk-3 nk-2 nk-1 nk nk+1 nk-+2 nk+3 nk+4 nk+5 Frequency n
Frequency tuning : action on the frequency condition nk=k c/2 L G 0(n) R 2 R 1 L L variation -> nkvariation Maximum tuning range c/2 L Gain 1/R 1 R 2 G 20(n) c/2 L nk-5 nk-4 nk-3 nk-2 nk-1 nk nk+1 nk-+2 nk+3 nk+4 nk+5 Frequency n
Frequency tuning : action on the frequency condition nk=k c/2 L G 0(n) R 2 R 1 L L variation -> nkvariation Maximum tuning range c/2 L Gain 1/R 1 R 2 G 20(n) c/2 L nk-5 nk-4 nk-3 nk-2 nk-1 nk nk+1 nk-+2 nk+3 nk+4 nk+5 Frequency n
Frequency tuning : action on the frequency condition nk=k c/2 L G 0(n) R 2 L variation -> nkvariation Maximum tuning range c/2 L R 1 L Gain G 20(n) 1/R 1 R 2 c/2 L nk-5 nk-4 nk-3 nk-2 nk-1 nk nk+1 nk-+2 nk+3 nk+4 nk+5 Frequency n
Frequency tuning : action on the frequency condition nk=k c/2 L G 0(n) R 2 L variation -> nkvariation Maximum tuning range c/2 L R 1 L Gain G 20(n) 1/R 1 R 2 c/2 L nk-5 nk-4 nk-3 nk-2 nk-1 nk nk+1 nk-+2 nk+3 nk+4 nk+5 Frequency n Piezo-electric transducer
Frequency tuning : action on the gain condition R 1 Gain medium G 0(n) Action on the spectral filter T(n) R 2 M 1 Gain condition : G 02(n) T 2(n) R 1 R 2 >1 Gain G 02(n)*T 2(n) Dn G 02(n) 1/R 1 R 2 n 1 Frequency n
Examples of frequency tuning Transmission filters Fabry Perot Etalon T(n) R 2 Output beam Anti reflection coating Order 1 M 2 M 1 Grating Laser diode Lens M 1 de r 0 Gratings Or R 1 Reflection filters R 2(n) Prisme M 2 T(n) Volume bragg grating R 2(n) R 1 M 1 L l=2 n. L Index modulation Temperature variation (dilatation)
Spectral width of single frequency laser nk=k c/2 L L variation -> nkvariation AN : L=30 cm, l=633 nm; DL=1 nm -> Dn/n=DL/L Dn=1, 6 MHz G 0(n) R 2 R 1 L Gain G 20(n) 1/R 1 R 2 c/2 L nk-5 nk-4 nk-3 nk-2 nk-1 nk nk+1 nk-+2 nk+3 nk+4 nk+5 Frequency n
Spectral width of single frequency laser nk=k c/2 L L variation -> nkvariation AN : L=30 cm, l=633 nm; DL=1 nm -> Dn/n=DL/L Dn=1, 6 MHz G 0(n) R 2 R 1 L Gain G 20(n) 1/R 1 R 2 c/2 L nk-5 nk-4 nk-3 nk-2 nk-1 nk nk+1 nk-+2 nk+3 nk+4 nk+5 Frequency n
Spectral width of single frequency laser nk=k c/2 L L variation -> nkvariation AN : L=30 cm, l=633 nm; DL=1 nm -> Dn/n=DL/L Dn=1, 6 MHz G 0(n) R 2 R 1 L Gain G 20(n) 1/R 1 R 2 c/2 L nk-5 nk-4 nk-3 nk-2 nk-1 nk nk+1 nk-+2 nk+3 nk+4 nk+5 Frequency n
Spectral width of single frequency laser nk=k c/2 L L variation -> nkvariation AN : L=30 cm, l=633 nm; DL=1 nm -> Dn/n=DL/L Dn=1, 6 MHz G 0(n) R 2 R 1 L Gain We see an average value of the frequency Dn G 20(n) 1/R 1 R 2 c/2 L nk-5 nk-4 nk-3 nk-2 nk-1 nk nk+1 nk-+2 nk+3 nk+4 nk+5 Frequency n
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