The mechanism of Q-switching is by turning on and off the laser resonator loss periodically. That is to say, by spoiling the resonator quality factor Q, the loss inside the cavity will oscillate periodically in order to obtain giant output pulses. So the Q-switching can also be called as the loss switching. One usually introduces the loss oscillation through using a modulated absorber.
Because the pump continues to deliver constant power at all time, at the high loss times, energy is stored inside the cavity in the form of an accumulated population inversion. During the on-time, the losses are reduced and the large accumulated population inversion is released, generating giant and short pulses of light as shown in Fig. 2.3.
Fig. 2.3 The loss modulation, population inversion and the pulse generation of Q-switch lasers [2.9]
As shown in figure 2.4, we identify that the shutter is opened at the point of t
= 0. The population inversion is far above threshold at that instant in the system. The spontaneous emission along the axis of the cavity is then enormously amplified so that the pulse quickly builds up to a sufficiently strong one through depleting the population inversion.
21
Fig. 2.4 The geometrical setup and the detailed process of pulse formation in the time domain for a Q-switched laser [2.10]
The giant pulse occurs on a very short time scale with a large number of stimulated photons. In view of this large increase in the photon flux, we realize that the population inversion will become depleted as the photon number increases. Consequently, one must keep track of the number of excited states as well as the number of photons.
We now make numerical predictions about the amplitude of the intensity produced by this Q switching operation. We can get rid of at least two of the transverse spatial coordinates by assigning an effective beam area A. We are
22
then left with the two dimensions z and t by ignoring any nonuniformity in the population density or the photon density along the z-axis of the simple cavity.
First of all, we have to inquire the time evolution of the photon number inside the cavity presuming that there are a few around to initiate the lasing process.
In one round trip the photon number will increase by a factor exp[2(N2-N1)σlg] and decrease owing to imperfect window transmission (Пj Tj), finite reflectivity (Пj Ri) and residual absorption (usually in the shutter) as exp-[2αsls]. The net change in Np during a round trip, the amplified result minus the starting value, divided by τRT (round trip time) is an excellent approximation to dNp/dt.
(2.6.1)
With some abbreviation and approximation, one has
changes the population inversion simultaneously. With a photon being produced, there is one atom changing its state from 2 to 1, which reduces the
23
inversion by 2 (for equal degeneracies) and thus reduces the gain. Now that we know how to model the time evolution of the photon number, the next step is to study the dynamics of the population inversion. The equations for the population of the upper and lower state are given by
Subtracting Eq.(2.6.4) from Eq.(2.6.3) and with some derivation, the formula of population inversion can be written as
(2.6.5)
The above equation could have been stated as a direct consequence of the formula of photon number since it merely states that if the number of photons increases by 1, then the population inversion must decrease by 2. By substituting a time scale normalized to the photon lifetime of the passive cavity by T =t/τp and dividing Eq.(2.6.2) by Eq.(2.6.5), one eliminates the time coordinate from the equation.
(2.6.6)
Now we multiply both sides by dn, integrate the left-hand side from the initial
24
value of the photon number Np(i) (which is negligible compared to what it will be) to the photon number Np(max) at the peak of the power pulse and simultaneously integrate the right-hand side from the initial value of the inversion, ni, to the threshold value nth. Thus we can find an elementary solution for the photon number Np in terms of the population inversion n as shown below.
(2.6.7)
(2.6.8)
From the above equation, we can further obtain the answer for the peak of the power pulse, output energy, and a reasonable estimation for its FWHM in terms of the photon number Np and population inversion n without using more complicated mathematical methods. The maximum output power can be expressed in a compact fashion by
(2.6.9)
25
[2.1] R. H. Stolen, J. Botineau, and A. Ashkin, “Intensity discrimination of optical pulses with birefringent filters”, Opt. Lett. 7, 512 (1982).
[2.2] M. Hofer, M. E. Fermann, F. Haberl, M .H. Ober and A. J. Schmidt, “Mode locking with cross-phase and self-phase modulation”, Opt. Lett. 16, 502 (1991).
[2.3] L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen,
“Ultrashort pulse fiber ring lasers,” Appl. Phys. B, vol. 65, pp. 277–294, 1997.
[2.4]P. D. Maker, R. W. Terhune: Phys. Rev. Lett. 12, 507 (1964) [2.5]. R. H. Stolen, J. Botineau, A. Ashkin: Opt. Lett. 7, 512 (1982)
[2.6] G. P. Agrawal, Nonlinear Fiber Optics, Academic Press, San Diego, (2001).
[2.7] H. A. Haus, E. P. Ippen, and K. Tamura, “Additive-Pulse Modelocking in Fiber Lasers,” IEEE J. Quantum Electron. 30, 200 (1994).
[2.8] H. A. Haus and A. Mecozzi, “Noise of Mode-Locked Lasers,” IEEE J.
Quantum Electron. 29,983 (1993).
[2.9] B. E. A. Saleh and M. C. Teich, “Fundamentals of Photonics,” John Wiley
& Sons, New York _1991_.
[2.10] Joseph T. Verdeyen, “Laser Electronics,” third edition, Prentice Hall Englewood Cliffs,New Jersey 07632
26
Chapter 3
Experimental results Before compression
3.1 Q-switched mode-locked
3.1-1 Experimental setup
Fig. 3.1 Schematic diagram of the Er-fiber laser
The schematic setup of Q-switched pulses generation from our erbium doped fiber laser with a ring cavity configuration is shown in Fig. 3.1. A laser diode with center wavelength of 980 nm is used to pump the 1.65 m long Er-doped single-mode gain fiber through a wavelength-division multiplexing
27
(WDM) coupler. The Er-fiber is very highly doped and the absorption coefficient is 80 dB/m @ 1530 nm. The isolator is for single direction wave propagation to prevent spatial hole burning and it is polarization-dependent.
Two polarization controllers with isolator can provide enough polarization dependent loss for Polarization Additive Pulse Mode-locking (P-APM). Over 400 m of single mode fiber is used inside the laser cavity to reduce the mode-locking repetition rate and to provide large dispersion and high nonlinearity. Finally, we use a 90/10 coupler to divide the light into the power meter (Newport inc.), oscilloscope (Wave Surfer 62 Xs, bandwidth 650 MHz, LeCroy) and optical spectrum analyzer (ADVANTEST Q8384.) for monitoring the state of laser.
3.1-2 Results and discussions
Stable Q-switched mode-locked (QML) pulses can be generated after properly rotating the angles of the polarization controllers (PCs) and adjusting the pump power to be less than 93mW. With a suitable pump power at 89mW, the QML pulse train shown in Fig. 3.2 is observed. Fig. 3.2 show that time spacing between adjacent Q-switched envelopes is about 446 us. Fig. 3.3 reveals the expanded symmetric single Q-switched envelope. Inside the envelope, the mode-locked pulses with a 2 s time spacing can also be obviously seen. The time trace of a single mode-locked pulse is shown in the inset of Fig. 3.3, from which the pulse width is estimated to be below 7 ns. Fig.
3.4 and Fig. 3.5 show that the laser is with a 500 kHz low mode-locking repetition-rate and 2.24kHz Q-switched repetition rate.
28 Fig. 3.2 Time trace of QML pulse trains
Fig. 3.3 Expanded single QML envelope, (Inset shows the time trace of a single mode-locked pulse)
29 Fig. 3.4 RF spectrum with three pulses
Fig. 3.5 Expanded single QML RF spectrum
30
The output optical spectrum is shown in Fig.3.6. We can see the spectrum have the self-similar-like characteristics normally observed in the all normal dispersion region [3.1], in which the plateau with steep edges on the pedestal can be clearly seen. The center wavelength is at the 1602 nm and the 3 dB bandwidth is about 5 nm. Since our laser works in the large anomalous dispersion region, we believe the experimental observation suggests a new self-similar-like operation state of the Er-fiber laser. We have also theoretically confirmed that the soliton pulse with a large nonlinear chirp in the form of will produce a flat-top spectral shape, which should provide a clue to understand the observed new phenomena [3.2].
Fig. 3.6 Optical spectrum of QML pulses (Center on 1602)
31
As the pumping power increases, the stable and regular QML pulse trains can still exist but the repetition rate of Q-switched envelope increases. Fig.
3.7(a) shows the time trace of QML pulse train at 131 mW pump power in which the period of Q-switched envelope becomes 290 s. The corresponding optical spectrum in Fig. 3.7(b) is similar to that in Fig. 3.6 but the bandwidth and amplitude of plateau region becomes smaller.
Nevertheless, the step edges in the two sides of plateau can still exist and the pedestal has the same slope like that in Fig. 3.6.
Fig. 3.7 (a) Time trace of QML pulse trains and (b) corresponding optical spectrum at 131 mW pump power
The measured width of the Q-switched envelope as the pumping power increases is shown in Fig. 3.8. The width of Q-switched envelope decreases slightly as the pumping power increases and the shortest width of about 62 s
32
can be obtained at the 122 mW pump power. At even higher pump powers the width and repetition rate will increase simultaneously. We also record the evolution of optical spectrum as the pump power increases and the results are shown in Fig. 3.9. As the pump power increased from 89 mW to 93.7 mW, the bandwidth of plateau above pedestal also increases. Then, the flat region in the top of plateau becomes curved at the 103 mW pump power. At even higher pump powers about 112 mW, the second floor plateau is generates above the original plateau. The steep edges in two side of plateau will become unapparent and finally the spectrum will become Gaussian distribution.
Fig. 3.8 Width of Q-switched envelope at different pumping powers.
33
Fig. 3.9 Evolution of optical spectrum at different pumping powers
34
For confirming our expectation theoretically, we simulated the optical spectrum of a soliton pulse with a large nonlinear chirp. We use mathematica to perform the simulation. The parameter b is representing the linear chirp and b2 is the higher order chirp. We expect the parameter of the higher order chirp b2 is large than the linear chirp parameter b. For this reason, we set b2 as 800 and b as 100 to simulate the pulse spectrum. Fig. 3.10 shows our results, with the appearance just like the experimental QML optical spectrum.
Fig. 3.10 Simulation result of the QML optical spectrum
35
Finally we use a tunable optical filter to confirm that the flat-top spectral shape is indeed caused by soliton pulses instead of assembling many continuous-wave components. Fig 3.11 shows the optical spectrum before filtering.
Fig. 3.11 Optical spectrum of QML pulses (Center on 1586nm)
First we filter out the edges of flat-top and keep the center spectrum of 1nm wide as seen in Fig. 3.12. After that we tune the filter to the left edge and right edge respectively, as in Fig. 3.13 and Fig. 3.14. The corresponding time traces are shown in Fig. 3.15, Fig. 3.16 and Fig. 3.17, in which the Q-switched envelopes are the same with the envelope width of about 65 s. These results indicate that the flat-top spectral shape is formed by the same Q-switched mode locked pulse instead of the combination of many continuous-wave components. In other words, the pulses produce all the wavelength components in the flat-top spectrum.
36
Fig. 3.12 Optical spectrum of QML after filtering (up curve is original spectrum) (middle remain)
Fig. 3.13 Optical spectrum of QML after filtering (up curve is original spectrum) (left edge remain)
37
Fig. 3.14 Optical spectrum of QML after filtering (up curve is original spectrum) (right edge remain)
Fig. 3.15 Expanded single QML envelope (middle remain)
38
Fig. 3.16 Expanded single QML envelope (left edge remain)
Fig. 3.17 Expanded single QML envelope (right edge remain)
39
3.2 Mode-locked pulse generation
In the previous section, the generation of stable Q-switched mode-locked pulses has been successful demonstrated. In this section, we want to study the characteristics of a passive mode-locked Er-fiber laser with over 400m single mode fibers inside the cavity to achieve a low pulse repetition rate of 500 kHz.
3.2-1 Experimental setup
90/10
Fig. 3.18 Schematic diagram of the Er-fiber laser
The basic setup is the same as that in the previous section. The 976 nm pump laser diodes are used to pump 1.65 m long Er-doped fiber through a WDM coupler. The fiber ring is including two polarization controllers with total length 340 cm. An isolator and 400m long signal mode fiber is added in the cavity to provide large net nonlinearity as well as large net anomalous
40
dispersion. Finally a 90/10 coupler is connected to the output coupler to divide the light into the power meter, oscilloscope, RF spectrum and optical spectrum analyzer for monitoring the state of the laser. However, in order to observe the optical spectrum before entering the Er-doped fiber we add a 99/1 coupler between the WDM and Er-doped fiber.
3.2-2 Results and discussions
The required pump power for generating mode-lock pulses is more than QML pulses. Above a certain threshold pump power, we can always operate the laser at a relatively stable continuous-wave mode-locking (CW-ML) state without pulse breaking by properly rotating the angles of the polarization controllers (PCs). The time traces of mode-locked pulses measured from the oscilloscope are shown in Fig. 3.19. The typical CW-ML pulse trains show the time interval of pulse separation is about 2 s. The corresponding repetition rate is 500 kHz, which can also be seen by the RF spectrum analyzer as illustrated in Fig. 3.20. Fig. 3.19 and Fig. 3.20 show that the mode-locked pulse train is relative stable in the time domain and the mode locked harmonic components can be clear seen in the RF spectrum.
41 Fig. 3.19 Time trace of pulse train
Fig. 3.20 RF spectrum of pulse train
42
In order to measure the output pulse-width, a high speed detector and 20G sampling oscilloscope are used. The expanded single pulse trace is shown in Fig. 3.21, which reveals that the pulse-width is below 1.8ns. Based on the parameters of a 500 kHz repetition rate, 1.87 ns pulse width and 3.27 mW average power, we estimated the peak power of the laser output is about 3.5 W.
Fig. 3.21 Expanded time trace
In addition, a relatively flat optical spectrum of the mode-locked pulses has been observed as shown in Fig. 3.22. The center wavelength is about 1585 nm and the 3dB spectrum bandwidth is 45 nm. We recognize that the optical spectrum obtained in our laser is relatively wider than typical mode-locked
43
single mode Er-doped fiber lasers. This is resulted from the net high third order nonlinearity of the 400 m long single mode fiber. The resulted 45 nm bandwidth from our simple laser configuration already can approach the 50 nm bandwidth performance of the reported frequency comb fiber laser [3.3].
Fig. 3.22 Optical spectrum
By carefully adjusting the polarization controllers we can also generate a square pulse shape. That because the intensity-dependent loss induced by NPR can have different characteristic responses. The round trip intensity transmission, T, of the system can be expressed as
(3.2.1)
Here is the azimuth angle of the polarizer is the rotation angle, and L
44
is beat length. One can drive an approximate expression for the beat length with a given power ( and )
(3.2.2)
Fig. 3.23 shows the numerically evaluated transmission as a function of power, with and . It can be seen that T(p) reaches the maximum value of 1 around p=2.5 and then starts to fall again. It may be these particular nonlinear switching characteristics that lead the laser to generate square-shaped pulses.
Fig. 3.23 Nonlinear transmission at [3.4]
45
From Eq.(3.2.2) we can solve a solution for the switching power as
(3.2.3)
As the result of Eq.(3.2.3), if one can increase the fiber length, the threshold
power can be reduced such that the square-shaped pulses may be generated.
Our experimental results are shown as follows. The expanded single pulse trace at the pump power of 233 mW is shown in Fig. 3.24. The pulse-width is about 7.5ns, operated under the cavity fundamental repetition rate of 500 kHz.
The optical spectrum is shown in Fig. 3.25 with the 3dB spectrum bandwidth of 5.7 nm
Fig. 3.24 Expanded single square-shaped pulse trace
46
Fig. 3.25 Optical spectrum of square-shaped pulses
Finally we compress the output laser pulses externally to generate ultarshort pulses with high peak powers. We use an erbium doped fiber amplifier (EDFA) for further boosting the optical power and use a section of dispersion compensating fibers (DCF) for linear pulse compression. The schematic setup is shown in Fig. 3.26, the polarization- independent isolator been connected to output is used to protect the laser and a 90/10 coupler is used to monitor original laser output. Then, the 400m DCF is used to compensate the dispersion. A pump laser diode with 980 nm center wavelength is used to pump 5 m long Er-doped fiber and its output is connected to the autocorrelator and optical spectrum analyzer for measurement. The dispersion values and units of parameters for some of the fibers used in the experiments are estimated as shown in Table. 3.1
47
Experimentally we have successfully used the dispersion compensating fiber (DCF) and EDFA to compensate the linear chirp of the laser output pulses. We have also observed that the nonlinear effects inside the EDFA may also have contributed to the chirp compensation. Fig. 3.27 and Fig. 3.28 show the characteristics of the compressed pulse. The pulse width decreases from nanosecond to femtosecond. Fig. 3.27 shows the autocorrelation trace of the compressed mode-locked pulse, and the pulse width from gauss fitting is about 230 fs. The laser output power increases to 31mW and the pulse peak power becomes 284kW. The corresponding optical spectrum is shown
48
in Fig. 4.3. The center wavelength is about 1572 nm and the 3dB spectrum bandwidth is 36 nm.
Fig. 3.27 Autocorrelation trace of the compressed pulse
Fig. 3.28 Optical spectrum after compression
49
3.3 Soliton pulses
3.3-1 Results and discussions
In our laser, the soliton pulses can be generated on under very low pump powers due to the long cavity length. When the pump power reaches about 60mW, the stable soliton pulses can be seen. Fig. 3.29 shows the time traces on the oscilloscope with the repetition rate of 500 kHz. Fig. 3.30 reveals the expanded pulses trace, in which two pulses seperated with a time period of 205 ns can be obviously seen. The soliton pulses breaks up because of the inherent limitations of the soliton regime. We can calculate that the pulse energy in the cavity is 25 pJ. The corresponding optical spectrum shown in Fig.
3.31 indicates that the center wavelength is on 1602.5 nm and the Kelly sidebands can be seen clearly. The distance between the two first-order side-peaks is 2 nm.
Fig. 3.29 Time traces of soliton pulses
50
Fig. 3.30 Expanded time traces of two soliton pulses
Fig. 3.31 Optical spectrum of soliton pulses (for two pulses)
51 move towards the trailing edge of right large peak. Chouli et al indicated that similar soliton dynamics seems to appear when the background noises are above a certain threshold, although the required threshold also depends on the settings of the polarization controllers. When the polarization controllers are fixed, a fine control of the amount of the CW background can trigger or stop the soliton dynamics [3.5].
Fig. 3.33 shows the expanded time traces of soliton pulses per round trip.
We estimate the number of solitons in the whole bunch is about 117. The recorded spectrum of the output is shown in Fig. 3.34. The measured number of solitons per round trip as the pumping power increases is shown in Fig.
3.35.
52
Fig. 3.32 Oscilloscope recording of soliton pulses
Fig. 3.33 Expanded time traces of soliton pulses per round trip
53 Fig. 3.34 Optical spectrum of soliton pulses
Fig. 3.35 Number of soliton pulses at different pumping power