Chapter 4 Experiments
4.3 Experimental Setup
In our experiment, the pumping source, passively mode-locked Nd:GdVO4 laser, is focused into a 1-m-long MF with about 35% couple efficiency by a 40X microscope objective lens. The experiment setup is shown in Fig. 4.4. A λ/2 plate is used to change the polarization state of the laser to get the widest spectral broadening. Finally we measured the output spectrum using an optical spectrum analyzer (OSA).
OSA Microstructured fiber Nd:GdVO4
1064 nm
Objective lens
40X
λ/2 plate
Fig. 4.4 The setup of our experiment.
Chapter 5 Results and Discussion
5.1 Simulated Dispersion Curve of the Microstructured Fiber
By the Mode Solutions mentioned in Chapter 4.2, we obtained the simulated dispersion curve and the mode pattern of our MF which are shown in Fig. 5.1. Our simulation result shows that the two zero-dispersion points are located at 790 nm and 1190 nm which slightly different from the provide specification from the suppler.
This may be due to the distortion of SEM, the shadows around the air holes. The shadows will influence the calculation of real size of air holes. However, our simulation result of the SC which will be shown in Fig. 5.3 is quite similar to the experiment result when using the parameters of the simulated dispersion curve. The parameters of the dispersion (including the higher order dispersion up to β6 ) at the 1062.9 nm are shown in Table 5.1.
600 700 800 900 1000 1100 1200 1300 1400 1500 -800
-600 -400 -200 0 200
Dispersion [ps/km.nm]
Wavelength [nm]
Fig. 5.1 The dispersion curve of our MF. The two zero-dispersion points are located at 790 nm and 1190 nm. The inset is the mode pattern of our MF.
Table 5.1 The parameters of dispersion at 1062.9 nm
β2 (ps2/km) β3 (ps3/km) β4 (ps4/km) β5 (ps5/km) β6 (ps6/km) -57.79207 -0.08328d0 0.00153 -9.20867*10-6 5.66594*10-8
5.2 The Reliability of our Simulation: Nonlinear Schrödinger Equation
The method we used to simulate the NSE has been described in Chapter 3. To ensure our simulation is reliable, we compared our simulation results with Ref [18].
In Ref [18], the authors simulated the contributions of various optical effects to the SC under the femtosecond pumping. There are four circumstances the authors simulated, only SPM, SPM + SS + HOD, SPM + SS + RS and SPM + HOD + RS + SS, respectively. The simulation results of these circumstances are shown in Fig. 5.2.
Under the same simulation parameters in Table 5.2, our simulation results are also shown in Fig. 5.3 and have a good agreement with Fig. 5.2. This indicates that our simulation of NSE is quite reliable.
Fig. 5.2 Simulation of four circumstances in Ref [18]. a) only SPM, b) SPM + SS + HOD, c) SPM+SS+RS and d) SPM+HOD+RS+SS
-40 -20
0 Pav= 4mW 10mW 16mW
-40 -20 0
Intensity [dB]
-40 -20 0
600 800 1000 1200 -40
-20 0
600 800 1000 1200
Wavelength [nm]
600 800 1000 1200
Fig. 5.3 Simulation result compared with Ref [18]. a) only SPM, b) SPM + SS + HOD, c) SPM+SS+RS and d) SPM+HOD+RS+SS
Table 5.2 The simulation parameters in Ref [18]
Pulse
width β2 (ps2/km) β3 (ps3/km) β4 (ps4/km) β5 (ps5/km) β6 (ps6/km) r (/m/km) 0.1ps -57.5 0.135 3.12*10-6 -2.9*10-7 3.69*10-10 100
5.3 The Supercontinuum Spectra: Comparison of Experiment and Simulation Results
In our experiment, we first use the CML state of the Nd:GdVO4 laser with 230 mW of average power to couple to our MF. The output spectrum is shown in Fig.
5.3. There are about 5 nm broadband resulted from SPM near the center. The peak power of the CML state is only about 42 W that is not enough to generate the SC.
1000 1040 1080 1120 -70
-60 -50 -40 -30 -20
Intensity [dbm]
Wavelength [nm]
Fig. 5.4 The output spectrum generated by CML state of Nd: GdVO4 laser.
In the next step, we use the QML state of Nd:GdVO4 laser to couple to the MF.
Under the same average power, the peak power of the QML pulse is about 14 times higher than the CML pulse. It can induce more nonlinear effects and therefore generate the SC. The spectrum generated by the QML pulses at 160 mW of average power is shown in Fig. 5.5. We can find that the peak power is large enough to induce the MI even though its average power is only 160 mW. The first Stokes and anti-Stokes components of MI are at 1081 nm and 1046 nm. The frequency difference between the pump and the Stokes component is about 4.8 THz which is close to Ωs = 5.28 THz (corresponding to the Stokes component at 1083 nm) calculated by the theory described in 2.1.3 with β2 = -57.79207, γ = 74 and Pp = 430 W.
The Stokes component is located within the spectrum of Raman gain and thus amplified. The amplified Stokes component can be regarded as pumping to induce the second or the even higher Stokes component. Therefore the spectrum shifts to the longer wavelength. This phenomenon is also called the intrapulse Raman
scattering mentioned in 2.1.4. The red-shift of spectrum suppresses the gain of anti-Stokes component and result in only one anti-Stokes component on the right side of the pump.
1000 1020 1040 1060 1080 1100 1120 1140 -70
-60 -50 -40 -30 -20
1046nm
Intensity [dbm]
Wavelength [nm]
160mW
1081nm Modulation Instability (MI)
Second order Stoke component
Fig. 5.5 The SC generated by QML pulses under 160 mW of average power.
Then we show the spectrum generated by QML pulses under 220 mW of average power in Fig. 5.6. Once the red-shift spectrum exceeds the zero-dispersion point located at 1190 nm, the higher-order dispersion will disturb the spectrum and therefore generate the dispersive wave at 1315 nm. The theory of HOD effect has mention in 2.1.6. Compared with the spectrum generated by CML pumping in Fig.
5.4, we can get the SC from 950 nm to 1450 nm by QML pumping with average pumping power of only 220 mW.
900 1000 1100 1200 1300 1400 -70
-60 -50 -40 -30 -20
Intensi ty [dbm]
Wavelength [nm]
220mW
Dispersive wave@ 1315nm
Zero Dispersion point @1190nm
Fig. 5.6 The SC generated by QML pulses under 220 mW of average power.
Finally, we show the spectrum generated by QML pules from 160 mW to 220 mW of average power in Fig. 5.7(a) to (d). Once the average power exceeds 230 mW, the laser system has transferred from the QML state to CML state. Figures 5.7(e) to (h) are the corresponding simulation SC spectra. The corresponding peak power of the experiment and the simulation is marked in Fig. 5.7.
Our simulation results [Fig. 5.7(e)-(h)] are quite similar to our experiment results.
Both show the red-shift of spectrum with higher-order dispersion. In our simulation, we sample 215 points in a time window of 120 ps, giving the wavelength window from 716 to 2059 nm. Each simulation step h is 50 µm normalized to the nonlinear interaction length and the simulated fiber length is 1 m. However, the peak power used in the simulation is not exactly the same as the experiment. It is because the peak power of the QML pulse in the experiment can not be measured precisely. The noise of our simulation is a little bit high. This may be due to the high sample points
up to 215 and the effect of boundary. In the case of femtosecond pumping, the sample points are only 210 and therefore there is less simulation noise in the case of picosecond pumping. Besides, the boundary condition of the simulation of NSE is the periodic boundary due to the use of the Fourier transform. Once the splitting pulse from the pump exceeds the end of the time window, it will restart shifting from the beginning of the time window and thus overlap the original signal. The original signal will be perturbed slightly and contribute to the noise in the simulation.
-70
900 1000 1100 1200 1300 1400 -50
900 1000 1100 1200 1300 1400 900 1000 1100 1200 1300 1400 900 1000 1100 1200 1300 1400
Fig. 5.7 The SC generated by QML pulse. The comparison of the experiment results (the upper row) and the simulation results (the lower row).
5.4 Numerical Results: the contribution of various optical effects to the Supercontinuum
To understand the contribution of various optical effects to the SC, we simulate four circumstances, SPM only, SPM + Raman, SPM + Raman + SS and SPM + Raman + SS +HOD, respectively, under peak power of 490 W, 600 W and 1200 W in Fig. 5.8. If we consider only the SPM effect [Fig. 5.8(a),(e),(i)], the spectrum is
symmetrically broadened due to the MI. The contribution of SPM to the SC is limited. Then we add the Raman effect into our simulation [Fig. 5.8(b),(f),(j)]. The peak power has exceeded the threshold of the Raman effect to shift the spectrum to the longer wavelength while the anti-Stokes components are suppressed. Figures 5.8(c)(g)(k) contain additional nonlinear effect of SS. The red shift of the spectrum in (c) and (g) is a little narrower than (b) and (f). This is because of the depletion of the red shift by the SS which we have mentioned in 2.1.5. The phenomenon of depletion in (k) will also appear at about 1900 nm. Finally, we add the effect of higher order dispersion (HOD) to generate the dispersive wave, that agree with the experiment results.
900 1000 1100 1200 1300 1400 -50
900 1000 1100 1200 1300 1400
(j)
900 1000 1100 1200 1300 1400
(k)
900 1000 1100 1200 1300 1400
Fig. 5.8 Four circumstances of simulation: SPM only ((a),(e),(i)), SPM+Raman ((b), (f),(j)), SPM+Raman+SS ((c),(g),(k)) and SPM+Raman+SS+HOD((d),(h),(i)).
Upper row from (a) to (d) is the simulation of 490 W peak power while the lower rows from (e) to (h) and (i) to (l) are corresponding to 600 W and 1200 W.
Conclusion and Future Works
We have demonstrated that the QML laser can be a great pumping source which can generate the SC from 900 nm to 1400 nm in MF under the average power of 220 mW. The peak power can be enhanced to about 14 times if we change the laser system from the CML state to the QML state. The major nonlinear effects contributing to the spectrum broadening are MI, stimulated Raman scattering and the HOD effect which were also confirmed in our simulation.
In our future work, we will increase the average power of QML laser system as high as possible to test the maximum spectral broadening. The potential of the QML laser has not been unleashed completely because we only tune our laser to 220 mW.
We also can use the CML laser with the same peak power of QML laser as pumping to figure out the difference of spectrum between the CML and QML pulse. Or we can double the frequency of QML pulses by KTP and couple the two kinds of QML pulses with different frequencies into the MF [40][41]. This may broaden the spectrum further. In the future work of our simulation, we can increase the speed of simulation by changing the compiler from Compaq Visual Fortran 6.6 to Intel Fortran compiler 9.0 and using the FFT function in the Intel math kernel library. The two kinds of software have been optimized to the Intel processor. We can also use Matfor to construct the interface where we can enter the parameters of input conveniently.
Appendix: Simulation of Dispersion of the Microstructured Fiber
“Mode solutions” developed by Lumerical is a powerful tool to simulate the dispersion profile of the MFs. It is constructed by the fully-vectorial optical mode solver based on the finite difference time domain (FDTD) Yee cell. One of the special properties of this software is the importing of SEM. By importing the SEM of MFs, we can easily get the dispersion profile of MFs. In the following, we will illustrate the steps how to use this software.
Step 1 Fist, we select “EDIT” tab and then “IMPORT” tab, the import dialog will appear. This dialog contains three parts: General, Rotations and Image import. In General, it can select the material of the fiber which is shown in Fig. A.1. In Rotation, it can rotate the SEM to the angle we want. In Image import, not only can import the SEM but also tune the scale of SEM after we import. We should notice that the image size of SEM should be symmetrical, such as 638*638 pixels, or the SEM will be distorted after importing.
Fig. A.1 The import dialog.
Step 2 Select the material of our MF. Usually, it is Corning 7980 Silica.
Fig. A.2 The General dialog which can select the material of the fibers
Step 3 After we select the Import image tab shown in Fig. A.1, the Image Import Wizard dialog will show up. We can change the contrast of SEM by tuning the threshold bar.
Fig A.3 The Image Import Wizard dialog
Step 4 After tuning the contrast of SEM, we should input the scale of SEM. We
pull the mouse to define a distance of 10 microns the same as the scale shown in the SEM. In fact, the cross section of MFs will be a little distorted after taking the picture of SEM. We can adjust the input of the scale to compensate the distortion.
Fig A.4 Input of the scale of SEM
Step 5 After importing the SEM, we should select a region to simulate.
Fig A.5 Selected region to simulate
Step 6 To select the analysis tab and to calculate the possible modes inside the MF.
Fig A.6 Calculation of modes existing inside the MF
Step 7 After calculating the modes, we should select a mode and simulate the dispersion of the MF. The data can be outputted to Matlab or the wordpad.
Fig A.7 Simulation of the dispersion of the MF
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