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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 15 — Jul. 18, 2011
  • pp: 14051–14059
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Scalable ultrahigh-speed optical transmultiplexer using a time lens

Keith G. Petrillo and Mark A. Foster  »View Author Affiliations


Optics Express, Vol. 19, Issue 15, pp. 14051-14059 (2011)
http://dx.doi.org/10.1364/OE.19.014051


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Abstract

We present a scalable approach to optical time division multiplexing using an all-optical transmultiplexer incorporating a time lens. With simply a single nonlinear device we numerically demonstrate direct conversion from time-division multiplexing (TDM) to wavelength division multiplexing (WDM) with an industry standard 100-GHz channel spacing. Data rates at 1.28 Tb/s are realized in simulation. Additionally, various pump shapes are investigated to minimize distortions and reverse operation of the device (WDM to TDM conversion) is shown.

© 2011 OSA

1. Introduction

Here we describe a device that alleviates the scaling penalty and bandwidth usage by implementing the concept of a time lens to perform the signal processing [13

13. M. A. Foster, “High-speed optical signal processing using temporal imaging,” presented at the 6th APS/DLS New Laser Scientist Conference, Rochester, New York, USA, 28–29 Oct. 2010.

,14

14. K. G. Petrillo and M. A. Foster, “Scalable 1.28-Tb/s transmultiplexer using a time-lens,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JTuI77.

]. Through the use of a single pulsed laser, dispersion, and four-wave mixing (FWM) it is possible to process all n channels simultaneously in a single device. This leads to a simple, compact, power efficient and therefore scalable design. Furthermore, the proposed device can function in both directions either converting from TDM to WDM or from WDM to TDM making it an ideal ultrahigh-bandwidth optical transmultiplexer. In this paper we present the theory of operation of this device. Through an independent research effort, this approach was also recently experimentally demonstrated by Mulvad et al. [15

15. H. C. H. Mulvad, E. Palushani, M. Galili, J. Xu, H. Hu, A. Clausen, L. K. Oxenløwe, and P. Jeppesen, “OTDM-WDM conversion based on time-domain optical Fourier transformation with spectral compression,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThN2.

,16

16. L. K. Oxenløwe, “Ultra-fast optical signal processing using optical time lenses and highly nonlinear silicon nanowires,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CThA5.

].

2. Space-time duality

The development of time-lens based ultrafast optical devices relies on the principles of the space-time duality. This duality originates from the analogy between paraxial diffraction and narrowband dispersion from the respective approximations of the wave equation in space and time [17

17. B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30(8), 1951–1963 (1994). [CrossRef]

,18

18. J. van Howe and C. Xu, “Ultrafast optical signal processing based upon space-time dualities,” J. Lightwave Technol. 24(7), 2649–2662 (2006). [CrossRef]

]. For this reason, many spatial imaging systems have direct temporal analogues. For example, a spatial lens can perform the Fourier transform of an object positioned one focal length from the lens. Likewise, a time lens can perform the Fourier transform of a section of a time domain signal after propagation through a dispersive focal length (Fig. 1
Fig. 1 Spatial and temporal Fourier processors. A spatial Fourier processor with focal length (f) is analogous to a temporal Fourier processor with dispersive focal length (β 2*L) to perform an all-optical Fourier Transform.
) [19

19. M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64(3), 270–272 (1994). [CrossRef]

,20

20. M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008). [CrossRef] [PubMed]

]. In the spatial system, the lens provides a quadratic spatial phase shift to the signal. Similarly, a time lens applies a quadratic temporal phase shift to a time domain signal. Temporal imaging concepts have been used for various experiments including optical waveform measurement, packet compression, and distortion compensation [17

17. B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30(8), 1951–1963 (1994). [CrossRef]

27

27. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Optical time lens based on four-wave mixing on a silicon chip,” Opt. Lett. 33(10), 1047–1049 (2008). [CrossRef] [PubMed]

]. Here we investigate the use of the temporal Fourier processor to convert between optical TDM and WDM formats.

3. Proposed system

A powerful and flexible approach to generating a temporal lens utilizes the nonlinear optical process of four-wave mixing (FWM) with an ultrafast pump pulse [27

27. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Optical time lens based on four-wave mixing on a silicon chip,” Opt. Lett. 33(10), 1047–1049 (2008). [CrossRef] [PubMed]

]. In this approach, the initially transform-limited pump pulse is chirped by twice the dispersive focal length of the system to generate the quadratic temporal phase required for the lens. Through the FWM interaction an idler wave is generated that possesses the information of the signal combined with the quadratic temporal phase shift of the pump. Therefore, isolation of the generated idler yields a lensed version of the input signal waveform.

In a temporal Fourier processor, the signal is first sent through the dispersive focal length of the system and then mixed with the chirped pump pulse. The FWM-generated idler is isolated with a spectral filter and passed through a second dispersive focal length yielding the Fourier transform of the input signal. Through this process the temporal signal is mapped to the frequency domain by the time-to-frequency conversion factor, which is given by the dispersive focal length of the system
ΔtΔω=|β2L|,
(1)
where Δω is the spectral shift corresponding to a temporal shift Δt, β 2 is the group velocity dispersion of the dispersive device, and L is the length of dispersive device [20

20. M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008). [CrossRef] [PubMed]

]. The dispersion for this system is typically implemented using optical fiber. For use as a transmultiplexer, the OTDM data-rate and desired WDM channel spacing fix the dispersive focal length of the fiber to
L=|12πRΔυβ2|,
(2)
where R is the OTDM data rate, Δυ is the desired WDM channel spacing, and β 2 is the group-velocity dispersion coefficient of the fiber.

Conversion from OTDM to WDM using the proposed transmultiplexer is depicted in Fig. 2
Fig. 2 Time lens transmultiplexer design. After suitable dispersion, a 1.28-Tb/s TDM signal is mixed with a 10-GHz pump in a single device yielding full demultiplexing to 128x10-Gb/s WDM channels
. A high-repetition-rate ultrafast pump laser is combined with the OTDM signal after propagating through their respective lengths of dispersion. The two signals experience FWM in a section of highly nonlinear fiber or integrated nonlinear waveguide. At the output, after a final length of dispersion, the WDM signal is produced as the FWM generated idler.

Here we eliminate the performance limitations of existing methods through application of the space-time duality to guide our system design. Specifically the incorporation of the initial dispersive focal length for the incoming signal allows for proper “focusing” of the temporal Fourier processor and leads to minimal cross-talk between adjacent channels despite using a relatively small industry standard channel spacing (e.g. 100 GHz) in the WDM output. The ability to directly generate a WDM signal with this small channel spacing is crucial for full demultiplexing of ultra-high speed OTDM signals up to and beyond 1.28 Tb/s within practical spectral bandwidths

4. Results

Stemming from Eq. (2), each data rate has a specific dispersive focal length. Third-order dispersion (TOD) management is critical to achieve error-free operation. The 160-Gb/s data rate is achieved using standard Corning SMF-28 single mode fiber to perform the dispersion. The 320-Gb/s and 640-Gb/s results require a TOD limited fiber (e.g. Corning model: DCM-D-080-04) that mitigates the TOD by a factor of 12 [20

20. M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008). [CrossRef] [PubMed]

]. For the 1.28-Tb/s data rate a fiber that reduces TOD by a factor of 48 relative to SMF-28 is required.

The eye diagrams for the TDM→WDM simulations are displayed in Fig. 4
Fig. 4 WDM output eye diagrams with each 10-Gb/s WDM channel overlayed. Three adjacent bits are shown with time relative to the center bit for input OTDM data rates of (a) 160-Gb/s, (b) 320-Gb/s, (c) 640-Gb/s, (d) 1.28-Tb/s
. The cumulative eye diagrams are produced by isolating each generated WDM channel of the spectrum individually and overlaying the eye-diagram of every channel. A random return-to-zero on-off keying input bit stream of 217 bits was simulated. A threshold was placed on the output bit streams for each wavelength channel to determine the status of the bit. These bit streams were then compared to their corresponding input TDM bit slots and no errors were found in the conversion process. Figure 5
Fig. 5 Generated WDM output spectrum with 100 GHz channel spacing for input OTDM data rates of (a)160 Gb/s, (b) 320 Gb/s, (c) 640 Gb/s, (d) 1.28 Tb/s
shows the spectra of the generated WDM signals for each data rate. In all cases a channel spacing of 100 GHz is generated. Therefore the full WDM spectral range is 1.6 THz, 3.2 THz, 6.4 THz, and 12.8 THz for the OTDM data rates of 160 Gb/s, 320 Gb/s, 640 Gb/s and 1.28 Tb/s respectively. As is shown, each WDM channel is well separated from the adjacent channels leading to minimal crosstalk as observed in the eye diagrams.

5. Discussion

5.1 Comparison with other ultrahigh-speed demultiplexers

Various devices exist to perform demultiplexing of OTDM signals. The primary reason behind investigating a time lens for this operation is the ability to reduce both the number of devices and the requisite spectral bandwidth compared to other approaches. Due to the time to frequency conversion factor of the temporal Fourier processor (Eq. 1), the time lens design allows greater control over the total bandwidth of the generated WDM channels while avoiding errors due to crosstalk. As an example of this benefit, we summarize the requirements for full FWM demultiplexing of a 1.28 Tb/s signal to multiple 40-Gb/s or 10-Gb/s channels in Table 1

Table 1. Resource comparison of current methods for 1.28-Tb/s demultiplexing using FWM

table-icon
View This Table
. In the table we list the required number of nonlinear devices and the approximate required spectral bandwidth including the input OTDM signal, FWM pump laser, and output WDM signal. As is shown, the time lens approach allows for spectrally efficient operation with a single nonlinear device.

5.2 Spectrum of the pump laser

The pump pulse spectral width is critical for operation with low distortion. If the pump pulses are spectrally narrow, there is a significant drop in the output power of the channels on the edge of the WDM spectrum. This is due to reduced power in the converted data pulses that temporally overlap with the pump pulse tails. In comparison, if the pump pulses are spectrally broad the eye diagrams show distortions resulting from the overlap of adjacent pump pulses. As shown in Fig. 6
Fig. 6 Spectrogram plots after initial dispersion for time lens pump pulses with (a) Gaussian and (b) super-Gaussian spectral shapes.
, initial tests using Gaussian pump pulses revealed that this scheme generated undesired temporal overlap between adjacent pump pulses after dispersion.

The temporal overlap leads to the generation of side pulses between the bit slots (see Fig. 7
Fig. 7 1.28 Tb/s TDM→WDM operation using a Gaussian spectrum for the pump pulse. Nondegenerate FWM occurs in the large regions of temporal overlap between the dispersed pump pulses and leads to the observed distortions between bits.
). The strength of these side pulses depends on the sharpness of the spectral cutoff imposed on the pump. The origin of this distortion can be understood as follows. The overlapping regions of adjacent pump pulses mix in the HNLF with TDM signals at the edge of the pump and through non-degenerate FWM produce a signal at the same frequency as the desired output from TDM signals near the center of the pump pulse. For certain WDM channels, this distortion is stronger than others due to the relative power of the overlapping pump pulses. For this reason, we choose to implement pump pulses with a super-Gaussian spectral shape which mitigates this form of distortion (see Fig. 4).

5.3 WDM to TDM conversion

As depicted in Fig. 8
Fig. 8 WDM to TDM conversion with the time lens transmultiplexer. After suitable dispersion, 128 10-Gb/s WDM channels are mixed with a 10-GHz pump in a single device yielding full multiplexing to 1.28-Tb/s TDM signal.
, one additional feature of this system is that the ability to operate in the reverse direction and convert from WDM to TDM (WDM→TDM) [37

37. X. Wu, A. Bogoni, S. R. Nuccio, O. F. Yilmaz, M. Scaffardi, and A. E. Willner, “High-Speed Optical WDM-to-TDM Conversion Using Fiber Nonlinearities,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1441–1447 (2010). [CrossRef]

]. For example, 128 10-Gb/s signals of equal frequency spacing can enter the system and leave as a single 1.28 Tb/s channel. The simulated WDM→TDM output eye diagrams for each data rate are displayed in Fig. 9
Fig. 9 Output eye diagrams for conversion from WDM to TDM using the transmultiplexer. Three adjacent bits are shown with time relative to the center bit for the data rates (a) 160 Gb/s, (b) 320 Gb/s, (c) 640 Gb/s, and (d) 1.28 Tb/s.
. The cumulative eye diagrams are produced by filtering the output signal and overlaying adjacent bits. For input signals of equal amplitude there is an 80% power fluctuation in the output TDM bit stream. This power fluctuation has been reduced to < 20% in our simulations by proper scaling of the input WDM channels. Aside from the scaling, the parameters of the simulation were identical to the TDM→WDM case including a super-Gaussian pump spectrum. The generated OTDM bit stream was compared to the input bit sequence and resulted in no errors over a thousand bits to confirm proper WDM→TDM conversion.

6. Conclusion

Simulations were performed for TDM→WDM and WDM→TDM signal conversion using a four-wave mixing time lens based temporal Fourier processor. OTDM data rates of 160 Gb/s, 320 Gb/s, 640 Gb/s and 1.28 Tb/s are simulated with a WDM data rate of 10 Gb/s per channel. Proper design of the dispersion lengths for the time lens allowed for a 100 GHz WDM channel spacing to be acquired. This allowed for a WDM bandwidth of only 12.8 THz to be used for demultiplexing the 1.28-Tb/s data rates. This approach to FWM demultiplexing of OTDM signals provides an unmatched combination of spectral efficiency and number of required nonlinear devices. This approach in conjuction with recently demonstrated ultrahigh-bandwidth chip-scale FWM [38

38. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006). [CrossRef] [PubMed]

40

40. A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express 18(3), 1904–1908 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-3-1904. [CrossRef] [PubMed]

] holds great promise for enabling compact and efficient ultrahigh-bandwidth OTDM systems.

Acknowledgments

This work was supported by start-up funds from The Johns Hopkins University.

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OCIS Codes
(060.4230) Fiber optics and optical communications : Multiplexing
(060.4510) Fiber optics and optical communications : Optical communications
(060.7140) Fiber optics and optical communications : Ultrafast processes in fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: May 26, 2011
Revised Manuscript: June 24, 2011
Manuscript Accepted: June 27, 2011
Published: July 7, 2011

Citation
Keith G. Petrillo and Mark A. Foster, "Scalable ultrahigh-speed optical transmultiplexer using a time lens," Opt. Express 19, 14051-14059 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-14051


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References

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