Chapter 2 Theories of GVD measurement method
2.5 Binary frequency-shift-keying (FSK) pulse light source
2.5.2 Operation of FSK
Vπ
Vπ
2 Vπ
±
Fig. 2.8 FSK modulator
The layout of a FSK modulator can be shown as in Fig. 2.8. The input CW light has a carrier frequency ωc. The frequency spectrum of “a” point has two peaks at ω ωc− RF and ω ωc + RF due to the amplitude modulation of the first modulator stage, which is illustrate by Fig. 2.9. Therefore, the main optical spectrum components to be considered are at ωc, ω ωc − RF and ω ωc + RF.
t
φ
cos((ω ωc − RF) )t cos((ω ωc + RF) )tωc
c RF
ω ω− ω ωc + RF Fig. 2.9 The double side band
When we inject the modulation signal with a 90° phase shit to the Mach
Zehnder Modulator (MZM) in the bottom of Fig. 2.8, the phases of the spectral components will be different. The phenomenon is shown in Fig. 2.10.
cos[(ωc −ωRF) ]t cos[(ω ωc+ RF) ]t
Fig. 2.10 Effects of the 90° phase shift
At the final stage of the modulator, the signals from two arms are added with a phase difference determined by the applied voltage of the modulator. When the modulation signal is at
2 Vπ
, the spectrum is illustrated in Fig. 2.11. The signal at
c RF
ω ω+ will be totally suppressed by the 180° phase difference.
cos[(ω ωc− RF) ]t cos[(ω ωc+ RF) ]t
− , the spectrum is illustrated in Fig. 2.12. This time the signal at ω ωc− RF will be totally suppressed by the 180° phase difference.
cos[(ω ωc− RF) ]t cos[(ω ωc+ RF) ]t
ωc
c RF
ω ω− ω ωc+ RF
cos[(ω ωc− RF)t−180 ]° cos[(ω ωc+ RF) ]t
ωc
c RF
ω ω− ω ωc+ RF
ωc
c RF
ω ω− ω ωc+ RF
Fig. 2.12 Sideband at ω ωc− RF is canceled
By the above operation method of FSK, we can get an output signal with double frequencies which can be switched in a controllable way [13].
Reference
[1] M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, "Ultra-high speed and long-distance TDM and WDM soliton transmission technology,”
IEEE J. Sel. Top. Quantum Electron., vol. 6, pp. 363-396, 2000.
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“Ultrafast all-optical logic gate using a nonlinear optical loop mirror based multi-periodic transfer function,” Opt. Express, vol. 16, pp. 2570-2577, 2008.
[4] C. R. Doerr, H. A. Haus, and E. P. Ippen, “Asynchronous soliton mode locking,” Opt. Lett., vol. 19, pp. 1958-1960, 1994.
[5] H. A. Haus, D. J. Jones, E. P. Ippen, and W.S. Wong, “Theory of soliton stability in asynchronous modelocking,” IEEE J. Lightwave Technol., vol.
14, pp. 622-627, 1996.
[6] W.-W Hsiang, C.-Y Lin, M.-F Tien, and Y. Lai, “Direct generation of a 10 GHz 816 fs pulse train from an erbium-fiber soliton laser with asynchronous phase modulation,” Opt. Lett., vol. 30, pp. 2493-2495 , 2005.
[7] J. N. Kutz, B. C. Collings, K. Bergman, W. H. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J.
Quantum Electron., vol. 34, pp.1749-1757 ,1998.
[8] H. A. Haus, D. J. Jones, E. P. Ippen, and W.S. Wong, “Theory of soliton stability in asynchronous modelocking,” IEEE J. Lightwave Technol., vol.
14, pp. 622-627, 1996.
[9] H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Structures for additive pulse mode locking,” J. Opt. Soc. Am. B, vol. 8, pp. 2068-2076 ,1991.
[10] D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A, vol. 27, pp. 3135 – 3145, 1983.
[11] W.-W Hsiang, C.-Y Lin, M.-F Tien, and Y. Lai, “Direct generation of a 10 GHz 816 fs pulse train from an erbium-fiber soliton laser with asynchronous phase modulation,” Opt. Lett., vol. 30, pp. 2493-2495, 2005.
[12] W.-W. Hsiang, C. Lin, N. Sooi, and Y. Lai, “Long-term stabilization of a 10 GHz 0.8 ps asynchronously mode-locked Er-fiber soliton laser by deviation-frequency locking,” Opt. Express, vol. 14, pp. 1822-1828, 2006.
[13] S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single Side-Band Modulation Performance of a LiNbO3 Integrated Modulator Consisting of Four-Phase,” IEEE Photon Tech. Lett., vol. 13, pp. 364-366, 2001.
Chapter 3
Experimental setup and results
3.1 The dispersion measurement system
The theory of our new dispersion measurement method has been explained in the previous chapter and in this chapter we will experimentally demonstrate the feasibility of the method. The pulse train from a wavelength-swept pulse light source will experience dispersion-induced periodic timing variation, which can be easily characterized by a RF spectrum analyzer. In this way the fiber GVD can be inferred accurately. The way of wavelength-sweeping can be sinusoidal, bi-wavelength sweeping, or some other sweeping formats. In this thesis work, the ASM is used as the sinusoidal format and FSK is used as the binary-step-wise format. The schematic setup of our proposed dispersion measurement system is shown in Fig. 3.1.
Fig. 3.1 Schematic setup of proposed dispersion measurement Wavelength-
D
3.2 The experimental setup with ASM laser source
The schematic setup of an asynchronous modelocked Er-fiber soliton laser is illustrated in Fig. 3.2.
Fig. 3.2 Schematic setup of a 10GHz asynchronous modelocked Er-fiber soliton laser
In this laser, the technique of hybrid modelocking is used. We put an electro-optic modulators (EO) phase modulator into the cavity of a passive mode-locked laser and keep the setup all-fiber. The EO modulators can be constructed as integrated-optical devices. These devices operate at higher speeds and lower voltages than the bulk devices. The optical waveguide is fabricated on an electro-optics substrate (often LiNbO3) by diffusing materials like titanium to increase the refractive index. The phase modulator needs a polarizer in the input
end to align the polarization axis of pulses with that of the EO crystal. The isolator is for single direction light propagation to prevent spatial hole burning.
It is also polarization-independent since the polarizer and the phase modulator provides enough polarization dependent loss for achieving polarization additive pulse modelocking (P-APM). The two polarization controllers are placed in the cavity to adjust the polarization state for achieving P-APM. In order to get more nonlinearity in the fiber cavity, high intra-cavity light intensity is needed. As a result, the method of bi-directional pumping is utilized in the experimental setup and about 350 mW of 980 nm pump is used in the experiment. An EO phase modulator is put in the fiber ring cavity to achieve active mode-locking. If the EO modulator is replaced with a polarization dependent isolator, the laser becomes a purely passive mode-locked laser.
The tunable bandpass filter is used to select the lasing wavelength of the laser.
In addition, it can cooperate with the self-phase modulation (SPM) effect in the cavity to suppress supermodes and to achieve a high supermode suppression ratio (SMSR). Besides, the wide bandwidth of the bandpass filter can support shorter pulses in the cavity so that the generated pulse width also can be shorter.
A section of 5.5 meters Erbium-doped fiber pumped by two 980 nm laser diodes acts as the gain medium of our laser. The output coupler is put behind the Er-fiber to get the greatest output power. The coupling ratio is 80/20 to couple 20% power inside the laser to the laser output. The chirp of the pulses is compensated with a length of negative group-velocity dispersion (GVD) fiber.
The feedback control circuit controlling the cavity length to lock the deviation frequency at a suitable value is used to stabilize the asynchronous mode-locked laser. The stabilization scheme is simple and economic due to the requirement of only electronics in the kHz range. It is composed of a photo
detector, a low pass filter, an amplifier, a frequency counter, a computer, a PZT driver, and a PZT. The signal obtained from the photo detector is amplified by the amplifier, and filtered out the unnecessary signals by the low pass filter.
Then the signals we want are sent to the frequency counter connected to the computer. The PZT driver controlled by the LABVIEW software of the computer applies the voltage on the PZT, to change the cavity length for stabilizing the mode-locked laser. The devices that been used in the fiber ring cavity are list in table 3.1.
Table 3.1 The devices in the fiber ring cavity
1. 980nm pump laser : maximum output power : 602mA x 1 : 450mA x 1 2. EO phase modulator
3. Tunable bandpass filter: 3dB bandwidth: 13.5 nm ; central wavelength:1530~1570 nm
4. Polarization independent isolator x 2 5. WDM coupler (980 nm/ 1550 nm) x 2 6. PM fiber : located at the EO phase modulator 7. Erbium-doped fiber: about 5.5 M
8. Dispersion shifted singlemode fiber: about 2M 9. Single mode fiber: about 19.33 M
10. Coupler: 80/20 x 1; 95/5 x 1 11. Polarization controller x 2 12. Photo detector
13. Amplifier
14. Low pass filter: frequency 500 Hz to 64000 Hz
15. Frequency counter: frequency DC to 225 MHz 16. PZT driver: voltage 0 V to 150 V
17. PZT
The asynchronously modelocked Er-fiber soliton laser is basically a periodic sinusoidal wavelength-scanning pulse light source. The laser can provide the required center frequency variation Δ to induce pulse timing λ variation for the GVD measurement. The measurement is done in three steps.
First we find the original pulse timing position variation δt0 from the RF spectrum of the laser output. Then, we determine the center frequency variation
λ
Δ from calibrating with a SMF fiber which GVD and length has been known.
Finally, we find the final pulse timing position variation δt1 after the test fiber from the final RF spectrum. The GVD can then be determined from δt0,δt1,
λ
Δ and the fiber length from Eq. (2.27). The system layout is shown as in Fig. 3.3.
L
Fig. 3.3 Schematic setup of dispersion measurement
3.2.1 Result and analysis with ASM
The ASM laser source has some inherent periodical timing variation.
When the laser light propagates through different type of fibers and length, additional periodical timing variation will be produced through the dispersion effect. A typical RF spectrum of the pulse train is shown in Fig.3.4. The magnitude of periodical timing variation will be changed by propagation but the frequency of periodical timing variation isn’t changed. The value of frequency is 19k Hz and is called the detuning frequency (deviation frequency) of ASM fiber laser.
19 kHZ
Δ
Fig. 3.4 The RF spectrum around the 10 GHz spectral harmonic
The central frequency (wavelength) variation of the pulse train can be determined by Eq. (2.27). The fitting curve is illustrated in Fig. 3.5. From the fitting the central wavelength variation value can be found.
Fig. 3.5 The relation between the length of SMF and timing variation
The Fig. 3.6 one can see that different lengths of SMF will have different magnitudes of sub-spectral peaks. The tendency of the curves at shorter length of SMF reveals the limit on the small GVD value measurement. It is mainly due to the original timing position variation from the laser itself.
Fig. 3.6 The magnitude difference between zero and first order spectral peaks as a function of the fiber length
The results of GVD measurement are listed in Table 3.2. The GVD of a LEAF fiber and a DCF fiber are found to be 4.2 (ps/nm/km) and 111. (ps/nm/km) respectively. The central wavelength variation Δ is 0.835 (nm) and the λ timing position variation from laser source δt0 is 2.74 (ps). The timing
position variation δt1 after connecting the test fibers (LEAF and DCF) are 3.05 (ps) and 5.16 (ps) respectively.
Table 3.2 Timing position variation and dispersion
Fiber type Fiber length (m) Δ (nm) λ δt01(ps) δt02(ps) |D| (ps/nm/km) LEAF 380 0.835 2.74 3.05 4.2
DCF 47 0.835 2.74 5.16 111.
3.3 Simulation and experiment of FSK
As stated in the previous section, the critical limit with respect to the smallest GVD measurement is the original timing position variation δt0 from the ASM laser source. In this section we try to build up a new measurement light source by CW light modulation instead of a pulse laser source. In this respect, the bi-wavelength sweeping light source is the simplest form to be tried. Thus we will use a FSK modulator and a Mach Zehnder Modulator to carry out the new measurement source for replacing the ASM laser. In Fig. 3.7 we adopt an EO modulation scheme that is similar to the recently developed scheme for generating high frequency Radio-Over-Fiber vector signals [1]. The original timing variation should be zero or very small for this kind of frequency modulated pulse light source.
MZ-a
90o Dual parallel
modulator
Fig. 3.7 FSK pulse light source
The system can be separated into three parts which are the light source, FSK modulator and Mach Zehnder Modulator . The light source is a continuous wave laser (CW laser) at 1550nm which can be considered as a signal carrier.
The FSK modulator can provide double frequency switch and the experimental measurement results are shown in Fig. 3.8, Fig. 3.9, and Fig.3.10.
1555.4 1555.6 1555.8 1556.0 1556.2 -70
-60 -50 -40 -30
Level (dB)
Optical frequency (nm)
Fig. 3.8 Double sideband with FSK modulator
In the double sideband case, the central frequency is at 1555.8 nm, which is determined by the CW laser. The wavelength difference between the two double side peaks is 0.322 nm
1555.4 1555.6 1555.8 1556.0 1556.2 -70
-60 -50 -40 -30 -20
Level (dBm)
Wavelength (nm)
Fig. 3.9 Single sideband at 1555.951 nm
1555.4 1555.6 1555.8 1556.0 1556.2
Optical frequency (nm)
Fig. 3.10 Single sideband at 1555.951 nm
Then, the Mach Zehnder Modulator driven by a pattern generator can produce 5G pulse trains. The optical spectra are in Fig. 3.11, Fig. 3.12 and Fig.
3.13.
1555.4 1555.6 1555.8 1556.0 1556.2 -80
Fig. 3.11 Double sideband with FSK modulator and MZM
Compared with Fig. 3.8 we can see that extra side peaks are generated in Fig. 3.11. and the frequency difference is about 5GHz. Since the MZM will produce phase modulation.
1555.4 1555.6 1555.8 1556.0 1556.2 -70
-60 -50 -40 -30 -20
Levrel (dBm)
Optical frequency (nm)
Fig. 3.12 Single sideband at right side with MZM
1555.4 1555.6 1555.8 1556.0 1556.2 -70
-60 -50 -40 -30 -20
Level (dBm)
Optical frequency (nm)
Fig. 3.13 Single sideband at left side with MZM
We have observed the RF spectra in 5GHz, 10GHz, 15GHz and 20GHz without connecting the test fiber respectively. The RF spectra are in Fig. 3.14, Fig. 3.15, Fig. 3.16 and Fig. 3.17.
4.997 4.998 4.999 5.000 5.001 5.002 5.003 -120
-100 -80 -60 -40 -20
Level (dBm)
Frequency (GHz)
Fig. 3.14 RF spectrum at 5GHz without connecting fiber
9.997 9.998 9.999 10.000 10.001 10.002 10.003 -130
-120 -110 -100 -90 -80 -70 -60 -50
Level (nm)
Frequency (GHz)
b_t_b_10G
Fig. 3.15 RF spectrum at 10GHz without connecting fiber
14.997 14.998 14.999 15.000 15.001 15.002 15.003
Fig. 3.16 RF spectrum at 15GHz without connecting fiber
19.997 19.998 19.999 20.000 20.001 20.002 20.003 -140
Fig. 3.17 RF spectrum at 20GHz without connecting fiber
From Fig. 3.14 to Fig.17, we can see four sidepeaks around the central frequency and the frequency difference between the peaks is 1MHz. There are some undesired sidepeaks in the figures. They may be due to the fact that the interference cancellation of the FSK modulator is not ideal and the fact that the central wavelength of the used tunable laser is drifting in time. One may be able
to select a more stable tunable laser and a more accurate band pass filter to solve the problem.
When the system is connected with a SMF fiber, the measurement figures are illustrated as Fig. 3.18, Fig. 3.19, Fig. 3.20 and Fig. 3.21.
4.997 4.998 4.999 5.000 5.001 5.002 5.003 -120
9.997 9.998 9.999 10.000 10.001 10.002 10.003 -120
Fig. 3.19 RF spectrum at 10GHz with 50m SMF
14.997 14.998 14.999 15.000 15.001 15.002 15.003
Fig. 3.20 RF spectrum at 15GHz with 50m SMF
19.997 19.998 19.999 20.000 20.001 20.002 20.003 -120
Fig. 3.21 RF spectrum at 20GHz with 50m SMF
When the light generated from the bi-wavelength sweeping light source goes through the test fiber, the GVD will cause sidepeaks around central frequency components. The relationship between the GVD and the magnitude ratio of sidepeaks has been derived in Eq. (2.29).
The measurement data can be compared with the analytic value and is
shown in Fig. 3.22.
Fig. 3.22 Side-peak ratio △ as a function of the fiber length: experiment (real) and theory (ideal)
From Fig. 3.22 we can understand that ideally the measurement sensitivity is larger for shorter length of test fibers. The reason is because the side-peaks in the RF spectrum don’t exist ideally and will be very sensitive to the dispersion-induced changes. In practice, there are still some magnitudes of side-peaks due to the imperfect of the modulators, which will limit the shortest fiber length (or the smallest dispersion) that can be measured.
In high frequencies, the measurement values seem to lose the accuracy because the high frequency terms are smaller and more sensitive to noises.
Figure 3.23 shows the electrical signal from the pattern generator and Figure 3.24 shows the optical signal from the pattern generator. The pulse width is 100
(ps) and the edge has some distortion. Such pulse shape distortion may also cause some deviation in high frequency signals, although they may be reduced by filtering.
Fig. 3.23 The electrical signal from pattern generator
Fig. 3.24 The optical signal from pattern generator
Although we have not succeeded in experimentally demonstrating the GVD measurement by using FSK signals, the feasibility of the measurement method has been verified by simulation. The simulation results are shown in Fig.
3.25.
1.0 1.5 2.0 2.5 3.0 3.5 4.0
differece between first order and zero order (dB)
Delay (ps)
Fig. 3.25 The simulation of GVD measurement
The main simulation parameters are listed in Table 3.3.
Table 3.3 Definition of simulation value
Numerical unit ps
Wavelength switch frequency 50 MHz
Pulse width 100 ps
Roundtrip time 200 ps
Time window 108 ps
If we consider the experimental conditions where the Δλ is 0.322 nm and the GVD of SMF is 17 ps/km/nm, we can draw the results as in Fig. 3.26.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 7
89 1011 12 1314 15 1617 1819 2021 2223
differece between first order and zero order (dB)
The length of SMF (km)
5 GHz 15 GHz 25 GHz 35 GHz 45 GHz
Fig. 3.26 Simulation of GVD measurement as a function of the SMF length In Fig. 3.26, the tendency of curves is the same as the analytic results in Fig.
3.22.
Reference
[1] C.-T. Lin, Y.-M Lin, J. Chen, S.-P. Dai, P. T. Shih, P.-C. Peng, and S. Chi,
“Optical direct-detection OFDM signal generation for radio-over-fiber link using frequency doubling scheme with carrier suppression,” Opt. Express, vol 16, pp. 6056-6063, 2008.
Chapter 4 Conclusions
4.1 Summary
In this thesis work, we have proposed and demonstrated a new group velocity measurement method. We use a periodic swept-wavelength pulse light source as the light source for measurement. Theoretically, by using this kind of light source the pulse timing position variation will be increased after the light has passed through a section of dispersive fiber. The pulse timing position variation can then be simply measured by a RF spectrum analyzer. In the experimental side, we have used two kinds of light source to verify the scheme.
One is a sinusoidal periodic swept-wavelength modelocked fiber laser source while the other is a periodic bi-wavelength sweeping pulse modulation light source. For the first case, an asynchronous modelocked Er-fiber soliton laser (ASM laser) has been used as the sinusoidal periodic swept-wavelength pulse light source. The detailed derivation and relation formula have been given in Chapter 2. The RF spectrum of the system is of a Bessel form. Successful experimental demonstration has been given in Chapter 3. For the latter case, we use a system consisted of a frequency shifting keying modulator (FSK modulator) and a Mach Zehnder Modulator (MZM) to be the periodic bi-wavelength sweeping pulse light source. The analytic formula has also been derived in Chapter 2. The RF spectrum of the system is of a sinusoidal form.
Successful simulation demonstration has also been given in Chapter 3. One interesting question then is to compare the measurement sensitivity of the two cases so that one can know how to increase the measurement sensitivity when needed. This will be given in the following section.
We can also compare the commercially available modulation phase-shift technique and the periodic wavelength-swept pulse light method developed in the present thesis. The compared characteristics are listed in Table 3.4.
Table 3.4 Comparison between the modulation phase-shift technique and the periodic wavelength-swept pulse light method
Measurement (ASM Er-fiber laser )
Light source Tunable laser Periodic
wavelength-swept pulse light source Observe signal Phase (RF signal) Pulse timing position
variation (light signal) Observe instrument RF network analyzer RF spectral analyzer Wavelength measurement GVD measurement range
unit length
0.1 ps/nm ~ 1 μs/nm 0.875 ps/nm ~ 25.5 ps/nm
Measurement accuracy (ps) ±0.16 ±0.125 Measurement accuracy
(ps/nm)
× ±0.175 High order dispersion measurable immeasurable
Measurement speed slower faster
Cost higher lower
From the table one can notice some important difference. The MPS can measure the higher order dispersion value owing to the higher wavelength measurement resolution. Thus, the periodic wavelength-swept pulse light method is more suitable to measure the group velocity dispersion (the second
order dispersion) for broadband test components. However, the periodic wavelength-swept pulse light method has better time delay measurement resolution. Also the measurement speed of periodic wavelength-swept pulse light method is faster than MPS because the MPS must scan the RF signal from 40 MHz to 3 GHz per wavelength. Finally, the cost for the MPS method is more expensive then that for the periodic wavelength-swept pulse light method because the MPS method uses a RF network analyzer in the system and the RF network analyzer is more expensive then the RF spectral analyzer.
4.2 Analysis
From Eq. (2.24) and Eq. (2.29) we can get Fig. 4.1 and Fig. 4.2, respectively.
From Eq. (2.24) and Eq. (2.29) we can get Fig. 4.1 and Fig. 4.2, respectively.