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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 18 — Sep. 1, 2008
  • pp: 13752–13757
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Coded output photonic A/D converter based on photonic crystal slow-light structures

Sunkyu Yu, Sukmo Koo, and Namkyoo Park  »View Author Affiliations


Optics Express, Vol. 16, Issue 18, pp. 13752-13757 (2008)
http://dx.doi.org/10.1364/OE.16.013752


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Abstract

A photonic analog-to-digital converter (PADC) utilizing a slow-light photonic crystal Mach-Zehnder interferometer (MZI) is proposed, to enable the optically coded output of a PADC with reduced device size and power consumption. Assuming an index modulation for the MZI on the Taylor’s PADC structure, limiting factors in device size, speed, and effective number of bits are derived considering the signal transition time of the light and the slow light dispersion effects. Details of the device design and results of a time domain assessment of the device performance is described with discussions on the feasibility of sub-mm size, 20GS/s operation of the device having the ENOB (effective number of bits) >5.

© 2008 Optical Society of America

1. Introduction

The realization of a high speed (>10GS/s) electronic analog-to-digital (A/D) converter has become a serious challenge for circuit designers. With the fundamental physical limitations associated with aperture jitter, thermal noise, and comparator ambiguity [1

1. R. H. Walden, “Analog-to-Digital Converter Survey and Analysis,” IEEE J. Sel. Areas Commun. 17, 539 (1999). [CrossRef]

], an increase in the universal measure of A/D converter performance (product of resolution and sampling rate) is near to the saturation regime. In this context, photonic means of digitizer, sampler [2

2. M. Westlund, P. A. Andrekson, H. Sunnerud, J. Hansryd, and J. Li, “High-Performance Optical-Fiber-Nonlinearity-based Optical Waveform Monitoring,” IEEE J. Lightwave Technol. 23, 2012–2022 (2005). [CrossRef]

], and A/D converters (PADC) have been a topic of intensive study as an attractive alternative for ultra-fast A/D converters. Especially for PADC, following serious research activities since early 1970s [3

3. G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15, 1955 (2007). [CrossRef] [PubMed]

, 4

4. H. F. Taylor, “An Optical Analog-to-Digital Converter-Design and Analysis,” IEEE J. Quantum Electron. 15, 210 (1979). [CrossRef]

], various principles and forms of operation have been suggested - which can be classified 1) in terms of the degree of photonic implementation; photonic sampled, photonic quantized, photonic sampled & quantized, and photonic assisted [3

3. G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15, 1955 (2007). [CrossRef] [PubMed]

], and 2) in terms of de-multiplexing means for analog signal; space, wavelength, time, and interferometric.

Of these, the interferometric PADC proposed by Taylor [4

4. H. F. Taylor, “An Optical Analog-to-Digital Converter-Design and Analysis,” IEEE J. Quantum Electron. 15, 210 (1979). [CrossRef]

] has been a structure generating most intensive follow-up studies because of its scalability (as the required number of interferometers/sources/detectors increases linearly with the ADC bits/resolutions), and compatibility with electronic interfaces (using electrical input signal and providing quantized output). As an additional attribute, Taylor’s PADC structure can be implemented with a low cost single wavelength laser source instead of a multi-wavelength source of higher functionality - which is an imperative for other competing approaches [5

5. F. X. Kärtner, R. Amatya, M. Araghchini, J. Birge, H. Byun, J. Chen, M. Dahlem, N. A. DiLello, F. Gan, C. W. Holzwarth, J. L. Hoyt, E. P. Ippen, A. Khilo, J. Kim, M. Kim, A. Motamedi, J. S. Orcutt, M. Park, M. Perrott, M. A. Popović, R. J. Ram, H. I. Smith, G. R. Zhou, S. J. Spector, T. M. Lyszczarz, M. W. Geis, D. M. Lennon, J. U. Yoon, M. E. Grein, and R. T. Schulein, “Photonic analog-to-digital conversion with electronic-photonic integrated circuits,” Proc. SPIE 6898, 689806 (2008). [CrossRef]

]. Still, with the exponential dependence of the interferometer (MZI) length to the number of bits (proportional to 2b), and correspondingly with the increase in the power consumption for the phase modulation, most of the demonstrations of Taylor’s PADC have focused on a low-bit and high sampling rate, not exceeding the effective number of bits (ENOB) of 4 (at 10GS/s) so far [3

3. G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15, 1955 (2007). [CrossRef] [PubMed]

].

In this paper, we suggest a new photonic crystal A/D converter design based on Taylor’s ADC concept. The uniqueness of our design is in the application of slow light advantages to the PADC with the introduction of photonic crystal Coupled Resonator Optical Waveguides (CROW) [6

6. J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled Resonator Optical Waveguides: toward the slowing and storage of light,” Opt. Photon. News 16, 36–40 (2005). [CrossRef]

]. By employing slow light, we obtain an efficient phase change with much shorter modulation length [7

7. M. Soljačić, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2059 (2002).

], to enable the reduction in the size/power consumption of the PADC (~ by factors of tens). To our knowledge, this is a new application of slow light, different from the traditionally proposed ones - such as interferometer [8

8. Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-Light Fourier Transform Interferometer,” Phys. Rev. Lett. 99, 240801 (2007) [CrossRef]

, 9

9. A. R. Shroff and P. M. Fauchet, “Optical Jitter and Pulse Distortion in High Bit-rate, Slow-Light Mach-Zehnder Interferometers,” OSA Slow and Fast Light topical meeting, Salt Lake City, UT, July (2007)

], buffer, delay line, or synchronizer [6

6. J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled Resonator Optical Waveguides: toward the slowing and storage of light,” Opt. Photon. News 16, 36–40 (2005). [CrossRef]

, 10

10. E. Parra and J. R. Lowell, “Toward Applications of Slow Light Technology,” Opt. Photon. News 18, 40 (2007). [CrossRef]

]. For investigating the properties of the suggested photonic crystal slow-light PADC, we analyze the performance limiting factors in terms of light transit time in the modulation region, as well as the pulse broadening effect (differential time delay) from the slow-light dispersion. Results show the feasibility of achieving a PADC with 20 giga-samplings per second (GS/s) and an ENOB of more than 5, under a silicon platform.

2. Principle/theoretical analysis

Figure 1 illustrates a schematic diagram of Taylor’s PADC [4

4. H. F. Taylor, “An Optical Analog-to-Digital Converter-Design and Analysis,” IEEE J. Quantum Electron. 15, 210 (1979). [CrossRef]

]. For each MZI, the necessary modulation region increases by a factor of 2 from the most significant bits. Optical outputs thus having a different period - as a function of the applied bias voltage strength (i.e, analog signal) - can be obtained from the output ports of different MZIs dedicated for each different bits, for the following conversion to a digitized gray coded output (with appropriate threshold/switch elements [11

11. R. A. Becker, C. E. Woodward, F. J. Leonberger, and R. C. Williamson, “Wide-band electrooptic guided-wave analog-to-digital converters,” Proc. IEEE 72, 802–819 (1984). [CrossRef]

]). Worth to note, by adjusting the amount of modulation to the MZI, it is also possible to get conventional binary output [4

4. H. F. Taylor, “An Optical Analog-to-Digital Converter-Design and Analysis,” IEEE J. Quantum Electron. 15, 210 (1979). [CrossRef]

]. For later use, we write the relationship between the resolution (b) of the Taylor’s PADC, and the required phase change (LLSB Δk, LLSB being the length of the modulation region for the least significant bit: LSB, Δk being the differential of wave vector from the waveguide index change) in the LSB-MZI;

LLSBΔk=2b1π.
(1)
Fig. 1. Schematics of Taylor’s PADC [3] and its output (for a 3-bit A/D converter. red line: decision threshold for the digital conversion). Bottom: slow-light implementation of 2×2 MZI.

Meanwhile, assuming the simultaneous application of an analog signal to the entire electrode, the net phase change felt by the optical signal is not given by the instantaneous strength of the analog signal, but is rather replaced by its averaged value over the transit time Tm (light signal propagation time in the modulated region Lm of the m-bit MZI) [12

12. F. J. Leonberger, C. E. Woodward, and D. L. Spears, “Design and development of a high-speed electrooptic A/D converter,” IEEE Trans. Circuits and Sys. 26, 1125–1131 (1979). [CrossRef]

]. Different lengths of Lm and Tm for different bits of MZI thus lead to a non-uniform response to the input analog signal for its output. These non-uniform responses for different bits, thus impose a limitation on the maximum signal bandwidth guaranteed for error-free operation of the ADC. Writing Tb as the transit time of light for the LSB MZI, where b the resolution of the PADC, we now can re-write the maximum signal bandwidth fs of the PADC [12

12. F. J. Leonberger, C. E. Woodward, and D. L. Spears, “Design and development of a high-speed electrooptic A/D converter,” IEEE Trans. Circuits and Sys. 26, 1125–1131 (1979). [CrossRef]

] as a function of the index change ratio ρ=(Δn/n), for future reference purpose,

fs<22b2π·Tb=22b2·υgπ·LLSB=2432bπσρ·f0
(2)

by using Tb=LLSB/υg, υg=Δω/Δk, LLSB=2b-1 π /Δk (Eq. (1), and (Δω/ω0)=σ (Δn/n)=σρ - here, σ is the fraction of mode energy stored in the modulated region [7

7. M. Soljačić, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2059 (2002).

], n is the refractive index of the dielectric and f0 is the frequency of the light source. Assuming a reasonable number of 1% refractive index modulation for λ 0=1550nm and σ=0.6, the PADC bandwidth becomes limited by the light propagation time Tb: to 11.5GHz at 6-bit resolution and to 1.44GHz at 8-bit resolution.

For the device size of PADC employing CROW, we now work on rewriting Eq. (1). Utilizing the dispersion relation of light in the CROW: ω(k)=ω 0(1+κcos(k·Λ)) and υg=/dk=κω 0Λsin(k·Λ) [6

6. J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled Resonator Optical Waveguides: toward the slowing and storage of light,” Opt. Photon. News 16, 36–40 (2005). [CrossRef]

] (κ the coupling coefficient; and ω 0 the resonant frequency of the CROW cavity). Equation (1) becomes (assuming the frequency of the signal light ~ ω 0)

LLSB=υgΔω2b1π2b1πκσρ,
(3)

which is plotted in Fig. 2(a). Can be seen, for the size reduction of Taylor’s PADC based on the CROW structure (determined by the modulation length required for the LSB MZI, the longest one) it is suggested to use the smallest κ available. However, understanding that a smaller coupling coefficient in the CROW results in a narrower bandwidth [6

6. J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled Resonator Optical Waveguides: toward the slowing and storage of light,” Opt. Photon. News 16, 36–40 (2005). [CrossRef]

], we naturally expect a limitation in the smallest κ accessible for the reasonable operation of the PADC.

ΔTm=dTmdωΔω=ddω(Lmυg)Δω
=LLSB·Δω2m1d(1υg)=2bm·π1υg2υgk=2bm1κf0cos(kΛ)sin2(kΛ).
(4)

Now noting that π/2 near the center of the CROW band and writing =π/2+ΔkΛ, where ΔkΛ≪1, Eq. (4) then can be approximated, with Δk=Δω/υg, as

ΔTm2bm1κf0·ΔkΛ=2bm1σρκ2f0sin(kΛ)2bm1σρκ2f0.
(5)

Treating the effect of the signal transit time (Eq. (2)) as the bit-dependent attenuation to the input sinusoid signal [12

12. F. J. Leonberger, C. E. Woodward, and D. L. Spears, “Design and development of a high-speed electrooptic A/D converter,” IEEE Trans. Circuits and Sys. 26, 1125–1131 (1979). [CrossRef]

] and then applying the differential delays (Eq. (5)) from the CROW dispersion considerations, we can now estimate the error in the ENOB (effective number of bits, the actual resolution one can derive from the ADC, contaminated with various noises) that originated from the introduction of CROW structure to Taylor’s PADC platform. Applying a fast Fourier transform to the digitized output of the CROW PADC (with transit time and dispersion effects), and then calculating the signal-to-noise and distortion ratio (SINAD), we show the calculated ENOB=(SINAD-1.76)/6.02 [1

1. R. H. Walden, “Analog-to-Digital Converter Survey and Analysis,” IEEE J. Sel. Areas Commun. 17, 539 (1999). [CrossRef]

, 3

3. G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15, 1955 (2007). [CrossRef] [PubMed]

], in Fig. 2(b).

Fig. 2. (a). Device length and (b) ENOB of the PADC plotted for different coupling coefficients, at various target resolutions. (1550nm, σ=0.6, ρ=1.0%, and Λ=2µm).

Can be seen, the reduction of the ENOB with smaller values of κ is evident implying the performance-size tradeoff for Taylor’s PADC, resulting from CROW bandwidth restrictions. For example, changing the κ from 0.02 to 0.005, it is possible to reduce the device size/power consumption by a factor of ~4, but only at the accompanied expense of an ENOB reduction of ~2 (for 10GHz, with 1 % index modulation). We also note that, there exists a maximum bound in the ENOB, dictated from the flight-time considerations only (without CROW, Eq. (2) - 5 bits for 10GHz (or 20GS/s) and 2 bits for 200GHz (or 400GS/s).

3. Results/discussion

Without loss of generality, two-dimensional square dielectric rod photonic crystal (PC) has been used as the basic platform, for the study of a slow-light PADC under Taylor’s principle. Dielectric rod of radius r=0.20a, with a lattice constant of a=550nm, and an effective refractive index neff (Si) of 3.23 were adopted. For the construction of the CROW, the dispersion relation (Fig. 3(a)) was calculated using the PWEM (Plane Wave Expansion Method). The radius of the defect in the CROW cavity was set at r=0.08a with a defect period of 3a, to provide a coupling coefficient κ of 0.0142 - considering restrictions both in the ENOB (related to differential time delay) and device size. Worth to mention, care has been taken in the wideband design of the 3dB directional splitter (Fig. 3(b)) [14

14. M. Koshiba, “Wavelength Division Multiplexing and Demultiplexing with Photonic Crystal Waveguide Couplers,” IEEE J. Lightwave Technol. 19, 1970–1975 (2001). [CrossRef]

] and the CROW-PC waveguide adapter (Fig. 3(c)). For the CROW-PC waveguide adapter, coupled mode theory (CMT) has been applied [15

15. U. Peschel, A. L. Reynolds, B. Arredondo, F. Lederer, P. J. Roberts, T. F. Krauss, and P. J. I. de Maagt, “Transmission and reflection analysis of functional coupled cavity components,” IEEE J. Quantum Electron. 38, 830–836 (2002). [CrossRef]

] to give a coupling efficiency > 95%.

Fig. 3. (a). CROW dispersion relation of the achieved design. (b) 3dB splitter (red rods tuned to r=0.18a) (c) CROW-PC waveguide adapter (purple and red rods tuned to r=0.22a and 0.15a).

With the large problem size extending to more than 100µm (=LLSB for a 3bit PADC), 2D FDTD analysis [16

16. A. Taflove and S. C. Hagness, Computational Electromagnetics: The Finite-Difference Time-Domain Method, (Boston, Artech House, 2000) 852.

] was carried out employing an effective index method [17

17. L. Yang, J. Motohisa, and T. Fukui, “Suggested procedure for the use of the effective-index method for high-index-contrast photonic crystal slabs,” Opt. Eng. 44, 078002 (2005). [CrossRef]

]. Push-pull index modulation (+/- 0.496%) was used to drive the MZI assuming a DC bias to both arms of the modulator, with the signal frequency set at the CROW center frequency f=0.3543(c/a). Figure 4 shows the operation of the 3-bit PADC (having different modulation lengths for each MZI), for a linearly increasing (within t=6.88ps~27.5ps) analog input signal. To note, outputs of each MZI can be digitized by setting decision thresholds, to produce coded output. For the current example, the threshold was set at 43% of the normalized LSB peak power.

Fig. 4. Demonstration of a 3-bit CROW PADC under a linear refractive index modulation (Media 1). The green and yellow regions show the modulation region (push-pull with different sign) of each MZI. For the figures on the right, the red dashed lines show the decision threshold.

Confirming the basic operation, now further to analyze the PADC operations at an ultra-high sampling rate, high-frequency (100 ~350GHz) sinusoidal analog signal has been tested to get the ENOB values at corresponding frequencies - following the procedures detailed earlier in this section. Figure 5(a) shows the 100GHz analog input signal overlaid on the digitized output. Also shown in Fig. 5(b) is the obtained ENOB of the 3-bit PADC structure (simulation bit limited by the computational capacity) plotted together with the theoretical ENOB values derived in Section 2. With the selection of a reasonable value for κ (0.0142), the differential time delay penalty from the CROW dispersion was minimized, leaving the signal transit time as the dominant source of error in the ENOB of the CROW PADC operation. Worth to mention, to counter the signal transit time and thus to get a higher ENOB (>3) for the PADC at these operation speed (>100GHz), a traveling-wave MZI with longer modulation length can be considered, possibly using Kerr nonlinearity, and co-propagating control optical analog signals.

Finally critical to mention, for the current study assuming electrical modulation, a realistic modulation speed and the material aspects of dielectrics need to be counted. For modulating the index of silicon with an electrical signal, a plasma dispersion effect (with a response time up to 20GHz) can be used [18

18. F. Gan and F. X. Kartner, “High-Speed Silicon Electrooptic Modulator Design,” IEEE Photon. Technol. Lett. 17, 1007–1009 (2005). [CrossRef]

, 19

19. A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007). [CrossRef] [PubMed]

]. Assuming 1% of the index change ratio ρ in air-hole type Silicon PC structures, ENOB=5 for the PADC operation was estimated at a 20GS/s sampling speed (from Fig. 2(a), with 10GHz analog signal, with κ=0.02 and at resolution b=6, σ=0.6, and Λ=2εm), giving the length of longest MZI smaller than 700µm.

Fig. 5. (a). Plot of the digitized output (black, magenta) from a 3-bit CROW PADC compared with its analog sinusoid input signal (yellow: 100GHz, cyan: 350GHz). (b) ENOB of the 3-bit PADC at different frequencies of analog input signals. The ENOB from the FDTD simulation (black) is compared to the ENOB values calculated from theory (in Section 2)

4. Conclusion

We proposed and analyzed a new and unique photonic A/D converter design using slow-light photonic crystal structures. Theoretical analysis on the performance limitation has been developed/and carried out considering both the signal transit time and CROW dispersion effect, to point out the trade-off in device size and penalties in the ENOB, associated with the differential time delay (from the CROW dispersion). Numerical assessment of the device performance shows the feasibility of a slow-light PADC with a reduced device size (up to a factor of 10 (~υg/c, when compared to those MZI employing a conventional waveguide) and higher ENOB/speed of operations (ENOB=5, 20GS/s for a silicon platform using a plasma dispersion effect).

Acknowledgment

This work is supported by the Samsung Advanced Institute of Technology and in part by Korea Science and Engineering Foundation (KOSEF, grant No. R01-2007-000-21036-0).

References and links

1.

R. H. Walden, “Analog-to-Digital Converter Survey and Analysis,” IEEE J. Sel. Areas Commun. 17, 539 (1999). [CrossRef]

2.

M. Westlund, P. A. Andrekson, H. Sunnerud, J. Hansryd, and J. Li, “High-Performance Optical-Fiber-Nonlinearity-based Optical Waveform Monitoring,” IEEE J. Lightwave Technol. 23, 2012–2022 (2005). [CrossRef]

3.

G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15, 1955 (2007). [CrossRef] [PubMed]

4.

H. F. Taylor, “An Optical Analog-to-Digital Converter-Design and Analysis,” IEEE J. Quantum Electron. 15, 210 (1979). [CrossRef]

5.

F. X. Kärtner, R. Amatya, M. Araghchini, J. Birge, H. Byun, J. Chen, M. Dahlem, N. A. DiLello, F. Gan, C. W. Holzwarth, J. L. Hoyt, E. P. Ippen, A. Khilo, J. Kim, M. Kim, A. Motamedi, J. S. Orcutt, M. Park, M. Perrott, M. A. Popović, R. J. Ram, H. I. Smith, G. R. Zhou, S. J. Spector, T. M. Lyszczarz, M. W. Geis, D. M. Lennon, J. U. Yoon, M. E. Grein, and R. T. Schulein, “Photonic analog-to-digital conversion with electronic-photonic integrated circuits,” Proc. SPIE 6898, 689806 (2008). [CrossRef]

6.

J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled Resonator Optical Waveguides: toward the slowing and storage of light,” Opt. Photon. News 16, 36–40 (2005). [CrossRef]

7.

M. Soljačić, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2059 (2002).

8.

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-Light Fourier Transform Interferometer,” Phys. Rev. Lett. 99, 240801 (2007) [CrossRef]

9.

A. R. Shroff and P. M. Fauchet, “Optical Jitter and Pulse Distortion in High Bit-rate, Slow-Light Mach-Zehnder Interferometers,” OSA Slow and Fast Light topical meeting, Salt Lake City, UT, July (2007)

10.

E. Parra and J. R. Lowell, “Toward Applications of Slow Light Technology,” Opt. Photon. News 18, 40 (2007). [CrossRef]

11.

R. A. Becker, C. E. Woodward, F. J. Leonberger, and R. C. Williamson, “Wide-band electrooptic guided-wave analog-to-digital converters,” Proc. IEEE 72, 802–819 (1984). [CrossRef]

12.

F. J. Leonberger, C. E. Woodward, and D. L. Spears, “Design and development of a high-speed electrooptic A/D converter,” IEEE Trans. Circuits and Sys. 26, 1125–1131 (1979). [CrossRef]

13.

Y.-H. Ye, J. Ding, D. Y. Jeong, I. C. Khoo, and Q. M. Zhang, “Finite-size effect on one-dimensional coupled-resonator optical waveguides,” Phys. Rev. E 69, 056604 (2004)

14.

M. Koshiba, “Wavelength Division Multiplexing and Demultiplexing with Photonic Crystal Waveguide Couplers,” IEEE J. Lightwave Technol. 19, 1970–1975 (2001). [CrossRef]

15.

U. Peschel, A. L. Reynolds, B. Arredondo, F. Lederer, P. J. Roberts, T. F. Krauss, and P. J. I. de Maagt, “Transmission and reflection analysis of functional coupled cavity components,” IEEE J. Quantum Electron. 38, 830–836 (2002). [CrossRef]

16.

A. Taflove and S. C. Hagness, Computational Electromagnetics: The Finite-Difference Time-Domain Method, (Boston, Artech House, 2000) 852.

17.

L. Yang, J. Motohisa, and T. Fukui, “Suggested procedure for the use of the effective-index method for high-index-contrast photonic crystal slabs,” Opt. Eng. 44, 078002 (2005). [CrossRef]

18.

F. Gan and F. X. Kartner, “High-Speed Silicon Electrooptic Modulator Design,” IEEE Photon. Technol. Lett. 17, 1007–1009 (2005). [CrossRef]

19.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007). [CrossRef] [PubMed]

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(200.4740) Optics in computing : Optical processing
(230.4555) Optical devices : Coupled resonators
(050.5298) Diffraction and gratings : Photonic crystals
(250.4110) Optoelectronics : Modulators

ToC Category:
Integrated Optics

History
Original Manuscript: June 24, 2008
Revised Manuscript: August 10, 2008
Manuscript Accepted: August 10, 2008
Published: August 21, 2008

Citation
Sunkyu Yu, Sukmo Koo, and Namkyoo Park, "Coded output photonic A/D converter based on photonic crystal slow-light structures," Opt. Express 16, 13752-13757 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-18-13752


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References

  1. R. H. Walden, “Analog-to-Digital Converter Survey and Analysis,” IEEE J. Sel. Areas Commun. 17, 539 (1999). [CrossRef]
  2. M. Westlund, P. A. Andrekson, H. Sunnerud, J. Hansryd, J. Li, “High-Performance Optical-Fiber-Nonlinearity-based Optical Waveform Monitoring,” IEEE J. Lightwave Technol. 23, 2012–2022 (2005). [CrossRef]
  3. G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15, 1955 (2007). [CrossRef] [PubMed]
  4. H. F. Taylor, “An Optical Analog-to-Digital Converter-Design and Analysis,” IEEE J. Quantum Electron. 15, 210 (1979). [CrossRef]
  5. F. X. Kärtner, R. Amatya, M. Araghchini, J. Birge, H. Byun, J. Chen, M. Dahlem, N. A. DiLello, F. Gan, C. W. Holzwarth, J. L. Hoyt, E. P. Ippen, A. Khilo, J. Kim, M. Kim, A. Motamedi, J. S. Orcutt, M. Park, M. Perrott, M. A. Popović, R. J. Ram, H. I. Smith, G. R. Zhou, S. J. Spector, T. M. Lyszczarz, M. W. Geis, D. M. Lennon, J. U. Yoon, M. E. Grein, R. T. Schulein, “Photonic analog-to-digital conversion with electronic-photonic integrated circuits,” Proc. SPIE 6898, 689806 (2008). [CrossRef]
  6. J. Scheuer, G. T. Paloczi, J. K. S. Poon, A. Yariv, “Coupled Resonator Optical Waveguides: toward the slowing and storage of light,” Opt. Photon. News 16, 36–40 (2005). [CrossRef]
  7. M. Soljačić, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2059 (2002).
  8. Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, J. C. Howell, “Slow-Light Fourier Transform Interferometer,” Phys. Rev. Lett. 99, 240801 (2007) [CrossRef]
  9. A. R. Shroff, P. M. Fauchet, “Optical Jitter and Pulse Distortion in High Bit-rate, Slow-Light Mach-Zehnder Interferometers,” OSA Slow and Fast Light topical meeting, Salt Lake City, UT, July (2007)
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