ECE 468 Fall 2017 Final Paper Turbo A/D Converter Utilizing Chaotic Nature of

Acousto-Optic Light Deflector

Madhu AshokUniversity of Rochester

Department of Electrical and Computer Engineering Submitted to Zeljko Ignjatovic

With analog-to-digital converters approaching the fundamental limits of flicker, thermal noise, and jitter, optical solutions may assist in increasing the design space. This paper explores an experimental design of A/D converters using a

chaotic filter from acousto-optic deflectors of a HeNe beam.

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Introduction

This paper explores the fundamental limitations of Analog-to-Digital Converters (ADC’s), by implementing a continuous-time (CT) chaotic optical system via acousto-optic light deflection of a HeNe laser source. A chaotic optical system is used to reduce thermal noise effects by adding white noise to the input of the comparators. The goal of the design is to increase the resolution-bandwidth and operating speed while keeping the physical design complexity minimal. The tradeoff of this system will be higher complexity at the digital decoder, which is a smaller bottleneck than aperture jitter noise from current ADC conventions [1]. For simplicity, we shall refer to this system as a TurboADC, which is defined by N uniformly distributed bits at the output of its internal comparators for a given signal [2].

In order to highlight the theoretical limitations of ADCs, the following three theories must be implemented [2]:

1. Capacity Theorem – The maximum rate of information at the output of an ADC with M

comparators and a sampling rate f ¿ is given by C ADC=M∗f ¿( bitssec )

2. Existence Theorem – One such ADC can be created to operate at C ADC

3. Necessary Condition – A required condition is a white autocorrelation function of the input to the internal comparators

In order to meet these conditions, the number of comparators (M ) and sampling rate of the chaotic filter (f ¿) must be maximized.

Background

Almost every American has an analog-to-digital converter in their pocket, not to mention the millions of ADCs required in industry for every signal processing application one can think of. The process of accurately converting analog signals into the digital domain has been pushing the boundaries set by the thermal and flicker noise limits in CMOS technology [3], which leads engineers to apply complex algorithms to reduce noise while maintaining high resolution. This comes at a cost of power or complexity in design, in addition to suffering from the jitter limitations. One way to circumvent these boundaries is to use light as a medium for noise shaping before optical comparators [4]. Given a reference voltage, V Ref , the light must behave chaotically from this initial condition, while maintaining operational speeds above tens of megahertz. A consideration for this application is acousto-optic modulation [5], which was developed for optical beam steering using Raman-Nath scattering from interactions of acoustic and optical wave fronts in the Bragg diffraction (θB) regime.

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Figure 1: Given a wavelength of light ❑L incident at θi=θd=θB from a propagating acoustic wave front with wavelength, 𝛬, diffraction will occur at an angle θd for the first order [6].

A piezo-electric transducer introduces acoustic plane waves with wavelength, Λ, generated from a varying input frequency, f ¿. The relationship between the diffracted angle, θd, and the input frequency can be derived from the following relationship between the wavelengths of acoustic and optical waves in the Bragg regime:

sin (θd )=( m❑L

2 Λ ) for m=...−2 ,−1 ,0 , 1 ,2 ,… ( 1 )

The diffraction order, m, becomes -1, 0, and 1 in the Bragg regime θB≅m❑L

n Λ (where n is the

index of refraction of the medium). In the case of air, we can simplify the expression in (1) with the identity of acoustic velocity (ν): f ¿ Λ=ν

sin (θd )=(m∗f ¿∗❑L

2 ν ) ( 2 )

The small angle approximation is taken, giving a reduced expression for the deflected angle between the two beams, α=2θd:

α2=(m∗f ¿∗❑L

2ν ) ( 3 )

α=f ¿❑L

νfor m=1 ( 4 )

Deflection from this process will introduce a path length difference, which can be quantified by:

OPL=∫C

❑

n (s ) ds

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The optical path length, OPL, is dictated by the integrated sum of the index of refraction, n (n ≈ 1 for air) with incremental path length, ds. Optical path length is related to phase delay, δ , by the following relationship:

δ=2π❑L

OPL ( 5 )

The proposed design implements a spherical mirror that collects deflected and m=0 order beams to a collimating fiber optic coupler. The mirror will allow the beams to be collocated, while adjusting path length difference based on the deflected angle, α .

Experimental A/D Design

Figure 2: Analog-to-digital converter using the chaotic nature of an acousto-optic deflector, which varies the deflection angle, α , with respect to an input reference voltage, V Ref . The first order m=1 beam varies in path length from the different deflection angles α .

The experimental design, shown above, collimates the m=0 and m=1 beams into an optical fiber that is fed back into the input HeNe source, inducing a feedback loop with the acousto-optic deflector.

Figure 3: Feedback loop for a HeNe beam summed with a non-linear filter with input of V Ref . The phase delay, δ , is a function of a reference voltage input condition.

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The output of the system can be sent to M comparitors, which is specified to be 750 resolvable spots in an ELF-D750 acousto-optic light deflector by Panasonic [7].

Figure 4: Te O2 crystal diagram for an acousto-optic deflector from Panasonic [7].

The Te O2 crystal operates at an acoustic center frequency of 75 MHz, with a -3-dB bandwidth of 50 MHz. Other acousto-optic devices have higher center frequencies in the hundreds of megahertz, but the implementation with a HeNe source at ❑L=632.8 nanometers is practical for prototyping. The advertised deflection angle range for the ELF-D750 is [2.7 ˚ ,5.4 ˚ ], allowing the radius of the mirror to be reduced. The output of the chaotic filter will be a beam from the feedback loop that can be sent to M comparitors.

Conclusion

The exact mapping of V Ref to phase difference (δ) would need to be verified experimentally. Currently in the Wilmot labs, there is a working HeNe source demonstrating the acousto-optic deflection phenomena, with a varying frequency generator causing the deflected beam to oscillate according to the input. The first two modes can be summed with a spherical mirror, collocating the focal points of the collimator and the mirror. The reflected rays can be coupled into an optical fiber that sums with the input HeNe beam. If time allowed, this would be the preferred experimental approach to an optical TurboADC. CMOS technology can fit into small chips, whereas a prototype of a TurboADC would need an optical bench. If the design concept is proven to work, it can be scaled to smaller laser diodes in cavities, which have shown to exhibit chaotic behavior [8-10]. The theoretical limit of a Te O2 acousto-optic modulator with

M=750 comparitors and a sampling rate of f ¿=75 MHz is C ADC=56.25 Gbitssec . These

approximations would need to be verified, as well as investigating methods to scale down the design.

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References

[2] Walden, Robert H. "Analog-to-digital converter survey and analysis." IEEE Journal on selected areas in communications 17.4 (1999): 539-550.

[3] Z. Ignjatovic and M. Sterling, “Information-Theoretic Approach to A/D Conversion.” In IEE Transactions on Circuits and Systems I: Regular Papers, vol. 60, no. 9, pp. 2249-2262, Sept. 2013.

[4] B. Murmann, “ADC Performance Survey 1997-2017,” [Online]. Available: http://web.stanford.edu/~murmann/adcsurvey.html.

[5] Khilo, Anatol, et al. "Photonic ADC: overcoming the bottleneck of electronic jitter." Optics Express20.4 (2012): 4454-4469.

[6] Young, Jr Eddie H., and Shi-Kay Yao. "Design considerations for acousto-optic devices." Proceedings of the IEEE 69.1 (1981): 54-64.

[7] McCarron, D. J. A guide to acousto-optic modulators. Technical report, Durham University, 2007.

[8] “EFLD250 Datasheet.” Datasheets Library | DatasheetLib.Com, www.datasheetlib.com/datasheet/677128/efld250_panasonic-corporation.html.

[9] Yano, T., et al. "TeO2 anisotropic Bragg light deflector without midband degeneracy." Applied Physics Letters 26.12 (1975): 689-691.

[10] Psaltis, Demetri, Hyuk Lee, and Gabriel Sirat. "Acousto‐electro‐optic light modulation." Applied Physics Letters 46.3 (1985): 215-217.

[11] Vanwiggeren, Gregory D., and Rajarshi Roy. "Communication with chaotic lasers." Science279.5354 (1998): 1198-1200.

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