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. Direct creation of a frequency comb 2. The dream: a purely dispersive mechanism, creates the soliton 3. The reality: needs an amplitude modulation 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.

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:

tRT Direct creation of a frequency comb 5w 4w 3w 2w w LASER CEO? CEP? Pulse duration tRT Mode bandwidth Number of pulses CEO? CEP? Pulse duration (for square spectrum) : 0.443 x \lambda/4c = 390 as CEO = 0 CEP changes with propagaton in air w 2w 3w 4w 5w W

Direct creation of a frequency comb

Ultrashort laser sources 1. Direct creation of a frequency comb 2. The dream: a purely dispersive mechanism, creates the soliton 3. The reality: needs an amplitude modulation 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.

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

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

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

e(t,0) eik(t)d e(t,0) Propagation in the time domain PHASE MODULATION 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)

e(DW,0) e(DW,0)e-ik(DW)z Propagation in the frequency domain 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:

PHASE MODULATION DISPERSION

PHASE MODULATION DISPERSION

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

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.

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

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).

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

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

Saturation Absorption saturation Gain saturation Stabilizes Starts mode-locking time I

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

Saturation changes the group velocity z z = vgt Saturable gain Saturable absorption

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

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

(… 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

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

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

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

…) 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

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

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

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

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: 1 0 1 - fNL 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).

n2I The ultrafast saturable loss: Kerr deflection 1 0 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 1 0 The deflection matrix is therefore simply: n2I For details see ????????????? This may be an interesting research topic

A third ultrafast cavity perturbation: Kerr astigmatism modification x d 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).

Ultrashort laser sources 1. Direct creation of a frequency comb 2. The dream: a purely dispersive mechanism, creates the soliton 3. The reality: needs an amplitude modulation 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.

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

Cavity Ray Path

Cavity mode can be defined by 2 apertures 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

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)‏ …)

Ultrashort laser sources 1. Direct creation of a frequency comb 2. The dream: a purely dispersive mechanism, creates the soliton 3. The reality: needs an amplitude modulation 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.

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)

Two pulse/cavity lasers for a better understanding of the mode-locked laser operation Is a mode-locked laser really a periodic modulation to the cw wave? TIME E The lone bullet in the resonator: FREQUENCY E 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? 5 mm 2 m

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

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

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

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

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 z signal With amplitude noise (and small n2): This is like listening to Chopin with an AM radio z SOLUTION: go to an FM station! This is what IPI is

Measurement of n2 BS D(n2) = 2 10-19 cm2/W 2 Delay EOM Ti:sapphire 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 10-19 cm2/W 2 Delay Repetition rate detector D1 EOM Ti:sapphire PPLN Beat Note detector D2 BS

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

IPI applied to magnetometry Resolution: 10 nT or Faraday rotation of 8x10-9rad Extracavity pump Femtosecond temporal resolution Intracavity probe saturable absorber dye jet TGG d G TGG = Terbium Gallium Garnet

D Periodic displacements: detecting ultrasound phonons. : 2 gate M Delay 1 M Periodic excitation Laser cavity D d Phonon or vibration excited on mirror D BEAT NOTE Time After excitation

The VECSEL approach Advantages: High power in a small package No problems with Q-switching INTRA-CAVITY SAM EXTRA-CAVITY VECSEL 53 53

Fiber implementation of IPI D P X Sensing element Reference arm SA

The route to the phase sensing by IPI has numerous bifurcations Start cw magnetometer Laser gyro Fresnel drag Electro-optical coefficient Phase sensor Optical accelerometer Nonlinear index measurement RF magnetometer Phonon visualization Nanomechanics vizualization Three dimensional nanoscope

The route to the phase sensing by IPI is a multiple lane highway. Extracavity Pumped OPO Intracavity Pumped OPO Ti:sapphire + saturable absorber dye Dye laser Fiber mode-locked laser VCSEL pumped OPO PHASE SENSOR

Ultrashort laser sources 1. Direct creation of a frequency comb 2. The dream: a purely dispersive mechanism, creates the soliton 3. The reality: needs an amplitude modulation 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.

The OPO: from the theoretician dream to the experimentalist nightmare. Population inversion gain Parametric gain A fs signal pulse propagating through the gain medium extracts more and more energy from the medium as it grows, because the gain has a long lifetime The signal pulse (at ws) only gains energy as long as the pump is present No fluorescence! Fluorescence noise Amplified spontaneous emission No amplified spontaneous emission Group velocity affected by saturation Control of group and phase Velocities intertwined

Population inversion gain Parametric gain TIME Ip TIME Ip TIME G A I N TIME G A I N

The OPO: a (theoretical) dream for IPI How to make a laser with two pulses circulating independently in the cavity? 1. External pumping, with pump cavity ½ length or signal cavity. Advantage: Stability – no feedback from OPO to pump Disadvantage: high power needed (> 1nJ/pulse) 2. Intracavity pumping Advantages: controllable crossing point, high power Disadvantage: instabilities Cure: SHG Instabilities in Intracavity Pumped Optical Parametric Oscillators and Methods of Stabilization} Andreas Velten, Alena Zavadilova, Vaclav Kubecek, and Jean-Claude Diels Applied Physics B 98:13-25 (2009) SHG OPO Pump cavity

The intracavity pumped OPO: an experimentalist nightmare

The intracavity pumped OPO: an experimentalist nightmare

Lasers for IPI: Optical Parametric Oscillators (OPO) How to make a laser with two pulses circulating independently in the cavity? 2. Intracavity pumping where pump and OPO cavities have a commun multiple Advantage: same stability as extracavity pumped Disadvantage: Each OPO pulse is pumped only once/2 round-trips. Not enough pump energy available SHG OPO Pump cavity

IPI and intracavity pumped OPO’s: an field full of promises… and of stumbling blocks For more details: Opo_and_NLloss.pdf A. Velten, A. Zavadilova, V Kubecek, and J.-C. Diels. “Instabilities in intracavity pumped optical parametric oscillators and methods of stabilization.” Applied Physics B, 98:13–24, 2010. "A. Velten, A, Schmitt-Sody and J.-C. Diels", "Precise intracavity phase measurement in an OPO with two pulses per cavity round-trip", Optics Letters, 35: 1181--1183, (2010).