HISTORIAS DE PRÍNCIPES Y MENDIGOS

Two different SHG crystals were used. First, based on the publication of the laser designer'^, we assumed 2ps pulses and were only interested in the autocorrelation intensity. We used a 5mm LiNbOa crystal with a long (50cm) focal length focusing lens to ensure correct phase matching. This configuration worked well and gave a strong SHG signal. Later, the pulses turned out to be shorter than 2ps and we where interested in the FROG signal, which requires spectral information. The LiNbOs crystal GVD (155.0541 fs/mm) stretches the pulses and the necessary phase matching condition narrows the SHG signal to the point where it does not hold enough spectral information and it becomes impossible to use it for the FROG phase retrieval algorithm. Since a thinner LiNbOs was not available to us we used a 0.3mm BBO crystal with a lower GVD (97 fs/mm) the pulse distortion was reduced from 775fs to 29fs and became negligible. The use of a thin SHG crystal has other advantages: higher bandwidth (since it is inversely proportional to the crystal thickness) and a reduced group velocity mismatch between the fundamental and the harmonic (further

Chapter 4 Frequency Resolved Optical Gating

us to use a short focal length lens (20cm). This allows for a much larger bandwidth of the autocorrelated pulse to be converted into second harmonic and therefore retain the information necessary for the FROG measure. Of course the intensity of the SHG signal was gready reduced by the weaker nonlinearity o f BBO compared to LiNbOs and by the shorter interaction length. But we were able to compensate using a shorter focal length lens as well as longer reading time and cooler CCD temperature.

^ C r y s t a l

Properties

LiNbOs BBO

Transparency range 420-5200nm 189-3500 nm

NLO coefficients ds3 = 37.84 pmA^ dsi = 5.104 pmA^ d22 = 2.464 pmA^

dll = 2.552 p n W dsi = 0.1276 pm/V d22< 0.1276 pmA^ Table 4-1: N L O crystal comparison

4.1.3 Preliminary Results

An autocorrelation trace measured with the LiNbOs crystal confirms the general shape and width of the pulse but is heavily distorted due to the crystal properties.

Chapter 4 _{Frequency Resolved Optical Gating} 4.0 3.5- 3.0- • D ^ o c w ^ . 5 - CO E o z >. '</) c 0 2.0- c 0.5- 0.0- 14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Time in picoseconds

Figure 4-2: Autocorrelation Trace with U N b 0 3 Crystal

4.2 Data acquisition

4.2.1 Spectrometer

We used an Oriel MS257 imaging monochromator with a focal length of 1/4 meter and holographic diffraction grating of 1800 lines per millimetre blazed for 500nm used with an Andor CCD array of 128x1024 pixels this spectrometer allows a maximum spectral resolution of 0. Inm. The CCD can be cooled down to -9 0 degree Celsius to reduce thermal noise and can be read at a maximum speed of 10ms. The CCD quantum efficiency is more than 10% from 250 to lOOOnm reaching 40% at 700nm while the diffraction grating efficiency is more than 20% from 300 to lOSOnm reaching 65% at 500nm. To maximise

Chapter 4 Frequency Resolved Optical Gating the signal detection and resolution the collection lens of the autocorrelator was chosen to match the NA of the spectrometer.

4.2.2 Delay line

Since we used dielectric mirror for the autocorrelator instead of retro-reflector, the delay line had to be perfectly aligned and uses a smooth and precise actuator. W e used the Coherent Ealing encoder driver system for these reasons. This system is both reliable and flexible since the error on position (follow-on error) is available at all time to monitor the exact position of the actuator, and it is also compatible with a manual translation stage which facilitates the initial alignment of the autocorrelator to find the position of zero relative delay between the two pulse where both legs of the autocorrelator are equal. It has a very high resolution and repeatability (lOOnm) unfortunately, its speed is limited to

12mm/min.

4.2.3 Experimental procedure

Measuring the FROG trace simply consists in taking the autocorrelation spectra at different delay. The measurement precision depends on the range of delay; the time step, and the CCD exposure time. The resolution in the frequency domain being fixed by the spectrometer resolution, the only way to increase the resolution of the whole measurement consists of increasing the time resolution by taking spectrums at closer delay. In order to optimise the parameters, it is useful to first maximise the signal intensity at zero delay. In practise since the soliton laser had problems of wavelength hopping due to thermal expansion as well as stability, it was necessary to keep the measurements relatively short in order to get a meaningful trace. A good compromise was obtained for time steps of 50fs although some measurements were possible with lOfs steps. The systematic error of 0.7fs on the delay line was averaged out on the whole length of the measurement making the average error on each step negligible. Background noise of dark current and scattered light

Chapter 4 Frequency Resolved Optical Gating

taken at large delay is subtracted for each delay. This also cancels the constant integral term in the expression of the intensity autocorrelation equation (2.126) to get the expression of the FROG trace equation (2.128).

4.3 Data

4.3.1 Acquisition

The data acquisition software is written in L a b V IE W ™ . Alt-the functions of the CCD, the delay line and the spectrometer can be computer controlled. The software developed for this experiment only includes the delay line and the CCD functions. It allows the configuration of the CCD in temperature and exposure time, the delay line position as well as the range, the steps of the measure. Background subtraction routine as well as calibration of the CCD array to wavelength is also available in a restricted way without using the spectrometer. The data is displayed at the end of the measurement is also saved in the form of an ASCII file containing the matrix of data with the relevant index information in real physical units to be imported in the FROG phase retrieval algorithm program. Binary files would have been a more efficient way of storing such data but it wouldn’t have been compatible with the spreadsheet format used by the algorithm. The raw data takes the form of a matrix where the column index represents the time delay and the line the wavelength. Before any manipulation the background noise and large delay spectrum are removed to leave only the FROG trace, which should ideally stand out of a null background. The data is represented in Figure 4-3 as an image with wavelength on the X-axis and time on the Y-axis.

Chapter 4

Frequen<y §gt0tfpg OpUqgl Gating

7 6 5 . 0 7 6 7 . 5 7 7 0 . 0 7 7 2 , 5

Saveiength in nanometers

250 375 500 625 75 0 875 1000

Intensity AU

Figure 4-3: FROG Raw data

In the raw data (Figure 4-3), the details of the trace are difficult to make out from the

background. The dark current and scattered light levels are still too high to see the

spectrum clearly. The data is still unusable in this form and needs to be filtered in order to

be able to exploit it with the phase retrieval algorithm.

Chapter 4

Mac^K; 0.25, MagY: 3 v f i j i ; ; •• •

■ ■ ... J i . i x ' '

Figure 4-4: Lom stpixel suhtraction

We transpose the matrix of data to represent it with time on abscissa and wavelength on

ordmate. A first filtration was also carried out, the lowest intensity pixel of the data set was

subtracted from the rest of the picture. Even with this very simple compensation for noise,

the SHG spectrum as a function of delay appears more clearly (in blue and green against

the red background). At large delay there is only a constant background SHG signal due to

the two separated pulses. At the centre of the trace near zero delay where the pulse

recombines, the intensity peak appears in blue with the fnnges due to the constructive and

Chapter 4

Frequency P

'

destructive interferences. But this is not yet a FROG trace, w t ' 'I

y

S

variable part for the signal with respect to the delay without

1

i » CW

< t.

lil

0.25, MagY: 3 Pixelfl00,45). 244

Figure 4-5: Background subtraction and FROG trace

Subtracting the constant SHG spectrum at large delays, the FROG trace finally appears.

Even before we subject it to the generalised projection algorithm to precisely retrieve the

pulse shape, we can already tell from the 5 peaks that we are dealing with a train o f 3

pulses which would be consistent with a soliton pulse and its “wings”^^’^^ The information

in the frequency domain is a little harder to interpret but from the 9 peaks we can similarly

Chapter 4 Frequency Resolved Optical Gating expect a spectrum of 5 peaks which is in agreement with the spectrum of the laser directly measured in (Figure 3-8).

This data can be further refined to clear up noise and speed up the algorithm with low pass Fourier filtration and resample of the time delay steps. But* both these operations will induce a loss of precision on the final result. Again a compromi^j^hisito be made between

processing speed and result accuracy. ? ^

■Pt. * . .

4.3.2 Retrieved pulse

* i

r - ' .

The following trace (Figure 4-6) was taken on the 16* Ju ly i^ O ^. The thermal induced Mode Partition Noise problems overcame allowed a clean s u b t r a S ^ ^ ^ ^ i e constant SHG signal and the laser remained stable for the duration of the rripasureniQ^l. ^ e temporal

.. '■

*

%

V’S' .

resolution was 25fs and the spectral 0.0675nm per pixel, ju st befow thfe- maximal optical

H

"

Chapter 4

_{Frequency R esoiy^}

_Ggtthy:

-15000 -10000 -5000 0 5000 Delay in femtoseconds

PTOi j

0 25 50 75 100 125 150 Intensity AU

Figure 4-6: Experimental FROG trace

The raw data has been filtered and formatted before we can finally retrieve the amplitude

and phase of the original pulse. Once cleaned up the FROG trace shows the complexity of

the pulse. It is now ready to be used in the phase retrieval algorithm.

Chapter 4

_Frequency

Y T " ' . r ' --15000 -10000 -5000 0 5000 Delay in femtoseconds 25 SO 75 100 Intensity AU

Figure 4-7: Retrieved FR O G tracein

Figure 4-7 represents the match to the experimental trace o f Figure 4-6 found by the

algorithm with an error of

-

0.01. The corresponding pulse is represented in the time

domain on Figure 4-8 and in the frequency domain on Figure 4-10. The main pulse and its

wings were fitted with a Gaussian profile and the chirp of the central peak with a power

profile.

Chapter 4

4.3.2.1 Time Domain

Frequency

Amplitude G aussian fit < 0.6-

S- 0.4

Time in picoseconds

Figure 4-8: fibre laserpulse in the time domain

The 3 peaks were fitted together with the Gaussian model and separately with the

Hyperbolic Secant. For this reason, there is no general error for the Hyperbolic Secant

model. But the individual fits of each peak all had values of

less than 0.0002.

Both the amplitude fit to a Gaussian and Hyperbolic Secant models are very good and it is

difficult to decide which correspond better to the experimental measurement. In Figure 4-9

the pulse shape reconstructed by the phase retrieval algorithm is compared to a Gaussian

pulse o f FWHM 500fs and to a Soliton pulse of FWHM 400fs in logarithmic scale. The

complete pulse fit were constructed using the best parameters obtain for each individual

Chapter 4 Frequency Resolved Optical Gating

peak in Table 4-2. It clearly shows that the pulse measured is closer to a Gaussian profile than to a hyperbolic secant one.

\ Fit Amplitude Amplitude Phase

Gaussian Hyperbolic Secant Power

\

y = yo + A^- Sech 1 1 1 1 y = > ’o + A - k - ^ c , r Parameter \ 0.00004 - 0.00323 0.9982 - 0.99708 I, Yo 0.0018 ±0 . 0 0 0 2 0 49.42992 ±0.0128 X cl (-4577 ± 8) fs (-4567 ± 8) fs - Peak 1

_{(535 ± 8) fs}

_{(467 ± 8) fs}

_- Ai 0.117 ±0.002 0 . 1 2 0 ±0 . 0 0 1 — —i Xc2 (-92.6 ± 0.9) fs (-83 ± 3) fs - (-157:6 ± 2) fsfr Peak 2 CO2 / P

(495.2 ± 0.9) fs

(396 ± 2) fs

P'= 1.90 ±0.03

A2 0.963 ± 0.002 1.016 ±0.005 1.30 ± 0.02 Xc3 (4150 ± 4) fs (4155 ± 8) fs - Peak 3 0D3

(494 ± 5) fs

(411 ± 8) fs

- A3 0.199 ±0.002 0.209 ± 0.003 -

Chapter 4 Frequency R esolved Optical Gating

Pulse Shape Comparison

0.1 T3 <D

I

0.01 u< O

z

0.001 0.0001 -6000 -4000 - 2000 0 2000 4000 6000 Time in FemtoSeconds

Figure 4-9: Experimental Data, Gaussian (plain) and Soliton model (dashed).

More information on the pulse is obtained from the chirp. Although it becomes noisy when the intensity is low for the two secondary peaks, it is well defined on the main one. It turns out to be negative and of power (1.90 ± 0.03). Considering the error on the pulse recovery from the generalised projection algorithm, we can consider it to be equal to two and therefore the pulse to be linearly chirped.

The FROG trace measured corresponds to a pulses consisting of 3 peaks with a Gaussian profile and a linear chirp. The output of the laser is therefore not a soliton pulse as that would have a hyperbolic secant profile and a constant chirp. The structure of the pulse is a consequence of several of the laser properties.

Firstly, if a pulse does not have a hyperbolic secant profile, it will be subject to the effect of modulation instability. In the time domain this will create sub-pulses leading and trailing it with an interval depending on the intensity of the original pulses and on the fibre nonlinear coefficient and dispersion. Therefore measuring the interval between the pulses and with the fibre optics parameters, (core radius, nonlinear refractive index, dispersion).

Chapter 4 Frequency Resolved Optical Gating

we can use equation (2.103) derived for the m odulation instability to estimate the pow er of the pulse.

C onsidering dispersion shifted fibre with; Core radius p = 10 ^im, nonlinear refractive index U2 = 2.31 10 m^W \ zero dispersion w avelength A-o = 1540 nm. W ith a m easured

delay betw een the pulses o f t = 4.4 psec corresponding by Fourier transform to a frequency shift of 1.43 THz (Qmax = 2ti / t ). With theses param eters and considering the equivalent resulting shift in a CW beam, we can estimate the pulse pow er at about 348m W .

U sing the sam e param eters, w e calculated the pow er required to form a first order soliton to be 2W. Clearly the pulse we measured does not have the necessary pow er to achieve soliton shaping.

Secondly, in order to be able to circulate in the cavity and be am plified, a pulse m ust obey the quantifying condition imposed by the NALM on its am plitude. The sub-pulses created by m odulation instability will also have to obey this condition. Now that we know the pulse peak power, we can use the NALM sw itching condition to deduce its gain, here 38dB. But a NALM switching curve exhibits a first m axim um below its minimum characteristic power; here the switching pow er o f 350m W gives a first maximum at 70m W . The am plitudes of the measured pulses verify the ratio of approximately 5 to 1 betw een the first two intensities allowed to circulate.

Only the tw o modulation instability generated pulses satisfying the NALM condition are allow ed to circulate alongside the m ain pulse, hence the three peaks observed. W ith higher pum ping power, the main peak pow er w ould have increased in increments of the N A LM condition. The second allowed pow er being at about 675mW, with 3 levels of peak powers, 5 pulses would have been allow ed to circulate in the cavity. A nd so on until the threshold value of 2W where the soliton regim e w ould have been finally attained.

Chapter 4

4.3.2.2 Frequency Domain

Frequency Resolved

<

tfi

c

o

c

Amplitude Gaussian fit 0.8- 0.2- 0.0- 1534 1536 1538 1540 1542 1544

Wavelength in nm

17

I

- 1 6

15«6

Figure 4-10: fibre laser pulse in the JhquetKj domain

The spectrum amplitude in Figure 4-10 is fitted with a Gaussian profile with 7 peaks while

the phase is fitted with an inverse power law. Again the agreement is quite good and

consistent with a Gaussian profile with a negative linear chirp. Details o f the fitting

parameters are resumed in Table 4-3.

Frequency Resolved Optical Gating

Amplitude Phase

Fit Gaussian Power

Parameter y y o + ( o ,4 n / l 1J i 0.00021 0.006 0.99595 0.98477 ! Yo 0 (19.55 ±0.05) rad; Xcl (1536.0 ± 0.1) nm (1535.08 ± 0.01) nn\ Peak 1 03] / Pi (0.7 + 0.3) nm (2.6 ± 0.1) Ai 0.024 ± 0.008 - 2 Xc2 (1537.52 ± 0.02) nm (1537.42 ± 0.02) nm Peak 2 _{CO2 / P2 (0.62 ± 0.04) nm (2.2 ±-0.3)} A2 0.148 ±0.008 -2 '' Xc3 (1539.165 ± 0.005) nm (1539.03 ± 0.01) nm Peak 3 _CO3 / P3 (0.61 ± 0.01) nm (2.1 ± 0.3) As 0.507 ± 0.007 - 2 Xc4 (1540.8201 0.003) nm (1540.814 ±0.009) nm Peak 4 _{CO4/ P4} (0.579 + 0.007) ran (1.8 ± 0.2) A4 0.716 ±0.007 - 2 Xc5 (1542.451 ±0.006) nm (1542.50 ± 0.01) nm Peak 5 (O5 / P5 (0.66 ± 0.01) nm (1.7 ± 0.2) A5 0.535 ± 0.008 - 2 Xc6 (1543.95 ± 0.01) nm (1544.30 ± 0.01) nm Peak 6 ₀)₆ /Pe (0.88 ± 0.03) nm (3.2 ± 0.2) A6 0.32 ± 0.01 - 2 Xc7 (1545.77 ± 0.07) nm - Peak 7 ( O 7 / P 7 (0.6 ± 0.1) nm - At 0.040 ± 0.007 -

Chapter 4 Frequency Resolved Optical Gating

The convergence of the phase retrieval algorithm depends on the initial guess made one the shape of the pulse, it is important to specify that no assumption are made. The first guess only consisted of intensity and phase noise. The Gaussian profile is only a product of the convergence of the algorithm and was reproduced several times with different data filtration and initial guess. It is not a computational artefact.

The spectrum peaks are separated by an average frequency shift o f 1.3 THz that compares well with the value of 1.43THz we found from the distance between the pulses in the time domain. This proves that the two independently retrieved expressions of the pulse are indeed Fourier transform of each other. The average phase chirp is (1.9±0.2) and also compares well with the value of (1.9±0.03) found in time domain fit.

We can also compare the FROG retrieved spectra in Figure 4-10 to the ones measured directly in Figure 4-8. Except from difference in wavelength due to the mode partition noise in measurements taken in different conditions at different times, we can see the same 7 peaks with the same bandwidth. This confirms the accuracy of the FROG measurement and the phase retrieval algorithm.

4.4

Conclusion

The details of our experimental set-up for SHG-FROG were explained and the measurement and analysis of the FROG trace from the hybrid fibre laser presented. The pulse amplitude can be well fitted by both a Gaussian and an Hyperbolic Secant profile, but the Gaussian presents a better agreement. And although there is still an uncertainty over the sign of chirp due to the nature of the SHG signal, it is clearly linear and incompatible with the characteristic constant phase of soliton pulses'^^. For both these reasons, we can say that the pulse measured is not a soliton but a Gaussian pulse with linear chirp.

Chapter 4 Frequency Resolved Optical Gating

The laser design worked well as far as producing ultra short mode-locked pulses. But the power was not sufficient to produce the nonlinear effect necessary for the formation of solitons. The laser operated only in the lowest energy allowed by the NALM. This was probably caused by excessive losses in the cavity due to poor or aging splices and the coupling on the SBR. These issues could have been addressed by a complete rebuilt of the

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