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Ultrashort laser sources. Nonlinear optics needs high intensities, and non-thermal effects. Ideal excitation: ultrashort pulses. Enjoy the theory, but…. …getting your hands dirty is something else!. Blessed the feeble minded, for they are theoreticians…. Ultrashort laser sources. 1.

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Ultrashort laser sources


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    1. Ultrashort laser sources Nonlinear optics needs high intensities, and non-thermal effects Ideal excitation: ultrashort pulses Enjoy the theory, but… …getting your hands dirty is something else! Blessed the feeble minded, for they are theoreticians…

    2. Ultrashort laser sources 1. Direct creation of a frequency comb 2. The dream: a purely dispersive mechanism, creates the soliton The reality: needs an amplitude modulation 3. Saturable absorption, Kerr lensing or Kerr deflection 4. Ideal laser medium versus ideal amplifier medium 5. Two pulse/cavity lasers 6. The OPO: from the theoretician dream to the experimentalist nightmare.

    3. Direct creation of a frequency comb A perfectly regular frequency comb is formed by nonlinear optics: w, 2w, 3w, 4w, 5w, ... But they are not in phase. If they can be put in phase, a pulse train with zero CEO is created. Reference:

    4. w 2w 3w 4w W 5w Direct creation of a frequency comb 4w 5w 3w 2w w LASER Pulse duration tRT Mode bandwidth Number of pulses CEO? CEP?

    5. Direct creation of a frequency comb

    6. Ultrashort laser sources 1. Direct creation of a frequency comb 2. The dream: a purely dispersive mechanism, creates the soliton The reality: needs an amplitude modulation 3. Saturable absorption, Kerr lensing or Kerr deflection 4. Ideal laser medium versus ideal amplifier medium 5. Two pulse/cavity lasers 6. The OPO: from the theoretician dream to the experimentalist nightmare.

    7. Phase Phase Phase modulation modulation modulation A purely dispersive mechanism, creates the soliton dispersion FIBER dispersion dispersion dispersion Dispersion Phase modulation LASER

    8. A purely dispersive mechanism, creates the soliton Electric field amplitude Nonlinear index leads to phase modulation (a) time z = v4t z = v3t z = v1t z = v2t distance z

    9. A purely dispersive mechanism, creates the soliton Electric field amplitude (b) Upchirped pulse in Negative dispersion medium time z = v2t (slow) z = v1t (fast)

    10. A purely dispersive mechanism, creates the soliton Propagation in the time domain PHASE MODULATION E(t) = e(t)eiwt-kz n(t) or k(t) e(t,0) eik(t)d e(t,0)

    11. A purely dispersive mechanism, creates the soliton Propagation in the frequency domain DISPERSION n(W) or k(W) e(DW,0) e(DW,0)e-ik(DW)z Retarded frame and taking the inverse FT:

    12. PHASE MODULATION DISPERSION

    13. PHASE MODULATION DISPERSION

    14. Characteristic field: Characteristic time: Normalized distance: Equation in the retarded frame Solitons: solutions of the eigenvalue equation

    15. A purely dispersive mechanism, creates the soliton The soliton as a “canal wave” Recreation of the observation of John Russell for the 150th anniversary of his observation in 1834.

    16. Phase Phase Phase modulation modulation modulation A purely dispersive mechanism, creates the soliton dispersion FIBER dispersion dispersion dispersion Dispersion Phase modulation LASER

    17. A purely dispersive mechanism, creates the soliton The elements of soliton control in the laser Tuning the wavelength, the mode and the CEO L. Arissian and J.-C. Diels, “Carrier to envelope and dispersion control in a cavity with prism pairs”, Physical Review A, 75:013824 (2007).

    18. The magic wand of saturation Starts mode-locking Changes the group velocity Couples intracavity pulses in amplitude in phase? Interacts with CEP! Ultrashort laser sources 1. Direct creation of a frequency comb 2. The dream: a purely dispersive mechanism, creates the soliton The reality: needs an amplitude modulation 3. Saturable absorption, Kerr lensing or Kerr deflection 4. Ideal laser medium versus ideal amplifier medium 5. Two pulse/cavity lasers 6. The OPO: from the theoretician dream to the experimentalist nightmare.

    19. Gain pressure at the bottom of the dam; saturates as the dam fills up and the flow released balances the influx Saturation Gain Medium Gain saturation is what stabilizes a laser.

    20. time Saturation Absorption saturation Gain saturation Stabilizes Starts mode-locking I 0

    21. Saturation starts mode-locking The ideal “saturation absorption” curve: Pulse energy

    22. Saturation changes the group velocity I z z = vgt Saturable gain Saturable absorption

    23. Saturation changes the group velocity Application creating two pulse trains of exactly the same repetition rate. In a ring cavity or in a linear cavity GAIN GAIN ABSORBER ABSORBER

    24. A B t1 z t2 t3 t4 t5 t =- z/c t = z/c t Saturation changes the group velocity, and couples intracavity pulses in amplitude Application: creating two pulse trains of exactly the same repetition rate.

    25. Saturation changes the group velocity, and couples intracavity pulses in amplitude and phase Application: creating two pulse trains of exactly the same repetition rate. It works… with a flowing dye jet What happens if you substitute MQW for the liquid dye jet? It is a whole new parenthesis. (… Nanostructures, the CEO and the CEP

    26. Nanostructures and the CEO. 2 pulse/cavity linear cavity, mode-locked by saturable absorbers. Beat note bandwidth unusually broad???? TEST: RECORD REPETITION RATE VERSUS CAVITY LENGTH

    27. Period of λ/2 Repetition rate versus cavity length, and other repetition rate mysteries MQW with equal spacing of λ/2 MQW with a non-periodic structure

    28. Repetition rate versus cavity length E1 E2 Modeling MQW E’1E’2 Propagation axis z MQW z-ct z-ct Time

    29. Repetition rate versus cavity length, and other repetition rate mysteries Nanostructures, the CEO and the CEP The position of the standing wave determines the magnitude of the interaction with a structure < l, therefore the change in group velocity. For details see: “group-phase_velocity_coupling.pdf” …) More material on the coupling in amplitude and phase between two Intracavity pulses in: two_pulse_walzing_in_a_laser_cavity.pdf

    30. Slow versus fast saturable absorber The ultrafast: Kerr lensing and Kerr deflection The magic wand of saturation Starts mode-locking Changes the group velocity Couples intracavity pulses in amplitude in phase? Interacts with CEP! Ultrashort laser sources 1. Direct creation of a frequency comb 2. The dream: a purely dispersive mechanism, creates the soliton The reality: needs an amplitude modulation 3. Saturable absorption, Kerr lensing or Kerr deflection 4. Ideal laser medium versus ideal amplifier medium 5. Two pulse/cavity lasers 6. The OPO: from the theoretician dream to the experimentalist nightmare.

    31. The ultrafast: Kerr lensing and Kerr deflection n = n0 + n2I Kerr deflection Kerr Lensing lossy ideal lossy Both mechanisms can provide the ideal “saturation absorption” curve:

    32. The ultrafast: Kerr lensing and Kerr deflection H. W. Kogelnik and T. Li, “Laser beams and resonators", Appl. Opt., 5: 1550-1567, (1966) Cavity analysis: classical textbooks

    33. 1 - fNL 1 0 1 The ultrafast saturable loss: Kerr lensing The beam waist should not be in the middle of the crystal Analysis: write the ABCD matrix of the cavity, starting from the nonlinear lens Multiply by the nonlinear lens matrix: For details: J.-C. Diels and W. Rudolph, “Ultrashort laser pulse phenomena, Fundamental, techniques on a fs time scale”, 2nd Edition, Chapter 5, Section 5.5 “Cavities” (Elsevier, 2006).

    34. 1 0 0 The ultrafast saturable loss: Kerr deflection Analysis: write the ABCD matrix of the cavity, starting from the nonlinear element Multiply by the nonlinear deflection matrix. At Brewster angle, the deflection from beam axis is proportional to n2I n2I The deflection matrix is therefore simply: n2I For details see ????????????? This may be an interesting research topic

    35. y x d A third ultrafast cavity perturbation: Kerr astigmatism modification 1 d 0 1 Propagation matrix: The ABCD matrix should be calculated in the plane xz and yz. The crystal thicknesses are (at Brewster angle) Different ABCD (and stability condition) in the xz and yz planes. The difference is intensity dependent. H.~W. Kogelnik, E.~P. Ippen, A.~Dienes, and C.~V. Shank. “Astigmatically compensated cavities for cw dye lasers.” IEEE Journal of Quantum Electron., QE-8:373--379 (1972).

    36. Ultrashort laser sources 1. Direct creation of a frequency comb 2. The dream: a purely dispersive mechanism, creates the soliton The reality: needs an amplitude modulation 3. Saturable absorption, Kerr lensing or Kerr deflection 4. Ideal laser medium versus ideal amplifier medium 5. Two pulse/cavity lasers 6. The OPO: from the theoretician dream to the experimentalist nightmare.

    37. Ideal laser medium versus ideal amplifier medium Long lifetime media Short lifetime media Crystalline host lasers Dye laser, semiconductor lasers Ti:sapphire, alexandrite, forsterite etc… High gain, low power Low gain, high power “Soliton” type operation possible, but strong tendency to Q-switching Operation dominated by gain, loss modulation “robust” operation Average power independent of repetition rate  High energy/pulse with long cavities Pulse energy independent of repetition rate > 1 nJ/pulse difficult (VECSL) ( … Degenerate self optimizing cavity Couder, Bartolemy 1994 Ideal amplifier

    38. Cavity Ray Path

    39. Couderc et. al. Setup • Cavity mode can be defined by 2 apertures • OR: Shape of pump defines cavity mode • Useful for diode pumping • Useful for VECSEL

    40. Advantages for the VECSEL • Use V shaped cavity with gain and MQW at focal length • Gain diameter determined by pump • Absorber diameter determined by best mode locking • Astigmatism may be a problem (might lead to elliptical beam)‏ …)

    41. Ultrashort laser sources 1. Direct creation of a frequency comb 2. The dream: a purely dispersive mechanism, creates the soliton The reality: needs an amplitude modulation 3. Saturable absorption, Kerr lensing or Kerr deflection 4. Ideal laser medium versus ideal amplifier medium 5. Two pulse/cavity lasers – a most powerful probe 6. The OPO: from the theoretician dream to the experimentalist nightmare.

    42. 5. Two pulse/cavity lasers A better understanding of the mode-locked laser operation The laser is more than a source: it is a powerful diagnostic tool Intracavity Phase Interferometry as a linear and nonlinear probe The two pulse/cavity laser as a two-level system (later)

    43. Two pulse/cavity lasers for a • better understanding of the mode-locked laser operation E TIME E 5 mm FREQUENCY 2 m Is a mode-locked laser really a periodic modulation to the cw wave? The lone bullet in the resonator: In a mode-locked laser, a wave packet of longitudinal dimension of mm, travels back and forth in a resonator of the order of one or two meter Why would this light bullet care whether its central wavelength would fit as a sub-multiple of the cavity length?

    44. Is a mode-locked laser really a periodic modulation to the cw wave? Does the light bullet care whether its central wavelength fits as a sub-multiple of the cavity length? Yes, it does! Because at each round-trip, the Doppler shift at each reflection equals the mode shift. The experimentalo proof is in the Intracavity Phase Interferometry

    45. D D DL LASER GAIN Dn n DL L = The principle of Intracavity Phase Interferometry M2 DL SOLUTION: go to an FM station! This is what IPI is Review in J. Phys. B, 42:183001 (2009) LASER M1 Michelson interferometer determines the position of M2 through intensity measurement I DL In presence of noise: listening to Chopin with an AM radio

    46. Fourier Transform 0.16 Hz f01 f02 Frequency Frequency (Hz) Intracavity Phase Interferometry (IPI) Interference of two pulse trains LASER CAVITY 1 2

    47. 0.2 0.1 0.85 0.86 0.88 0.89 0.87 Time (seconds) DL(pm) 0.01 0.02 -0.04 -0.03 -0.02 -0.01 Dn DL = n L Example of data D Expanded scale (measurement) Fourier transform D(Dn)=

    48. z z Z-scan versus Intracavity Phase Interferometry (IPI) Measurement of n2 is a measurement of phase Most phase measurements convert the phase in intensity, hence sensitive to amplitude noise Example: zscan D signal With amplitude noise (and small n2): This is like listening to Chopin with an AM radio This is what IPI is SOLUTION: go to an FM station!

    49. PPLN D1 D2 Measurement of n2 1. External pumping, with pump cavity ½ length or signal cavity. EOM: Pockel’s cell to induce an intensity difference I1-I2 between the two OPO pulses Optimum resolution from 0.16 Hz bandwidth: D(n2) = 2 10-19cm2/W 2 Delay Repetition rate detector Ti:sapphire EOM Beat Note detector BS

    50. Requires a … z-scan No scan required Intensity measurements on continuous beam Requires single shot determination of the intensity Frequency measurement Intensity measurement Amplitude noise sensitive Not affected by amplitude noise OPO tunable Dispersion of n2 Measurement of n2 --- IPI vs z-scan Z-scan I P I Single intensity difference provides n2 (larger dynamic range)