## Abstract

We propose a novel “orthogonal” TDM transmission scheme using an optical Nyquist pulse that enables us to achieve an ultrahigh data rate and spectral efficiency simultaneously without any intersymbol interference (ISI). We analytically describe the principle of orthogonal TDM, and demonstrate a 160 Gbaud optical orthogonal TDM transmission using 40 GHz optical Nyquist pulses. Tolerance to GVD and the dispersion slope is significantly improved by virtue of the orthogonality, reduced bandwidth, and minimum ISI.

©2012 Optical Society of America

## 1. Introduction

Optical time division multiplexing (OTDM) technology using ultrashort optical pulses makes it possible to realize ultrahigh-speed transmission at single-carrier bit rates of 1 Tbit/s and beyond [1]. However, the long-distance transmission of such ultrashort pulses remains a major challenge because of their high susceptibility to chromatic dispersion (CD) and polarization mode dispersion (PMD), which become especially significant with large bandwidths. Therefore, signal bandwidth reduction is an important subject in relation to ultrahigh-speed transmission.

At the same time, intensive efforts have been made to improve spectral efficiency by adopting a coherent multi-level modulation format, such as quadrature amplitude modulation (QAM) and orthogonal frequency division multiplexing (OFDM). Recently, a combination of OTDM and QAM has attracted a lot of attention with a view to increasing the symbol rate beyond the bandwidth limitation of electronics and simultaneously improving spectral efficiency [2–4]. However, typical pulse waveforms such as Gaussian or sech waveforms have rapidly decreasing tails, which generally occupy a large bandwidth in the frequency domain. This makes it difficult to improve the spectral efficiency of OTDM-QAM transmission.

In wireless transmission systems, the Nyquist filtering technique has been widely used to reduce the signal bandwidth while avoiding the problem of intersymbol interference (ISI) effects [5]. The Nyquist filter features minimal ISI because of its impulse response with zero crossing at every symbol period. Recently, the adoption of a Nyquist filter was proposed for digital coherent optical transmission [6] and this approach has been successfully applied to highly spectrally efficient multi-level QAM transmissions [7,8]. Since ideally this scheme enables the signal bandwidth to equal the symbol rate, it is possible to reduce the WDM channel spacing to the symbol rate. Such a dense WDM transmission scheme is sometimes called Nyquist WDM [9,10]. The Nyquist WDM takes advantage of the orthogonality between WDM channels to achieve an interchannel crosstalk-free operation by prefiltering the spectrum into a rectangular profile [11,12]. In these demonstrations, the Nyquist filter is employed for a baseband data sequence in a digital signal processor (DSP), and therefore the symbol rate cannot exceed the speed of electronic devices [9–11].

If we can generate an ultrashort optical pulse whose shape is the same as the impulse response of the Nyquist filter, which we call an “optical Nyquist pulse”, we can obtain enormous advantages in terms of increasing both the spectral efficiency and the symbol rate. Optical Nyquist pulses can be easily multiplexed to a higher data rate even exceeding the bandwidth limitation of electronics by employing conventional OTDM. As we will show later, this TDM with Nyquist pulses can be identified as optical “orthogonal” TDM, in contrast to the orthogonality between WDM channels as in OFDM or Nyquist WDM [9–12]. Since the signal bandwidth is significantly reduced without ISI, we can expect a great improvement in the tolerance to CD and PMD. In addition, by applying the optical Nyquist pulses to coherent OTDM-QAM transmission, we can simultaneously achieve an ultrahigh bit rate and spectral efficiency.

In this paper, we propose a novel optical orthogonal TDM transmission scheme using an optical Nyquist pulse train. We present the principle of orthogonal TDM analytically, and identify analogies with digital-to-analog conversion or OFDM transmission based on the sampling theorem. An ultrahigh-speed orthogonal TDM transmission at 160 Gbaud is demonstrated by employing the OTDM of the optical Nyquist pulses, which are generated by using a spectrum manipulation technique. The advantage of the proposed scheme is confirmed in terms of improved tolerance to second- and third-order dispersion with minimal ISI effects.

## 2. Principle of orthogonal TDM using optical Nyquist pulses

Figure 1
shows the principle of the proposed OTDM scheme using optical Nyquist pulses, and compares it with a conventional digital Nyquist filtering technique. The conventional scheme is based on the ISI-free shaping of a baseband data signal in a DSP as shown in Fig. 1(a). The shaped data sequence is sometimes referred to as a “Nyquist pulse,” but it should be noted that this is not a typical isolated pulse. By contrast, in the proposed scheme shown in Fig. 1(b), we first generate an optical Nyquist pulse train at a repetition rate of *f _{s}*, in which the pulse shape is set at a much shorter waveform than 1/

*f*for OTDM. The pulse waveform and spectrum are given by the impulse response and transfer function of a raised-cosine Nyquist filter, respectively, which are defined as [13]

_{s}*T*= 1/(

*N f*) is the symbol period, and α (0 ≤ α ≤ 1) is known as a roll-off factor [5]. By serial time interleaving the Nyquist pulse train with a delay

_{s}*T*and optically multiplexing it

*N*times, it is possible to obtain an ultrahigh-speed optical Nyquist pulse train at a symbol rate of

*N f*.

_{s}Figure 2(a)
shows the waveform of a Nyquist pulse *r*(*t*) with different α values. It can be seen that the pulse is accompanied by an oscillating tail, but the amplitude goes to zero at every symbol interval. These characteristics mean that there is no ISI between neighboring symbols. The oscillating tail converges to zero faster for larger α values. Figure 2(b) shows the Nyquist pulse spectrum for different α values. Note here that *R*(*f*) is the spectral profile of the electric field of the Nyquist pulse. The tail of the spectrum goes to zero in a finite bandwidth, *B* = (1+α)/*T*. A smaller α is beneficial for bandwidth reduction but at the expense of a reduced margin in terms of ISI in the time domain. When we set α at zero, the Nyquist pulse becomes a sinc function, which oscillates over an infinite time.

Figure 3 shows the pulse width Δτ and spectral width Δν of the Nyquist pulse, which are defined as the full width at half maximum, and the time-bandwidth product ΔτΔν for different α values. Δν can be explicitly obtained as follows

whereas Δτ was calculated numerically. Equation (2) indicates that Δν decreases for a large α. This is opposite to the relationship between α and the signal bandwidth*B*described above, which is defined in terms of the actual spectral occupancy. It is therefore important to distinguish

*B*and Δν when discussing the signal bandwidth of the Nyquist pulse.

The TDM of optical Nyquist pulses has several interesting properties as regards orthogonality and an analogy with the sampling theorem. We define the time interleaved optical Nyquist pulses as *ϕ _{n}*(

*t*) =

*r*(

*t*−

*nT*) and the symbol data at

*t*=

*nT*as

*g*. When α = 0, according to the sampling theorem, the TDM Nyquist data train

_{n}*u*(

*t*) = ∑

*g*(

_{n}ϕ_{n}*t*) is equivalent to an analog signal

*g*(

*t*), where

*g*(

*t*) is given by the interpolation of

*g*[5]:

_{n}The relationship between *g*(*t*) and *g _{n}* (=

*g*(

*nT*)) is shown schematically in Fig. 4(a) . From this observation, the generation of a TDM Nyquist data train can also be viewed as a digital-to-analog conversion from

*g*to

_{n}*g*(

*t*) in the optical domain. Based on this property,

*g*can be detected from the OTDM data train with sufficiently narrow optical gating at

_{n}*t*=

*nT*, as shown schematically in Fig. 4(b). This optical gating corresponds to a “sampler” for analog signals.

It should also be noted that the time interleaved optical Nyquist pulses, *ϕ _{n}*(

*t*) =

*r*(

*t*−

*nT*), satisfy the orthogonality condition when α = 0,

*g*in terms of

_{n}*g*(

*t*) and

*ϕ*(

_{n}*t*):

The relationship between *g*(*t*), *g _{n}*, and

*ϕ*(

_{n}*t*) shown in Eqs. (3)-(5) can be compared with the generation and demodulation of OFDM signals, which take advantage of the Fourier series expansion. The one-to-one correspondence between O-OTDM and OFDM is shown in Table 1 with respect to signal representation, orthogonality, and signal demodulation.

For a general α value, the integral of Eq. (4) can be calculated as

*x*) = sin(

*x*)/

*x*. When

*n*≠

*m*, the right-hand side of Eq. (6) is sufficiently small but is generally a non-zero value, and hence the orthogonality is not rigorously satisfied theoretically. Nevertheless, the integral converges to zero for a large |

*n*−

*m*|, and the convergence is faster with a larger α. This indicates that the quasi-orthogonal property is maintained in Nyquist pulses even when α ≠ 0.

## 3. Generation of an optical Nyquist pulse train and its orthogonal TDM signal

To demonstrate high-speed orthogonal TDM, we generated an optical Nyquist pulse and undertook an OTDM transmission experiment using the setup shown in Fig. 5
. A Nyquist pulse with *T* = 6.25 ps and α = 0.5, which was designed for 160 Gbaud transmission, was generated at a repetition rate of 40 GHz from a 1.8 ps Gaussian pulse by using a spectrum manipulation technique based on the spatial intensity and phase modulation of spectral components using a liquid crystal spatial modulator [14]. The generated Nyquist pulse waveform and optical spectrum are shown in Fig. 6(a) and (b)
, respectively. It can be seen that the pulse shape accurately fits the Nyquist profile given by Eq. (1).

We then modulated these pulses with 40 Gbit/s DPSK and multiplexed them from 40 to 160 Gbit/s using a planar-lightwave circuit (PLC)-based bit interleaver as a conventional OTDM multiplexer. The obtained optical orthogonal TDM signal is shown in Fig. 6(c). Here the power is normalized by the peak power in Fig. 6(a). The numerically calculated OTDM waveform of the Nyquist pulse with a random data sequence is shown in Fig. 6(d). The OTDM waveform appears greatly distorted due to interference, but it can be clearly seen that there is no ISI at any symbol interval, and a constant level is maintained as indicated by the blue dots.

The 160 Gbaud Nyquist pulse was demultiplexed to 40 Gbaud by using a nonlinear optical loop mirror (NOLM) with a switching gate width of 1.0 ps. As we described in the previous section, such a narrow switching gate functions as a “sampler”, and allows us to extract only the part of the signal unaffected by ISI. The switching gate width was optimally chosen in terms of both residual ISI and OSNR in the demultiplexed signal, as too narrow switching gate causes excessive loss. The NOLM was composed of a 100 m highly nonlinear fiber (HNLF) with γ = 17 W^{−1} km^{−1}, a dispersion slope of 0.03 ps/nm^{2}/km, and a zero-dispersion wavelength of 1548 nm. The control pulse source was a 40 GHz PLL operated mode-locked fiber laser (MLFL) emitting a 720 fs pulse at 1563 nm [15], which was synchronized with a 40 GHz clock extracted from the transmitted data using an electro-optical PLL clock recovery circuit. At the NOLM output, the demultiplexed signal was separated from the control pulse with a 15 nm optical filter, and received with a preamplifier, followed by demodulation with a one-bit delay interferometer (DI) and balanced detection. The demultiplexed 40 Gbaud pulse waveforms before and after the demodulation are shown in Fig. 7
. These waveforms indicate that the Nyquist pulse was demultiplexed with clear eye opening without affected by ISI from adjacent OTDM channels.

## 4. Dispersion tolerance of optical orthogonal TDM transmission

To demonstrate the advantage of the proposed scheme for high-speed OTDM transmission with respect to dispersion tolerance, we first transmitted the 160 Gbit/s Nyquist pulses in a fiber with uncompensated group-velocity dispersion (GVD), and compared the propagation characteristics with those of a 160 Gbit/s, 1.8 ps Gaussian pulse transmission. We used a 200-m standard single-mode fiber (SSMF) with a GVD of 3.4 ps/nm as the transmission fiber. Figure 8(a) shows the transmitted 160 Gbit/s Nyquist pulse waveform, and Fig. 8(b) shows the corresponding result with a Gaussian pulse waveform. The Nyquist pulse was more tolerant to GVD-induced distortion, where the ISI-free regime was maintained at every symbol interval even in the presence of GVD. On the other hand, with a Gaussian pulse, GVD caused a strong pulse overlap and resulted in a complicated interference pattern. These observations were also clearly reflected in the numerical results.

We measured the BER for the transmitted signal under GVD for 40 Gbit/s tributaries, as shown in Fig. 9 . There was a significant error floor with a Gaussian pulse, and a large BER variation was observed depending on the tributary, which indicates the influence of ISI. By contrast, with a Nyquist pulse, low-penalty performance was achieved with a small BER variation among different tributaries.

We also confirmed that the Nyquist pulse is advantageous in terms of reducing the effect of third-order dispersion (TOD). We evaluated the TOD-induced distortion of 160 Gbaud OTDM signals for various TOD values, β_{3}*L*. Since it is not easy to change the TOD values of optical fibers over a wide range while maintaining zero dispersion, TOD was generated by using a programmable optical filter with a constant intensity profile and a phase profile that was designed to follow the function exp(*i*β_{3}*L*ω^{3}).

Figure 10
compares 160 Gbit/s Nyquist and Gaussian waveforms for TOD values of β_{3}*L* = 20, 25 and 30 ps^{3}, corresponding to dispersion slopes of 12.3, 15.4 and 18.5 ps/nm^{2}, respectively. The corresponding waveforms obtained with numerical simulations are shown in Fig. 11
. It can be seen that, with the Nyquist pulses, distortions occur mainly outside the symbol points, and each symbol can be clearly identified regardless of the TOD magnitude. On the other hand, Gaussian pulses are easily distorted due to a large TOD as shown on the right.

The BER characteristics corresponding to Figs. 10 and 11(a)–(c) are shown in Fig. 12 . The BER is considerably degraded with a Gaussian pulse especially for a larger TOD, while almost identical BER performance is achieved with a Nyquist pulse regardless of the TOD values. These results clearly show the advantage of orthogonal TDM transmission as regards improved dispersion tolerance, which is attributed to both the reduced bandwidth of the Nyquist pulses and their ISI-free property as a result of the orthogonality. It should be noted that a Gaussian pulse, which occupies the same spectral width (20 dB bandwidth) as the Nyquist pulse, has a pulse width of 5.5 ps. The duty ratio of the Gaussian pulse is 88%, and that of the Nyquist pulse is 83%. The ΔνΔτ product of the Nyquist pulse is as large as 0.72 for α = 0.5, as shown in Fig. 3(b), compared with a Gaussian pulse of 0.44. A comparison of the Nyquist and Gaussian pulses with the same spectral efficiency is shown in Fig. 13 . Since theduty ratio of a 160 Gbaud signal becomes as large as 88% with the Gaussian pulse, it is difficult realize OTDM. However, the Nyquist pulse can be easily interleaved even with a duty ratio of 83%.

## 5. Conclusion

We proposed a novel orthogonal TDM scheme using optical Nyquist pulses to achieve an ultrahigh data rate and spectral efficiency simultaneously while avoiding the ISI effects. By employing the 4-OTDM of a 40 Gbaud optical Nyquist pulse train, we successfully generated a 160 Gbaud orthogonal TDM signal in the optical domain. An increased tolerance to dispersion and the dispersion slope was demonstrated by virtue of the orthogonality, reduced bandwidth, and minimum ISI. This scheme is potentially scalable to a higher symbol rate per channel of, for example, 1 Tbaud, and is expected to greatly reduce susceptibility to CD and PMD impairments in ultrahigh-speed transmissions. It also offers the possibility of achieving a spectral efficiency approaching the Shannon limit by using coherent optical Nyquist pulses for QAM.

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