Subfemtosecond hybrid synchronization between
ultrafast Yb and Er fiber laser systems
by controlling the relative injection timing
Bo-Wei Tsai,1Shang-Ying Wu,2Chieh Hu,3Wei-Wei Hsiang,1,* and Yinchieh Lai2,41
Department of Physics, Fu Jen Catholic University, Taipei 24205, Taiwan
2Department of Photonics & Institute of Electro-Optical Engineering, National Chiao-Tung University, Hsinchu 30010, Taiwan
3Additive Manufacturing & Laser Application Technology Center, ITRI South Campus, Tainan 73445, Taiwan
4
Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan *Corresponding author: 069179@mail.fju.edu.tw
Received May 2, 2013; revised July 21, 2013; accepted August 6, 2013; posted August 8, 2013 (Doc. ID 189903); published August 30, 2013
We report experimental as well as theoretical investigation of the key factors that influence the relative timing jitter between hybrid synchronized ultrafast Yb and Er fiber laser systems. Experimental results show that, within the achievable synchronization range, the synchronization performance varies significantly with the relative injection timing between the 1μm master and 1.5 μm slave pulses. This observation is in agreement with the insights obtained from the theoretical analysis, which identifies the retiming effect as a function of the initial condition of the master– slave pulse collision. By controlling the relative injection timing with a low-bandwidth intracavity feedback, relative timing jitter as low as 0.87 fs (within 1.9 MHz bandwidth) is successfully obtained. © 2013 Optical Society of America
OCIS codes: (320.7090) Ultrafast lasers; (140.4050) Mode-locked lasers; (140.3510) Lasers, fiber; (320.7110) Ultrafast nonlinear optics.
http://dx.doi.org/10.1364/OL.38.003456
Optical pulse timing synchronization is a crucial step for developing new techniques in ultrafast science and tech-nology. Some important examples include time-resolved imaging and spectroscopy, fs optical parametric ampli-fiers (OPA), and coherent pulse synthesis, as well as
pre-cise timing distribution [1–3]. Both the passive and active
synchronization techniques have been actively explored to lock the repetition rates of two ultrashort pulse lasers. In active synchronization schemes, complicated setups of precise pulse timing detection and high-speed intra-cavity feedback are typically required for achieving
low timing jitters [4,5]. In contrast, the passive
synchro-nization schemes based on the shared cavity or pulse injection configuration can take advantage of the instan-taneity of the nonlinear optical cross-phase modulation (XPM) to implement a high-speed synchronization
feed-back [6–8]. As a further extension, it is expected that
passive synchronization assisted by a low-bandwidth intracavity feedback should be able to suppress the fast timing fluctuations as well as remove the slow timing drifts. The scheme should be capable of achieving long-term sub-fs synchronization with low-cost feedback devices. However, such a hybrid synchronization ap-proach with sub-fs precision was only demonstrated on
the solid-state lasers [7]. For ultrafast fiber laser systems,
it is still a challenge to obtain sub-fs synchronization by
the hybrid synchronization technique [6,8].
In this Letter, we report experimental as well as theo-retical investigation of the key factors that influence the
relative timing jitter between the 1μm Yb and 1.5 μm Er
fiber laser systems synchronized by the pulse injection technique and with a low-bandwidth intracavity feed-back. It is found experimentally that the synchronization performance can vary significantly with respect to the
relative injection timing between the 1 μm master and
1.5μm slave pulses. A simple theoretical analysis based
on the linearized evolution equations of the laser pulse parameters has also been derived to examine the effects of the two-color pulse collision on the retiming force for achieving synchronization. By controlling the relative injection timing with a low-bandwidth intracavity feed-back, such that the slave pulse experiences the maximum retiming force, a relative timing jitter as low as 0.87 fs (1.9 MHz bandwidth) between the two-color ultrafast fiber laser systems can be obtained.
Figure 1shows the experimental setup of the hybrid
synchronization between the fs Yb and Er fiber laser amplifier systems with the pulse repetition rates of ∼43.28 MHz. The homebuilt mode-locked Er fiber and Yb fiber lasers are both based on the nonlinear polarization rotation technique, and their output pulses
Fig. 1. Experimental setup of the hybrid synchronized Er and Yb fiber laser amplifier systems. BS, beam splitter; DM, dichroic mirror; BPF, optical bandpass filter; PD, photodiode; LPF, elec-tric low-pass filter; PI, proportional-integral controller; PZT, piezoelectric transducer; M, mirror; WDM, wavelength division multiplexer (WDM1,1560∕1030 nm; WDM2, 1560∕976 nm); LD, laser diode; ISO, polarization independent isolator; PBS, polari-zation beam splitter; FC, fiber collimator; WP, wave plates. 3456 OPTICS LETTERS / Vol. 38, No. 17 / September 1, 2013
are amplified by the single-cladding Er-doped (OFS EDF 80) and double-cladding Yb-doped (LIEKKI, Yb1200-10/ 125DC) fiber amplifiers, respectively. The net intracavity dispersions of the stretched pulse Er fiber and
self-similar Yb fiber lasers are∼ − 0.023 ps2 and ∼0.011 ps2,
respectively. The anomalous intracavity dispersion of the Er fiber laser is required for being a slave laser in the pas-sive synchronization scheme. After amplification the
1.5μm pulses are compressed by the single-mode fiber
(SMF 28) to ∼70 fs with the pulse energy of 1.5 nJ.
For the 1 μm amplified pulses, dechirp is achieved by
the transmission grating pair (1000 lines∕mm) and, after
compression, the pulse energy of 9 nJ and pulse duration
of∼110 fs can be obtained. The hybrid synchronization
procedures begin with the injection of a small part of the output power of the Yb laser amplifier system into the slave Er fiber laser via the two wavelength division
multi-plexers (WDM1). The remaining of the 1 μm output is
combined with the 1.5μm pulses from the Er fiber laser
amplifier system to be incident on a nonlinear BBO crystal. Within a suitable range of the extracavity delay
between the 1 μm master and 1.5 μm slave pulses, the
sum-frequency generation (SFG) signals can be gener-ated and used for the measurement of the timing jitter as well as for the intracavity feedback control. The feed-back loop consists of a proportional-integral controller and a piezoelectric transducer (PZT) driver, and the cav-ity length of the Er fiber laser is adjusted by the PZT wound with SMF 28. By locking the SFG signals at the middle height of the cross correlation trace, the slow tim-ing drift, which is the main characteristic of the passive synchronization under the environmental perturbations, can be effectively removed. The bandwidth of the intra-cavity feedback of the PZT servo is less than 3 kHz, and the measurement bandwidth of the relative timing jitter is determined by the low-pass filter of 1.9 MHz. It should be noted that, because the extracavity time separation
be-tween the 1 and 1.5 μm pulses is fixed by the feedback
loop, the detuning of the extracavity delay via the
retro-reflector (see Fig.1) will, accordingly, change the relative
injection timing between the two color pulses inside the
Er fiber laser [9].
Although the hybrid synchronization can be achieved over a wide range of the extracavity delay, we find that the corresponding relative timing jitter may vary signifi-cantly. This reveals that the relative injection timing be-tween the master and slave pulses inside the Er fiber laser can affect the synchronization performance.
Figure 2(a) demonstrates the successful locking of the
relative pulse timing with the turn-on of the feedback.
Figure2(b)shows the measurement results of the cross
correlation trace and the minimum relative timing jitter
obtained by optimizing the position (offset is 40 μm) of
the extracavity delay with the injection power of 30 mW. The amplitude-to-time conversion ratio near the middle
height of the cross correlation trace is 14.75 fs∕V, and
the amplitude fluctuation of 58.91 mV in Fig.2(b)
corre-sponds to the relative timing jitter of 0.87 fs. When the offset position of the extracavity delay is moved from
40 to 160μm, as shown in the inset of Fig.2(b), the
am-plitude fluctuation and its corresponding timing jitter are increased to 129.2 mV and 1.91 fs, respectively. Within all the locking range of the hybrid synchronization, the
relative timing jitter measured with respect to different extracavity delays for the two injection powers of 15
and 30 mW are shown in Fig. 2(c). Besides the effects
from the extracavity delay, it can be seen that the relative timing jitter measured from the 30 mW injection power is smaller than those obtained from the 15 mW injection power. An injection power higher than 30 mW has been tried to get an even smaller relative timing jitter. How-ever, the instability of the mode-locking of the Er fiber laser prevents the better synchronization performance from being obtained, possibly due to the excess
nonlin-ear polarization rotation introduced by the 1μm injection
pulse. In addition to the relative timing jitter, the optical spectra of the slave Er fiber laser are also measured con-currently with the different delays for the case of the
30 mW injection power, as shown in Fig.2(d). Compared
to the free-running spectrum of the mode-locked Er fiber laser, only redshift of the center wavelength can be observed in our hybrid synchronization experiment, as
also shown in Fig.2(e).
Besides the time domain measurement of the relative timing jitter, the frequency domain analysis has been per-formed as well to identify the timing jitter suppression originating from the active or passive synchronization mechanisms. To achieve this, the cross correlation signal under the hybrid synchronization is connected to an rf
spectrum analyzer (Agilent E4402B with UKB), and Fig.3
shows the power spectrum density (PSD) of the cross correlation output with respect to different frequency
ranges. The blue (bottom) curve of Fig. 3(a) is the
measurement result under the stable hybrid synchroniza-tion. When the gain of the PI servo exceeds the stable value, obvious oscillations appearing around 3 kHz can be seen from the green (middle with three large peaks)
curve in Fig.3(a). Therefore the bandwidth of the active
0 50 100 0 1 2 3 0 5 10 0 2 4 Feedback off Cross-Co rre la tor Amplitud e (V) Time (s) Feedback on Offset: 40 µm Offset: 160 µm C ros s-Correlat or Am pl it ude (V ) Time (s) Timing jitter 0.87 fs (1.9 MHz BW) -200 0 200 (b) Delay (fs) 0 5 10 15 20 2 3 4 A m pl it u de (V ) Time (s) (a) 0 80 160 0.8 1.2 1.6 2.0 2.4 2.8 1550 1555 1560 1565 1570 1575 0.50 0.75 1.00 0 80 160 0.5 1.0 1.5 2.0 Offset (µm) (e) (c) 15 mW 30 mW
Relative Timing Jitter (
fs) Offset (µm) (d) Int ensit y (a.u.) 0 µm 40 µm 80 µm 120 µm 160 µm No Injection Wavelength (nm) Wavelength Shift ( n m)
Fig. 2. (a) Demonstration of successful feedback; (b) mea-sured cross correlation trace and the timing jitters; (c) meamea-sured timing jitters of the slave Er fiber laser with different extracav-ity delay and injection power of 15 and 30 mW; (d) measured optical spectra of the slave Er fiber laser with different extrac-avity delay and injection power of 30 mW; (e) shift of the center wavelength versus the distance offset.
synchronization is less than 3 kHz. The gray (top) curve
in Fig.3(a)shows the case with a relative timing jitter of
∼10 fs when the 1 μm injection power (∼2.5 mW) is al-most completely blocked. It indicates that, for frequen-cies above 1 kHz, passive synchronization plays the dominant role to suppress the relative timing jitter. The PSD of the cross correlation output from 10 kHz to the Nyquist frequency (21.6 MHz) is measured by using another detector with a broader bandwidth, as shown in
Fig. 3(b). Above 100 kHz, the slope of the PSD, i.e., the
blue (top) curve in Fig.3(b), begins to decay with a slope
close to 1∕f2, which exhibits the typical timing jitter
characteristics of mode-locked fiber lasers [10,11]. This
means that the locking bandwidth of the passive synchro-nization should be at least 100 kHz in our experiment. Moreover, like other mode-locked fiber lasers, the part of the PSD with a frequency higher than a few MHz will not contribute significantly to the overall integrated rel-ative timing jitter. Although the detection floor, the black
(bottom) curve in Fig.3(b), is much lower than the PSD
of the cross correlation output, the measurement resolu-tion of the relative timing jitter is mainly limited by the amplitude noise of the SFG signal itself, which
corresponds to∼0.35 fs in our experiment.
The theoretical analysis aimed to clarify the above ex-perimental observations has also been carried out. First of all, the net XPM-induced frequency shift from the
master–slave pulse collision in the common fiber section
is numerically calculated with respect to the different in-jection timing. The effect serves as a retiming force on the slave Er fiber laser for achieving synchronization. The theoretical model is based on the coupled nonlinear Schrödinger equation, and the numerical method of
fourth-order Runge–Kutta in the interaction picture
(RK4IP [12]) are utilized to obtain the net single-pass
XPM-induced frequency shift as well as its first-order derivative with respect to the timing separation between the slave and master pulses when they enter the
copro-pagation fiber section, as illustrated in Fig. 4(a). The
obtained results are shown in Fig.4(b). The parameters
used in the simulation are estimated to be close to the actual experimental condition (fiber length: 0.9 m,
1.5μm; pulse: 300 fs, 0.2 nJ; 1 μm pulse: 200 fs, 0.74 nJ;
GVD: 23 ps2∕km at 1 μm and −11 ps2∕km at 1.5 μm,
respectively; nonlinear coefficient: 1.5 W−1km−1; pulse
walk-off: −1.7 ps∕m [9]). It can be clearly seen in
Fig.4(b)that, due to the GVD and pulse walk-off effects,
the net single-pass XPM-induced frequency shift is not exactly antisymmetric and may lead to the experimental
results in Fig.2when one examines the pulse dynamics
of the slave Er fiber laser that acquires the retiming force from the successive collisions with the injection pulses.
The fluctuations of the timing position Δt0;Er and
center wavelength ΔωEr of the slave pulse can be
de-scribed by the linearized evolution equations, similar to those of a typical active frequency-modulation
mode-locked laser [13]: TR dΔωEr dT − 4dr 3τ2ΔωEr f0δtΔt0;Er− Δt0;Yb; (1) TR dΔt0;Er dT 2diΔωEr; (2)
where dr represents the gain bandwidth filtering effect,
f0δt denotes the first-order derivative of the net
XPM-induced frequency shift at the equilibrium separation
(δt ¯t0;Er− ¯t0;Yb) between the master and slave pulse,
τ is the pulse width, di is the GVD, Δt0;Yb is the timing
fluctuations of the injection pulse, TRis the cavity round
trip time, and T is on a time scale of the cavity round trip time. Here, for simplicity, we have ignored the noise sources of the Er fiber laser itself. The frequency
re-sponse of the slave pulse’s timing fluctuation Δt0;Er to
the injection pulse’s timing fluctuation Δt0;Yb can be
easily obtained from solving Eqs. (1) and (2) in the
fre-quency domain such that the power spectral density of
the relative timing jitter can be expressed as [14]
hjΔt0;ErΩ − Δt0;YbΩj2i Ω 44drΩ 3τ2TR 2 h Ω22f0δtdi T2R 2 3τ4drΩ2TR 2i hjΔt0;YbΩj2i. (3)
Equation (3) clearly indicates that the relative timing
jitter can be reduced by increasing the value of f0δt,
the first-order derivative of the net XPM-induced shift. Because the derivative value varies significantly with
the relative injection timingδt, this explains why the
rel-ative timing jitter depends on the extracavity delay in our hybrid synchronization experiment. It is also in agree-ment with the observation that the minimum relative
-1 0 1 2 3 -0.6 -0.4 -0.2 0.0 0.2 (a) Frequ en cy Sh ift (THz ) δt (ps) 1.5 µm 1.5 µm 1 µm 1 µm WDM1 WDM1 0 (b) -6 -4 -2 0 2 Deriva tive (TH z /ps) δt t
Fig. 4. (a) Schematic illustration of the two-color pulse colli-sion; (b) calculated single-pass XPM-induced frequency shift and its first-order derivative versus the relative position be-tween the master and slave pulses when entering the SMF of 0.9 m. 104 105 106 107 -110 -100 -90 -80 RF Intensity (dBm) Frequency (Hz) hybrid synchronization dectection floor (b) 2 4 6 8 10 -80 -60 -40 -20 RF In te nsi ty (d Bm) Frequency (kHz) (a)
Fig. 3. Frequency domain analysis of the cross correlation out-put under the hybrid synchronization. (a) Blue curve (bottom): the stable hybrid synchronization; green curve (middle): the hybrid synchronization with an excess gain of the PI servo; gray curve (top): the hybrid synchronization with only 2.5 mW injec-tion power. (b) Blue curve (top): the stable hybrid synchroni-zation; black curve (bottom): the detection floor.
timing jitter and stable hybrid synchronization are only
accompanied by the redshift in the slave pulse’s center
wavelength. As shown in Fig.4(b), the more stable
syn-chronization range is the region with the larger positive
first-order derivative f0δt, which corresponds to the
re-gion with the red (or negative) frequency shift f δt. The
value of f0δt, as well as the current locking bandwidth
of the passive synchronization in our experiment, is still
lower than the fast PZT servo (∼180 kHz) or an
electro-optic modulator (> the Nyquist frequency) [2,15].
How-ever, from the theoretical analysis presented above, the passive synchronization locking bandwidth can be increased without affecting the stable mode-locking by simultaneously shortening the copropagation fiber length and increasing the injection pulse energy.
The individual timing jitters of the mode-locked Er fi-ber and Yb fifi-ber lasers in our experiment have not been characterized experimentally. According to their values of the intracavity dispersion, it is reasonable to estimate that individual timing jitters of the two fiber laser systems
are within the fs range [10–11]. Nevertheless, due to the
passive synchronization effect, i.e., the first term on the
right hand side of Eq. (3), the sub-fs relative timing jitter
can be obtained in our experiment. In [11] it was shown
that the mode-locked fiber lasers with the close-to-zero intracavity dispersion are able to have the attosecond
timing jitters. From Eq. (3), it is expected to obtain a
lower relative timing jitter than our current results if the individual timing jitters of the master and slave fiber lasers can be further minimized by optimizing the intra-cavity dispersion. Recently, an alternative approach based on a single Er fiber laser with the two-branch am-plifiers and highly nonlinear fibers has achieved an unprecedented synchronization accuracy with a 43-as relative timing jitter between the two-color pulses and demonstrated the successful synthesis of a single-cycle
pulse [16,17]. Nevertheless, the synchronization
tech-niques that directly lock the two ultrafast laser systems with different wavelengths are still needed, especially for the cases in which the wavelengths of the two-color pulses cannot be obtained simultaneously from super-continuum generation in highly nonlinear fibers.
To conclude, we have experimentally and theoretically investigated the key factors that influence the timing jit-ter between two ultrafast fiber lasers synchronized by the pulse injection technique. By controlling the relative tim-ing position between the injection and the slave pulses,
an ultrasmall relative timing jitter of 0.87 fs (1.9 MHz bandwidth) between the Yb fiber and Er fiber fs lasers has been achieved. This hybrid synchronization scheme provides a very flexible configuration for the synchroni-zation between two fiber laser systems as well as for the remote optical-to-optical timing distribution.
This work is supported by the National Science Coun-cil of Taiwan under the contracts NSC 99-2112-M-030-002-MY3 and NSC 99-2221-E-009-045-MY3 and by the ITRI South under the contract B200-101JE1. The authors also gratefully acknowledge the technical support from Dr. Jen-Long Peng.
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