Open Access
Add to BibSonomyAbstract
Photonic analog-to-digital conversion and optical quantization are demonstrated, based on the spectral shifts of orthogonal frequency division multiplexing subcarriers and a frequency-packed arrayed waveguide grating. The system is extremely low-energy consuming since the spectral shifts are small and generated by cross-phase modulation, using a linear-slope high-speed and low-jitter pulse train generated by a mode locked laser diode. The feasibility of a 2, 3 and 4-bit optical quantization scheme is demonstrated.
© 2014 Optical Society of America
1. Introduction
The steep increase of the information data volume transmitted over telecomunication networks, which is going to grow more and more in the next future, as a larger percentage of the population gains access to broadband internet, calls for a constant capacity enhancement in the core fiber.
Digital coherent optical transmission is one of the main technologies that can increase the network capacity, by incorporating ultrahigh-speed and sophisticated digital signal processing (DSP) into wavelength division multiplexing (WDM) communications. To compensate for chromatic and polarization mode dispersion at 40G and 100G speeds, advanced DSP devices and algorithms, as well as energy-efficient and fine-resolution analog to digital (A/D) converters are required [1]. Electrical devices cannot support large multi-bit amplitude resolution and high sampling rates, due to their timing jitter and comparator ambiguity [2–4]. Photonic A/D converters, that are able to quantize, sample, as well as encode directly in the optical domain, can overcome these main limitations, with a reduced power consumption. High-speed optical sampling approaches have been demonstrated [5,6], and a large number of different optical intensity quantization schemes have been proposed in literature, following the progressive availability of reliable devices, such as a highly nonlinear fibers (HNLF) [7–11], nonlinear optical loop mirrors [12,13], Mach-Zehnder interferometers [14], and semiconductor optical amplifiers [15,16]. Other advantage of the optical quantization schemes are the simplicity of implementation and the reduced insertion losses [17].
About ten years ago, soliton approaches, based on soliton frequency shifts or higher-order soliton formation, were proposed for optical multi-level thresholding [8]. These schemes use a single nonlinear effect for all the bits at a single line, and a 10 GS/s, 32-level (5-bit) quantization scheme using spectral shift and compression has been experimentally demonstrated [9]. However, this method is quite power hungry, due to the spectral compression required to increase the bit resolution; in addition, a large spectral shift is needed to change the power values at the outputs of an arrayed waveguide grating (AWG)-based demultiplexer, since WDM channels are 100 GHz spaced in the ITU grid. To overcome the energy issue related to a large spectral variation, a dense spectral slicing scheme with a specially designed AWG for orthogonal frequency division multiplexing (OFDM) has been recently proposed [18,19]; in that case, the OFDM subcarriers spacing was 40 GHz and the proof-of-concept of 10GS/s, 3-bit A/D conversion has been experimentally demonstrated.
In the present paper, we present a further improvement of the proposed spectral slicing A/D conversion, using a newly designed frequency packed (FP)-AWG device, where the spacing between adjacent subcarriers is further reduced to minimize the required spectral shifts, and therefore the overall energy consumption. In addition, spectral bandwidth compression is no longer required and the A/D conversion and quantization is efficiently achieved using a linear-slope pulse-train and cross phase modulation (XPM). Finally, the proposed approach is more efficient and flexible than the previous approach [19], since the sampling rate B and the quantization resolution are completely independent.
The reminder of this paper is organized as follows: in Section II, the spectral shifts of OFDM subcarriers are numerically and experimentally evaluated and the 2, 3 and 4 bit optical quantization cases are numerically evaluated in Section III, analyzing also the performance of the quantized transfer function.
2. OFDM subcarrier spectral shifts
2. 1 Numerical simulation
Shifting WDM wavelengths, 100 GHz separated, using nonlinear effects requires very large power. To overcome this limitation, in [19] the signal after the HNLF is demultiplexed by an AWG device that implements OFDM filters, with 40 GHz subcarrier spacing. In the new A/D converter of Fig. 1, we further reduce the power requirements, using a FP-AWG: the bit resolution is increased, without reducing the sampling rate B. The scheme of Fig. 1(a) illustrates the working principle of the proposed A/D converter that is based on frequency shifts of OFDM subcarriers induced by the XPM effect. Figure 1(b) shows the simulated OFDM time symbol and linear-slope pulse train, whereas Fig. 1(c) illustrates the effect of XPM on the OFDM symbol and the corresponding spectra.
Fig. 1 (a) A/D converter scheme based on spectral shifts induced by XPM, and a FP-AWG. (b) Symbol corresponding to one of OFDM subcarrier and linear-slope pulse train. (c) XPM effect on an OFDM symbol and corresponding spectra. [FBG: fiber Bragg grating; OBPF: optical band pass filter; XPM: cross phase modulation; NDF: negative dispersion fiber; PDF: positive dispersion fiber; AWG: arrayed waveguide grating; ATT: attenuator; PD: photo detector; Ts: sampling time duration]
To evaluate the photonic quantization performance of the proposed A/D converter, we assume that the input signal is the peak power Pp that induces different shifts on the OFDM subcarriers. The sampled analog pulse can be obtained by an optical sampler (based on the four wave mixing effect) inserted additionally in front of FBG#1 in Fig. 1. Otherwise, if the analog input to the A/D converter is a RF signal, a laser source and a modulator should be inserted in front of FBG#1.
In the A/D converter scheme of Fig. 2(a), the spectral shifts of an OFDM subcarrier (generated by the fiber Bragg grating (FBG)#2) at wavelength λ2 = 1550 nm) are obtained using a linear-slope pulse-train (generated by the FBG#1 at λ1 = 1560 nm) and the XPM effect. The two signals are properly filtered, combined together and sent to a HNLF, that converts the amplitude variation of the linear-slope pulse train into a frequency shift of the OFDM subcarrier. We observe this approach is similar to the one used to perform code conversion in an optical code-based system [20]; in fact an OFDM subcarrier is equivalent to a code generated/processed by an AWG-based multiport encoder/decoder [18]. Figure 2(b) shows the linear-slope pulse train for different values of peak power Pp, obtained through numerical simulations, and Fig. 2(c) report the simulated OFDM symbol. Figures 2(d) and (e) describe the simulations of the spectral shifted OFDM subcarrier for Pp = 0 and for Pp = 120 mW, respectively.
Fig. 2 (a) Architecture of the A/D converter; the OFDM subcarriers are generated by FBG#2 and the linear-slope train by FBG#1; the XPM effect is achieved using HNLFs. (b) simulated linear-slope pulse train for different values of peak power Pp. (c) simulated OFDM symbol (d) simulated OFDM subcarrier for Pp = 0 (e) simulated shifted OFDM subcarrier for Pp = 120 mW.
The spectral occupancy of an OFDM subcarrier and the linear-slope pulse train are shown in Fig. 3, as well as the spectral broadening due to the XPM effect. An optimization process is required to select the proper values of λ1, λ2, Δλ1 and Δλ2, and the optimal wavelength allocation guidelines are reported in Table 1. If λ1 and λ2 are too close, (small values of λ2 -λ1), there is a low crosstalk tolerance for the control pulse; if we increase their distance (large values of λ2 -λ1) we observe small spectral shifts due to the group velocity delay GVD effect. Therefore, to reach a tradeoff, λ1 = 1560 nm and λ2 = 1550 nm have been selected for the sampled analog and the probe pulses, respectively; in this way, the GVD and crosstalk effects are minimized.
Fig. 3 Numerical simulations of the wavelength allocation of the OFDM subcarrier and the linear slope signal.
Table 1. Wavelength allocation, spectral shifts and power requirements
To reduce the crosstalk, the spectrum of the OFDM subcarrier is filtered by an optical band-pass filter (OBPF) with bandwidth Δλ2 = 2.6 nm. On the other hand, an OBPF with bandwidth Δλ1 = 3.2 nm is used to remove the off-band spectral content of the spread linear-slope pulse train; both filter bandwidths are shown in Fig. 3. These OPBF bandwidths are obtained again following the optimization process shown in Table 1, in order to reduce the spectral broadening due to self-phase modulation (SPM) effect, while keeping the linear slope. In fact a small value of Δλ1 brings to the linear slope break and a large value to a wide spectral broadening due to the XPM effect. On the other hand, we observe small spectral shifts if Δλ1 is too small, and low crosstalk tolerance for the control pulse if this parameter is too large.
Finally, to mitigate the walk-off effect in the HNLF, we use a chain of fibers, with alternate positive and negative dispersion coefficient values, as reported in Table 2; the connection losses between the HNLFs have been neglected, for the sake of simplicity.
Table 2. HNLFs parameters.
The optical sampled Gaussian pulse with T0 = 2 ps width and Pp peak power, generated by the light source#1 at wavelength λ1 = 1560, is converted by the FBG#1 into a linear-slope pulse train, composed of N = 8 chips with the same phase, increasing amplitudes |al| = (l = 0,1,.. N-1), and ∆τ = 3.2 ps chip interval
The last chip amplitude |aN-1| equates the peak power Pp. After the OBPF, each chip pulse spreads in time and interferes with the adjacent ones, as sketched in Fig. 2(b), where the simulated waveform of the linear-slope pulse train is plotted for different values of Pp.
The Gaussian probe pulse with T0 = 2 ps width and intensity I2 is generated by the light source#2 at λ2 = 1550 and converted into an optical OFDM signal by the FBG#2. The OFDM symbol is composed of N = 8 chips with same amplitude and phase, delayed of ∆τ = 3.2 ps
The simulated time waveform of the OFDM subcarrier is plotted in Fig. 2(c).
The two signals El(t) and Es(t) are combined together by a coupler and the XPM effect in the HNLF changes the chip phases, as a function of the peak power Pp
Here γ and Leff are the HNLF nonlinear coefficient and effective interaction length, respectively. To numerically evaluate the group velocity dispersion and the nonlinear effects in the HNLF, we use the split-step-Fourier method.
Figure 4(a) shows the wavelength shift as a function of the peak power Pp, and we observe that there is a nearly linear relation between these two parameters; small departures from linearity are important in A/D converter and should be compensated. We also remark that the optical power of the shifted OFDM subcarrier depends on the spectral envelope of source#2 and a short probe pulse with broad spectrum reduces the power losses in the shifted OFDM subcarrier, as it is shown in Fig. 2(d).
Fig. 4 (a) Numerical simulations of the center wavelength shift vs input peak power, (b) peak spectral power transition vs input peak power.
Figure 4(b) shows the power loss as a function of the peak power Pp: the corresponding slope depends on the spectral broadening due to XPM effects, as well as on the width T0 of the probe pulse of source#2. Furthermore, a dash-line circle evidences an anomalous behavior, since the spectrum broadening of the control signal, due to the SPM effect, is strongly influenced by the probe signal spectrum, as it is shown in Fig. 3. Therefore, the spectral shift region is restricted to a limited interval in the C-band.
A passive AWG device can be designed to implement the discrete Fourier transform and used in all-optical OFDM systems to optically generate and process N OFDM carriers, where N is the number of the input/output ports and of the grating arms [21]. In a standard OFDM scheme, the maximum spectral efficiency is 1, and it is achieved when the channel spacing equates the bit rate B. To increase the spectral efficiency in FP-OFDM systems, we can design an AWG, where the channel spacing is reduced with respect to the reference value B. The FP-AWG device has a number of output ports larger than the number of the grating arms and the subchannel spacing is reduced with respect to a conventional AWG for OFDM systems.
2. 2 Experimental validation
Figure 5(a) shows the experimental setup that we used to evaluate the spectral shifts of the OFDM subcarriers. Two mode-locked laser diodes (MLLD), with 9.95328 GHz repetition rate, and pulse width T0 = 2 ps at central wavelengths of λ1 = 1560 nm and λ2 = 1550 nm have been used. The amplified spectrum from MLLD#1 is tailored by an additional 5-nm OBPF to remove the off-band amplified spontaneous emission noise.
Fig. 5 (a) Experimental setup. (b) Measured linear-slope pulse train; (c) Measured OFDM symbol (d) Measured signal after the HNLF. [MLLD: mode locked laser diode; CLK: clock; ATT: attenuator; PC: polarization controller; POL: polarizer; SSFBG: super structured fiber Bragg grating]
Since the FBG#1 that generates the linear-slope pulse train was not available in the laboratory, we use a 1 x 8 coupler and a 8 x 1 combiner, together with a set of N = 8 delay lines with ∆τ = 3.2 ps and attenuators (ATT). Therefore, the timing and peak power of each pulse can be separately adjusted to form the linear-slope pulse train shown in Fig. 5(b), that is fed into an OBPF with bandwidth Δλ1 = 3.2 nm.
A 2-ps probe pulses from MLLD#2 is sent to a FBG#2 that generates an OFDM subcarrier with a sinc-like shaped spectrum. The total length of FBG#2 is 2.6 nm and it generates OFDM symbols composed of 8 chips; the length of the section to generate a chip is 0.326 mm. In addition, the grating period is 536 mm and the average effective index is 1.45. The time waveform of the OFDM symbol is almost rectangular and it is shown in Fig. 5(c), even though the interference between chip pulses and the effect of the OPBF, with bandwidth Δλ2 = 2.6 nm to reduce the crosstalk due to SPM effect, prevent that a box-like waveform can be measured.
The OFDM subcarrier can be generated either by a conventional AWG or by the FBG#2; the number of AWG input/output ports (that equates the waveguide arms) is N = 8 and it is also the number of chips in the OFDM symbol. Since the chip interval is ∆τ = 3.2 ps, the AWG free spectral range is FSR = 1/∆τ = 312.5 GHz, and the OFDM subcarrier spacing is FSR/N = 39.06 GHz.
The OFDM subcarrier and the linear-slope pulse train are combined together by a 3dB coupler and the timing of the last signal has been adjusted by a delay line, to precisely overlap with the OFDM symbol. In addition, also the two polarizations are matched, using polarization controllers (PC) and the signal measured after the HNLF is shown in Fig. 5(d)
The average power of the linear-slope pulse train and the OFDM subcarrier launched into the HNLF are 17.5 dBm and −1.3 dBm, respectively; the HNLFs parameters are reported in Table 2. The overall loss of the HNLFs is 13 dB.
Figure 6(a, b) show the OFDM spectrum after the HNLF, for two different values of the average power. The spectral shift generated by the XPM effect are evident, and only the spectral shifted OFDM subcarrier passes through the 2.7-nm OBPF. The OFDM spectra are almost sinc-like, as their shapes are affected by the 2-ps width and repetition rate of the MLLD; we observe that the spectrally shifted OFDM carrier preserves its sinc-like shape.
Figure 7 shows the measured frequency shifts (i.e. the variation of the wavelength corresponding to the main-lobe of the OFDM subcarrier) versus the average power from MLLD#1. The measured data confirm that the wavelength shift varies linearly with the power of the linear-slope pulse train.
3. Numerical analysis of optical quantization
The optical sampling rate B should be carefully selected, to avoid degradation in the quantization transfer function due to inter-symbol interference (ISI). In fact, after the FBG#2 (or a conventional AWG), the OFDM symbol is composed of N chips with chip interval Δτ (symbol duration N Δτ). When it is received by another AWG, the convolution of the OFDM symbols occurs, and the time duration of the signal at the AWG output ports is 2(N-1) Δτ [18,22]. Therefore, the sampling rate should satisfy the condition B < 1/[2(N-1)Δτ]. For instance, in the case FSR = 1/∆τ = 312.5 GHz and N = 8, the maximum sampling rate is B < 1/[2(N-1)Δτ] = 22.14 GHz. This limitation can be overcome using a femtosecond-class pulse light source and pulse compression. In addition, the ISI effect in the HNLF can be neglected by compensating the total dispersion using a sequence of HNLFs with alternate positive and negative dispersion values.
The A/D resolution (expressed in number of bits) depends on the spectrum of the transmitted OFDM subcarrier that is spread due to the XPM effect, and the bandwidth FSR/N of the transfer function at the AWG outputs (OFDM subcarrier spacing). The number of the AWG output ports used is 2#bits-1 that equates the number of required photo detectors (PD). It is evident that a tradeoff should be reached for the number of the AWG outputs, to increase both sampling rate and bit resolution.
To make these two parameters independent from each other, we reduce the OFDM subcarrier spacing and use a FP-AWG that generates OFDM symbols, where the number N of chips (i.e. number of the grating arms) is smaller than the number of input/output ports N’ [22]. Figure 8 shows the spectra of a conventional AWG and FP-AWG devices, for different values of N’; the channel spacing is B’ = FSR/N’.
Fig. 8 Simulated AWG output spectra (a) 8-port standard AWG, (b) 24-port FP-AWG, (c) 56-port FP-AWG.
Using a FP-AWG, the sampling rate should still satisfy the condition B < 1/[2(N-1)Δτ]. On the other hand, the A/D resolution can be estimated by evaluating the ratio between the OFDM carrier bandwidth (FSR/N) and the channel spacing of a FP-AWG (FSR/N’). Therefore it is k = N’/N + 1 = 2#bits-1, that is also the number of the required PDs (AWG output ports connected to PDs). In case of 4-bit quantization, considering FSR = 312.5 GHz, N = 8 and N’ = 56, the OFDM subcarrier spacing is FSR/N’ = 5.57 GHz (and it is FSR/N = 39.06 GHz in a conventional AWG). The output spectra of FP-AWG for 2, 3 and 4-bit quantization are shown in Fig. 8. Table 3(a, b, c) reports the 2, 3 and 4-bit A/D conversion table.
Table 3. Code lookup table (a) 2 bit, (b) 3 and (c) 4 bit.
The quantization transfer functions at the AWG output ports have a Gaussian shape, but with different maximum peak values; to make them uniform, we use an ATTs array. Figure 9 show the input peak power/output average power transfer functions, also with compensated relative power ratios and threshold levels; all the ATT values are shown in the inset of Figs. 9. The offset input peak power is set to 0 mV. The vertical axis value is normalized with respect to the output power from port#8. To increase the energy efficiency, we used two different threshold values for 2-bit quantization; in all the other cases, the same threshold has been considered for all the outputs, to simplify the system implementation.
Fig. 9 Simulated quantization transfer functions (a) two bits (w/ and w/o compensation), (b) three bits (w/ and w/o compensation), (c) four bits (w/o compensation), (d) four bits (w/ compensation).
To estimate the resolution performance, we calculate the differential nonlinearity (DNL) and integral nonlinearity (INL) errors, and the effective number of bits resolution (ENOB) associated to the signal-to-noise ratio (SNR). The DNL and INL are defined as
All these parameters have been numerically evaluated by the quantization transfer functions of Fig. 9 and are plotted in Fig. 10, considering amplitude compensation. Table 4 reports the least significant bit (LSB), the maximum INL and maximum DNL for 2, 3 and 4-bit quantization cases. In the ENOB estimation, we suppose an oversampling, when the input bandwidth is smaller than half of the sampling rate B; the input sampled values have a uniformly distributed density function [13]. The ENOB is calculated following the formulation of Ref [13]. that allows a comparison between all-optical and electrical A/D conversion with a PD
where PS and PN are the root-mean-square power of the optical signal and optical noise without the DC component Here, PFS, PStep-i are the full-scale power range, and the quantization noise with nonlinear error, respectively. The values of PS, PN and ENOB are also reported in Table 4.Table 4. Performance evaluation of transfer function.
5. Conclusions
We have proposed and demonstrated an energy-efficient photonic A/D converter based on spectral shifts of OFDM subcarriers and optical quantization using a new FP-AWG device. The proposed approach increases the resolution, without affecting the sampling rate, compared to previous schemes. We have experimentally demonstrated OFDM subcarrier spectral shifts generated by a linear-slope pulse train and XPM effect. The quantization transfer function is equalized using ATTs array, and we have evaluated the nonlinear error and the ENOB.
Acknowledgment
This work was presented in part at ECOC2014, Cannes, France, September 2014. The authors would like to thank Mr. R. Matsumoto, Mr. H. Terauchi, Dr. T. Konishi and Dr. A. Maruta of Osaka University for their kind cooperation. The research is supported by the Japan Society for the Promotion of Science (JSPS). This work was partially supported by the NICT R&D programs, “Basic Technologies for High-Performance Opto-Electronic Hybrid Packet Router” (2011-2016) and the European Community’s Seventh Framework Programme (FP7/2007-2013) under Grant 318714 (ASTRON).
References and links
1. H. F. Haunstein, W. Sauer-Greff, A. Dittrich, K. Sticht, and R. Urbansky, “Principles for electronic equalization of polarization-mode dispersion,” J. Lightwave Technol. 22(4), 1169–1182 (2004). [CrossRef]
2. M. Chu, P. Jacob, J.-W. Kim, M. R. LeRoy, R. P. Kraft, and J. F. McDonald, “A 40 Gs/s time interleaved ADC using SiGe BiCMOS technology,” IEEE J. Solid-State Circuits 45(2), 380–390 (2010). [CrossRef]
3. B. E. Jonsson, “A survey of A/D-converter performance evolution,” in IEEE Int. Conf. Electronics Circ. Syst. (ICECS), Athens, Greece, 768–771, Dec. 2010. [CrossRef]
4. R. Walden, Analog-to-digital conversion in the early twenty-first century (Wiley Encyclopedia of Computer Science and Engineering, 126–138, Wiley, 2008).
5. T. R. Clark and M. L. Dennis, “Toward a 100-GSample/s photonic A-D converter,” IEEE Photon. Technol. Lett. 13(3), 236–238 (2001). [CrossRef]
6. C. Schmidt-Langhorst and H.-G. Weber, “Optical sampling techniques,” J. Opt. Fiber Commun. Rep. 2(1), 86–114 (2005). [CrossRef]
7. T. Konishi, K. Tanimura, K. Asano, Y. Oshita, and Y. Ichioka, “All-optical analog-to-digital converter by use of self-frequency shifting in fiber and a pulse-shaping technique,” J. Opt. Soc. Am. B 19(11), 2817–2823 (2002). [CrossRef]
8. C. Xu and X. Liu, “Photonic analog-to-digital converter using soliton self-frequency shift and interleaving spectral filters,” Opt. Lett. 28(12), 986–988 (2003). [CrossRef] [PubMed]
9. T. Satoh, K. Takahashi, H. Matsui, K. Itoh, and T. Konishi, “10-GS/s 5-bit real-time optical quantization for photonic analog-to-digital cpnversion,” IEEE Photon. Technol. Lett. 24(10), 830–832 (2012).
10. S. Oda and A. Maruta, “A novel quantization scheme by slicing supercontinuum spectrum for all-optical analog-to-digital conversion,” IEEE Photon. Technol. Lett. 17(2), 465–467 (2005). [CrossRef]
11. T. Nishitani, T. Konishi, and K. Itoh, “Optical coding scheme using optical interconnection for high sampling rate and high resolution photonic analog-to-digital conversion,” Opt. Express 15(24), 15812–15817 (2007). [CrossRef] [PubMed]
12. K. Ikeda, J. M. Abdul, H. Tobioki, T. Inoue, S. Namiki, and K. Kitayama, “Design considerations of all-optical A/D conversion: Nonlinear fiber-optic sagnac-loop interferometer-based optical quantizing and coding,” J. Lightwave Technol. 24(7), 2618–2628 (2006). [CrossRef]
13. Y. Miyoshi, S. Takagi, S. Namiki, and K. Kitayama, “Multiperiod PM-NOLM with dynamic counter-propagating effects compensation for 5-bit all-optical analog-to-digital conversion and its performance evaluations,” J. Lightwave Technol. 28(4), 415–422 (2010). [CrossRef]
14. J.-M. Jeong and M. E. Marhic, “All-optical analog-to-digital and digital-to-analog conversion implemented by a nonlinear fiber interferometer,” Opt. Commun. 91(1–2), 115–122 (1992). [CrossRef]
15. M. Scaffardi, E. Lazzeri, F. Fresi, L. Poti, and A. Bogoni, “Analog-to-digital conversion based on modular blocks exploiting cross-gain modulation in semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 21(8), 540–542 (2009). [CrossRef]
16. H. Wen, H. Wang, and Y. Ji, “All-optical quantization and coding scheme for ultrafast analog-to-digital conversion exploiting polarization switches based on nonlinear polarization rotation in semiconductor optical amplifiers,” Opt. Commun. 285(18), 3877–3885 (2012). [CrossRef]
17. G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15(5), 1955–1982 (2007). [CrossRef] [PubMed]
18. G. Cincotti, N. Wada, and K. Kitayama, “Characterization of a full encoder/decoder in the AWG configuration for code-based photonic routers-part I: modeling and design,” J. Lightwave Technol. 24(1), 103–112 (2006). [CrossRef]
19. T. Kodama, R. Matsumoto, A. Maruta, and K. Kitayama, “Energy efficient optical quantization scheme with orthogonal spectral slicing by AWG for OFDM,” in Optical Fiber communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC 2013), JW2A.17, Anaheim, USA, Mar. 2013. [CrossRef]
20. T. Kodama, N. Wada, G. Cincotti, and K. Kitayama, “Tunable optical code converter using XPM and linear-slope pulse streams generated by FBGs,” Opt. Lett. 39(2), 355–358 (2014). [CrossRef] [PubMed]
21. G. Cincotti, “Generalized fiber Fourier optics,” Opt. Lett. 36(12), 2321–2323 (2011). [CrossRef] [PubMed]
22. A. Abrardo and G. Cincotti, “Design of AWG devices for all-optical time-frequency packing,” J. Lightwave Technol. 32(10), 1951–1959 (2014). [CrossRef]
