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Ultrafast all-optical switching in a highly nonlinear fiber with a longitudinally varied zero-dispersion wavelength was investigated theoretically and experimentally. We describe fiber-matched methodology for construction of a fast, low energy photon switch. The design relies on static and dynamic models and allows performance target selection, under constraints of physical fiber characteristic. The new design methodology was used to construct one-pump switch in the highly efficient parametric mixer. We demonstrate that such a parametric gate can operate at 100 GHz rate, with 2 aJ control energy, while achieving better than 50% extinction ratio. Theoretical analysis and experimental measurements indicate that accurate mapping of the fiber local dispersion is critical in optimizing the bandwidth and control energy of the switch. Switching performance limits are discussed and means for impairment mitigation are described.
© 2014 Optical Society of America
1. Introduction
The idea of practical, direct light manipulation originates in 1980s when Smith [1] articulated the notion of all-optical switching devices that could overcome total energy consumption and speed limitations inherent to electronic switching devices. Since then, all-optical switching has been demonstrated in a number of different platforms, but, arguably, none of these offered performance that is compelling enough to displace conventional electronic devices. One of the main reasons for the lack of performance is that majority of all-optical switching devices reported to date rely on index modulation, dictating high power per switching event. Furthermore, the integrity of the switched signal, a critical consideration in communication links, is often ignored. However, with progress across multiple physical platforms, optical switching can now be realized at significantly lower energy. In a number of recent publications [2–8] high-speed switching devices that are triggered by low photon count have been developed, motivating another look at the utility of optical switching devices. A cross-section of recently reported work is summarized in Table 1.
Table 1. Optical Switching Devices: Recent Reports4
In contrast to the work reported only a decade ago, the advance is reflected in energy levels: the probe energy per bit has reached a single photon level and the total device energy that of fJ. As expected from the diversity of physical platforms and operating principles, the underlying response time and dissipation vary widely. While the devices employing photonic-crystal nanocavity [6,7] consume low energy per pulse, these have relatively long switching time and high coupling and propagation loss. Conversely, the technologies reported in [2,4,8] are comparatively fast, but require high pump energies for optimal performance. In [3,5] probe energy/pulse has reached few-photon level, but have long switching time, high loss and require cryogenic environment, thus adding to the overall energy dissipation. Summarizing the above overview one can conclude that while the optical switching indeed shows considerable progress, a tradeoff between the total invested energy and the switching time (bit rate) is seen across all platforms.
This report investigates and demonstrates fast, atto-Joule all-optical switching at telecom wavelength band (1550 nm). We specifically chose silica fiber parametric mixer (FPM) [9] engineered for very high efficiency. This class of devices has traditionally been used as signal amplifiers and wavelength converters and, in this role, are recognized as fiber optic parametric amplifiers (FOPA) [10]. Endowed by large, ion-independent bandwidth and ultrafast Kerr response, FPMs have been used in applications such as frequency combs [11], super-continuum generation [12] and signal processing [8,9]. Inherent femtosecond silica nonlinear response is the key motivation for the FPM use in development of a direct light gate that aims to operate at high bit rate and with low-power signal. Of equal importance is that FPM also offers long interaction length, thus relaxing the requirement for the total invested energy. Optical switching in a highly nonlinear fiber was previously demonstrated using continuous wave (CW) pump and pulsed signal [8,9]. However, complex dynamics of a short pulse propagation in the vicinity of zero-dispersion wavelength of the fiber in such an operating regime conceals the FPM process, thus inhibiting the switching operation. Therefore, it is critical to demonstrate that the switching is still possible employing short pulses for both the pump and the signal wave. Here we show that an 8.1 pJ pump pulse can be switched by 2.2 aJ control signal resulting in the extinction ratio (ER) of more than 3 dB, while more than 5 dB ER can be achieved with 5.4 aJ control. Finally, the transfer response of FPM switching architecture allows for a control of a 100 Gbps-fast OOK input.
2. Pump depletion in efficient parametric mixer induced by small-signal
2.1 Theory
In the simplest implementation, an all-optical switch can be realized, at least in principle, by controlling the pump state in a high-gain FOPA. Since the gain mechanism relies on the power transfer from the pump to the signal and idler waves, even a small input should lead to measurable depletion of the pump at the output of the device, as illustrated in Fig. 1. Pump depletion is a direct function of the signal input power: even a very weak signal can initiate a strong change of the pump level if the parametric exchange is made to be very efficient. The operation of the FOPA in the depleted pump regime was investigated theoretically by Chen [13], while the stability of states was later studied by Cappellini [14]. While simple, this model provided for an insight to energy transfer among continuous waves in the nonlinear fiber and is often used to estimate the pump depletion levels.
Fig. 1 Pump depletion mediated by four wave mixing in highly nonlinear fiber in the presence of weak signal. HNLF-highly nonlinear fiber.
In practice, there are more than three waves participating in the mixing process, thus limiting the predictive accuracy of such approach. Nevertheless, the three wave model gives a good insight to the photon exchange governed by the following set of equations [14]:
where Aj, j = 0,1,2 is the amplitude of the pump, signal and idler respectively, ϕj the phase of the pump, signal and idler respectively, γ nonlinear parameter. The condition leading to a complete pump depletion involves the parameters [10]: where ΔkNL is nonlinear phase mismatch, ΔkL linear phase mismatch, Δω frequency separation between the pump and the signal and β(2) and β(4) second and fourth order dispersion coefficient respectively; furthermore, in Eq. (6) no idler is assumed at the input (phase insensitive operation). As opposed to the well-known phase matching condition in the linear operating regime (ΔkNL = 2γA02) which leads to gain maximization, the condition given by Eq. (6) is designed to minimize the pump power level [10]. Therefore, strong, broadband pump depletion can be obtained when the linear phase mismatch cancels the nonlinear phase mismatch contribution. Maximum energy transfer from the pump to the signal and the idler (maximum pump depletion) is dependent on the dispersion properties and the nonlinear coefficient of the fiber, fiber length, frequency separation between the pump and the signal and the pump and signal and idler power levels. Thus, for given fiber parameters, there exist an optimum pump power level and pump/signal wavelength positioning that will result in the maximum depletion (switching) performance.2.2. Switch design
As stated above, the three-wave model has only limited accuracy because higher order mixing products were not taken into account. Consequently, in order to increase the prediction accuracy, the photon switching must be described by a model that can incorporate higher-order terms and account for impairment mechanisms expected in a physical fiber. Broadband nonlinear Schrödinger description, while computationally expensive, can account for the loss, dispersion fluctuation, multiple-tone generation and is used as a second step in the design process.
2.2.1. Static response
Switching bandwidth of the FPM device is largely defined by the physical characteristics of the fiber. In order to estimate its bandwidth, the static system response needs to be characterized first. The simplest technique for the static transfer response relies on the continuous-wave (CW) pump and the tunable probe that can be used to estimate the switch bandwidth. To model the device, 31.6 dBm CW pump centered at 1554 nm was combined with a white noise source; the noise source representing vacuum fluctuations had a level of fluctuations of 0.5 photons per mode and was a basis for parametric fluorescence generation. The system was analyzed by a commercial nonlinear Schrödinger solver (NLS) [15] incorporating split-step Fourier method [16] using the rigorously characterized fiber parameters. The generalized nonlinear Schrödinger equation is given by Eq. (27) in the Appendix. The interaction of multiple frequency components was simulated over 41 THz bandwidth, 3 times wider than the modulation instability bandwidth at a given pump power level, to increase the predictive accuracy of the model, including the effect of parametric fluorescence on pump integrity, which depends mainly on the modulation instability bandwidth. Optical signal to noise ratio (OSNR) of the pump used in the simulation was 47 dB, measured in the 0.1 nm resolution bandwidth, matching typical OSNR of the amplified 1550 nm diode. The switch transfer response was mapped by varying both wavelength and power of the CW probe in the 1560-1575 nm and −40 dBm to −20 dBm ranges, respectively. Pump-signal interaction along the 520-m-long HNLF with nonlinear parameter (γ) of 12.3 W−1km−1, propagation loss of 1.1 dB/km and global zero-dispersion wavelength (ZDW) of 1548 nm was simulated and used to calculate the power of all generated waves. Furthermore, the HNLF had longitudinal ZDW fluctuations modeled after the experimentally measured fiber possessing ZDW map shown in Fig. 2(a). Due to severe effect of the ZDW fluctuations on the FPM [17], including the longitudinal ZDW profile is critical for an accurate modeling of the system. The experimentally obtained ZDWL profile was modeled using 200 different fiber sections of equal length and with constant ZDWL. The system response was obtained by successively solving the NLS for each fiber section. At the output of the HNLF, the pump was filtered using a 2 nm optical band-pass filter (OBPF) and detected. Extinction ratio (ER), defined here as the ratio of the pump power in the presence and in the absence of the signal was measured and the resulting contour map is plotted in Fig. 2(b).
Fig. 2 (a) Longitudinal ZDW profile and the corresponding dispersion profile at the pump wavelength used in the static transfer characterization; (b) Calculated ER power-wavelength contour map. Δλ indicates wavelength offset between the pump and the control signal.
As seen in Fig. 2(b), when the power of the signal was set to −30 dBm, the optimum control wavelength was 1566 nm. More importantly, this selection guarantees the minimum 3 dB ER across the entire 5.5 nm bandwidth. In other words, the calculation indicates that the switch can be controlled by 1.4 ps signal shaped by a rectangular pulse with a peak power of −30 dBm, and should possess a minimum 3 dB ER at the output. Interestingly, the map plotted in Fig. 2(b) allows for a straightforward design of a switch: given the minimum extinction ratio and the desired switch speed (bandwidth), it is possible to uniquely select the control power and center frequency with respect to the pump.
2.2.2. Dynamic response
Having characterized the bandwidth of the system using static analysis, further investigation of the switching response was performed in the time domain using pulsed input. Consequently, the CW pump and signal were replaced by optical pulses. There are several effects characteristic for the dynamic pulse interaction that place additional challenge in a switch design, the first one being the dispersion induced pulse breakup. Namely, it has been shown [18,19] that pulses propagating at zero dispersion wavelength are highly affected by third-order dispersion. An interplay between the nonlinearity and the dispersion causes splitting of a pulse initially centered at the ZDW to frequency downshifted soliton-like wave and up shifted dispersive wave, leading to clear frequency separation. Wai et al. [19] suggested that the effect could be eliminated by controlling the pump position with respect to the ZDW, as well as the pulse duration. Since the system bandwidth is drastically affected by the pump spectral position, it is preferable to refrain from using the pump wavelength as a free design parameter. Any pulse breakup could be avoided by increasing the pump pulsewidth, thus limiting the pump repetition rate and switching time of the device. Another, preferred way to circumvent this impairment is to use a fiber with specifically tailored dispersion over the wavelength range of interest. Consequently, for the purpose of this experiment, we chose to minimize soliton radiation impairment by limiting the switching speed to 100 GHz, dictating 5 ps gating window. Other, equally important effects that affect switch performance are the walk-off of the interacting waves, soliton pulse compression and evolution. The average walk-off parameter d12 can be estimated from [10,16] d12 = |β2(ωp)Δω + β3(ωp)Δω2/2|, where β2(ωp) = −1.9⋅10−28 s2/m and β3(ωp) = 4.1⋅10−41 s3/m, and is found to be 0.003 ps/m at the signal frequency and 0.0002 ps/m at the idler frequency. All the mentioned effects are included in the simulation [15].
The switching response was further characterized using a pulsed input signal to determine the optimum operating conditions. The pump was generated by a source which produced a pulse train centered at 1554 nm. Pulses had a peak power of 31.2 dBm, pulsewidth of 5.4 ps and repetition rate 10 GHz. The signal consisted of transform-limited 2.3 ps pulses with 10 GHz repetition rate, centered at 1565 nm. The chosen temporal width of the signal pulse guarantees the temporal overlap of the interacting waves along propagation, however some extinction ratio deterioration, compared to CW operation, can certainly be expected. The signal peak power was varied from −30 dBm to −14 dBm using 4 dB steps while keeping the rest of simulation parameters unchanged with respect to the static case. At the output of the HNLF, the pump was filtered using a 2 nm OBPF and both time and frequency domain outputs of the device were subsequently analyzed and plotted in Figs. 3(a)-3(e) and 4(a)-4(e).
Fig. 3 Spectrum at the output of the system in case when signal is not present at the input (dotted curve) and the case when the signal is present (solid curve); Control signal peak power corresponds to (a) −14dBm, (b) −18dBm, (c) −22dBm, (d) −26dBm, (e) −30dBm.
Fig. 4 Time response of the system in case when signal is not present at the input (dotted curve) and the case when the signal is present (solid curve); Control signal peak power corresponds to (a) −14dBm, (b) −18dBm, (c) −22dBm, (d) −26dBm, (e) −30dBm, with corresponding histograms.
The switching was achieved by energy transfer from the pump to the signal, the idler and higher order mixing waves via the four wave mixing process, clearly seen in the spectra in Figs. 3(a)-3(e). In the absence of the signal, represented with dashed curve, only amplified spontaneous emission noise is present. Presence of the signal containing few photons within the envelope of the pulse can clearly be distinguished from the noise as seen in Fig. 3(e).
The results in the time domain are plotted in Figs. 4(a)-4(e) using the averaged pump waveform with the signal on and off, with the two corresponding histograms. These histograms were generated from 56730 samples, and were obtained by repeating the NLS simulation seeded by independent noise source realizations, while maintaining the deterministic simulation parameters. We note that the main purpose of the histogram is to calculate the average ER and estimate the error, rather than emphasizing the statistical properties of the pump wave at the output of the system. The histogram shape strongly depends on the pump peak power, pump excess noise, impulse response of the detection system (which is not included in the simulation) and the temporal width of the window used to collect the histogram samples; therefore, the study of the statistical properties of the system requires strict system characterization and might be the topic of the future work. In order to mimic experimental conditions, the samples were collected at the pulse center within a 1.5 ps timing window. The results indicate that the pump waveform can indeed be switched with an only 2.2 atto-Joule-strong signal, as seen in Fig. 4(e). While not shown here, it is important noting that the noise performance can be significantly improved when the lower pump power is used, with modestly higher signal powers. Finally, we emphasize that the case calculated here is still very far from the optimal switching design that requires specifically tailored fiber characteristics.
In the final step in the system characterization, the switching performance was completed by measuring the ER using Eqs. (8)-(17) in the Appendix. Additionally, the relation between the signal power and the photon number (energy) is given by Eq. (24) in the Appendix. The results of this characterization, for different input signal pulse energies are presented in the Table 2. The error in the ER measurement is represented with a 97.7% confidence interval. It can be seen that a control pulse containing 17 photons resulted in a 2.86 dB average ER. The temporal response of the system is dominated by the input pump pulsewidth. Because of the high input peak power and operation close to the ZDW of the fiber in the anomalous dispersion regime, the pump evolves into a high order soliton-like pulse. On the one hand, the pump evolution of this type has the advantage of pulsewidth reduction and peak power enhancement. The reduced output pulsewidth is important for temporal response of the system which will be limited by the input pulsewidth only, while a higher peak power increases the system ER . On the other hand, the high order soliton pulses suffer from increased peak power fluctuations, due to the peak-power-dependent pulse compression, leading to increased pump output peak power fluctuations, as compared to the CW regime.
Table 2. Extinction Ratio
3. Experimental results
3.1. Static system response
After the design outlined in Section 2, the switching device was experimentally realized with the setup shown in Fig. 5. The system switching performance was first characterized with respect to the ER as a function of the signal spectral position and the power. A tunable laser source, positioned at 1554 nm, was used as the pump seed and was modulated to generate long, quasi-CW pulses in order to suppress any residual stimulated Brillion scattering (SBS). This pump pulse was 1 ns long and was repeated at 51.2 ns intervals. The amplitude-modulated pump was amplified by an erbium-doped fiber amplifier (EDFA) and filtered using a 1 nm optical band-pass filter (OBPF) in order to filter out amplified spontaneous emission (ASE) noise from the EDFA. The resulting OSNR of the pump at the HNLF input was 47 dB, measured within 0.1 nm resolution bandwidth. The pump peak power was controlled by a variable optical attenuator (VOA) and set to 31.6 dBm.
Fig. 5 Experimental setup: Static measurement performed by quasi-CW pump (L2) and CW signal (L1); Dynamic measurement was performed by replacing pump and signal sources by mode-locked laser and cavitless pulse source (insertion indicated by dashed line). Acronyms: MLL-Mode Locked Laser, A-amplifier, L tunable laser, OBPF- Optical Band Pass Filter, C- Coupler, WDM – Wavelength division multiplexer, HNLF - Highly Nonlinear Fiber, VOA - Variable Optical Attenuator, MZM - Mach Zehnder modulator, PPG - Pattern Generator, PD – Photo diode, SO – Sampling oscilloscope, OSO - Optical Sampling Oscilloscope.
The signal was generated by a CW tunable external cavity laser, L1, and was swept both in wavelength and power from 1559 to 1569 nm and −40 dBm to −20 dBm respectively. Amplified pump and the attenuated signal were combined and launched into a 520 m long HNLF with nonlinear coefficient 12.3 W−1km−1, propagation loss of 1.1 dB/km and longitudinal ZDW profile shown in Fig. 4(a). Longitudinal ZDW variations in the HNLF were measured using the counter-colliding Brillouin scanner technique [20]. The pump was filtered using 2 nm OBPF at the output of the HNLF and detected by a photodiode (PD) and a sampling oscilloscope (SO). Pump ER was measured using the oscilloscope: sampling point at the center was identified and used in order to eliminate the roll-off at the edges imposed by the finite response time of the modulator and the pattern generator.
The pump ER measurement was plotted as contour wavelength-power map in Fig. 6, similar to the form adopted during the design mapping shown in Fig. 2(b). We note that the results of the static measurement are in a good agreement with the model prediction shown in Fig. 2(b). The optimal wavelength for the input signal with power of −30 dBm was measured at 1565 nm. More importantly, this selection guarantees the minimum 3 dB ER across the entire 5 nm bandwidth.
Fig. 6 Measured ER power-wavelength contour map. Δλ indicates separation of the pump and the control signal.
While not detailed here, it is important to note that the optimum ER-bandwidth performance was found at the pump wavelength of 1554 nm. Shorter pump wavelength resulted in the ER decrease, while bandwidth reduction is observed at the longer pump wavelength.
3.2. Dynamic system response
In the second set of experiments, the temporal response of the system was characterized by positioning the pump and the signal according to parameters obtained from the static measurement. The experimental setup shown in Fig. 5 had the CW signal/pumps from the static measurement architecture eliminated, replacing them by pulsed sources. To capture the fast transients, the detection system incorporated a wide bandwidth optical sampling oscilloscope (OSO). The pump was generated using a cavity-less pulse source [21] centered at 1554 nm, producing 5.4 ps long pulses with a repetition rate of 10 GHz. The control signal was represented by mode locked laser (MLL) at 1564 nm, with a pulsewidth of 2.4 ps and repetition rate of 40 GHz; its power was controlled by a variable optical attenuator (VOA). The pump peak power was calibrated at the input of the HNLF using the method described in the Appendix, and was set to 31.7 dBm with an error of ± 0.7 dB using a VOA. The average power of the control pulse was measured with an optical power meter at the calibration point (A) in Fig. 5; the calibration accounted for the power ratio between the measurement point A and the input of the HNLF. At the output of the HNLF, the pump was filtered using two consecutive 2 nm OBPF, and was attenuated before being detected by the OSO.
The experimental results from the temporal and spectral domain measurements are shown in Figs. 7(a)-7(e) and 8(a)-8(e). We note an excellent agreement between the simulation results shown in Figs. 3(a)-3(e) and 4(a)-4(e), and the measurements, both in temporal and spectral domains. In the absence of the input signal, represented with a dashed curve in Fig. 7, the output of the switch is characterized by the amplified spontaneous emission noise. As predicted by the model, the presence of a weak, 17-photon pulse [corresponding to Fig. 7(e)] can clearly be distinguished from noise in the spectral measurement.
Fig. 7 Measured spectrum at the output of the system in case when signal is not present at the input (dotted curve) and the case when the signal is present (solid curve); Control signal peak power corresponds to (a) −14.5dBm (b) −18.5dBm, (c) −22.5dBm, (d) −26.5dBm,(e)-30.4dBm.
Fig. 8 Measured temporal response of the system in case when signal is not present at the input (dotted curve) and the case when the signal is present (solid curve); Control signal peak power corresponds to (a) −14.5dBm, (b) −18.5 dBm, (c) −22.5dBm, (d) −26.5 dBm, (e) −30.4dBm, with corresponding histograms.
The results of temporal response measurements are presented in Figs. 8(a)-8(e) where averaged output of the device, in presence and absence of the input (control) signal is plotted. Figure 8 also shows corresponding histograms for high- and low-level outputs with both input conditions. It can be noticed that the high-level histogram experiences asymmetry which comes from the noise induced pump depletion. The difference in the measured and the simulated histogram is attributed to the error of the pump peak power calibration, temporal width of the histogram widow, pump excess noise and impulse response of the system. The exact matching of the histogram shape requires a rigorous study and is out of the scope of this work. By varying the control signal energy from 2.2 aJ to 84 aJ, the experiment indicates that the pump can be switched with ER ranging between 3.1 dB and 7.7 dB.
The ER of the pump maintained at constant peak power (31.7 dBm) was measured following the procedure described in Section 2, while the signal probe power level was varied. Results are summarized in the Table 3 and Fig. 9. In the Table 3, results are presented with an error given within the 97.7% confidence interval.
Table 3. Extinction Ratio*
The pump input pulse energy was constant and maintained at 8.1 ± 0.8 pJ throughout the measurement. In the presence of the control signal, the pump beam was switched and the ER of 3.10 ± 0.03 dB and 5.40 ± 0.05 dB was measured when signal was at 2.2 ± 0.2 aJ and 5.4 ± 0.5 aJ respectively. Equivalently, this corresponded to an average of 17 ± 2 and 42 ± 4 photons per control (signal) pulse. At higher signal peak powers, we observe pump power noise reduction, as expected from the nonlinear transfer function of the system.
4. Discussion
At high control powers, the experimentally measured pump ER was lower than that predicted by the theory: at −22 dBm input signal, this difference was nearly 3dB. The main reason for discrepancy was attributed to the low sensitivity and the limited dynamic range of the OSO, as well as the timing jitter of the pump pulse used in the experiment. Furthermore, signal and idler walkoff have a significant contribution to the ER degradation. Depending on the dispersion profile of the fiber, the group velocities of the pump, signal and idler differ, ultimately resulting in a measurable finite temporal misalignment. Although increasing the signal pulsewidth might relieve the influence of the walk-off on the ER, it also elevates the signal energy. Thus, reliance on a HNLF with low local dispersion over the wavelength range of interest would be preferred way of overcoming the described issue. In addition to the aforementioned ER impairment mechanism, the pump amplitude noise is directly converted to the signal amplitude noise and further transferred to higher order idlers via gain fluctuation. Finally, it is the coupled signal/idler phase noise (via the cross phase modulation (XPM) and FWM), that impairs the system performance by means of a broadened switching window. Additionally, the pump phase noise is equally important as it leads to amplitude-phase noise conversion via self phase modulation (SPM) and XPM, which cannot be neglected in the high-saturation regime. In general, if not controlled, the phase noise of the three original waves present at the HNLF input could decrease the overall ER when working with short signal pulses. The output pump amplitude fidelity is highly sensitive to the mixer figure of merit (defined by the γPL product) and input signal power, imposing a direct tradeoff between the high ER and pump amplitude integrity at low input signal power levels. Furthermore, output pump integrity additionally depends on the pump signal to noise ratio, pump excess noise, dispersion properties of the fiber and pump pulse width. Lastly, while the effect of the parametric fluorescence on the switching performance strongly depends on the described parameters, it is expected a γPL>>10 results in the absence of the two well defined states. However, these limitations can obviously be controlled by reducing the pump power level.
The switch limitation that cannot be predicted by the static analysis comes from the third order dispersion induced pulse breakup. Indeed, in the presence of a finite β3, the switching speed is limited by the input pump pulsewidth, and was found to correspond to 5.4 ps at the power level used in this experiment (31.7 dBm). This limitation can, in principle, be circumvented by engineering HNLF with tailored high-order dispersion over the wavelength range of interest.
As a final observation, we note that in contrast to the low speed / CW case, on the same platform [9], where the pump can be controlled with as low power as that corresponding to an average of 3 photons, this task becomes distinctly more challenging for a pulsed pump. An ER close to 3 dB has been achieved for a 2.2 aJ signal in this work, while the similar effect was achieved with half the signal energy in the CW pump case. This discrepancy can be relieved by a further effort in fiber dispersion engineering.
5. Conclusion
We have theoretically investigated and experimentally demonstrated ultrafast all-optical switching in a highly efficient parametric mixer. The experimental measurements fully affirm the low-energy potential of the platform, allowing the control of a high power pulse by 17 photons on the average and achieve the extinction ratio (ER) of 3 dB. A higher ER was readily achievable: 42 photons corresponded to the ER of 5.4 dB. The switch performance was limited by the walkoff of the interacting waves and amplitude and phase noise inherent to the pump/signal seeds. The maximal signal (pump) rate was limited by the third order dispersion of the HNLF that induced pump pulse breakup and was measured at 5.4 ps for the implemented experimental system. This effect can be readily reduced by dispersion engineering, allowing for increase of the switch speed. The total switching energy for the demonstrated system corresponded to 8.1 pJ/pulse for the pump and 2.2 aJ/pulse for the signal and was dominated by the pump pulse level necessary to match the conventional HNLF type. In addition to engineering a new HNLF fiber, further reduction in pump energy can be achieved with shorter pulses but requires a further third order dispersion engineering to prevent the pulse breakup. We note that the switch represents an all-fiber platform that operates at telecom wavelengths and possesses a negligible (<1dB) loss, allowing for its seamless insertion and selective use without impairing the existing lightwave links. Finally, the demonstrated all-fiber switch possesses physical footprint compatible with the OTU standard [21] and offers a low dissipation alternative to electronic switching at high rates.
7. Appendix
7.1 Error estimation
The average extinction ratio and the corresponding error were calculated using standard error estimation [22,23]. The relative frequency fi, the mean μ and the standard error estimate ε of two output power levels of the pump were calculated using histograms:
where n is the total number of points and ni is a number of points at the power level mi and t is a number given by Student t distribution. For n = 56730 and 84% confidence interval, t number is equal to 1, while for 97.7% confidence interval, t number is 2, thus making the error twice larger. Extinction ratio and the corresponding error were calculated using the following set of equations [22,23]: Power meter used in the experiment has an error ΔPPM = ± 3%, which makes the average and peak power error: where Pave is the average power; PPM power meter power reading; Rcal calibration power ratio between point A in Fig. 5 and HNLF input for signal power calibration and point B and HNLF input for pump power calibration; Ppeak peak power; Rcal2 calibration power ratio between the peak and the average power (method described below). The average number of photons in the signal pulse and the error were estimated using following equations: where T is the period of the signal, h is the Planck constant and ν is signal frequency. Additionally, signal energy is calculated as the product of the signal average power Pave and the period T (Es = PaveT).The optical sampling oscilloscope was calibrated using CW light centered at 1554 nm. Measured transfer function represented is given by Eq. (26) obtained from the fit.
One method to calibrate peak power is by matching the value of the pulse peak power to the CW reference level using OSO. The ratio of the average power of the pulse and that of the CW reference (corresponding to the peak power of the pulse), labeled as Rcal2 in the Eq. (20), can be used to monitor the peak power. This was experimentally implemented at the point B on Fig. 5, where the average power of the pulse was measured. Additional calibration between the point B and the HNLF input was needed to have an accurate estimate of the peak power at the HNLF input.
7.2 Generalized nonlinear Schrödinger equation
The propagation of multiple frequency components was modeled by universal fiber [15] utilizing generalized nonlinear Schrödinger equation [16]. The equation describes the forward propagating field and is given by:
where is a complex envelope of the field, α is an attenuation coefficient, is a differential operator that accounts for the dispersion in a linear medium, is a nonlinear operator governing the nonlinear effects. The mentioned operators are given by: While the model supports higher order nonlinear effects and Raman scattering, these were not considered in the simulations shown in this work, as these effect do not significantly contribute to the system response, but considerably extend the simulation time.Acknowledgment
This work has been supported by Intelligence Advanced Research Projects Agency (IARPA).
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