Download Multiwavelength pulse generator using time

1470
OPTICS LETTERS / Vol. 29, No. 13 / July 1, 2004
Multiwavelength pulse generator using time-lens compression
James van Howe, Jonas Hansryd, and Chris Xu
School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853
Received January 15, 2004
We demonstrate a novel method of generating a multiwavelength pulse train by use of time-lens compression.
In addition to pulse compression, this time lens simultaneously displaces the pulses according to their center
wavelengths, resulting in a temporally evenly spaced multiwavelength pulse train. We further demonstrate
a new aberration-correction technique based on the temporal analog of a spatial correction lens to improve
the quality of the compressed pulses. Through the use of cw distributed-feedback lasers and electro-optic
phase modulators, the all-fiber system allows complete tunability of temporal spacing, spectral profile, and
repetition rate. © 2004 Optical Society of America
OCIS codes: 200.4960, 070.1170, 060.4230, 320.7080.
Optical wavelength-division multiplexing (WDM) parallel processing has shown great promise for ultrafast
real-time sampling1 – 4; however, the complexity of
the sampling source, which requires linear time –
wavelength mapping, hampers practical implementation.3,5 Previous approaches to obtaining such
a linearly chirped multiwavelength source, i.e., a
source that generates a periodically repeating multiwavelength pulse train with precise interpulse
spacing, relied on femtosecond mode-locked lasers
to provide the necessary spectral bandwidth and
required spectral slicing, spectral f lattening, and
adjustable time delay.1,2 We demonstrate a novel
method for generating a linearly chirped multiwavelength pulse train through use of a time lens.6 – 9
In addition to pulse compression, this time lens simultaneously displaces the pulses according to their
center wavelengths, resulting in a temporally evenly
spaced multiwavelength pulse train. Furthermore,
we demonstrate a new aberration-correction technique
to improve the quality of the compressed pulses.
A time lens, in analogy to a spatial lens, works by imposing a quadratic phase on an incoming electric f ield
in time instead of space.6 – 8 Our method utilizes sinusoidally driven LiNbO3 phase modulators to generate
this phase prof ile. We f irst generate four temporally
overlaid 33% duty cycle 10-GHz pulse trains, using four
cw distributed-feedback (DFB) lasers (Fig. 1). For a
single period and wavelength, we assume a Gaussian
electric f ield:
E 苷 E0 exp共2t2 兾2T0 2 兲 ,
electric field is simply
µ
∂
1 1 iC t2 .
E 苷 E0 exp 2
2
T0 2
(3)
Equation (3) describes a standard linearly chirped
Gaussian pulse. With a fiber of length Z and dispersion parameter b2 to provide the linear dispersion
needed for compression, the minimum pulse width is
obtained when the output pulse is chirp free10:
Z 苷 Zcf 苷
C
LD ,
1 1 C2
(4)
where LD 苷 jT0 2 兾b2 j is the dispersion length of the
fiber. Fulfilling this condition results in an output
pulse width
T苷 p
T0
.
1 1 C2
(5)
The analysis above for a single wavelength applies to a
multiwavelength system as well, except that a carrierfrequency-dependent time delay is introduced because
of dispersion. Although Vp of a phase modulator
depends on the carrier wavelength (Vp ~ l), variation
of Vp is negligible (,1%) in our experiment because
of the narrow wavelength span needed. For an
N-wavelength system of evenly spaced frequency Dn,
(1)
where T0 is the 1兾e pulse half-width, and impose a
phase,
∂
µ
2Ct2 ,
2pt
V
艐
cos
Dw 苷 p
2Vp
Tm
2T0 2
(2)
where V is the peak-to-peak drive voltage, Vp is the
drive required for a p phase shift, Tm is the modulation period, and C 苷 共2p 3 V兾Vp 兲 共T0 2 兾Tm 2 兲. We have
expanded the cosine to second order and neglected the
constant phase term. After phase modulation, the
0146-9592/04/131470-03$15.00/0
Fig. 1. Experimental setup for generating a multiwavelength pulse train. Pulse trains were generated with and
without a correction lens. The final compressed pulse
train is also illustrated schematically. PC, pulse carver;
MZ, Mach– Zehnder modulator; PMs, phase modulators.
© 2004 Optical Society of America
July 1, 2004 / Vol. 29, No. 13 / OPTICS LETTERS
the time delay between adjacent frequency pulses as a
result of dispersion is
Dt 苷 2pb2 Zcf Dn .
(6)
The condition for evenly spaced pulses after chirp-free
pulse compression can be met if
Dt 苷 Tm
µ
∂
1
1 n 苷 2pb2 Zcf Dn ,
N
(7)
where n is an integer number n 苷 0, 1, 2 . . . . For successful WDM parallel processing, adjacent frequency
pulses must not overlap spectrally, a condition that can
always be satisf ied by choosing the appropriate value
of n. Equation (7) denotes the simplicity and f lexibility of such a system. Driving the phase modulator(s)
at the desired modulation period and voltage determines Zcf . This in turn determines the necessary
frequency spacing Dn for even pulse spacing, easily
obtained with independently controlled cw DFB lasers.
The experimental setup is shown in Fig. 1. Although more wavelength channels can be incorporated,
we use four wavelengths for the purpose of demonstration. The four cw DFB lasers (ILX 79800D) are
spaced 835 GHz (艐6.7 nm) apart so that no spectral
overlap occurs after compression [n 苷 1 Eq. (7)].
After the WDM, we use a Mach – Zehnder modulator
(JDS Uniphase OC-192) as a standard pulse carver;
i.e., it is biased at maximum transmission and driven
with a 5-GHz sinusoid. This generates four temporally overlaid 10-GHz 33% duty cycle pulse trains.
The overlaid pulse trains are temporally compressed
and displaced by the time-lens system, which consists of two low-Vp phase modulators (Sumitomo
T.PMH1.5-11) driven synchronously at 4.5Vp each
by a 10-GHz sinusoidal drive, and a 1.1-km spool
of standard single-mode fiber with dispersion of
18.7 ps兾nm. The optical spectra before and after
the time lens are shown in Fig. 2. The close match
between measurement and theory demonstrates the
reliability and predictability of our system. We measure the temporal spacing of the multiwavelength
pulses two different ways: (1) by use of an oscilloscope (Agilent 86109A) (Fig. 3) and (2) by taking the
second-order cross-correlation trace with an interferometric autocorrelator (Fig. 4). Because the impulse
response function of the oscilloscope is limited to
18 ps, as shown in Fig. 3(a), we expected and observed
a 40-GHz sinusoid when all channels were measured
simultaneously [Fig. 3(b)]. The cross-correlation
trace, which has femtosecond resolution, gives the
more accurate measurement of the pulse spacing.
Figure 4 shows a spacing of 25 ps with a small variation of 60.3 ps. This variation agrees with what
is expected as a result of a nonzero dispersion slope
of the SSMF, which can be eliminated by proper
dispersion slope compensation. The experimental
cross-correlation trace shows a remarkable match to
theory (Fig. 4, inset). The difference in height of the
large peaks can be explained by a slight walk-off over
the large 100-ps delay of the autocorrelator. The
1471
lower height of the lower peaks in the experimental
trace can be explained by the incoherence between the
DFB lasers, which the theoretical trace does not take
into account. Figure 5(a) shows the autocorrelation
trace of a single-frequency pulse train. By use of
a deconvolution factor obtained through numerical
modeling, a deconvolved pulse width of 2.6 ps and
hence a compression ratio of 13 is achieved. We
note that this compression is approximately a factor
of 2 smaller than that predicted by Eq. (5) (艐22).
The discrepancy is due to the approximation of the
sinusoidal phase modulation as quadratic. Simply,
the quadratic approximation of a cosine wave is
totally invalid beyond the inf lection point, where the
curvature of the phase modulation changes sign.
Any departure from an ideal quadratic phase in
a time-lens system introduces aberrations. Proper
Fig. 2. Optical spectra before and after the time lens in
the absence of the correction lens, resolution bandwidth of
0.01 nm. The dashed spikes represent the initial spectra
of the cw DFB lasers: (a) calculated, (b) measured.
Fig. 3. Oscilloscope time traces of (a) each wavelength
channel measured separately then overlaid, and (b) all
channels measured simultaneously. There is no averaging on (a) or (b). The impulse response of the oscilloscope
is 18.0 ps.
Fig. 4. Cross-correlation trace demonstrating even pulse
spacing. Inset, theoretical trace.
1472
OPTICS LETTERS / Vol. 29, No. 13 / July 1, 2004
Fig. 5. Autocorrelation trace of a single-wavelength channel (a) without a correction lens, autocorrelation FWHM
3.5 ps, and (b) with a correction lens, autocorrelation
FWHM 4.2 ps. Taking into account the deconvolution
factors gives pulse widths of 2.6 and 3.0 ps, respectively.
imaging relies on the quadratic phase f iltering supplied by dispersion, as well as the quadratic phase
modulation imposed on the incoming electric f ield.8
Higher-order dispersive or modulation terms will only
distort the image. Aberrations from higher-order dispersion can be neglected in our system. Third-order
dispersion, for example, is estimated to introduce only
a 0.3% delay of the half-maximum spectral component of a compressed pulse from its ideal location.8
The leading aberration in our setup comes from
higher-order phase modulation terms. This distortion is responsible for the sidelobes that are visible
in the autocorrelation trace of the compressed pulses
[Fig. 5(a)]. The approximation of the cosine phase
modulation drive as quadratic is valid only under a
small portion of the cusp of the sinusoid. Restricting
the temporal object to a time aperture of ta 艐 Tm 兾2p
is suggested to keep the next higher-order term
negligible (approximately 2% of the quadratic term).6
However, there are two penalties associated with such
a restriction. First, it is necessary to begin with
much shorter pulses. In our system, input pulses
would need to be less than 16.0 ps. This corresponds
to a duty cycle of 16% or less, which is difficult to
achieve with the pulse carving technique. Second,
and perhaps more importantly, restricting the time
aperture leads to a much smaller compression ratio.
Our calculations show that a compression ratio of only
4 can be achieved with a 16.0-ps input pulse. We
demonstrate a new approach to eliminating aberration
without significantly sacrif icing the compression
ratio. Instead of restricting the time aperture, we
add a correction lens, which is analogous to aberration correction in spatial imaging (Fig. 1). The
correction lens consists of another phase modulator
but this time driven at 1.0Vp by a 20-GHz sinusoidal
drive (twice the frequency of the compression lens
and 11% of the drive). Fourier analysis allows any
periodic function to be decomposed into a sum of
harmonics. Our correction lens essentially adds the
next harmonic in the Fourier decomposition of a
quadratic. The suppression of the sidelobes, shown
in Fig. 5(b), demonstrates the effectiveness of the
correction scheme. The slightly smaller compression
ratio of 11 in the aberration-corrected system is
explained by the fact that the additional lens acts
as a weak negative lens. In helping the system
assimilate a truer parabolic drive, the correction
lens gives a chirp with a sign opposite to that of the
compression lens, thereby decreasing compression
strength slightly. A new dispersion of 23.0 ps is used
to satisfy the chirp-free condition, requiring a new
frequency spacing of 680 GHz for even pulse spacing.
Further aberration correction can be added to the
system by incorporating lenses of higher-order Fourier
harmonics. The limit to the amount of correction
desired is determined by the bandwidth limitations of
the LiNBO3 phase modulators (currently #50 GHz for
commercial devices). Although a separate correction
stage is used in our setup, we note that it is possible
to combine the compression and correction drive
voltages into a single rf drive and therefore use a
single broadband phase modulator to obtain the same
results. In addition, the f iber spool can be replaced
with other dispersive devices such as a fiber Bragg
grating, making the system even more compact and
eliminating the potential problem of slow timing jitter
(wander) from temperature f luctuations.
In conclusion, we have demonstrated a novel multiwavelength pulse generator based on time-lens compression with aberration correction. Our system is
all-fiber and relies on linear optics, allowing easy
use and near-exact reproducibility and predictability.
Our source not only reduces the complexity of previous
systems but also adds f lexibility and control. The
power and wavelength of the cw DFB lasers can be
independently and precisely tuned to achieve the
desired spectral prof ile and temporal spacing, and the
repetition rate of the pulses can be continuously varied
electronically over a large range. We anticipate that
the growing technological advances in phase modulators will extend this technique toward generating even
shorter pulse widths at higher repetition rates.
J. van Howe’s e-mail address is [email protected].
References
1. J. U. Kang and R. D. Esman, Electron. Lett. 35, 60
(1999).
2. A. S. Bhushan, P. V. Kelkar, B. Jalali, O. Boyraz, and
M. Islam, IEEE Photon. Technol. Lett. 14, 684 (2002).
3. P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J.
Hargreaves, R. D. Younger, J. L. Wasserman, F. J.
O’Donnell, K. G. Ray, and R. C. Williamson, IEEE
Trans. Microwave Theory Technol. 49, 1840 (2001).
4. P. Rabiei and A. F. J. Levi, J. Lightwave Technol. 18,
1264 (2000).
5. C. Xu and X. Liu, Opt. Lett. 28, 986 (2003).
6. B. H. Kolner, IEEE J. Quantum Electron. 30, 1951
(1994).
7. A. A. Godil, B. A. Auld, and D. M. Bloom, IEEE J.
Quantum Electron. 30, 827 (1994).
8. C. V. Bennett and B. H. Kolner, IEEE J. Quantum
Electron. 37, 20 (2001).
9. L. F. Mollenauer and C. Xu, in Conference on Lasers
and Electro-Optics (CLEO), Vol. 73 of OSA Trends in
Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), paper CPDB1.
10. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San
Diego, Calif., 2001).