We demonstrate a fiber-based slow light system using a carbon disulfide (CS2) filled integrated liquid-core optical fiber (i-LCOF). Using 1 meter of i-LCOF we were able to delay 18ps pulses up to 34ps; a delay of 188% of the pulse width. This experimental setup serves as a foundation for slow-light experiments in other nonlinear liquids. Numerical simulations of pulse-propagation equations confirmed the observed delay and a simplified method is presented that can be applied to calculate induced delay for non-cw Stokes pulses. The system is all-fiber and compact with delays greater than a pulse width, indicating potential application as an ultrafast controllable delay line for time division multiplexing in multiGb/s telecommunication systems.
©2013 Optical Society of America
The rapid growth of the global telecommunication infrastructure is largely due to the success of optical fibers. Fibers are now mass-produced to exhibit extremely low transmission loss and wide-bandwidth, which recently allowed >100-Tb/s to be transmitted over 165km . While many functions necessary for advanced optical networking have been demonstrated, a fast tunable optical delay line has remained an elusive capability. The basis of optical group delay is the time required for a pulse to propagate through a given medium, depending either on the length of the medium or its group index. A tunable optical delay requires a variation of the group delay by taking advantage of sharp spectral features in the material’s transmission spectrum . The relationship between optical transmission in a medium and the group velocity experienced by a pulse can be determined using the Kramers-Kronig relation . Slow light has a promising future for controllable optical delays, with pioneering results being demonstrated in gases and solids through the use of electromagnetically induced transparency and coherent population oscillation, respectively [4, 5]. A brief tutorial on the different methods of achieving slow-light effects such as the ones mentioned are well covered by Khurgin in . He also suggests applications for slow light like, e.g., optical buffers, tunable time delays, optical switches, microwave photonics, and enhanced light-matter interaction.
Besides direct atomic transitions, stimulated Brillouin scattering (SBS), stimulated Raman scattering (SRS), and parametric amplification  are other interesting mechanisms for creating slow light. These nonlinear optical effects have the wavelength selectivity property required for WDM networks. They can be implemented by the use of available highly nonlinear fibers, which can be integrated with existing fiber optical systems. SBS-based slow light has previously been demonstrated for nanosecond pulses [8, 9]; this is mainly due to the long, nanosecond lifetime of acoustic waves. This bandwidth limitation is the major hurdle blocking the use of SBS for real applications. Yet, this limitation has been overcome through the use of a double-Brillouin pump method achieving 10.9ps delay for 37ps pulses . Though impressive, this technique required that many pump lasers be used simultaneously, which increases the complexity and cost of the system. Likewise, SRS-based slow light has been used to realize an all-optical tunable pulse delay based on a Raman amplifier pumped by an optical parametric oscillator . In that work, 430fs pulses were delayed by up to 370fs, which corresponds to a fractional delay of 85% of the input pulse width. The ultrafast Raman response time in silica optical fiber (~10fs) limits the delay efficiency available at realistic operating bandwidths of fiber communication systems. Slow light based on parametric amplification, which may provide a suitable response time, is very sensitive to variation of fiber dispersion along the fiber.
In this paper, we demonstrate slow-light using stimulated Raman amplification in an integrated liquid core optical fiber (i-LCOF) filled with carbon disulfide (CS2). CS2 has a Raman response time of a few picoseconds, which bridges the gap between the low speed of SBS and the extreme speed of Raman amplification in silica fiber. We have been able to delay 18ps pulses up to 34ps, a delay of 188% of the pulse width. This experimental setup serves as a foundation for slow-light experiments in other nonlinear liquids. We also performed numerical simulations of pulse-propagation equations, which also confirmed the observed delay. The system is all-fiber based and compact with delays greater than a pulse width, exhibiting potential application as an ultrafast controllable delay line for time division multiplexing in multiGb/s telecommunication systems.
Experiment setup and results
To slow down a pulse of light using SRS, we need to use another pulse of light as the pump source whose frequency is up-shifted by the Raman resonance energy shift in the nonlinear medium. To achieve this goal we start with a mode-locked (ML) fiber laser with carbon nanotube saturable absorber (provided by Kphotonics, LLC). The ML laser’s design is similar to what was reported in . The laser generates a 50MHz pulse train at ~500fs pulse duration. A narrow band picosecond pulse train is generated from the ML fiber laser by amplification in an EDFA and spectral filtering with a narrowband fiber Bragg grating (FBG). This picosecond laser pulse train will be used as the pump in our slow light experiment (Fig. 1). To generate the signal pulses we used an i-LCOF filled with CS2 to generate the first order Raman Stokes line which is automatically down shifted from the pump by the Raman shift in CS2 (which is at about 656cm−1). The fabrication of the i-LCOF and its use as a Raman medium has been previously discussed in . The core diameter of the LCOF is ~2µm. The inset of Fig. 1 shows the spectrum at the output of the i-LCOF where the generated signal at around 1729nm is clearly visible. The pump and signal pulse trains are automatically synchronized since they are generated from a single ML laser.
The FBG filter has a FWHM spectral bandwidth of ~0.14nm that corresponds to about 22ps transform-limited pulse in the time domain. The narrow band picosecond 1553nm pump is created and then split into two branches (Fig. 1). The pulses in the first branch, which contain 90% of the average power, enter the i-LCOF filled with CS2 to generate the 1729nm Stokes signal. The remaining 10% in the second branch is amplified to create the pump for the slow light Raman amplifier using a second i-LOCF where the generated 1729nm pulses in the first branch will be delayed. The length of the first i-LCOF where the 1729nm pules are generated is ~1m and it has a transmission of ~30% at 1553nm. The high transmission loss is mainly due to significant mode-mismatch in the two gap-splices between the LCOF and the standard optical fiber . Due to the large Raman cross-section of liquid CS2, we observed an impressively low Raman generation threshold pulse energy of only ~0.1nJ. The average power of the signal pulses is <1mW so self-phase modulation can be ignored. The transform limited temporal width of the 1729nm signal pulses is ~18ps.
We used the Fourier-transform spectral interferometry (FTSI) method  to be able to accurately measure the amplification-induced delay in the signal pulses. For this purpose we create a reference pulse by splitting the 1729nm signal before entering the i-LCOF amplifier. The reference and signal pulses are later recombined using a 50/50 fiber coupler to provide spectral interference, which can be measured using a high-resolution optical spectrum analyzer (OSA). Since the 1729nm pulses are created from stimulated Raman scattering seeded by noise, in order to get good spectral interference contrast, it is important to interfere the signal pulse with its other half but not with the neighboring pulses in the pulse train. Thus, the optical paths for the signal and reference arms should be equal. A variable delay line is implemented in the reference path to put the time delay between the reference pulse and the signal pulse to be within the measurable range and to calibrate the system. The temporal separation measurable with our FTSI technique is limited by the 0.01nm resolution of the OSA and the spectral width of the Stokes pulse (0.174nm at FWHM), which represents a pulse separation range from about 60ps to 1ns. To calibrate the system we interfered the two 1729nm pulses (the reference pulse and the signal pulse) using the variable delay line in the reference arm. The set (known) value of the delay can be then compared to the delay extracted from the FTSI data acquired with the OSA. We observed ~ ± 3ps error between the set time delay (with the tunable delay line) and the measured delay using FTSI.
The second i-LCOF (Raman amplifier) is also a 1m CS2-filled i-LCOF with a transmission of ~15%. The transmission loss in the second i-LCOF is higher due to imperfection in the gap-splices. It does not, however, represent a major problem in our experiment. Before the Raman amplifier, the pump and signal must be overlapped in time. To achieve that, the pump and signal pulses are first roughly overlapped in time by using a 50GHz oscilloscope which provides a precision of ± 15ps. A mechanical variable delay line is then used for fine adjustment of the temporal overlap of the pump and signal. For efficient amplification, both the pump and signal must have the same polarization orientation so a fiber polarization controller for the pump is implemented to attain the maximum signal gain. Furthermore, by carefully optimizing the scan speed of the OSA, good fringe visibility can be achieved.
Let us consider the intensities of both the test signal, |Esig|2, and reference, |Eref|2, at a given frequency ω. The interaction of these two fields as they arrive at the OSA can then be calculated as 14]. γ for CS2 i-LCOF at 1550nm has been calculated in  to be ~900 (W km)−1. The delay induced by the XPM is estimated to be ~3fs, which is clearly negligible compared to the delays achieved.
Figure 2(a) shows representative spectral interference data between the reference and signal pulses at two different P0 acquired from the OSA. The Fourier transform of the data shown in Fig. 2(a) yields the temporal separation of the pulses (amplified signal and reference) as shown in Fig. 2(b). We can see that the signal is within the temporal-bandwidth limit mentioned above. We measured the delay by first interfering the signal and reference pulses without amplification to calculate their initial separation. We then increase the pump power launched into the Raman amplifier to induce a net optical gain and as a result a delay on the signal pulse. FTSI is repeated to re-calculate the reference and signal pulse separation. Finally, we subtract the pulse separation value with gain present from the initial separation (without gain) to attain the induced delay at a set pump power.
The result of the measurement of the induced pulse delay due to Raman amplification is plotted in Fig. 3(a) as a function of pump power. The pulse delays are measured in picoseconds and with respect to the pump peak power (at 1553 nm). We obtain a maximum pulse delay of 34 ± 6.5ps at P0 = 1.93W (Fig. 3(a)) which corresponds to a fractional delay of 1.88 and a gain of 21.5dB (Fig. 3(b)).
In order to explain the observed Raman-induced slow-light effect, we numerically solve the simultaneous propagation of the pump and Stokes pulses along the LCOF. As the primary goal, we determine the delay of the Stokes pulse. The theoretical description is based on the coupled nonlinear Schrödinger equations (NLSE) in the slowly varying envelope approximation for pump Ap(z,t) and Stokes As(z,t) pulses as given by Eqs. (10)-(11) in . These equations explain a multitude of nonlinear effects [3, 14], including Raman amplification and delay . As general parameters, these sets of equations include the dispersion (βp and βs at the pump and Stokes wavelengths, respectively), linear losses (αp and αs), Kerr nonlinearities (γp and γs), and walk-off parameter dwo, all of which are related to the optically active medium, i.e. CS2 in our case. Moreover, the Raman response is included and characterized through the Raman shift Δν = 656cm−1 and linewidth (FWHM) δν = 0.7cm−1 . As a basic mechanism, the Raman spectral resonance induces a change of refractive index and hence leads to a delay and amplification of the Stokes pulse .
In addition to the numerical evaluation of the full propagation equations, we also develop an analytical expression. Specifically, we approximate the overlap integral which is responsible for the pump-Stokes Raman interaction and given by the right hand side of (2)14], hR is the Raman-response function, and ΩR is the frequency difference between pump and Stokes. As an approximation, it is convenient to assume a CW pump that remains undepleted and thus does not suffer any distortion during interaction , yielding the Fourier transformed expression20]. In particular, when we additionally demand that the Stokes is a CW-pulse, Eq. (4) reduces to the CW result
In the experimental and theoretical configuration, the pump and Stokes are given as Gaussian pulses with individual durations and peak powers when entering the LCOF. As previously stated, the pump (Stokes) has a duration (FWHM) of 22(18)ps. Here, the Stokes pulse has virtually no power when entering the LCOF, i.e., it is initially noise but builds up through the Raman interaction. We allow a temporal misalignment between pump and Stokes at the input of the LCOF, i.e., there can be an initial time offset between the pulses. The wavelengths of pump and Stokes (1553.15nm and 1729.34nm, respectively) are determined to match the Raman response frequency of CS2, i.e. ~656cm−1.
The system parameters are fixed to describe CS2-filled LCOFs. The dispersion is computed from a simple step-index model [21, 22] and the relevant Sellmeier coefficients of the materials . Systematic measurements of linear refractive index as well as the absorption spectra of some interesting nonlinear liquids were also recently reported in . As a result, the second-order dispersion for the pump (Stokes) is β2 ≈ 105 ps2/km (~117ps2/km) and the walk-off is given by dwo = 14.5ps/m inside the LCOF . We set the linear losses to zero because we do not see appreciable absorption at the working wavelengths and consider a fiber of length 1m and 2μm core diameter. The nonlinearity γ is fixed such that the Raman gain coefficient gR ~2.7x10−11m/W at the pump wavelength , as extracted from inverse-Raman-scattering measurements.
The temporal alignment of the Stokes and pump must be varied to maximize the induced delay of the system. Because of the capabilities of the experimental setup, the misalignment was controllable to within ± 15ps, which is vital for understanding the observed delays. Figure 4 presents the effects of misalignment on Stokes delay in our system at different P0. It is clear that aside from P0, the alignment of the pulses prior to LCOF can directly affect the resulting delay. The walk-off parameter dwo has an effect on this temporal alignment throughout the amplifier. The Stokes pulse propagates at a faster group velocity than the pump so placing it just prior to the pump would extend the interaction of both pulses throughout the LCOF. The maximum measured experimental delay was 34ps at P0 = 1.93W which corresponds to about −15ps misalignment, agreeing well with our possible misalignment error.
Figure 5 displays the Stokes’ induced delay with respect to the pump peak power for our numerical (solid line), pulsed analytical (shaded), and CW analytical (dashed line) calculations. The numerical calculations are conducted by solving the NLSE directly; the pulsed and CW analytical solutions are acquired from (4) and (5), respectively. The maximum delay calculated was 34.5ps for P0 = 3.5 W. A reduction in delay beyond the maximum is due to pump-pulse deformation in the nonlinear medium.
Figure 6 displays the evolution of the Stokes pulse with respect to the pump as it propagates through the LCOF. The system’s reference point is the pump (blue thin curve) and the Stokes is aligned such that it enters the LCOF before the pump by 15ps. Five frames are plotted according to different propagation lengths, i.e., z = 0, 0.25, 0.5, 0.75, and 1 meter. Each frame displays two Stokes fields: the pulse that does interact with the pump and experiences the induced delay (red thick curve) and the one that does NOT interact with the amplifier and thus separates away from the pump because of the dwo (gray shaded area). The pump peak power is 1.5W and the gain observed through the amplifier was ~20dB, which agrees with the measured data in Fig. 3(b). A bar indicates the acquired delay, given by the time difference of average pulse positions as indicated by vertical lines, and the corresponding delay value is written explicitly. It becomes clear from this figure that the experienced total delay is a combination of the induced Raman delay and the walk-off parameter.
To test the effectiveness of the analytical solutions, we looked at the case of a pump pulse with a 300ps pulse duration, as shown in Fig. 7, which shows the Stokes delay with respect to the pump peak power. The red line is the numerical solution, the yellow shaded area is the pulsed analytical result and the dashed line is the CW analytical result. In the inset, we computed the pump-Stokes interaction after a 1-meter propagation where the grey shaded area is the Stokes without pump, the red line is the Stokes with pump (numerics), the yellow shaded area is the Stokes with pump computed analytically, and the blue line is the pump. From the Stokes’ delay with respect to P0 one can see by comparing to Fig. 5 that we can achieve higher delay values when we use temporally wider pump pulses. This is a limiting factor to our experimental observations where the pump temporal width is determined by the FBG. Likewise, the numerical and analytical solutions agree very well in comparison with Fig. 5; the CW analytical result still overestimates the delay but by less due to the longer pump duration. It must be noted that this is true only for low P0 and as P0 grows the pump profile experiences nonlinear deformations within the LCOF thereby limiting the induced delay. Viewing the inset, it can be seen that the analytical expressions reproduce the numerical values very well; in particular, the asymmetric temporal lineshape and absolute optical power of the Stokes are reproduced very accurately. This demonstrates that (4) can be used efficiently to compute realistic delay values even for finite Stokes-pulse durations.
We have analyzed and demonstrated an all-fiber-based ultrafast all-optical tunable delay. By using CS2-filled LCOFs, we were able to both generate and amplify the signal pulses and take advantage of the CS2 picosecond response time and high nonlinearity. The LCOF’s high confinement also allowed for a dramatic reduction in propagation length for the amplifier, which allowed us to overcome other possible nonlinear effects and delays. By using similar pulse durations for both the signal and pump, we show the capability of delaying pulses individually in a pulse train with delay values well beyond the signal duration. Our results demonstrate a delay of 34ps at a pump peak power of 1.93W. The delay values measured agree with a theoretical estimate of the optimal misalignment between signal and pump pulses of about −15ps before the Raman amplifier. This slow light system could be useful for optical time division multiplexing (OTDM) where multiple channels of bit rate B are transmitted by sharing the same frequency but are divided by bit slots rate NB, where N is the number of channels . By using a pulse-to-pulse delay configuration, it is possible to shift an individual bit to an adjacent channels slot without incurring any alterations to the other channels. Similarly, selectively shifting an entire channel could be possible after the OTDM transmitter. These delays could be implemented for multiGb/s OTDM signals.
The authors would like to thank Roland Himmelhuber and Dmitriy Churin for useful discussions. We thank Yevgeniy Merzlyak for fabricating the LCOFs used in the system and the Technology Research Initiative Fund (TRIF) through the Photonics Initiative for graduate student support. This work was supported by the DARPA ZOE program (Grant No. W31P4Q-09-1-0012), the CIAN ERC (Grant No. EEC-0812072) and the AFOSR COMAS MURI (FA9550-10-1-0558).
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