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We propose a novel optical quantizing and coding for ultrafast analog-to-digital (A/D) conversion using nonlinear optical switches based on Sagnac interferometer. The feasibility of a 3-bit A/D conversion at 10-Giga-sample-per-second (Gsps) is experimentally demonstrated. Multi-period transfer function of the Sagnac interferometer type nonlinear fiber-optic switch, which is a key to the quantizing and coding, is experimentally realized for the first time to the authors’ knowledge. The proposed optical quantizing and coding, combined with existing optical sampling techniques, will enable ultrafast photonic A/D conversion without high-speed electronics, potentially in the frequency region of well over a few hundred Gsps.
©2005 Optical Society of America
1. Introduction
Although a 3-bit electrical analog-to-digital (A/D) conversion operating at 24 Giga-sample-per-second (Gsps), was reported recently [1], it would be difficult in general to realize ultrafast electrical A/D conversion exceeding a few tens Gsps as the speed is limited due to ambiguity of comparator and jitter of sampling window etc [2]. Optical A/D conversion has been studied for more than two decades to overcome these electrical limitations [3]. The process of A/D conversion consists of sampling, quantizing, and coding. Some techniques of optical sampling have come to reality [4–6], however, very few schemes have been proposed for optical quantizing and coding techniques [7, 8]. In order to realize ultrafast optical A/D conversion operating at much higher sampling rates than the electronic limits, it would be essential to make use of ultrafast optical phenomena. In fact, the Kerr nonlinearity of silica is as fast as a few femto seconds [9], which translates into a few hundred terahertz bandwidth.
In this paper we propose a novel optical quantizing and coding for ultrafast A/D conversion using nonlinear optical switches based on Sagnac interferometer [10]. The feasibility of a 3-bit A/D conversion at 10-Gsps is experimentally demonstrated. Multi-period transfer function of the Sagnac interferometer type nonlinear fiber-optic switch, which is a key to the quantizing and coding, is experimentally realized for the first time. Because the Kerr nonlinearity of silica fiber is exploited for composing the key parts of the proposed scheme, it could operate potentially at much higher sampling rates than 10 Gsps.
2. Principle of all-optical A/D conversion
A block diagram of the proposed N-bit long optical quantizing and coding scheme for all-optical A/D converter and examples of temporal pulse trains at some points are shown in Fig. 1. Optical pulses sampled from an analog signal are split and launched into an array of N encoders, respectively followed by an array of N thresholders. Each encoder has a different transfer function with respect to input optical power. The different transfer functions realize encoding and quantizing, while the thresholders increase the on-off ratio of the transfer functions by rejecting residual “0” pulses and reduce the variance of the height of “1” pulses. Then, synchronized parallel digital signals appear after the thresholders as shown in the rightmost part of Fig. 1. In the proposed scheme, we are going to use Sagnac interferometer-type nonlinear switches as encoders as well as thresholders, of which transfer functions are therefore assumed to be sinusoidal. Figure 2 shows an example of transfer functions of the encoders. The encoder 1, 2, and 3 have half-, single-, and two-period transfer functions respectively. Ideally, the transfer functions have to be of rectangular response, as indicated by the shaded areas in the upper side of Fig. 2. In order to convert the sinusoidal responses of the Sagnac interferometers into rectangular ones, another set of Sagnac interferometers are used as thresholders. As a result, the transfer functions are approximately modified to be of rectangle by the cascaded use of sinusoidal transfer functions. Although imperfection remains, the input pulses then come out as parallel digital output pulses that are in fact of a Gray-code uniquely determined by the input level as exemplified in the lower side of Fig. 2 where the number of bit, N, is three for ease of understanding. If the quantization is in 2N levels, one input sampled optical pulse is then converted to specific N-bit optical Gray-coded digital parallel signals.
Each encoder consists of an optical switch based on nonlinear Sagnac loop. The detailed scheme is shown in Fig. 3. This optical switch is comprised of a 3dB coupler, a WDM coupler, a highly nonlinear fiber (HNLF) [11, 12], two polarization controllers (PCs), a circulator, and an optical bandpass filter (BPF). The PC placed in the Sagnac loop adjusts the polarization to maximize the on-off ratio of the interferometer. This switch has three ports; one control pulse input, one probe pulse input, and one switched output port of the probe pulse. The output level is determined by the amount of the cross-phase modulation (XPM) exerted by the control pulse onto the probe pulse. Consequently, the output level is sinusoidal with respect to the level of the input control pulse. Therefore, in order for this device to work as the encoder, the sampled pulses operating at λ2 are launched as the control pulses into the Sagnac loop via the WDM coupler, synchronized with the local probe pulses operating at λ1. It is noted that each of the sampled pulses was temporally stretched so as to uniformly induce a XPM across the entire probe pulse traveling clockwise. The polarization of sampled pulses is so adjusted by the PC as to induce maximum XPM. The phase shift of the probe pulse traveling clockwise, ϕXPM-CW, and the probe pulse traveling counterclockwise, ϕXPM-CCW, can be written such that ϕXPM-CW=2γPpeakL, and ϕXPM-CCW=2γPaveL, respectively, where γ is nonlinear coefficient, Ppeak is the peak power of each of the control pulse, Pave is the average power of the control pulse train and L is the length of HNLF.
Fig. 2. Transfer functions and corresponding quantizing rule of Encoders 1, 2, and 3, (upper) and relation of input power of analog pulse to output bit pattern (Gray code) of the encoders (lower).
In order to grasp the whole picture of the operating principle, let us here neglect for simplicity the fiber loss, changes in state of polarization and pulse shape, and walk-off due to the fiber dispersion. When the phase difference between the clockwise and the counterclockwise traveling probe pulses |ϕXPM-CW-ϕXPM-CCW|, becomes (2n+1)π, the probe pulse is entirely transmitted to the output port, while for |ϕXPM-CW-ϕXPM-CCW| of 2nπ, the probe pulses are entirely reflected back to the input port. Transmitted optical power of probe pulse T becomes sinusoidal and is written as
where P is the maximum output average power of probe pulses train. This periodical characteristic is suitable to realize the Gray coding in the proposed all-optical A/D conversion, as was explained above with Fig. 2. The circulator prevents the back flow of the reflected probe pulse and the control pulses. The BPF removes the sampled control pulses and transmits only the probe pulses. The thresholders employed here are the so-called NOLM, or a nonlinear optical loop mirror [9].
The above discussions are based on a simple model that is not always valid in practical cases. In order to experimentally achieve such a sinusoidal response from a scheme shown in Fig. 3, some design issues have to be considered. For example, the use of the different wavelength of control and probe pulse means the existence of walk-off problem due to dispersion. The walk-off not only limits the effective fiber length but also significantly influences the shape of transfer function. Because the sinusoidal response with high on-off ratio is essential, the effects of walk-off should be as minimal as possible. In order to resolve this issue, the temporal expansion of control pulses is effective, as we shall do in the following experiment. Also, allocating wavelengths and its fiber dispersions should be carefully considered. In particular, such consideration becomes crucial to realize multi-period transfer functions for which a large XPM is necessary. Another issue is power consumption. The increase of “γL” and decrease of duty ratio is required to realize low power consumption A/D conversion. Decreasing duty ratio results in the use of shorter control pulses, but it makes the walk-off issue more serious. The use of the HNLF with low dispersion slope [11, 12] greatly helps to increase the power efficiency as well as mitigate the walk-off issue.
3. Experimental demonstration
Figure 4 shows the experimental setup for 10-Gsps 3-bit optical quantizing and coding. We used a 10 GHz regenerative passively mode-locked fiber ring laser (FRL) operating at 1552 nm for the control pulses, or the ‘emulated’ input sampled pulses. The probe pulses with a carrier wavelength of 1568 nm and a temporal width of 3 ps, synchronized with the control pulses, were generated via four-wave mixing (FWM) of this FRL by co-injecting a 1560 nm CW laser diode output into a short HNLF [13]. A dispersion compensating fiber (DCF) was used to broaden the temporal pulse width of the control pulse up to 11 ps. The variable optical attenuator (VOA) after the DCF was used to change levels of optical pulses, emulating sampled pulses from an analog signal input. The optical delay lines (ODLs) were used to adjust the delay so as to overlap the probe pulses with the control pulses. Attenuators (ATTs) were used to properly adjust the relative periodicity of the transfer functions among the encoders so that Encoders A, B, and C provide half-, single-, and two-period transfer functions, respectively at the maximum level of control pulses. Length, L, and nonlinear coefficient, γ, of HNLFs of Encoders A, B, and C were 380 m, 403 m, and 406 m, 17.5 W-1 km-1, 12.0 W-1 km-1, and 12.0 W-1 km-1 respectively. The induced phase difference between the CCW- and CW-probe pulse in the loop is approximately estimated to be 2 γ(Ppeak-Pave)L, according to the discussions regarding Eq. (1), when the fiber loss, walk-off, pulse shape changing, and polarization rotation in fibers are neglected. The ratio of “2 γ(Ppeak-Pave)L” of three encoders had to be 1 to 2 to 4 to realize half-, single-, and two-period transfer functions, and each power of control pulse was changed to adjust the ratio in this experiment. The characteristics of three thresholders were almost identical. The gains of EDFAs were adjusted to the proper values around 23 dB. 10dB-ATTs were used for the thresholders to introduce asymmetrical losses inside the loops for self-switching operation of the NOLMs. The L and γ of HNLF used in the thresholders were 830 m, and 19 W-1 km-1 respectively. The transfer function of one of the NOLMs (thresholders) is shown in Fig. 5. This nonlinear response can improve the transfer functions of the encoders.
Fig. 6. Experimental results of the transfer functions of the encoders. The left column indicates the encoder outputs, and the right column indicates the thresholder outputs.
The experimental results of the transfer functions of Encoders A, B, and C are shown in the left part of Fig. 6. To the authors’ knowledge, this is the first observation of multi-period transfer functions up to two periods. The average power of the control pulses is measured at the output of VOA, or the input of the A/D converter, as indicated by “X” in Fig. 4. The non-zero ‘null’ levels in the transfer functions may be due to the unwanted nonlinear phenomena in optical fiber, unstable polarization and fluctuations of pulse intensity and timing. Further studies should clarify the causes in more detail and provide a solution to obtain an ideal multi period transfer function. The experimental output results of Thresholders A’, B’, and C’ are shown on the r.h.s. of Fig. 6. We can see improved transfer functions, which have almost zero ‘null’ levels. The pulse widths were measured at the output of the thresholders, and autocorrelation traces are shown in the inset of Fig. 6. The measured FWHM temporal pulse widths are indicated in the insets respectively. The autocorrelation traces of thresholder A’, B’, and C’ were obtained when average powers of control pulses were 500mW, 800mW, and 500mW respectively. Every output signal kept the initial pulse width approximated as 3ps and no significant changes in pulse shape were observed. Figure 7 shows reconstructed output digital pulses at 200 mW, 700 mW, and 1000 mW average powers of control pulse, which are obtained from measured pulse width and measured average power, assuming Gaussian pulse shapes. It is thus confirmed that 3-bit A/D conversion is successfully achieved. To further suppress residual pulses of “0”, either cascaded thresholders or optical 2R technique could be incorporated.
4. Conclusion
We have proposed a novel all-optical quantizing and coding scheme for photonic A/D conversion. The multi-period transfer function of nonlinear fiber-optic switch has been obtained for the first time. A 10-Gsps, 3-bit-long quantizing and coding have been successfully demonstrated. To realize ultrafast A/D conversion, one needs narrower pulse width of the control pulses and the probe pulses, as it surely leads to not only reduction in the average power, but also high-speed pulse repetition. Though walk-off problem between the control pulse and the probe pulse, which was approximately 3 ps in our experiment, is a matter of concern, it can be reduced by some techniques such as adopting dispersion managed optical fiber in Encoders. The proposed optical quantizing and coding, combined with existing optical sampling techniques without high-speed electronics, will enable ultrafast photonic A/D conversion of potentially multi-level quantizing more than 3-bit in the frequency region of well over a few hundreds Gsps because of ultrafast fiber nonlinearity.
Acknowledgments
This work was supported by Japan Science and Technology Agency (JST). K. Ikeda acknowledges a support from Inoue Foundation for Science. The authors thank T. Inoue for helpful discussions.
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