By Andre Vatarescu

**Overview**

While modulation formats based on phase-shift keying have received a significant amount of attention, they may not be the most cost-effective approach for high-speed applications like 40 Gbps. One alternative leverages amplitude-shift keying to meet network requirements at a lower cost.

Recent articles in Lightwave have discussed various phase-shift keying (PSK)-based modulation formats as potential future options for 40/100-Gbps optical transmission. These formats are related to electrical modulation techniques and have been adapted to the optical domain—leading to complex devices and complicated modes of operation. This article outlines a simple and effective optical amplitude-shift keying (ASK) modulation technique. The technique applies a time-dependent electrical spectral structure to an electro-optic modulator to generate optical pulses, consisting of a time-varying number of photons, without broadening the spectral distribution of the input optical carrier. To a degree, the approach adopts the positive elements of direct modulation of a distributed-feedback (DFB) semiconductor laser but discards the negative element of frequency chirp.

**Physical aspects**

The spectral distribution of a signal—be it electrical or optical—is determined by the physical processes that generate the signal. Quite often the real spectrum is different from the Fourier transform of the signal. In optical communications, the spectrum coming out of a directly modulated semiconductor is different from the spectrum emitted by an electro-optic modulator, even when the two devices are driven by the same electrical signal.

The Wigner spectrum describes a particular case of signals whose spectrum varies with time, i.e., W(f, t). The amplitude of the spectral components is switched on and off. A well-known time-varying spectrum is the chirped frequency generated by a directly modulated semiconductor laser. A directly modulated single longitudinal-mode DFB laser, as indicated by Sato et al.1, gives rise to a pulse through modulation of the number of photons emitted, and there is no Fourier spectrum to shape the pulse. The theoretical grounds for the possibility of going below the Fourier limit with time-varying spectra are presented by Loughlin and Cohen.2

Conventionally, the Fourier spectrum S(f), which is time independent, is used to shape a pulse s(t). But the same pulse s(t) can also be generated by using a Wigner spectrum W(f, t). Optically, only the envelope amplitude is detected, and so the intensity | W(f, t) |2 can represent a pulse that comprises a single optical spectral component.

One may ask next: Isn’t the uncertainty principle violated? The answer is that the uncertainty principle in quantum mechanics involves quantum operators acting on wave functions—and there is no quantum operator for time, which is a parameter. Whatever energy–time uncertainty is derived, it can be accommodated by relating the energy to the number of photons in the pulse and the time variance to the arrival of the photons at the photodetector.

The question now is how to generate such an electrical signal and translate it into an optical signal. To this end, one uses the properties of an electro-optic modulator.

Although conventionally electro-optic modulation is described in terms of a phase modulation of the optical carrier, physically the process involves the generation of optical sidebands on either side of the optical carrier. One way of generating a Wigner-type spectrum is to modulate the level of electrical spectral power applied to the electro-optic modulator. This in turn leads to time-varying amplitudes of the sidebands. This approach, along with adequate optical filtering, can work at low bit rates (1 to 5 Gbps) but is impractical at speeds exceeding 5 Gbps. As we will see, a different approach is available based on other properties of the electro-optic modulator.

**Wigner-type pulse propagation**

One can illustrate, with a simple example, the physical structure of the Wigner spectrum that can be generated. Take a continuous wave (CW) optical beam and direct it to a photodetector. A steady-state (DC) photocurrent is generated. Next, drop a mirror across the beam to reflect photons away and prevent them from reaching the photodetector. As the photocurrent goes down to zero, an electrical signal has been generated. The modulation of the beam involves only its number of photons, without modifying their energy or frequency distribution. (How this can be done at speeds of 40 Gbps will be revealed later.)

Now, use a standard singlemode fiber (SMF) to propagate the Wigner-type optical pulse. Given the narrow spectral distribution of the optical pulse, the chromatic dispersion and the second-order polarization-mode dispersion (PMD) of a standard SMF will not present any difficulty. For the differential group delay (DGD) of the PMD, a pulse duty cycle of less than 100% will be necessary. (It would appear that a standard SMF has lower PMD than dispersion-shifted fibers.) The narrow spectrum also reduces interchannel crosstalk, provided the optical filter is properly designed.

As for nonlinear effects, the Brillouin interaction (or scattering) will have to build up from noise because the narrow optical spectrum does not have two spectral lines shifted from each other by the Brillouin frequency (10–12 GHz). Therefore, there are no photons to be scattered backward, e.g., through Rayleigh scattering, so as to provide a stimulating signal. (The Stokes wave can provide some gain for an adjacent optical channel properly placed.) In addition, a highly dispersive SMF impedes the four-wave mixing interactions.

**Designing wavelet-based 40-Gbps transmission links**

A transmission system that combines mixed time-frequency signal representations with the properties described earlier is already under development. The transmission system includes a standard 40-Gbps intensity modulator and a standard direct detection receiver. The novelty consists of introducing a simple spectrum converter in the electronic driver of the electro-optic modulator.

The conventional approach of shaping signal waveforms, e.g., pulses, by means of controlling and tailoring the corresponding Fourier spectrum of the signal runs into the limitations associated with the Fourier analysis. The separation between the time domain and the frequency domain leads to the pulse duration being inversely proportional to the Fourier spectral bandwidth needed to shape the pulse.

In contrast, by mixing the time and frequency domains, the spectrum becomes a function of time, which provides an additional and significant element in shaping signals. In this context, wavelets—defined as short-duration sinusoidal waves—can break away from the Fourier constraints. The modulation format used will be on-off keying (OOK) or binary ASK with a return-to-zero (RZ) pulse structure to mitigate the effect of PMD. The spectral efficiency will be higher than that of dual-polarization quadrature phase-shift keying (QPSK).

The development is intended for multihaul networks operating at 10 Gbps and the emerging 40-Gbps fiber-optic transmission systems. It will use commercially available components and devices. Three elements stand out:

- 1. the very narrow physical distribution of the optical spectrum that enables the elimination of dispersion-compensation modules
- 2. reduction in the crosstalk between adjacent optical channels, leading to enhanced optical signal-to-noise ratio and the elimination of forward-error correction codes
- 3. simplification of the electronic driver, which will be designed in terms of digital combinational logic circuits rather than analog circuits that require complex spectral shaping configurations

In the quest for an optimal modulation format for a bit rate of 40 Gbps, the suppression of the optical carrier—in order to reduce the degradations induced by nonlinear effects in optical fibers—singled out DPSK as the preferred technique. However, the need for phase-decoding and dispersion compensations, particularly for RZ pulses, increases the cost of deployment and operation.

The wavelet approach to high-speed optical pulse modulation has the ability to deliver high-quality transmission with simple setup configurations and reduced operational costs.

**Andre Vatarescu**, PhD, *is R&D coordinator at Fibre-Optic Transmission of Canberra, Australia. He can be reached at andre_vatarescu@yahoo.com.au.*

**References**

- 1. K. Sato. S. Kuwahara, Y. Miyamoto, “Chirp characteristics of 40-Gb/s directly modulated distributed-feedback laser diodes,” J. Lightwave Technol., Vol. 23, Issue 11, pp. 3790–3797, Nov. 2005.
- 2. P.J. Loughlin, L. Cohen, “The uncertainty principle: global, local, or both?,” IEEE Transactions on Signal Processing, Vol. 52, Issue 5, pp. 1218–1227, May 2004.

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