# Extreme temporal multiplexing of Mbit/s data-packets into Gbit/s data sequences through nonlinear temporal focusing

Julien Fatome, Miro Erkintalo, Stéphane Coen

► To cite this version:

Julien Fatome, Miro Erkintalo, Stéphane Coen. Extreme temporal multiplexing of Mbit/s data-packets into Gbit/s data sequences through nonlinear temporal focusing. Optical Fiber Technology, 2024, 87, pp.103857. 10.1016/j.yofte.2024.103857. hal-04871819

HAL Id: hal-04871819

https://hal.science/hal-04871819v1

Submitted on 7 Jan 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Extreme temporal multiplexing of Mbit/s data-packets into Gbit/s
data sequences through nonlinear temporal focusing

Julien Fatome¹,*, Miro Erkintalo², and Stéphane Coen²

¹ Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS-Université de Bourgogne, Dijon, France

² Department of Physics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand

**Abstract.** This study expands upon an innovative, all-optical, real-time, nonlinear temporal compression technique based on a counter-propagating degenerate four-wave mixing interaction in a birefringent optical fibre. Specifically, we provide a proof-of-principle demonstration of an advanced time-interleaving procedure, enabling the multiplexing of a 10-Mbit/s data packet within a 10-Gbit/s data sequence, achieving a record compression factor of 4350 alongside the demonstration of time-reversal capabilities. The proposed approach is scalable, holding promise for dynamic optical networks, buffering applications, and the generation of ultrafast waveforms.

**Keywords:** Optical fibre; Nonlinear optics; Optical Communications; Polarization; All-optical signal processing.

# 1. Introduction

Our world today is inundated with an exponential surge in digital optical data [1-2]. Dealing with this escalating demand for global capacity in fibre networks requires researchers to develop novel strategies for switching, interleaving, buffering, and compressing optical data. This is crucial to establish the temporal granularity of data packets at the physical layer. Specifically, the ability to modify the timescale of optical data or waveforms beyond the current bandwidth limitations of conventional optoelectronic technologies is an essential functionality targeted in various applications, including optical communications [3-4], spectroscopy [5], or sensing [6]. To achieve this objective, numerous studies have been conducted to magnify the timescale of short temporal events, enabling their detection with conventional low-bandwidth electronics [7-8]. In particular, the concept of time-lens [9] has opened up new frontiers in photonics, unveiling transient phenomena and nonlinear dynamics previously inaccessible. Examples include the real-time detection of rogue waves [10-11], single-shot spectroscopy [12], or the self-organization of mode-locked lasers [13].

In contrast, a comparatively small number of works have been dedicated to the converse process — the temporal compression of arbitrary light-waves [14-20]. This capability holds potential applications in many scientific fields where cost-effective generation of ultrafast optical waveforms is necessary. Whilst mature technological solutions to achieve temporal compression are still lacking, there have been notable proof-of-concept demonstrations reported in the literature, predominantly relying on optical buffers and delay lines [15-17]. Manipulations of data packet duration have been also experimentally achieved using supercontinuum generation, followed by spectrum-slicing and time-shifting, allowing the temporal compression of four-bit

packets from 10 to 40 Gbit/s [18]. However, these techniques are based on time-interleaving procedures and do not affect the pulse duration. Consequently, the initial pulse width must be carefully selected to match the output compressed repetition-rate. Moreover, these methods are not applicable for the compression of arbitrary optical waveforms.

To overcome these challenges, a distinctive approach leverages the space-time duality of electromagnetic waves, and consists in turning the time-lens technique backward into a temporal focusing telescope [19-20]. Using this phenomenon, Foster and coworkers demonstrated a 27-compression factor for ns-waveforms and 10-Gbit/s data packets [20]. However, the focusing capabilities of time-lens apparatus are fundamentally restricted by practical limitations of focal length and lens aberrations due to high-order dispersion effects [8, 20].

Very recently, a novel experimental scenario has emerged, which exploits a specific four-wave-mixing (FWM) interaction within a polarization-maintaining birefringent optical fibre (PMF). Originally proposed by A. Starodumov in reference [21], we have recently presented an initial demonstration of this effect in ref. [22]. Remarkably, these proof-of-concept experiments have leveraged the technique to achieve ultra-high temporal compression factors, ranging from three to four orders of magnitude for both data sequences and arbitrary optical waveforms [21-22]. In this contribution, we leverage this innovative compression technique to manipulate the temporal timescale of Mbit/s optical data sequences. Specifically, we present a proof-of-principle demonstration of an advanced time-interleaving procedure, enabling the multiplexing of a 10-Mbit/s data packet within an incident 10-Gbit/s data sequence. This is achieved through an extreme ×4350-temporal reduction of the initial µs-signal waveform.

<footnote>* Corresponding author: jfatome@u-bourgogne.fr</footnote>
## 2. Principle of operation

The fundamental principle of our scheme is depicted in Fig. 1. The temporal compression technique relies on the nonlinear interaction that takes place between two counter-propagating light waves in a birefringent optical fibre, which is characterized by two well-defined (slow and fast) polarization axes. From one side of the fibre, the low-bandwidth Mbit/s optical signal to be compressed (depicted in orange) is injected with a polarization state aligned at 45° relative to the slow and fast birefringent axes. Simultaneously, from the opposite end, a short readout pulse (in green) is injected and propagates along the slow polarization axis of the fibre. Additionally, a fast Gbit/s data sequence is polarization multiplexed and propagates orthogonally to the readout pulse along the fast-birefringent axis. This Gbit/s data sequence is specifically prepared with a vacant time-slot dedicated to containing the temporally compressed, ultrafast replica of the counter-propagating Mbit/s data packet. When the readout pulse overlaps with a part of the incoming Mbit/s signal (step 1 in Fig. 1), a nonlinear FWM interaction results in the generation of a new signal (depicted in blue). This signal, co-propagating and orthogonally polarized to the readout pulse, is also co-polarized with the fast Gbit/s data sequence. The resulting compressed bit produced during this interaction has the typical duration of the readout pulse, and by carefully adjusting the initial delay between the readout pulse and the Gbit/s data sequence, we ensure that this compressed bit is contained within the

vacant time-slot of the sequence. Owing to the group-velocity mismatch due to fibre birefringence, this newly generated signal propagates at a different speed than the readout pulse (but same speed than the Gbit/s data sequence), gradually walking away from the readout pulse (step 2). This dynamic process ensures a continuous resetting of the system for subsequent bit compressions. This entire process iterates as the readout pulse sweeps along subsequent parts of the incoming Mbit/s data packet (step 3), thus interleaving an ultrafast replica of the slow input pattern into the initial vacant time-slot within the propagating Gbit/s sequence. Note that injecting the readout pulse along the fast birefringent axis, instead of the slow one, introduces a time-reversal operation in addition to the compression process.

The compression factor $M$ experienced by the input Mbit/s data is primarily determined by the rate at which the generated signal walks away from the readout pulse, and is given by $M = 2n/|\Delta n|$, where $n$ and $\Delta n$ are respectively the group index and index difference between the two axes of the birefringent fibre [22]. Consequently, standard PMFs yield compression factors ranging from $10^3$ to $10^4$, while optical fibers or integrated waveguides specifically designed for this purpose could extend that range from $10^2$ to $10^5$. Finally, in terms of length, the PMF needs to be longer than half the spatial extent of the input low-bandwidth pattern and it is noteworthy that the shortest temporal feature that can be generated is determined by the readout pulse duration.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Principle of operation for time-interleaving of Mbit/s data packets within Gbit/s data sequences.</figcaption></figure>

## 3. System modelling

We begin by discussing the numerical model that will be used to simulate our experimental system. To this end, we consider the counter-propagating interaction of optical

beams centred at the same frequency, $\omega$, within a conventional birefringent optical fibre [23-26]. The nonlinear Schrödinger equations that govern the evolution of the amplitudes of the four field envelopes considered here can be expressed in the following form:

$$ \left\{ \begin{aligned} (\partial_t + v_{g_x} \partial_z) E_x &= i\gamma \left[ |E_x|^2 + \frac{2}{3} |E_y|^2 + 2|\overline{E_x}|^2 + \frac{2}{3} |\overline{E_y}|^2 \right] E_x + i \frac{2\gamma}{3} E_y \overline{E_y} E_x^* \\ (\partial_t + v_{g_y} \partial_z) E_y &= i\gamma \left[ |E_y|^2 + \frac{2}{3} |E_x|^2 + 2|\overline{E_y}|^2 + \frac{2}{3} |\overline{E_x}|^2 \right] E_y + i \frac{2\gamma}{3} E_x \overline{E_x} E_y^* \\ (\partial_t - v_{g_x} \partial_z) \overline{E_x} &= i\gamma \left[ |\overline{E_x}|^2 + \frac{2}{3} |\overline{E_y}|^2 + 2|E_x|^2 + \frac{2}{3} |E_y|^2 \right] \overline{E_x} + i \frac{2\gamma}{3} \overline{E_y} E_x E_y^* \\ (\partial_t - v_{g_y} \partial_z) \overline{E_y} &= i\gamma \left[ |\overline{E_y}|^2 + \frac{2}{3} |\overline{E_x}|^2 + 2|E_y|^2 + \frac{2}{3} |E_x|^2 \right] \overline{E_y} + i \frac{2\gamma}{3} \overline{E_x} E_y E_y^* \end{aligned} \right. \quad (1) $$
Here, the optical fields ($E_x; E_y$) represent the polarization components of the forward incident Mbit/s data packet propagating along both axes of the birefringent fibre, whilst ($\overline{E}_x; \overline{E}_y$) correspond to the backward waveforms consisting of the readout pulse propagating along the slow birefringent axis and both the compressed replica and the fast Gbit/s data sequence along the fast axis. The variable $z$ denotes the spatial coordinate along the PMF, $\gamma$ represents the nonlinear Kerr coefficient and $v_{g(i)}$ describes the group-velocity of the waveforms along the slow ($x$) and fast axes ($y$) of the birefringence fibre. Note that the last term in Eqs. (1) represents the degenerate FWM interaction, which is responsible for an energy exchange between the two polarization components of each beam and is the driving force behind the temporal compression mechanism. Additionally, it is important to note that the effect of chromatic dispersion has been neglected in our model. Indeed, the dispersive length associated with all the waveforms under investigation [26], especially the readout pulse, was found to be one order of magnitude longer than the length of the fibre under-test.

## 4. Experimental setup

To realize a proof-of-concept demonstration of the temporal interleaving scheme, we use the experimental setup depicted in Fig. 2. It primarily comprises of a 103-m-long birefringent fibre ($\Delta n = 6.67 \times 10^{-4}$, $\gamma = 3$ W⁻¹

¹km⁻¹), enclosed between two optical circulators. The 10-Mbit/s data packet intended for compression and multiplexing is generated using a 1551-nm continuous-wave (CW) laser carved in the temporal domain through an intensity modulator (IM) driven by a 10-Mbit/s RF data sequence. An Erbium-doped fiber amplifier (EDFA) is employed to increase the peak power of the incoming waveform to the Watt level. A polarization controller (PC) then ensures alignment of the waveform's polarization at 45° with respect to both birefringent axes of the PMF. From the opposite side of the fibre, 6-ps readout pulses, centred at the same wavelength as the Mbit/s data pattern, are generated by a mode-locked laser. The repetition rate of the laser is adjusted to 2 MHz, enabling a single pulse to propagate through the fibre at any given time. An additional EDFA boosts the peak power of the readout pulses, whilst a polarizing beam splitter (PBS) determines the axis of the birefringent fiber (fast or slow) along which the pulses are injected. Concurrently with the readout pulse, a 1551-nm, few mW-level, 10-Gbit/s data stream is combined along the orthogonal birefringent axis. This data stream is specifically configured with a 200-ps vacant time-slot to hold the temporally compressed replica of the counter-propagating Mbit/s data packet. Finally, at the system output, a PBS separates the readout pulse and the resulting multiplexed 10-Gbit/s sequence before detection by means of a fast-photodiode connected to a 63-GHz bandwidth real-time oscilloscope.

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Experimental setup. PC: Polarization controller, Cir: Circulator, PBS: Polarizing beam splitter, EDFA: Erbium-doped fibre amplifier, PPG: Pulse pattern generator, IM: Intensity modulator, CW: Continuous wave.</figcaption></figure>

## 5. Experimental results

Figure 3 illustrates typical experimental results obtained from a 10-Mbit/s input data packet, comprising a 9-bit-long sequence with the pattern '110011010,' interleaved within a 10-Gbit/s data sequence. From one side of the PMF, as depicted in Fig. 3(a) (yellow curve), the initial 10-Gbit/s data sequence is configured with a 200-ps vacant time-slot designed for the time-interleaving of the counter-propagating compressed 10-Mbit/s data packet. Initially, its polarization state is aligned along the fast birefringent axis of the PMF, with an average power set to 10 mW. For reference, the autocorrelation trace of the readout pulse is also presented in black in Panel (a). The readout pulse is initially injected along the slow

birefringent axis, with its peak power set to 3.4 W. At the opposite end of the fibre, the original 10-Mbit/s sequence to be compressed and interleaved is depicted in Fig. 3(b) (in red) and spans over a 0.9-µs temporal window. Its peak power was increased to 12 W before injection into the PMF with a polarization state aligned at 45° relative to the birefringent axes.

We initially assessed the output signal when the polarization of the readout pulse is aligned along the slow birefringent axis of the PMF. As depicted in Figure 3c, it is evident that the 10-Gbit/s data sequence now incorporates a compressed replica of the counter-propagating Mbit/s data packet, interleaved within the 200-ps span with an increase of the bit rate from 10 Mbit/s to 43.5 Gbit/s and a shortening of the individual bits from

<footnote>* Corresponding author: jfatome@u-bourgogne.fr</footnote>
50 ns to less than 13 ps (limited by the temporal resolution of our detection apparatus). The associated compression factor is evaluated as $M = 4350$, demonstrating a good agreement with the theoretical prediction of 4378. Our experimental findings also exhibit excellent consistency with numerical simulations (grey dashed lines in Figs. 3(c-d) based on the set of four coupled nonlinear Schrödinger equations described in Eqs. (1). Finally, Fig. 3(d) illustrates the scenario in which the readout pulse propagates along the fast birefringent axis of the PMF, whilst the 10-Gbit/s data sequence is now swapped along the slow axis. In this configuration, the compressed replica is time-reversed, while the rest of the 10-Gbit/s data sequence remains remarkably preserved. Though expected, it is noteworthy that this seemingly straightforward swapping of polarization axes results in such a non-trivial functionality.

<figure><img src="image_4.png" /><figcaption>**Fig. 3.** (a) Input profile of the 10-Gbit/s data sequence (depicted in yellow) and autocorrelation trace of the readout pulse (in black). (b) Intensity profile of the counter-propagating 10-Mbit/s data packet designated for compression and interleaving. (c) Output intensity profile (shown in blue) of the 10-Gbit/s data sequence measured along the fast birefringent axis of the PMF when the polarization of the readout pulse is aligned along the slow axis, demonstrating the inclusion of a ×4350 compressed replica of the 10-Mbit/s data packet. (d) Similar to (c) but when the polarization states of the readout pulse and the 10-Gbit/s</figcaption></figure>

sequence are swapped, showcasing time-reversal capabilities on top of temporal compression. In both (c) and (d), grey dashed lines correspond to numerical simulations provided by Eqs. (1).

Finally, we assessed the conversion efficiency of the compression/interleaving process with respect to the input peak power of the Mbit/s data packet. For this purpose, as illustrated in Fig. 4(a) in red, two 50-ns pulses, separated by 250 ns, were employed to calibrate our system. Similar to the previous experiment, the peak power of the readout pulse was kept constant to 3.4 W. In Fig. 4(a), the resulting compressed replica is shown in blue when the peak power of the Mbit/s data packet was increased to 36 W. We confirmed the achievement of a compression factor of 4350, with a corresponding optical peak power of the compressed signal of 22 mW. For a more in-depth analysis, the blue circles in Fig. 4(b) show the experimentally measured conversion efficiency of the compression process, defined as the ratio between the peak powers of the compressed signal and readout pulse as a function of the input data peak power — the readout pulse peak power remains constant to 3.4 W. It is notable that a compressed replica is consistently generated, providing that both the incident data and the readout pulse are present in the fibre. Furthermore, we can observe that the efficiency of the compression process follows a square law as anticipated by the FWM term of Eqs. (1), which is directly proportional to the data intensity [21]. This results in a milliwatt peak power for the compressed signal at the system output. Note that the level of conversion efficiency is well corroborated by our numerical simulations based on Eqs. (1) and illustrated by the black solid line in Fig. 4(b).

<figure><img src="image_5.png" /><figcaption>**Fig. 4.** (a) Intensity profile of two incident 50-ns pulses (in red) compared with their corresponding ×4350-compressed output replicas (in blue). (b) Conversion efficiency and corresponding peak power of the compressed pulses measured at the system's output as a function of the injected data peak power. The experimental results are represented by blue circles, whilst the black solid line corresponds to numerical simulations based on Eqs. (1).</figcaption></figure>

## 6. Conclusion

In conclusion, we have shown that the all-optical, real-time temporal compression technique demonstrated in ref. [22] can be extended to enable simultaneous temporal compression and data interleaving. This all-optical, real-time temporal compression technique is based on successive counter-propagating four-wave mixing interactions occurring in birefringent optical fibres [21-22]. Our experimental results include an advanced time-interleaving procedure, enabling the multiplexing of a 10-
Mbit/s data packet within a 10-Gbit/s data sequence, achieving a record compression factor of ×4350 alongside the demonstration of time-reversal capabilities. The versatility of this method extends to various photonic platforms, encompassing birefringent fibres, multimode fibres, and integrated photonics, with potential scaling factors ranging from $10^2$ to $10^5$ [27-30]. Beyond communication applications, this conceptually simple light-by-light temporal squeezing system holds promise in diverse scientific fields, enabling the generation of ultrafast optical data, pulse trains, or waveforms from cost-effective, low-bandwidth off-the-shelf sources.

**Declaration of competing interest.** The authors declare no competing interests.

**Data availability.** Data will be made available on reasonable request.

**Acknowledgments.** JF and SC acknowledge the financial support from the CNRS, IRP Wall-IN project (CNRS research collaboration agreement n°241655). SC and ME acknowledge the financial support from The Royal Society of New Zealand, in the form of Marsden Funding (18-UOA-310).

## References

1. D. J. Richardson, "Filling the light pipe," *Science* **330**, 327-328 (2010).

2. P. J. Winzer, D. T. Neilson, and A. R. Chraplyvy, "Fiber-optic transmission and networking: the previous 20 and the next 20 years," *Opt. Express* **26**, 24190-24239 (2018).

3. A. Mahjoubfar et al. "Time stretch and its applications," *Nature Photon* **11**, 341-351 (2017).

4. G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, "Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules," *Science* **356**, 50-54 (2017).

5. E. Roussel et al. "Observing microscopic structures of a relativistic object using a time-stretch strategy," *Sci Rep* **5**, 10330 (2015).

6. M. Lei, W. Zou, X. Li, and J. Chen, "Ultrafast FBG interrogator based on time-stretch method," *IEEE Photon. Technol. Lett.* **28**, 778-781 (2016).

7. C. V. Bennett, R. P. Scott, and B. H. Kolner, "Temporal magnification and reversal of 100 Gb/s optical data with an up-conversion time microscope," *Appl. Phys. Lett.* **65**, 2513-2515 (1994).

8. M. A. Foster et al. "Silicon-chip-based ultrafast optical oscilloscope," *Nature* **456**, 81-84 (2008).

9. B. H. Kolner, "Space-time duality and the theory of temporal imaging," *IEEE J. Quantum Electron.* **30**, 1951-1963 (1994).

10. M. Närhi et al. "Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability," *Nat Commun* **7**, 13675 (2016).

11. P. Suret et al. "Single-shot observation of optical rogue waves in integrable turbulence using time microscopy," *Nat Commun* **7**, 13136 (2016).

12. K. Goda, B. Jalali, "Dispersive Fourier transformation for fast continuous single-shot measurements," *Nature Photon* **7**, 102-112 (2013).

13. G. Herink, B. Jalali, C. Ropers, and D. Solli, "Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate," *Nature Photon* **10**, 321-326 (2016).

14. M. H. Asghari, and B. Jalali, "Experimental demonstration of optical real-time data compression," *Appl. Phys. Lett.* **104**, 111101 (2014).

15. S. Rangarajan, H. N. Poulsen, and D. J. Blumenthal, "All-Optical Packet Compression of Variable Length Packets From 40 to 1500 B Using a Gated Fibre Loop," *IEEE Photon. Technol. Lett.* **18**, 322-324 (2006).

16. H. Toda, F. Nakada, M. Suzuki, and A. Hasegawa, "An optical packet compressor based on a fibre delay loop," *IEEE Photon. Technol. Lett.* **12**, 708-710 (2000).

17. P. Toliver, K.-L. Deng, I. Glesk, and P. R. Prucnal, "Simultaneous optical compression and decompression of 100-Gb/s OTDM packets using a single bidirectional optical delay line lattice," *IEEE Photon. Technol. Lett.* **11**, 1183-1185 (1999).

18. H. Sotobayashi, K. Kitayama, and T. Ozeki, "40 Gbit/s photonic packet compression and decompression by supercontinuum generation," *Electron. Lett.* **37**, 110-111 (2001).

19. P. J. Almeida, P. Petropoulos, B. C. Thomsen, M. Ibsen, and D. J. Richardson, "All-optical packet compression based on time-to-wavelength conversion," *IEEE Photon. Technol. Lett.* **16**, 1688-1690 (2004).

20. M. Foster et al. "Ultrafast waveform compression using a time-domain telescope," *Nature Photon.* **3**, 581-585 (2009).

21. A. N. Starodumov, "Pulse train compression up to terabit rates using four-wave mixing in birefringent fibre," *Optics Commun.* **124**, 365-372 (1996).

22. N. Berti, S. Coen, M. Erkintalo and J. Fatome, "Extreme waveform compression with a nonlinear temporal focusing mirror," *Nature Photon.* **16**, 822-827 (2022).

23. M. Guasoni et al. "Line of polarization attraction in highly birefringent optical fibres," *J. Opt. Soc. Am. B* **31**, 572-580 (2014).

24. V. V. Kozlov et al. "Nonlinear repolarization dynamics in optical fibers: transient polarization attraction," *J. Opt. Soc. Am. B* **28**, 1782-1791 (2011).

25. S. Pitois, G. Millot, and S. Wabnitz, "Nonlinear polarization dynamics of counterpropagating waves in an isotropic optical fiber: theory and experiments," *J. Opt. Soc. Am. B* **18**, 432-443 (2001).

26. G. P. Agrawal, "Nonlinear Fibre Optics," 5th ed., Academic Press, Oxford, (2013).

27. Y. Jung, G. Brambilla, K. Oh, and D. J. Richardson, "Highly birefringent silica microfiber," *Opt. Lett.* **35**, 378-380 (2010).

28. T. Yang et al. "High birefringence photonic crystal fiber with high nonlinearity and low confinement loss," *Opt. Express* **23**, 8329-8337 (2015).

29. J. Zhou et al. "Electro-optically switchable optical true delay lines of meter-scale lengths fabricated on Lithium Niobate on insulator using photolithography assisted chemo-mechanical etching," *Chin. Phys. Lett.* **37**, 084201 (2020).

30. H. Zhang, M. Bigot-Astruc, L. Bigot, P. Sillard, and J. Fatome, "Multiple modal and wavelength conversion process of a 10-Gbit/s signal in a 6-LP-mode fibre," *Opt. Express* **27**, 15413-15425 (2019).