Fibre nonlinearity as a monitor of ultrashort pulse characteristics

1. Fibre nonlinearity as a monitor of ultrashort pulse characteristics Rama Chari CAT, Indore 452013 R R Dasari Distinguished lecture series, Feb 28,2005

2. Complete measurement of an ultrashort pulse entails measuring the amplitude ( or intensity ) and the phase in either the spectral or temporal domain. If we do not have a detector faster than the pulse then it is not possible to measure the intensity and phase both by linear measurements alone. Fastest available detectors have a response time ~ few ps. Expensive or cumbersome or both. The way out : Use the pulse to gate itself using optical nonlinearities.

3. Several methods already in use . • Autocorrelation : intensity and interferometric • Frequency resolved optical gating (FROG) and its various versions • Spectral phase interferometry for direct electric field reconstruction (SPIDER)

4. Intensity Autocorrelation • Autocorrelation width proportional to pulse width • Proportionality constant depends on pulse shape • Pulse shape only be reliably determined in simple cases • No direct signature of chirp (rely on TBP which depends on shap)

5. Interferometric Autocorrelation • Directly sensitive to chirp • Width of fringes not pulse width but 1/spectral width • Contains Intensity Autocorrelation • Harder to directly fit • Algorithms like MOSAIC can be used to generate an interferometric autocorrelation  trace whose shape is far more sensitive to chirp than IAC.

6. FROG • One of the most popular techniques for sub-ps pulses. • A spectrogram of the autocorrelation is recorded and iterative methods are used to retrieve the pulse phase and amplitude. • Fairly robust and well proven technique. • Can be used in real time with fast algorithms.

7. SPIDER • Interferometric technique for phase and amplitude measurement. • Iterative method not required. • Experimentally more complicated to set up.

8. Pulse propagation in single mode optical fibres • Chromatic Dispersion : change in temporal width of the pulse • group velocity vg = c/[n+(dn/d)] • group velocity dispersion parameter 2 = d/ d(1/ vg) • For  < D, 2 > 0 , normal dispersion • For  > D, 2 < 0 , anomalous dispersion • In normal dispersion regime, pulse broadens as it moves along the fibre .

9. blue red t Tout = Tin [ 1+ (z/LD)2 ]1/2

10. Self phase modulation : Spectral broadening and modulation • Refractive index n eff = n () + n2I • Time dependent phase change NL(t) = n2k0L |E(t)|2 • Instantaneous frequency (t)-0 = -d NL/dt • Consequences : chirp, broadening, modulations • Other nonlinear effects : XPM, SRS etc

11. In normal dispersion regime • Dispersion effects dominant at low powers, longer fibre lengths. • L > LD=T02/|2| • Nonlinearity dominant at higher powers, shorter fibre lengths. • L >LNL = 1/P0 • Intermediate regime : both nonlinearity and GVD effects have to be considered.

12. For a 10 ps, 1.06 m pulse, LD is ~ 8 Km. For a 100 fs, 800 nm pulse, LD is ~ 28 cm. For a 1.06 m, 10 ps pulse with energy 0.2 nJ LNL is ~2.5 m For a 800 nm, 100 fs pulse with energy 1 nJ LNL is ~5 mm

13. If fibre length is comparable to both LD and LNL, then both nonlinearity and GVD have to be considered. The nonlinear Schrodinger describes the pulse propagation V is the envelope function= Af(t/t0) z0 is the normalized length = 0.322 (2c220/ |D()) A =  (P/P1) P1=(nc Aeff/16  z0 n2).10-7 W

14. This equation has to be solved numerically. Considering only the lowest order nonlinearity, the nonlinear refractive index, n2, causes a phase change of =n2E2 k0 L . One outcome of this phase change is the generation of new frequencies in the pulse spectrum and the appearance of the modulation fringes in the spectrum due to interference of frequency components generated from the different parts of the pulse . The input pulse parameters affect the features in the fiber-broadened spectra and this effect can be used to estimate the input pulse parameters as we show below.

15. Features of the fibre-broadened spectra Taking typical parameters of a picosecond Nd-YAG laser Eq.1 is solved for different input pulse parameters. The fiber length is kept at 100 m. First we consider a transform limited Gaussian input pulse. The Gaussian pulse shape function f(t/t0) had the following form: f (t/ t0) = exp [1 + ic) (t/ t02)2 where : to =  /1.665 ,  - FWHM of the Gaussian pulse and t is in the time frame of the pulse

17. A time asymmetry in the input pulse makes the end peaks asymmetric.

18. Spectra for different symmetric pulse shapes. The shapes are (a) Gaussian, (b) faster than Gaussian, (c) slower than Gaussian

19. Experimental and calculated spectra for a 7 ps laser pulse.

20. The starting point of these calculations was the measured autocorrelation width and the pulse peak power as estimated from the average power measurements. First a transform limited gaussian pulse with these parameters was taken as the guess input pulse and its spectrum after traversing the fiber was calculated using Eq.1. This calculated spectrum (dashed line in (a)) differs markedly from the experimental spectrum (solid line curves). A comparison of the characteristics of this calculated spectrum with the experimental spectrum gave a guideline on how to modify the input pulse parameters like shape, asymmetry and chirp to obtain a spectrum similar to the experimental one. With this indication a suitable input pulse was selected and the output spectrum recalculated. In most cases, only a few trials were sufficient to generate a spectrum reproducing the main features of the experimental spectrum.

21. The 7 psec. Pulses of CW Nd:YVO4 are best described by a pulse with a temporal shape which has a trailing edge faster than Gaussian and has a chirp of +1.

22. Stability monitoring of laser pulses Changes in pulse characteristics show up strongly in the spectrum after the pulse traverses a length of fibre. Therefore the difference between two pulses can be identified simply by comparing their fibre-broadened spectra. A quantitative estimate can be done of just how sensitive the spectra are to changes in pulse parameters.

23. A normalized difference spectrum can be defined as Idiff() = (Iref()– Icurr() ) / Iref() where Icurr () is the spectrum of the pulse being compared with the reference pulse and Iref() is the reference spectrum corresponding to the reference pulse.

27. CW mode-locked Ti:S laser 100 fs, 82 MHz 7.7 micron silica fibre Triax 180 spectrograph

29. Power change of 2%

30. Spectrum change with addition of 6 mm of quartz in the beam path Pulse power : 923 W

31. Conclusion • Fibre nonlinearity can serve as a sensitive sensor for changes in ultrashort pulse parameters. • Advantages: • Requires low power. • Sensitive to change in any parameter. • On-line, single measurement. • Simple to implement. • Limitations • Complete characterisation of the pulse not simple.

32. Acknowledgements Experiments Computation Vijay Shukla Mahesh Chandran Fozia Aziz S M Oak