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We propose and demonstrate a novel all-optical digital-to-analog (D/A) conversion using pulse pattern recognition based on optical correlation processing. It is composed of pulse pattern recognition based on correlation processing and intensity adjustment using an optical attenuator. We obtain a single pulse as a result of pulse pattern recognition by using correlation processing between a target digital signal and a prepared correlation filter function. The obtained single pulse can be promptly fed to an output port as a corresponding analog signal through adequate intensity adjustment. Experimental results show that four-bit digital signals with 1.65ps interval can be successfully converted to analog signals corresponding to input digital signals.
©2005 Optical Society of America
1. Introduction
Recent advances in optical fiber communications require high-speed optical digital signals such as amplitude shift keying (ASK) and phase shift keying (PSK) signals over 100 Gb/s. To connect continuous analog signals in nature to high-speed digital signals in conventional technology, high-speed analog-to-digital (A/D) and digital-to-analog (D/A) conversion techniques are indispensable [1]. Since, however, the speed of electronic signal processing is limited to about 100 GHz due to the RC delay bottleneck, it is difficult to realize high-speed A/D and D/A conversion with electronic signal processing. For the realization of high-speed A/D and D/A conversion, optical approaches have attracted much attention recently [2–10]. In the case of A/D conversion, optical techniques have been proposed [2–8] and all-optical approaches are adopted to some of them [6–8]. On the other hand, there are few investigations of optical D/A conversion technique [9–10]. In these methods, they apply a different intensity weighting factor to each bit of a digital signal and sum the intensities of all bits. Since, however, the corresponding analog value of a digital signal is mostly concentrated to the most significant bits (MSBs), the influences of intensity jitters of the MSBs might cause a tremendous error of an output analog signal. In addition, since they require electronic synchronization or control, their operation speeds are still limited by electronic processing. To completely overcome these problems, a new method without a different intensity weighting factor and any electronic processing is desirable.
In this paper, we propose a novel all-optical D/A conversion using pulse pattern recognition based on correlation processing. In this scheme, we suppress the influences of intensity jitters of the MSBs by treating a digital signal as a pulse pattern with a uniform intensity weighting factor. We demonstrate the proposed all-optical D/A conversion.
2. Principle and simulation
Figure 1 shows a schematic diagram of the proposed all-optical D/A conversion. The D/A conversion scheme for N-bit digital signals is composed of 2N -1 D/A conversion modules. It is composed of pulse pattern recognition based on optical correlation processing and intensity adjustment using an optical attenuator. Each D/A conversion module is for one target digital signal. The D/A conversion module outputs an analog signal only if the target digital signal inputs. An input N-bit digital signal is first split into 2N -1 duplicates to provide input digital signal to every D/A conversion modules. Hereafter, we focus on one D/A conversion module for one target digital signal. One duplicate of an input digital signal is dispersed and divided into a decomposed spectral distribution using a dispersion device. In this frequency domain, we realize pulse pattern recognition of a target digital signal using a correlation filter. A pulse pattern of a N-bit digital signal hi(t)(i = 1,2, …, 2N - 1) is given by
where, k, τ and δ(t) are the number of bits of the digital signal, the bit interval and the Dirac delta function, respectively. Equation (1) suggests that we can treat N bit pulses as one pulse pattern hi(t) with a uniform intensity weighting factor. The correlation signal between the correlation filter function f(t) and the input digital signal hi(t) is described by
where ci(t) and F(ω) are the output correlation signal and the Fourier transform of the correlation filter function f(t). Equation (3) suggests that we can control a waveform of a correlation signal ci(t) by changing a correlation filter function F(ω). For recognition of a target digital signal hi(t),we set an appropriate correlation filter function F(ω) so that a correlation signal Ci(t) becomes a single pulse whose maximum intensity is higher than those of nontarget ones from other modules. The obtained single pulse can be promptly fed to an output port as an analog signal through adequate intensity adjustment. In general, the simplest correlation filter F(ω) for recognition of a target pulse pattern is a matched filter. However, because the maximum intensities of correlation signals of some nontarget patterns are close to that of a target one by a matched filter, we cannot output a single pulse from only a desired module. Thus, in this scheme, the capability of the correlation filter F(ω) is the most important issue to obtain a single pulse from only a desired module. To solve this issue, the design technique of multiple object discriminant filter (MODF) is one promising method[11]. To design the correlation filter F(ω), we use a design technique of MODF with a simulated annealing (SA) algorithm [12], which is an iterative algorithm for solving optimization problems. The effect of MODF is very remarkable except time lag signals that have the same pulse pattern as that of a target digital signal. However, concerning time lag signals, an optical time gate can easily eliminate undesirable outputs. Thus, if we prepare 2N - 1 D/A conversion modules, all N-bit digital signals can be converted to corresponding analog signals using pulse pattern recognition based on correlation processing.
Fig. 2. Simulation result of the maximum intensity of a correlation signal of each four-bit digital signal in case of using the designed correlation filter and the matched filter to recognize a digital signal [0001].
Fig. 3. Simulation result of the maximum intensity ratio of a correlation signal of a target digital signal to those of nontarget digital signals in case of each target digital signal.
To confirm that a designed filter can output a single pulse as a result of correlation processing, we design the correlation filter F(ω) and simulate the correlation process between a digital signal and a designed correlation filter function. In this simulation, we set four-bit digital signals except time-lag digital signals as input digital signals. Figure 2 shows the simulation result of the maximum intensity of a correlation signal of each four-bit digital signal in case of using the designed correlation filter and the matched filter to recognize a digital signal [0001]. Figure. 3 shows the simulation result of the maximum intensity ratio of a correlation signal of a target digital signal to those of nontarget ones in case of each target digital signal. From these results, we can say that it is possible to output a single pulse from a target digital signal with a high peak power using the designed correlation filter.
3. Experiment and result
To demonstrate the proposed all-optical D/A conversion, we executed preliminary experiments. Figure 4 shows the experimental setup of the proposed all-optical D/A conversion. An experimental setup is composed of two parts; digital signal generation and D/A conversion. We used an ultra-short pulse from a femtosecond fiber laser as a light source. The pulse width, the center wavelength and the repetition rate were 300 fs, 1560 nm and 50 MHz, respectively. The ultra-short pulse was split into two pulses by the beam splitter (BS1). One was used as a source pulse for digital signal generation and the other as a reference pulse for the measurement of an output signal waveform. In a digital signal generation part, we generated a four-bit digital signal with 1.65 ps interval by adjusting the each path length of Michelson interferometers. The generated digital signal was fed to an all-optical D/A conversion part. An all-optical D/A conversion part was composed of 600 lines/mm diffraction grating, 100 mm and 200 mm focal length cylindrical lenses, a designed correlation filter and an optical ND filter. In this experiment, the designed correlation filter with phase quantized by 6 levels was fabricated by electronbeam lithography. The incident angle of the digital signal was set so that the center wavelength component could be diffracted with the angle 0 degrees. The input digital signal was dispersed into a decomposed spectral distribution using the grating (G) and the cylindrical lens (CL2) and was input to the designed correlation filter and the optical ND filter. In this experiment, we measured the temporal waveform of an output analog signal using an interferometric time-of-flight cross correlation technique [13] to confirm the operation of each D/A conversion module.
Figure 5 shows the experimental result of the maximum intensity of a correlation signal of each four-bit digital signal in case of using the designed correlation filter to recognize [0001]. Figure 6 shows the maximum intensity ratio of a correlation signal of a target digital signal to those of nontarget ones in case of each target digital signal.The intensity jitter of the correlation signal in Fig. 6 is within the range of that of the light source. Although we can successfully obtain the different maximum intensity of a correlation signal between that of a target digital signal and those of nontarget ones, the correlation signals of nontarget ones are not zero. Since, however, the lowest maximum intensity ratio of a correlation signal of a target digital signal to those of nontarget ones is 1.91:1, we can remove undesired correlation signals of nontarget digital signals using an adequate optical thresholder[14]. From these results, we can see that the fabricated designed correlation filters can recognize each target digital signal. Figure 7 (a)–(h) show the output analog signals for all four-bit digital signals except time-lag signals. Experimental result in Fig. 7 agree well with the theoretical analog value within the intensity jitter of the light source. From these results, we can see that an analog signal is output with corresponding to an input digital signal.
Fig. 4. Experimental set up of the proposed all-optical D/A conversion, G : Grating, M : Mirror, BS : Beam splitter, CL2, 5, 8 : 200 mm focal length cylindrical lens, CL1, 3, 4, 6 : 100 mm focal length cylindrical lens, CL7 : 40 mm focal length cylindrical lens, POL : Polarizer.
Fig. 5. Experimental result of the maximum intensity of a correlation signal of each four-bit digital signal in case of using the designed correlation filter to recognize a digital signal [0001].
Fig. 6. Experimental result of the maximum intensity ratio of a correlation signal of a target digital signal to those of nontarget ones in case of each target digital signal.
Fig. 7. Experimental result of the output analog signal in case of each input digital signal : (a) [0001], (b) [0011], (c) [0101], (d) [0111], (e) [1001], (f) [1011], (g) [1101], (h) [1111].
4. Conclusion
We have proposed the novel all-optical D/A conversion using pulse pattern recognition based on optical correlation processing. The capability of the D/A conversion strongly depends on that of the correlation filter for pulse pattern recognition. To obtain a single pulse from only a desired D/A conversion module, we have optimized and fabricated a correlation filter for pulse pattern recognition and demonstrated the all-optical D/A conversion. Preliminary experimental results showed that the all-optical D/A conversion could be achieved in case of four-bit digital signals with 1.65 ps interval. In this scheme, because we treat a digital signal as a pulse pattern with a uniform intensity weighting factor, we realize the signal processing without the tremendous dependence on the condition of each bit. In addition, since the proposed system can passively achieve optical signal processing without any electronic signal processing, it would be available for the realization of a seamless interconnection between optical analog and digital signals.
References and links
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