40GS/s Optical analog-to-digital conversion system and its improvement

doi:10.1364/OE.17.009252

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40GS/s Optical analog-to-digital conversion system and its improvement

Qingwei Wu, Hongming Zhang, Yue Peng, Xin Fu, and Minyu Yao »View Author Affiliations

Optics Express, Vol. 17, Issue 11, pp. 9252-9257 (2009)
http://dx.doi.org/10.1364/OE.17.009252

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▸ Article Outline
– Abstract
1. Introduction
2. Principle of operation
3. Experiment results
4. Improvement of our optical ADC system
4. Conclusion
– References and links

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Abstract

An optical analog-to-digital conversion system is proposed and demonstrated. Using time- and wavelength- interleaved optical sampling pulse train; sampling rate of 40GS/s is realized. 2.5GHz sinusoidal electrical analog signal is sampled and quantized using this system, achieving an effective number of bits of 3.45 bits. A novel technology that can dramatically improve the bandwidth of this system will also be presented in this paper, which manifests that our system can realized high bandwidth of more than 50GHz using commercially available LiNbO₃ phase modulator.

1. Introduction

Digital signal processing (DSP) technology is evolving very fast, and has been driving lots of applications with extreme bandwidth requirement. However, as the key interface between the analog signals and digital ones, due to the timing issue and device technology, the electrical analog-to-digital converter (ADC) is developing relatively rather slowly [1

R. H. Walden, “Analog-to-digital converter survey and analysis,” J. Sel. Areas Commun. 17(4), 539–550 (1999). [CrossRef]

]. Due to the ultra-short and ultra-stable optical sampling pulses, the potential of using optical technology in ADC has attracted researchers’ interest for many years [2

G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15(5), 1955–1982 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-5-1955. [CrossRef] [PubMed]

–8

W. Li, H. Zhang, Q. Wu, Z. Zhang, and M. Yao, “All-optical analog-to-digital conversion based on polarization-differential interference and phase modulation,” Photon. Technol. Lett. 19(8), 625–627 (2007). [CrossRef]

In 2005, an interferometric ADC scheme was proposed [7

J. Stigwall and S. Galt, “Interferometric analog-to-digital conversion scheme,” Photon. Technol. Lett. 17(2), 468–470 (2005). [CrossRef]

], and one improvement of it was illustrated in [8

]. Using only one phase modulator, both schemes are much simpler than the famous Taylor’s scheme [3

H. Taylor, “An optical analog-to-digital converter-Design and analysis,” J. Quantum Electron. 15(4), 210–216 (1979). [CrossRef]

]. The key issue in both interferometric ADC approaches is to realize the desired phase shift between the transmission characteristics of each two adjacent channels in order to achieve optical quantization. It is realized through free-space adjustment in [7

J. Stigwall and S. Galt, “Interferometric analog-to-digital conversion scheme,” Photon. Technol. Lett. 17(2), 468–470 (2005). [CrossRef]

] and fiber stretching in [8

]. In this paper, we will propose another approach to achieve this desired phase shift, utilizing electronically controlled fiber squeezer. Compared with both [7

J. Stigwall and S. Galt, “Interferometric analog-to-digital conversion scheme,” Photon. Technol. Lett. 17(2), 468–470 (2005). [CrossRef]

] and [8

], the desired phase shift will be much easier to be realized and controlled. 40GS/s optical ADC system using this proposed approach will be implemented. 2.5GHz sinusoidal electrical analog signal will be sampled and quantized, achieving an effective number of bits (ENOB) of 3.45 bits. We will also present a novel pre-compensation technology that can improve the bandwidth of our system considerably.

2. Principle of operation

Figure 1(a) is the illustration of polarization interference, as described in [8

]. Through adjusting the polarization controller (PC), there will be two polarization states along x and z axes with the same amplitude in the phase modulator. The phase difference between these two polarization states will be linearly changed with the voltage of electrical analog signal. Using an in-line analyzer at the output of the phase modulator, and adjusting its axis at 45° to both x and z axes, polarization interference will be realized. And a sinusoidal interferometric transmission characteristic will be obtained, the phase of which is determined by the original phase difference between these two polarization states without phase modulation.

Fig. 1 (a). Illustration of polarization interference and (b) A segment of fiber submitted to a literal force per unit length f.

Dividing the output of the phase modulator with a 1 × N polarization maintaining optical coupler into N channels before polarization interference happens, and then each channel passes through a fiber squeezer. As shown in Fig. 1(b), when single-mode fiber (SMF) is submitted to a lateral force per unit length f, it will induce birefringence between two polarization states, shown as follows [9

T. Ōkoshi, Optical Fibers (Academic, New York, 1982).

B_{f} = 3.63 \times 10^{- 12} \frac{f}{A} .

(1)

where A is the radius of the fiber. This induced birefringence means extra phase difference between these two polarization states after travelling through certain length of fiber. Piezoelectric ceramics are used to squeeze the N-channel fibers. Different driving voltage will induce different birefringence, as a result of which, different phase differences between two polarizations will be obtained, which will determine the phase shift of each channel. Figure 2(a) shows the measured relation between the phase differences and applied voltages of a homemade fiber squeezer. Figure 2(b) illustrates the relation between the voltage accuracy and the ENOB, from which we can see that when the theoretic resolution is lower than 6 bits, the requirement of the voltage accuracy is tens of mV, which can be easily realized using nowadays stable electronic voltage source. And because of the very good rigidity of the piezoelectric ceramics, the phase shift can be very stable. And using some feedback techniques, the phase shift stability can be further improved.

Fig. 2 (a). Phase difference vs. applied voltage (b) ENOB vs. voltage accuracy.

Through adjusting the voltage applied on each fiber squeezer, the ith channel can induce an extra phase difference of i × π/N (i = 1,2,…,N) between these two polarization states. After polarization interference, the transmission characteristics of each two adjacent channels will have a phase shift of π/N. Four-channel transmission characteristics are illustrated in Fig. 3 . The phase shift between each two adjacent channels is π/4. From this figure, we can see that, using these 4 channels and setting half of the maximum output as the threshold, 8 quantization levels can be realized to the voltage span of 2V _π (V _π is the half wave voltage the phase modulator). If there are N channels, and the phase shift between each two adjacent channels is π/N, 2N quantized levels can be realized, corresponding a theoretic resolution of log₂(2N).

Fig. 3 Transmission characteristics of four channels with a phase shift of π/4.

Figure 4 shows our presented 40GS/s optical ADC system. Time- and wavelength- interleaved optical pulse train with a repetition rate of 40GHz performs as the sampling pulse source. Two polarization states with the same amplitude will exit in the phase modulator. After demultiplexing, each wavelength will be divided into 8 channels, and the optical fiber of each channel will be pressed by a fiber squeezer to induce desired extra phase difference between these two polarization states. Polarization interference will happen when the pulses pass through the in-line analyzer array. A polarization beam splitter can perform as an in-line analyzer. The sampled pulses will then be detected and digitized into digital values using electric comparators. And the processing unit will convert the quantization codes shown in Fig. 3 into normally used binary output. Each wavelength channel will be a 10GS/s and 4-bit optical ADC. And combining the time-interleaved four wavelengths, sampling rate of 40GS/s can be achieved, with a resolution of 4 bits. If more channels are phase shifted, high resolution can be obtained.

Fig. 4 Schematic illustration of the presented 40GS/s optical ADC system

3. Experiment results

3.1 Time- and wavelength- interleaved 40GS/s sampling pulse source

Figure 5 illustrates the experiment setup of the time- and wavelength- interleaved optical sampling pulse source and the measured waveform at each stage. Four continuous wave light sources are modulated by an electro-absorption modulator (EAM: CIP 10G-PS-EAM-1550- Optical Sampling Window Generator), generating pulses with a repetition rate of 10GHz and full width of half maximum (FWHM) of 20ps. After appropriate phase modulation and passing through SMF with specifically designed length, FWHM of the pulses will be compressed to 15ps, and at the same, time interval of 25ps between two adjacent wavelengths is realized due to the dispersion effect of the SMF. As shown at the right bottom of this figure, waveforms of compressed pulses of four different wavelengths are recorded and superimposed together. The time domain waveform of the multiplexed 40GS/s pulses is also shown at the right bottom of this figure. Timing jitter of this pulse source is 300fs, and its amplitude fluctuation is 2%.

Fig. 5 Experiment setup of sampling pulse source and measured waveforms at each stage.

If the optical pulses are further compressed using some other technologies, or we use narrower multi-wavelength pulse source, and there are more wavelengths, much higher sampling rate can be achieved using the time- and wavelength- interleaved structure.

3.2 40GS/s optical ADC system experiment

Using our presented optical ADC system in Fig. 4, 2.5GHz sinusoidal electrical analog signal is sampled and quantized. 40GS/s time- and wavelength- interleaved pulse train generated in Fig. 5 performs as the sampling pulse source. After sampling stage in the phase modulator, the pulses will be demultiplexed into four wavelength channels. Then each wavelength will be divided into 8 channels, and each channel will have a fiber squeezer, performing as the phase shifter. Through adjusting the voltages applied on all the fiber squeezers, desired π/8 phase shift between each two adjacent channels will be realized. We use the oscilloscope to record the waveforms for all the channels, and superimposed together the four waveforms of different wavelengths with the same phase shift. Figure 6 shows the recorded waveforms of the corresponding eight phase shifts, from 0 to 7π/8. Four different colors in this figure represent four different wavelengths of the sampling pulse source.

Fig. 6 Measured waveforms of 40GS/s pulses for different phase shifts.

Setting half of the maximum output as the threshold, the quantization codes and 20 corresponding digitized values can be obtained using software digitization. These digitized values are shown as the dots in Fig. 7 . Only 20 digitized values are not enough to analyze their spectrum. In order to evaluate the performance of this ADC, a “Sine-wave Curve Fitting” method can be utilized [10

J. Michael, Demler, High Speed Analog-to-Digital Conversion (Academic, San Diego, 1991).

]; and a corresponding fitting sine-wave curve can be developed, shown as the solid line in Fig. 7. After calculation, we obtain a signal-to-noise ratio (SNR) of 22.53dB, corresponding to an ENOB of 3.45 bits. It should be noted that, to fully analyze the performance of this ADC, real-time digitizing and spectrum measurement should be carried out, which is now in progress in our research project.

Fig. 7 Digitized values (dots) and corresponding fitting sine-curve wave (solid line).

4. Improvement of our optical ADC system

Ultra-short and ultra-stable optical sampling pulses can be obtained. As a result, the sampling pulse source is not the biggest factor that can influence the bandwidth of this system. And nowadays, bandwidth of the commercially available LiNbO₃ modulator can be as high as 50GHz. Through some special technology, this bandwidth can exceed 100GHz [11

J. Li and S. He, “Broadband optical modulator of fiber type,” Opt. Express 13(3), 842–846 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-842. [CrossRef] [PubMed]

]. Furthermore, the electro-optic polymer modulator can have a high bandwidth of 150-200GHz [12

M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee, “Broadband modulation of light by using an electro-optic polymer,” Science 298(5597), 1401–1403 (2002). [CrossRef] [PubMed]

Another factor that will significantly influence the bandwidth of our presented ADC is the possible walk-off between two polarization states in the phase modulator. When there are two polarization states in the phase modulator, the electrical analog signal will modulate both of them with different modulation efficiencies. If there is some walk-off between these two polarization states, their sampled voltages will be different. We only consider the walk-off in the effective electro-optic interaction range, which is the region of the electrode. Assumed that there is no walk-off when the optical pulses enter the electrode region, as shown in Fig. 8(a) , and taking into account the different modulation efficiencies of two polarization states, then the effective sampled voltage differences after pulses travelling through this region will be:

Fig. 8 Walk-off and its influence without (a) and with (b) pre-compensation.

Δ V = [\frac{1}{Δ T} \int_{t_{i}}^{t_{i} + Δ T} A \sin (ω t) d t - A \sin (ω t_{i})] \times \frac{α}{1 - α}

(2)

where ΔT is the walk-off introduced in the electrode region (length: ΔL), and α is relative the modulation efficiency of x polarization compared with that of z polarization, which is between 0.25 and 0.33. This voltage difference must be smaller than Q/2 (Q is the smallest quantizing step size). When ΔL = 1cm and α = 0.3, the bandwidth limit of our present system for different resolutions is shown in Fig. 9 (solid line), which manifests that, when the resolution is 5 bits, its upper bond of bandwidth is only 4.67GHz.

Fig. 9 Bandwidth limit without (solid line) and with (dashed line) pre-compensation.

However, if there is already a walk-off of ΔT/2 when the two polarization states enter into the electrode region and the slower pulses must enter prior to the faster ones. We call this as pre-compensation technology, and it is shown in Fig. 8(b). The effective sampled voltage difference will then be:

Δ V = [\frac{1}{Δ T} \int_{t_{i} - Δ T / 2}^{t_{i} + Δ T / 2} A \sin (ω t) d t - A \sin (ω t_{i})] \times \frac{α}{1 - α}

(3)

And now, under the same condition, the bandwidth limit of this system will be Fig. 9(dashed line). When the resolution is 5 bits, upper bond of the bandwidth can be as high as 60GHz, which is much higher than the bandwidth without pre-compensation. In our 40GS/s optical ADC system, pre-compensation is realized by adding a specific length of polarization maintaining fiber (PMF) before the phase modulator, and the PMF’s slow and fast axes are opposite to those of the phase modulator. With pre-compensation, the upper bond bandwidth of our presented system using commercial LiNbO₃ modulator can be dramatically improved to more than 50GHz.

4. Conclusion

In conclusion, we have presented a new proposal of 40GS/s optical ADC system. Time- and wavelength- interleaved optical pulse train with repetition rate of 40GHz performs as the sampling pulse source. Using narrower optical pulses and more wavelengths, our system has the feasibility of realizing a much higher sampling rate. The phase shift between two adjacent channels needed for optical quantization is achieved by an electronically controlled fiber squeezer. Compared with formally proposed approaches, it is more stable, and much easier to be realized and controlled. We have also proposed a novel pre-compensation technology, which can dramatically extend the bandwidth of our system to more than 50GHz.

This work was supported by the National High Technology Research and Development Program of China (2007AA01Z271).

References and links

1.	R. H. Walden, “Analog-to-digital converter survey and analysis,” J. Sel. Areas Commun. 17(4), 539–550 (1999). [CrossRef]
2.	G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15(5), 1955–1982 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-5-1955. [CrossRef] [PubMed]
3.	H. Taylor, “An optical analog-to-digital converter-Design and analysis,” J. Quantum Electron. 15(4), 210–216 (1979). [CrossRef]
4.	A. Yariv and R. G. M. P. Koumans, “Time interleaved optical sampling for ultra-high speed A/D conversion,” Electron. Lett. 34(21), 2012–2013 (1998). [CrossRef]
5.	P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” Trans. Microw. Theroy Tech. 49(10), 1840–1853 (2001). [CrossRef]
6.	H. Chi and J. Yao, “A photonic analog-to-digital conversion scheme using Mach-Zehnder modulators with identical half-wave voltages,” Opt. Express 16(2), 567–572 (2008). [CrossRef] [PubMed]
7.	J. Stigwall and S. Galt, “Interferometric analog-to-digital conversion scheme,” Photon. Technol. Lett. 17(2), 468–470 (2005). [CrossRef]
8.	W. Li, H. Zhang, Q. Wu, Z. Zhang, and M. Yao, “All-optical analog-to-digital conversion based on polarization-differential interference and phase modulation,” Photon. Technol. Lett. 19(8), 625–627 (2007). [CrossRef]
9.	T. Ōkoshi, Optical Fibers (Academic, New York, 1982).
10.	J. Michael, Demler, High Speed Analog-to-Digital Conversion (Academic, San Diego, 1991).
11.	J. Li and S. He, “Broadband optical modulator of fiber type,” Opt. Express 13(3), 842–846 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-842. [CrossRef] [PubMed]
12.	M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee, “Broadband modulation of light by using an electro-optic polymer,” Science 298(5597), 1401–1403 (2002). [CrossRef] [PubMed]

OCIS Codes
(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems
(200.4560) Optics in computing : Optical data processing
(230.0250) Optical devices : Optoelectronics

ToC Category:
Optical Devices

History
Original Manuscript: March 23, 2009
Revised Manuscript: April 26, 2009
Manuscript Accepted: May 9, 2009
Published: May 18, 2009

Citation
Qingwei Wu, Hongming Zhang, Yue Peng, Xin Fu, and Minyu Yao, "40GS/s Optical analog-to-digital conversion system and its improvement," Opt. Express 17, 9252-9257 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-11-9252

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References

R. H. Walden, “Analog-to-digital converter survey and analysis,” J. Sel. Areas Commun. 17(4), 539–550 (1999). [CrossRef]
G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15(5), 1955–1982 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-5-1955 . [CrossRef] [PubMed]
H. Taylor, “An optical analog-to-digital converter-Design and analysis,” J. Quantum Electron. 15(4), 210–216 (1979). [CrossRef]
A. Yariv and R. G. M. P. Koumans, “Time interleaved optical sampling for ultra-high speed A/D conversion,” Electron. Lett. 34(21), 2012–2013 (1998). [CrossRef]
P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” Trans. Microw. Theroy Tech. 49(10), 1840–1853 (2001). [CrossRef]
H. Chi and J. Yao, “A photonic analog-to-digital conversion scheme using Mach-Zehnder modulators with identical half-wave voltages,” Opt. Express 16(2), 567–572 (2008). [CrossRef] [PubMed]
J. Stigwall and S. Galt, “Interferometric analog-to-digital conversion scheme,” Photon. Technol. Lett. 17(2), 468–470 (2005). [CrossRef]
W. Li, H. Zhang, Q. Wu, Z. Zhang, and M. Yao, “All-optical analog-to-digital conversion based on polarization-differential interference and phase modulation,” Photon. Technol. Lett. 19(8), 625–627 (2007). [CrossRef]
T. ?koshi, Optical Fibers (Academic, New York, 1982).
J. Michael, Demler, High Speed Analog-to-Digital Conversion (Academic, San Diego, 1991).
J. Li and S. He, “Broadband optical modulator of fiber type,” Opt. Express 13(3), 842–846 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-842 . [CrossRef] [PubMed]
M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee, “Broadband modulation of light by using an electro-optic polymer,” Science 298(5597), 1401–1403 (2002). [CrossRef] [PubMed]

Betts, G. E.
Chi, H.
Erben, C.
Galt, S.
Gill, D. M.
Gopalan, P.
Hargreaves, J. J.
He, S.
Heber, J. D.
Juodawlkis, P. W.
Katz, H. E.
Koumans, R. G. M. P.
Lee, M.
Li, J.
Li, W.
McGee, D. J.
O’Donnell, F. J.
Ray, K. G.
Stigwall, J.
Taylor, H.
Twichell, J. C.
Valley, G. C.
Walden, R. H.
Wasserman, J. L.
Williamson, R. C.
Wu, Q.
Yao, J.
Yao, M.
Yariv, A.
Younger, R. D.
Zhang, H.
Zhang, Z.

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