WO2016141945A1

WO2016141945A1 - All-optical conversion between an ofdm signal and a nyquist-wdm signal

Info

Publication number: WO2016141945A1
Application number: PCT/DK2016/050067
Authority: WO
Inventors: Pengyu Guan; Leif Katsuo Oxenløwe
Original assignee: Danmarks Tekniske Universitet
Priority date: 2015-03-10
Filing date: 2016-03-09
Publication date: 2016-09-15
Also published as: CN107408988A; CN107408988B

Abstract

The present invention provides an optical signal converter for converting an optical N-subcarrier OFDM input signal to an optical M-channel Nyquist-WDM output signal, comprising a first phase modulator configurable to apply a linear chirp, a dispersive element configurable to apply a second-order dispersion, and a second phase modulator configurable to apply a linear chirp. A similar optical N-channel Nyquist-WDM to an M-subcarrier OFDM output signalis also provided, along with methods corresponding to the two converters.

Description

All-optical conversion between an OFDM signal and a Nyquist-WDM signal Technical field

The present invention relates to optical orthogonal frequency division multiplexing signals and optical Nyquist wavelength division multiplexing signals, and more particularly to conversion of signals between the two types.

Background of the invention

Due to the rapid traffic growth in optical communication networks, intensive efforts have been made to use the available bandwidth of optical fibers more efficiently.

Recent studies have focused on orthogonal frequency division multiplexing (OFDM) and Nyquist wavelength division multiplexing (Nyquist-WDM), due to their high spectral efficiency (SE), which enable a channel spacing equal to the symbol rate. Fig. la illustrates a spectrum of an OFDM signal. It consists of closely spaced sinc-shaped subcarriers that overlap in the frequency domain. The waveforms (not shown) for each subcarrier are substantially square and closely spaced. Fig. lb illustrates a spectrum of a Nyquist-WDM signal. It consists of closely spaced but non-overlapping individual channels. For each Nyquist-WDM channel, the waveforms (not shown) are sinc-shaped and overlap in time. These multiplexing techniques have been used to demonstrate high SE super-channels with Tbit/s capacity. The capability to switch between OFDM and Nyquist-WDM networks could become very important for the next generation communication systems. However, such functionality is at present not possible without complex optical/electrical/optical (OEO) conversions. Both Nyquist-WDM system technology and OFDM system technology are being investigated for commercial communication systems. If employed side by side, it will most likely become very important to have an efficient tool for converting signals between these two types of systems.

Summary of the invention

In a first aspect, the invention provides an optical signal converter for converting an optical V-subcarrier OFDM input signal to an optical A7-channel Nyquist-WDM output signal. The OFDM-to-Nyquist-WDM converter comprises: - a first phase modulator configurable to apply a linear chirp with a chirp rate K₁ to the OFDM input signal to obtain a first intermediate signal,

- a dispersive element coupled to receive the first intermediate signal and

configurable to apply a second-order dispersion D to the first intermediate signal to obtain a second intermediate signal,

- a second phase modulator coupled to receive the second intermediate signal and configurable to apply a linear chirp with a chirp rate K₁₂ to the second intermediate signal,

wherein :

- the chirp rate K₁ is selected in accordance with (1 - r )^■ 2nNf_sAv_0FDM/M <

K₁ < (1 + r )^■ 2nNf_sAv_0FDM/M, Av_0FDM being a subcarrier spacing of the OFDM input signal, f_s being a symbol rate of the OFDM signal, and parameter r fulfilling 0 < r ≤ 0.2,

- the chirp rate K₁₂ is selected in accordance with (1 - r )^■ 2nNf_sAv_0FDM/M <

K₁₂ < (1 + r )^■ 2nNf_sAv_0FDM/M,

- the dispersion D is selected in accordance with (1 - r )^■ 2nNf_sAv_0FDM/M < - <

(1 + rj^■ 2nNf_sAv_0FDM/M, and

- the respective linear chirps are applied with a repetition rate of f_PM=f_s/M.

Such a converter is capable of providing what can be thought of as a "complete optical Fourier transformation" (complete OFT). It enables both time-to-frequency and frequency-to-time conversions at the same time, thus performing an exchange between the temporal and spectral profiles from input to output. It avoids OEO conversion, since the entire transformation takes place optically. The invention is therefore a (relatively) simple solution.

Maximum spectral efficiency is often obtained when K₁ = K₁₂ = 1/D = 2nNf_sAv_0FDM/M. However, reasonable conversion efficiency is obtainable when the values differ from this value, in other words r may be selected to be different from 0 as also indicated in the broadest embodiment of the first aspect. The choice of r within the range is therefore not, as such, subject to any particular essential method or condition in the broadest embodiment. In practice a certain value of r will provide the best possible performance and that value could therefore advantageously be used. As in many other situations within the field of the present invention, "best possible performance" is determined for a specific setup in part by trial and error, as the person skilled in the art will readily recognize. Examples of provision of chirp rates and dispersion is illustrated later in the present specification. The example uses four-wave-mixing to provide the phase modulation and dispersion-compensating fiber to provide the dispersion D₁. Note that during use of the first aspect of the invention, the subcarrier spacing of the OFDM input signal and the symbol rate f_s of the OFDM signal are known. The chirp rates K₁ and K₁₂ and dispersion D are then determined using the equations above, and then suitable hardware is configured to provide the determined chirp rates and dispersion. As mentioned above, an example later in the present specification illustrates the invention.

The phase modulation is applied across a phase modulation window having length

The phase modulation window preferably begins and ends between symbols.

In a second aspect, the invention provides an optical signal converter for converting an optical V-channel Nyquist-WDM input signal to an optical A7-subcarrier OFDM output signal. The Nyquist-WDM-to-OFDM converter comprises:

- a first phase modulator configurable to apply a linear chirp with a chirp rate K₂₁ to the Nyquist-WDM input signal to obtain a first intermediate signal,

- a dispersive element coupled to receive the first intermediate signal and

configurable to apply a second-order dispersion D₂ to the first intermediate signal to obtain a second intermediate signal,

- a second phase modulator coupled to receive the second intermediate signal and configurable to apply a linear chirp with a chirp rate K₂₂ to the second intermediate signal,

wherein:

- the chirp rate K₂₁ is selected in accordance with (1 -r₂)^■ 2nNf_sAv_N__WDM/M <

K₂₁ < (1 + r₂)^■ 2nNf_sAv_N__WDM/M, Av_N__WDM being a channel spacing of the Nyquist-WDM input signal, f_s being a symbol rate of the Nyquist-WDM signal, and parameter r₂ fulfilling 0 < r₂ < 0.2,

- the chirp rate K₂₂ is selected in accordance with (1 -r₂)^■ 2nNf_sAv_N__WDM/M < K₂₂ < (1 + r₂)^■ 2nNf_sAv_N__WDM/M,

- the dispersion D₂ is selected in accordance with (1 -r₂) -2nNf_sAv_N__WDM/M < J < (1 + r₂)^■ 2nNf_sAv_N__WDM/M, and - the respective linear chirps are applied with a repetition rate of f_PM=f_s/M.

Similarly to the first aspect, maximum spectral efficiency is often obtained when K₂₁ = K₂₂ = 1/D₂ = 2nNf_sAv_N__WDM/M. Again, however, reasonable conversion efficiency is obtainable when the values differ from this value. Embodiments having r_x, r₂ in the interval from 0 to 0.1 provide higher spectral efficiencies. The discussion relating to the choice of r above applies equally well to the choice of r₂. It also applies to the further aspects below.

Note that during use of the second aspect of the invention, the channel spacing of the Nyquist-WDM input signal and the symbol rate f_s of the Nyquist-WDM signal are known. The chirp rates K₂₁ and K₂₂ and dispersion D₂ are determined using the equations above, and then suitable hardware is configured to provide the determined chirp rates and dispersion. As mentioned above, an example later in the present specification illustrates the first aspect of the invention. However, the considerations are entirely the same going from optical Nyquist-WDM input signal to an optical OFDM signal.

Four-wave mixing is often considered a problem in wavelength-division multiplexing schemes, because signals produced due to the mixing interfere with intentionally generated signals. Even so, embodiments of the optical signal converters are in some cases strongly simplified when the first intermediate signal is an idler signal resulting from first four-wave-mixing the input signal with a linearly chirped first pump pulse in an optical fiber, and the second phase modulator provides a second four-wave mixing of the second intermediate signal with a second linearly chirped pump pulse in an optical fiber.

Converters described above that comprise a pump pulse generator configurable to produce the first and the second pump pulse is a product in which the four-wave- mixing process can be optimized from the beginning. It does away with the need for providing external equipment for providing pump pulses. Furthermore, in such embodiments the phase modulators and dispersive element can be optimized for the converter application that is at the core of the present invention. Note that in the first phase modulator, interaction between the input signal and the first pump pulse generates an idler signal that is phase-conjugated relative to the input signal. Four-wave-mixing-based embodiments are even more advantageous if they are configured so the second pump pulse is adapted to substantially eliminate a phase conjugation resulting from the first four-wave-mixing. In such embodiments, the output signal is non-phase-conjugated with respect to the input signal. The output signal is non-phase-conjugated (i.e. not phase conjugated) with respect to the input signal for the simple reason that the second pump pulse provides a phase conjugation on top of the phase conjugation generated by the first pump pulse, thereby in effect cancelling that phase conjugation. The second pump pulse can, in some situations, be adapted for instance by propagating it in a dispersion-compensating fiber (DCF).

By using an optical fiber having said second-order dispersion as the dispersive element, the system is further simplified.

A third aspect of the invention provides a method for converting an optical V-subcarrier OFDM input signal to an optical A7-channel Nyquist-WDM output signal. The method comprises:

- obtaining a first intermediate signal by applying a linear chirp with a chirp rate K₁ to the OFDM input signal,

- obtaining a second intermediate signal by applying a second-order dispersion D to the first intermediate signal,

- applying a linear chirp with a chirp rate K₁₂ to the second intermediate signal, wherein :

K₁₂ < (1 + r )^■ 2nNf_sAv_0FDM/M,

(1 + rj^■ 2nNf_sAv_0FDM/M, and

A fourth aspect of the invention provides a method for converting an optical /V-channel Nyquist-WDM input signal to an optical A7-subcarrier OFDM output signal. The method comprises: - obtaining a first intermediate signal by applying a linear chirp with a chirp rate K₂₁ to the Nyquist-WDM input signal,

- obtaining a second intermediate signal by applying a second-order dispersion D₂ to the first intermediate signal,

- applying a linear chirp with a chirp rate K₂₂ to the second intermediate signal, wherein :

- the chirp rate K₂₁ is selected in accordance with (1 - r₂)^■ 2nNf_sAv_N__WDM/M < K₂₁ < (1 + r₂)^■ 2nNf_sAv_N__WDM/M, Av_N__WDM being a channel spacing of the Nyquist-WDM input signal, f_s being a symbol rate of the Nyquist-WDM signal, and parameter r₂ fulfilling 0 < r₂ < 0.2,

- the chirp rate K₂₂ is selected in accordance with (1 - r₂)^■ 2nNf_sAv_N__WDM/M < K₂₂ < (1 + r₂)^■ 2nNf_sAv_N__WDM/M,

- the dispersion D₂ is selected in accordance with (1 - r₂) - 2nNf_sAv_N__WDM/M < ^₂ < (1 + r₂)^■ 2nNf_sAv_N__WDM/M, and

The same considerations as discussed with respect to the first and second aspects of the invention apply equally to the third and fourth aspects.

Note that the OFDM-to-Nyquist-WDM and the Nyquist-WDM -to-OFDM converter (and corresponding methods) are identical in many respects. Considering the case Av_0FDM = Av_N__WDM, it is clear that the same chirp and dispersion parameters can be used whether converting from OFDM to Nyquist-WDM, or vice versa.

Brief descriptions of the drawings

Figure la illustrates a spectrum for an optical OFDM signal. Figure lb illustrates a spectrum for an optical Nyquist-WDM signal.

Figure 2 illustrates a basic principle underlying embodiments of the present invention.

Figure 3a and 3b illustrate optical signal converters in accordance with aspects of the present invention.

Figure 4a illustrates a conversion of a four-subcarrier OFDM signal to a four-channel Nyquist-WDM signal. Figure 4b illustrates a conversion of a four-subcarrier OFDM signal to a two-channel Nyquist-WDM signal.

Figure 5a illustrates a conversion of a four-channel Nyquist-WDM signal to a four- channel OFDM signal. Figure 5b illustrates a conversion of a four-channel Nyquist-WDM signal to a two- channel OFDM signal.

Figure 6a shows in more detail the conversion of a four-subcarrier OFDM signal to a four-channel Nyquist-WDM signal.

Figure 6b shows in more detail the conversion of a four-subcarrier OFDM signal to a two-channel Nyquist-WDM signal.

Figure 7 illustrates the principle of an embodiment of the invention, along with an OFDM transmitter and a Nyquist-WDM receiver.

Figure 8 illustrates an experimental for demonstrating conversion of an 8-subcarrier 640 Gbit/s OFDM super-channel to an 8x80-Gbit/s Nyquist-WDM channel. Figure 9 results of the OFDM to Nyquist-WDM conversion with the setup in Fig. 8.

Figure 10 shows performance of the conversion.

Detailed description of selected embodiments

Fig. 2 illustrates a basic principle underlying embodiments of the present invention, namely an optical signal processor that is capable of performing a "complete optical Fourier transformation" ("complete OFT"). It enables both time-to-frequency and frequency-to-time conversions at the same time, thus performing an exchange between the temporal and spectral profiles from input to output. It turns out that this is particularly useful in the context of co-existence of OFDM systems and Nyquist-WDM systems. SI is the OFDM signal, with the waveform on top, the spectrum below. The waveform consists of substantially square pulses, and the spectrum is composed of sinc-shaped individual spectra, one for each OFDM subcarrier. S2 is the Nyquist-WDM signal that is associated with the OFDM signal SI. The waveforms are sinc-shaped, and the spectrum consists of substantially square, non-overlapping channels. Fig. 3a illustrates an OFDM-to-Nyquist-WDM converter 300 in accordance with an embodiment of the invention. It has a first phase modulator 301, which receives the OFDM input signal and applies a linear chirp. This results in a first intermediate signal that is provided to a dispersive element 303. The dispersive element applies a second- order dispersion, resulting in a second intermediate signal. The second intermediate signal is provided to a second phase modulator 305 that applies a linear chirp. The result is a Nyquist-WDM signal at the output.

Preferably, the phase modulators and the dispersive element are enabled using optical fiber. Fig. 3b illustrates an Nyquist-WDM-to-OFDM converter 310 in accordance with an embodiment of the invention. It has a first phase modulator 311, which receives the Nyquist-WDM input signal and applies a linear chirp. This results in a first intermediate signal that is provided to a dispersive element 313. The dispersive element applies a second-order dispersion, resulting in a second intermediate signal. The second intermediate signal is provided to a second phase modulator 315 that applies a linear chirp. The result is a an OFDM signal at the output.

Fig. 4a and 4b illustrate OFDM-to-Nyquist-WDM conversion in more detail.

The chirp rate K determines the scaling factor between the time and frequency domains according to: At = 2nAf/K. In order to obtain maximum spectral efficiency, the chirp rate should be configured to K = 2nAv_OFDM ². The quadratic phase modulation preferably has a repetition rate f_PM of f_s/N for a conversion from an V-subcarrier OFDM signal to an V-channel Nyquist WDM signal. In other words, the phase modulation is applied over windows that are nominally T_PM = l/f_PM. This is shown with dashed lines in the Figs. 4a and 4b. Because of the characteristics of OFDM signals, the converted signal is in fact

substantially a Nyquist WDM signal when the chirp rate and dispersion are selected as described above. In practice a short guard internal needs to be inserted between every N OFDM symbol slots for the transition of the quadratic phase modulation.

In the following, the symbol rate for an /V-subcarrier OFDM signal will be denoted f_s, the OFDM symbol slot will be denoted AT_0FDM, and the OFDM subcarrier spacing be denoted Av_0FDM. For an /V-channel Nyquist-WDM signal, AT_N__WDM will be used to denote the Nyquist-WDM symbol slot, and the Nyquist-WDM channel spacing will be denoted

Av_N__WDM .

Fig. 4a shows application of a phase modulation across four OFDM pulses. The application of the chirp is what ultimately gives rise to the four Nyquist-WDM channels shown on the right side of the figure. The square shape of the OFDM waveforms is in a sense replicated in that the Nyquist-WDM spectrum consists of four square spectra (the Nyquist-WDM channels). The sinc-shaped subcarriers are, in the same sense, converted to sinc-shaped waveforms in the Nyquist-WDM signal. The invention is in part based on the realization that these two particular signal formats, OFDM and Nyquist-WDM, are each other's Fourier transform and can be switched between using an OFT, where the characteristics of the OFT have been carefully designed.

The present invention can also be used to convert an OFDM signal with N subcarriers to a Nyquist-WDM signal with M channels, where N and M are not equal. The repetition rate f_PM of the quadratic phase modulation is instead set to f_s/M. The chirp rate is selected as K = 2nNf_sAv_0FDM/M for maximum spectral efficiency. The result is a Nyquist- WDM signal with a symbol rate of Nf_s/M.

Fig. 4b is similar to Fig. 4a, but now the phase modulation is applied across two pulses rather than four as in Fig. 4a. Selecting the chirp properly results is two Nyquist-WDM channels having twice the bandwidth of the Nyquist-WDM channels in Fig. 4a. This leads to the waveforms having eight pulses instead of four within the same time interval.

Figs. 5a and 5b illustrate conversion of Nyquist-WDM signals to OFDM signals.

In the following, the symbol rate for an V-channel Nyquist-WDM signal will be denoted f_Sl AT_N__WDM will be used to denote the Nyquist-WDM symbol slot, and the Nyquist-WDM channel spacing will be denoted Av_N__WDM . The OFDM symbol slot will be denoted AT_0FDM, and the OFDM subcarrier spacing be denoted Av_0FDM.

In order to convert an V-channel Nyquist WDM signal to an A7-subcarrier OFDM signal, the chirp rate should be selected as K = 2nNf_sAv_N__WDM/M. The repetition frequency f_PM of the quadratic phase modulation should be set to f_s/M. The resulting symbol rate for the generated OFDM signal is Nf_s/M. The principles for converting Nyquist-WDM to OFDM are exactly the same as conversion from OFDM to Nyquist-WDM, and thus Figs. 5a and 5b will not be described in further detail, except to mention that Fig. 5a illustrates, similarly to Fig. 4a, phase modulation across four pulses, and Fig. 5b illustrates, similarly to Fig. 4b, phase modulation across two pulses.

To illustrate how the transformation rearranges data, Fig. 6a illustrates an OFDM signal with four subcarriers, numbered chl-ch4. The top of the figure shows four OFDM "pulses" pl-p4. The dashed lines illustrate the phase modulation window (see description above). Since there are four subcarriers, each "pulse" pl-p4actually comprises four separate symbols, one for each OFDM subcarrier. To illustrate this, each "pulse" contains a number for each of the four OFDM subcarriers, 16 numbers in all (four "pulses" times four subcarriers).

The first pulse contains numbers 1-4. Each number can be thought of as a symbol. Symbol 1 is carried on OFDM subcarrier chl, symbol 2 on OFDM subcarrier ch2, and so on. The second pulse contains symbols 5-8, where 5 is carried on chl, 6 on ch2, and so on. The third pulse contains symbols 9-12, where 9 belongs to chl, through number 12 which belongs to ch4. Finally, the fourth pulse contains numbers 13-16, where 13 is carried on chl, 14 on ch2, 15 on ch3 and 16 on ch3.

In the frequency domain, symbols 1-4 are encoded sequentially on the four subcarriers, as are 5-16, as illustrated. This selection is arbitrary, but the symbols are useful for illustrating how the phase modulations and dispersion in a sense rearranges the symbols.

Fig. 6a illustrates how the OFDM signal is transformed when the phase modulation is applied across the four pulses of the OFDM signal. The phase modulation is configured to cause a shift in frequency across the four pulses (i.e. the phase modulation window covers four pulses), the shift being in accordance with the applied linear chirp.

Due to the linear chirp, the data in the four pulses are shifted in frequency with respect to each other. This means that the data in pi, i.e. symbols 1-4, are translated at the output to an N-WDM channel CHI, symbols 5-8 to an N-WDM channel CH2 shifted according to the chirp, symbols 9-12 to an N-WDM channel CH3 shifted yet again by the same amount, and symbols 13-16 are translated to a fourth N-WDM channel CH4. Each channel contains, as a function of time, the four symbols that were simultaneous in the OFDM signal. Bandpass-filtering CH2, for instance, a pulse train (indicated as Pl- P4) will emerge which consists of sequential symbols that actually represent symbols 5- 8. They coincide in the OFDM signal, but after conversion they are arranged in order in time, shifted with respect to one another. This means that if symbols 1-4 are thought of as belonging to a single OTDM channel, that channel can be extracted by obtaining, by filtering, the corresponding WDM channel, say CHI. The symbols will be arranged sequentially in time. This implies on the one hand that the conversion is very well suited for conversion of an OFDM signal that is obtained by time-multiplexing individual channels. However, arrangement of symbols in an OTDM fashion is not a prerequisite for operating the invention. It merely turns out that OTDM translates well into separate Nyquist-WDM channels.

Fig. 6b illustrates conversion of the same 16 symbols into two Nyquist-WDM channels rather than four. To contain the symbols, the Nyquist-WDM channels are twice as broad. This is obtained by providing twice as much chirp across the four pulses, pairwise. The chirp causes a channel shift twice that in Fig. 6a. The phase modulation window is shown with dashed lines. In Fig. 6a, the phase modulation window covers four pulses, whereas two phase modulation windows now cover the four pulses, each window covering two pulses. The first pulse, pi, ends up in a first Nyquist-WDM channel CHI, and the second pulse, p2, ends up in a second Nyquist-WDM channel

CH2. The separation (and channel width) is designed to be twice as large as the OFDM subcarrier width. The total bandwidth is maintained, but the two channels, rather than four as in Fig. 6a, are twice as broad as those in Fig. 6a.

In the time domain, 8 pulses (indicated as P1-P8) are the result of the conversion.

There are two signals, one for each Nyquist-WDM channel. The symbols they represent are shown in the figure. CHI comprises symbols 1-4 and 9-12, and CH2 comprises symbols 5-6 and 13-16. Each channel in the Nyquist-WDM signal therefore contains symbols from two OFDM pulses pl-p4 (each of which is really four pulses in this example, as described above). Experiment

Figs. 7-9 shows a demonstration of conversion of an optical OFDM signal to an optical Nyquist-WDM signal. In this demonstration, an 8-subcarrier 640 Gbit/s DPSK (differential phase-shift keyed) OFDM signal is simultaneously converted to eight 80- Gbit/s Nyquist-WDM channels. The total signal bandwidth of 800 GHz for the OFDM signal remains unchanged after conversion, maintaining a spectral efficiency of 0.8 symbol/s/Hz. As described above, an OFDM signal is composed of sinc-shaped subcarrier spectra with rectangular waveforms, and a Nyquist-WDM signal is composed of WDM channels with rectangular spectra and sinc-shaped waveforms. The OFDM to Nyquist-WDM conversion is, as described above, realized by exchanging the temporal and spectral profiles using an embodiment of the present invention. Fig. 7 includes an all-optical OFDM transmitter, an embodiment of the invention

(labeled "Complete OFT" in Fig. 7), and a Nyquist-WDM receiver. In the all-optical OFDM transmitter, a multi-carrier transmitter generates a number of channels with frequency spacing Av at symbol rate f_s fs ( "A" in Fig. 7), where Av = Nf_s and N is 8 in the present demonstration. The multi-carrier channels with flat-top temporal waveforms are bit-wise synchronized. A rectangular temporal gate with width T_ps=l/Av₁ is then used to select the center of the overlapping waveforms, resulting in sinc-shaped multicarrier channels in the frequency-domain with a half zero-crossing width (HZCW) equal to Av ( "B" in Fig. 7). The signal is then OTDM-multiplexed by a factor N (=8), resulting in an OFDM signal with a symbol rate equal to the channel spacing ("C" in Fig. 7), where, as mentioned, Av = Nf_s. Considering the discussion of Figs. 6a and 6b, it can be readily seen that the conversion from OFDM to Nyquist-WDM is particularly useful for OTDM-organized signals and conversion from N subcarriers to N Nyquist-WDM channels (i.e. same number). Filtering out a particular Nyquist-WDM channel, data from a corresponding one of the OTDM channels can be extracted by optical sampling. The filtering and optical sampling is described below.

The complete OFT for OFDM to Nyquist-WDM conversion is based on two quadratic phase-modulation stages ("time lenses") with chirp rate K, separated by a dispersion medium of D = /?₂£. The parameters are related as described above. The OFDM signal is converted to a Nyquist-WDM signal with channel spacing Av₂ depending on the choice of K (and, in turn, D). To achieve the maximum spectral efficiency after conversion, the chirp rate K should be set equal to K = 2πΑν². In the present experiment, a short guard interval (GI) is inserted in each OFDM symbol slot for the transition of the quadratic phase-modulation, and K is set to a value slightly less than 2πΑν ².

The present experiment can be thought of as illustrating OFDM to Nyquist-WDM conversion at a super-channel level, not at the subcarrier-level, in the sense that an individual Nyquist-WDM channel is converted from the corresponding OFDM temporal tributary. Above, it was described how individual symbols are "rearranged" in practice.

In the receiver, the converted Nyquist-WDM super-channel is first WDM-demultiplexed into individual Nyquist-WDM channels ("E") using a rectangular optical band-pass filter (OBPF) with bandwidth equal to the channel spacing Δν₂. The demultiplexed Nyquist- WDM channel is subsequently sampled at the inter-symbol-interference (ISI)-free point using a narrow optical sampling gate. Finally, the sampled signal ("F" in Fig. 7) is detected by a base-rate receiver. As the converter is transparent to the data-format, it can be used with more complex modulation formats, such as quadrature amplitude modulation (QAM) at various levels of complexity (i.e. number of symbols).

The experimental setup is shown in Fig. 8. Eight distributed feedback laser diodes (DFB-LDs), centered from 1547.2 nm to 1552.8 nm with 100 GHz spacing, are used in the transmitter. The outputs of the CW lasers are DPSK-modulated with a 10 Gbit/s 2³¹-1 PRBS in a Mach-Zehnder modulator (MZM). A 10-ps rectangular temporal gate is used to simultaneously shape all multi-carrier channels into 100 GHz HZCW sinc- shaped multi-carrier channels. The temporal gate is implemented by a non-linear polarization-rotating loop (NPRL) using a 10-ps rectangular control pulse. The obtained eight 10-Gbaud sinc-shaped multi-carrier channels are then OTDM-multiplexed to 80 Gbaud using an OTDM multiplexer, resulting in an 8-subcarrier 640 Gbit/s OFDM super- channel with SE at 0.8 symbol/s/Hz, as shown in Fig. 9(a). Fig. 9(a) also shows the 8 OFDM subcarriers with 100 GHz spacing obtained from the individual CW lasers, where the characteristic sinc-shape can be observed. The resulting OFDM waveform is shown in Fig. 9(b), where the 80-Gbaud rectangular-shaped OFDM waveform is obtained. The bit slot is 11.5 ps including a 1.5-ps GI, and an extra 8-ps GI between every 8 tributaries for the OFT operation (i.e. the OFDM to Nyquist-WDM signal conversion).

The quadratic phase modulation is implemented based on a four-wave mixing (FWM) process in a highly nonlinear fiber (HNLF) using linearly chirped rectangular pump pulses. The pump pulses are obtained from a 10 GHz mode-locked laser (MLL) at 1557 nm followed by spectral broadening in a dispersion-flattened HNLF (DF-HNLF). To obtain linearly chirped pumps, the output spectrum of the DF-HNLF is filtered using a wavelength selective switch (WSS), and each pump is subsequently propagated in an appropriate length of dispersive fiber. Pumpl is dispersed in 1700 m of SMF to achieve a chirp rate K= 0.055 ps^~2 for conversion of the 11.5 ps temporal spacing to a 100 GHz frequency grid (K < 2πΑν ² due to the insertion of a GI). As the data-signal is phase- conjugated after the first FWM process, pump2 is dispersed in 290 m of dispersion compensating fiber (DCF) having the opposite dispersion value of the 1700 m SMF, in order to achieve the same chirp rate K. The central wavelengths of the pumps are set at 1562 nm. They could be set at different wavelengths, allowing conversion from one spectral position to another. In the present experiment, the Nyquist-WDM ends up at the same location as the original OFDM signal, as shown in Fig. 9(c) and described below. The first FWM output is shown in Fig. 9(c). After extraction with a 14 nm OBPF, the idler is dispersed in 115 m DCF (Fig. 8), then combined with pump2 (Fig. 8) and coupled into HNLF2 (Fig. 8) for the second FWM process. The resulting spectrum is also shown in Fig. 9(c). The generated idler is the Nyquist-WDM super-channel converted from the OFDM signal. Fig. 9(d) shows a zoom-in on the idler, where 8 rectangular Nyquist-WDM channels with 100 GHz spacing can be observed, and the SE remains at 0.8 symbol/s/Hz after conversion.

In the receiver, a 100 GHz rectangular OBPF is used to demultiplex each Nyquist-WDM channel as shown in Fig. 9(d). Each 80-Gbit/s Nyquist-WDM channel contains eight 10- Gbit/s Nyquist tributaries. Fig. 10(a) shows the waveform of a WDM-demultiplexed 80- Gbit/s Nyquist-WDM channel, where 8 minimum-ISI positions with 11.5-ps spacing are clearly observed. These minimum-ISI positions correspond to the nulls of the sinc- shaped tributary waveforms. The minimum-ISI position in each 11.5-ps tributary time- slot is then sampled in the NOLM, using a 1.3-ps wide control pulse for gating. Finally, the bit error rate (BER) of each tributary is measured in a 10-Gbit/s pre-amplified DPSK receiver including a delay line interferometer (DLI) and a balanced photo-detector.

Fig. 10(b) shows the receiver sensitivities at BER= 10^~9, which is achieved for all 64 10- Gbit/s DPSK tributaries within the 8 converted Nyquist-WDM channels. As a BER curve example, one of the best Nyquist tributaries (W5- T5: tributary 5 from Nyquist-WDM channel 5) is plotted in Fig. 10(c). BER< 10^~9 is achieved with a receiver sensitivity of - 35.7 dBm. For reference, the BER curves of the same tributary without adjacent tributaries and neighboring Nyquist-WDM channels are also shown in Fig. 10(c) respectively, as well as a 10 Gbit/s DPSK baseline. The power penalty for the best tributary is 5 dB for the full system (including all-optical OFDM generation, OFDM to Nyquist-WDM conversion and optical sampling), of which 2.3 dB is due to the ISI from the adjacent tributaries and 2 dB is due to the neighboring Nyquist-WDM channels.

The spectral efficiency remains unchanged at 0.8 symbol/s/Hz after conversion, which is close to the binary single channel theoretical limit of 1 symbol/s/Hz.

Claims

1. An optical signal converter (300) for converting an optical V-subcarrier OFDM input signal to an optical A7-channel Nyquist-WDM output signal, comprising :

- a first phase modulator (301) configurable to apply a linear chirp with a chirp rate K₁ to the OFDM input signal to obtain a first intermediate signal,

- a dispersive element (303) coupled to receive the first intermediate signal and configurable to apply a second-order dispersion D to the first intermediate signal to obtain a second intermediate signal,

- a second phase modulator (305) coupled to receive the second intermediate signal and configurable to apply a linear chirp with a chirp rate K₁₂ to the second intermediate signal,

wherein :

- the chirp rate K₁ is selected in accordance with (1 - r )^■ 2nNf_sAv_0FDM/M < K₁ < (1 + r )^■ 2nNf_sAv_0FDM/M, Av_0FDM being a subcarrier spacing of the OFDM input signal, f_s being a symbol rate of the OFDM signal, and parameter r fulfilling 0 < r ≤ 0.2,

- the chirp rate K₁₂ is selected in accordance with (1 - r )^■ 2nNf_sAv_0FDM/M < K₁₂ < (1 + r )^■ 2nNf_sAv_0FDM/M,

(1 + rj^■ 2nNf_sAv_0FDM/M, and

2. An optical signal converter (310) for converting an optical /V-channel Nyquist-WDM input signal to an optical A7-subcarrier OFDM output signal, comprising :

- a first phase modulator (311) configurable to apply a linear chirp with a chirp rate K₂₁ to the Nyquist-WDM input signal to obtain a first intermediate signal,

- a dispersive element (313) coupled to receive the first intermediate signal and configurable to apply a second-order dispersion D₂ to the first intermediate signal to obtain a second intermediate signal,

- a second phase modulator (315) coupled to receive the second intermediate signal and configurable to apply a linear chirp with a chirp rate K₂₂ to the second intermediate signal,

wherein : - the chirp rate K₂₁ is selected in accordance with (1 - r₂)^■ 2nNf_sAv_N__WDM/M < K₂₁ < (1 + r₂)^■ 2nNf_sAv_N__WDM/M, Av_N__WDM being a channel spacing of the Nyquist-WDM input signal, f_s being a symbol rate of the Nyquist-WDM signal, and parameter r₂ fulfilling 0 < r₂ < 0.2,

An optical signal converter in accordance with claim 1 or 2, wherein the first intermediate signal is an idler signal resulting from first four-wave-mixing the input signal with a linearly chirped first pump pulse in an optical fiber, and the second phase modulator provides a second four-wave-mixing of the second intermediate signal with a second linearly chirped pump pulse in an optical fiber.

An optical signal converter in accordance with claim 3, further comprising a pump pulse generator configurable to produce the first and the second pump pulse.

A converter in accordance with claim 3 or 4, wherein the second pump pulse is adapted to substantially eliminate a phase conjugation resulting from the first four- wave-mixing, whereby the output signal is non-phase-conjugated with respect to the input signal.

An optical signal converter in accordance with one of the preceding claims, wherein the dispersive element comprises an optical fiber having said second-order dispersion.

An optical signal converter in accordance with one of the preceding claims, wherein parameter r_{l r} if applicable, and/or parameter r₂, if applicable, is in the interval from 0 to 0.1.

8. An optical signal converter in accordance with one of the preceding claims, wherein N = M.

9. A method for converting an optical V-subcarrier OFDM input signal to an optical M- channel Nyquist-WDM output signal, comprising :

K₁₂ < (1 + r )^■ 2nNf_sAv_0FDM/M

(1 + rj^■ 2nNf_sAv_0FDM/M, and

10. A method for converting an optical /V-channel Nyquist-WDM input signal to an

optical A7-subcarrier OFDM output signal, comprising :

- obtaining a first intermediate signal by applying a linear chirp with a chirp rate K₂₁ to the Nyquist-WDM input signal,

- the chirp rate K₂₁ is selected in accordance with (1 - r₂)^■ 2nNf_sAv_N__WDM/M < K₂₁ < (1 + r₂)^■ 2nNf_sAv_N__WDM/M, Av_N__WDM being a channel spacing of the Nyquist-WDM input signal, f_s being a symbol rate of the Nyquist-WDM signal, and parameter r₂ fulfilling 0 < r₂ < 0.2, - the chirp rate K₂₂ is selected in accordance with (1 - r₂)^■ 2nNf_sAv_N__WDM/M < K₂₂ < (1 + r₂)^■ 2nNf_sAv_N__WDM/M,