Acousto-optic Spectrum Analyzer

The New Type of Optoelectronic Device

Sergey Mantsevich

, Vladimir Balakshy

and Yury Kuznetsov

Physics, M. V. Lomonosov Moscow State University, Leninskye Gory 1, 119991, Moscow, Russian Federation

Keywords: Acousto-optic Interaction, Feedback, Optical Radiation Spectrum, Collinear Diffraction, Acousto-optic

Filter.

Abstract: The new optoelectronic system combining calcium molybdate collinear acousto-optic cell and positive

electronic feedback is proposed and examined both experimentally and theoretically. The feedback signal is

formed at the cell output due to the optical heterodyning effect with the use of an unconventional regime of

collinear cell operation. It is shown that the feedback circuit parameters enable controlling spectral

characteristics of the acousto-optic cell, resulting in enhancing the maximal spectral resolution and the

accuracy of optical wavelength determination. This system may be treated as the optical radiation spectrum

analyzer, as the spectrum of electric signal in the feedback circuit is related with the light spectrum on the

system input.

1 INTRODUCTION

Acousto-optic (AO) interaction is one of the main

effects used for optical radiation parameters control

and examination. The phase diffraction grating

induced inside the AO cell by acoustic waves allows

controlling the propagation direction, amplitude,

frequency and polarization of an optical wave

(Goutzoulis, Pape 1994).

AO systems with feedback is the class of

optoelectronic instruments that expand the scope of

optical information processing problems that can be

solved by AO methods. This type of AO systems is

comparatively new and poorly studied. It is known

that the introduction of feedback allows to improve

characteristics of conventional devices and to create

absolutely new devices of laser physics and optical

information processing (J. Chrostowski, 1982; Poon,

1989, Balakshy, 1996).

The feedback in these systems is hybrid: an

optical signal in one of the diffraction maxima at the

AO cell output is transformed by a photodetector

into an electrical signal that controls magnitude

(Balakshy, 2014) or frequency (Balakshy 1995,

Balakshy, 1999) of an acoustic wave excited in the

cell. The behaviour of the feedback AO systems is

extremely complicated. Diverse oscillations

(including harmonic, self-modulation and chaotic

ones) can be excited (Balakshy, 2014).

The AO feedback systems have two important

features. First, such systems are basically distributed

because the time of acoustic wave propagation in the

cell is compared with the period of oscillations.

Second, these systems are principally nonlinear and

the character of nonlinearities affects the system

behaviour. The nonlinearities, concerned in the first

place with the AO cell, give rise to diversity of

regimes, but, at the same time, they complicate the

analysis of the systems.

In this paper, an electronic feedback is added to

the collinear AO cell fabricated of calcium

molybdate crystal (CaMoO

) (Harris et.al., 1970;

Balakshy, 2009).

The resulting system is unique and has no

analogues among the known AO devices

The theoretical and experimental analysis is

carried for this optoelectronic system. It is shown

that the positive feedback makes it possible to

control the shape of the filter transmission function

and to suppers the function side lobes resulting in

significant enhancement of the spectral resolution

and the accuracy of optical wavelength

determination. The examined system may be treated

as optical spectrum analyzer.

Mantsevich S., Balakshy V. and Kuznetsov Y.

Acousto-optic Spectrum Analyzer - The New Type of Optoelectronic Device.

DOI: 10.5220/0006151402370244

In Proceedings of the 5th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2017), pages 237-244

ISBN: 978-989-758-223-3

237

2 LIGHT INTENSITY

MODULATION

The system operation is based on the effect of light

intensity modulation effect, predicted and observed

experimentally in (Balakshy, 2009; Balakshy 2012).

It was reported there that the special case of

collinear AO interaction exists that can provide

intensity modulation of the output optical radiation

at the frequency of the traveling acoustic wave. This

peculiarity gives the possibility to introduce the

feedback circuit to feed the AO cell transducer by

the modulated signal from photodetector.

The scheme of conventional collinear AO filter

is presented at figure 1.

Figure 1: Collinear AO filter scheme.

In the conventional variant of AO collinear filter

(Harris et.al., 1970; Balakshy, 2009), polarization of

the incident light is set in accordance with the crystal

eigenmode polarizations (polarization angle α is

equal to 90° or 0° with regard to the Y axis). In the

process of AO interaction, the light polarization

changes to the orthogonal one (anisotropic

diffraction). Therefore, crossed analyzer

(polarization angle α is equal to 90° or 0°,

respectively) let pass only the diffracted optical

radiation.

The transmission function of the filter used in the

experimental setup is presented at figure 2, the filter

passband equals 0.9nm in this case.

Figure 2: Transmission function of conventional collinear

AO filter.

Quite another situation appears in the special

case, when the incident optical wave has

polarization which differs from the eigenmode

polarizations. In this case, the wave, entering the AO

cell, is split into two waves with amplitudes 





(ordinary mode) and 





(extraordinary mode)

which are polarized along the Y and Z

crystallographic axes. These waves diffract in the

acoustic field independently and with equal

efficiency. The ordinary wave 





is scattered into

the +1

diffraction order, forming the waves 





(the

zeroth order with ordinary polarization) and 





(the +1

order with extraordinary polarization). The

extraordinary optical wave 





diffracts in a similar

manner into –1

order, forming the waves 





and







. The optical waves of the zeroth order 





and







have the frequency ω equal to the frequency of

the incident light, whereas the waves 





and 





have frequencies ω+ and ω- , respectively.

The analyzer oriented at the angle  let pass

through only a part of the light components. The

beatings of the components with frequency shift and

unshifted components result in the modulation of

output light intensity with ultrasound frequency. The

light intensity on the system output may be written

as the sum of three components:





|















cos

















sin



(1)





=







cos



Ω



Φ







cos



2Ω



2Φ



(2)

Amplitudes of I

and I

components depend on

the polarizer and analyzer orientations. The I

component has intensity modulation with ultrasound

frequency aroused in the AO cell. That is why it may

be used to feed the AO cell transducer with feedback

circuit. The magnitude of this component is

described by equation:





=





sin

√



∙





cos





√







(3)

where =Γ







, Γ is the Raman-Nath parameter

(AO coupling coefficient) which is proportional to

the acoustic wave amplitude and =



2 

⁄









is the dimensionless phase mismatch [1]. In the

last equation l is the AO interaction length, f –

ultrasound frequency, f

is the phase matching

frequency for the given optical wavelength, V is the

acoustic wave velocity along X crystallographic

axis. The AO filter transmission function for I

component is presented at figure 3.

PHOTOPTICS 2017 - 5th International Conference on Photonics, Optics and Laser Technology

238

Figure 3: AO collinear filter transmission function for

component.

It is possible to see the intensity modulation with

 frequency. Also the shape of transmission

function differs from the conventional one. It has flat

top, higher side lobes and wider passband (1.5nm at

3dB level).

3 FEEDBACK INFLUENCE

The existence of I

component modulated with

ultrasound frequency makes it possible to introduce

feedback circuit (figure 4) (Balakshy et.al., 2016,

Mantsevich et.al. 2016).

Figure 4: AO spectrum analyzer scheme.

An optical beam from laser 1 passes through

polarizer 2 and enters collinear AO cell 3. A

longitudinal acoustic wave is excited in the cell by

piezoelectric transducer 4 and after the reflection

propagates along X axis. The light beam passes

through the cell along the X axis as well. The regime

of travelling acoustic waves is ensured by acoustic

absorber 5. The diffracted radiation was registered

by photodetector 7 and its output signal at the

frequency f was sent through feedback 8 to the

transducer together with the signal of HF generator

9. The feedback circuit had tuneable gain factor to

30dB and phase shifter which provided phase tuning

to an optimal meaning. The spectrum of electric

signal in the feedback circuit is defined by the

optical spectrum on the AO cell input and may be

registered by the RF spectrum analyzer.

The feedback appearance changes dramatically

the shape of transmission function presented at

figure 2. Also tuning the circuit gain factor it is

possible to control the shape and passband of the

system transmission function. One of the

transmission functions obtained in the experiment is

presented at figure 5.

Figure 5: AO filter transmission function with feedback.

The transmission function side lobes disappeared

and the transmission band δf noticeably narrowed.

The sharpening of the spectral characteristic occurs

because the feedback coefficient is proportional to

the photodetector signal amplitude. For the

oscillogram presented in figure 5, =4.8 kHz,

=0.075 nm and contrast =60 ( is a ratio of

the transmission coefficient at the characteristic

maximum to the transmission in the first side

lobe). Thus, the narrowing of the AO filtration band

is as great as 20 times, that corresponds to the same

increasing the accuracy of the optical wavelength

measurement. In our experiments, the maximal

narrowing δf ranged up to approximately 40 times.

4 THEORETICAL MODEL

Considering the second section of the paper and fig.

4 it is possible to write the following equation

describing the photodetector 7 output signal at Ω

frequency (Balakshy et.al., 2016, Mantsevich et.al.

2016).









=







=

cos



Ω



(4)

Acousto-optic Spectrum Analyzer - The New Type of Optoelectronic Device

239

where σ is the detector sensitivity. The voltage at the

AO cell transducer may be written in the form









sinΩtσ



cos



Ωtφ



χ



=Γ



Γ





⁄

(5)

if the feedback circuit has the amplification

coefficient μ. In equation (5) U



is the HF generator

signal magnitude, χ is the phase shift in the phase

shifter and γ is the transducer conversion factor.

The conditions of phase equation (6) and

magnitude balance equation (7) for the examined

system are the following:

Ω

√







√



=2

(6)









√



2

∙

∙



4cos





√













√



2

=1

(7)

where =Γ







is like in the equation (3).

Equations (6) and (7) form the nonlinear system

relatively to the variables Γ (normalized magnitude

of ultrasound signal) and R (normalized ultrasound

frequency). The solution of this system of equations

permits to analyze the behavior and characteristics

of the examined optoelectronic system.

4.1 Transmission functions simulation

We will examine the influence of feedback circuit

on the collinear AO filter spectral characteristics in

this part of the paper. The transmission functions are

calculated by substitution into equation (3) the

values of Γ and R parameters obtained from

numerical solution of equations (6) and (7) system.

The equation (5) gives the transmission function

shape, defining the AO diffraction efficiency,

spectral passband and contrast.

We assume that the optical wavelength of

incident radiation is 655nm, the AO interaction

length in the cell is 4 cm, the detector sensitivity is

σ=0.7, the transducer conversion factor γ=0.9

(such parameters meet the characteristics of the

experimental set up).

The transmission functions I







simulations for

various values of feedback circuit gain μ and

generator signal magnitude defined by Raman-Nath

parameter Γ



were carried at first. The results of

computations are presented at figure 6a,b.

(a)

(b)

Figure 6: AO collinear cell with feedback circuit

transmission functions. a – Raman-Nath parameter Γ



π10

⁄

. b - Γ



=π 400

⁄

Figure 6 represents transmission functions of

collinear AO cell simulated for various feedback

gain μ (it should be noted that the value of gain

coefficient μ is normalized and didn’t match with

experimental one) for two Ramam-Nath parameters



=π 10

⁄

(figure 6a) and Γ



=π 400

⁄

(figure 6b).

Such magnitudes of Γ

indicate that the acoustic

power from generator is lower in 100 and 16·10

times correspondingly than needed to obtain

maximal diffraction efficiency at the traditional case

of collinear AO cell running without feedback.

The following conclusions can be drawn after

examining the dependences at figure 6. Firstly,

increasing the feedback gain it is possible to achieve

maximal diffraction efficiency for arbitrary value of

parameter. Secondly, the magnitude of system

with feedback transmission function side lobes is

determined by the magnitude of AO collinear cell

transmission function without feedback obtained for

the same Γ

parameter (curve 2 at figure 6a and

PHOTOPTICS 2017 - 5th International Conference on Photonics, Optics and Laser Technology

240

curve 1 at figure 6b). Thus, reducing Γ

and

simultaneously increasing μ the spectral contrast κ

can be improved. For example, κ=14.5 for curve 5

at figure 6a, this vale significantly exceeds spectral

contrast of conventional collinear filter. Spectral

contrast equals 145 for the curve 5 at figure 6b and

this value is higher than values ever mentioned in

literature (Mazur et.al., 1996). Thirdly, comparing

various curves at figure 6 we may conclude that for

every Γ

value exists optimal gain value that

provides minimal passband of the system.

Maximal AO diffraction efficiency ζ=I





⁄

reduce with the decrease of system passband. The

passband of transmission function 3 at figure 6a is in

1.3 times less than for the conventional collinear AO

filter with the same interaction length but with

diffraction efficiency near 56%. For the curve 2 at

figure 6b passband is in 3.5 times narrower than for

the collinear AO filter without feedback but the

diffraction efficiency will be about 46%.

Our simulations have shown that 0.05nm

passband may be achieved, but the diffraction

efficiency in this case reduces to 6%. The passband

of the curve 5 at figure 6b is 20% narrower than for

the traditional collinear AO filter with the same AO

interaction length but the diffraction efficiency is

still maximal and spectral contrast =145. These

parameters indicate that system with feedback has

great advantages for spectroscopic applications.

4.2 Spectral resolution determination

Let’s pretend that the optical radiation containing

two optical wavelengths λ

and λ

passes through the

examined system. We will simulate the spectral

dependences of optical signal on the output of AO

cell for such incident radiation for the following

cases: collinear AO filter in traditional geometry

(figure 7a) (Harris et.al.,1970), collinear AO filter

with special orientation of polarizer and analyzer

(figure 7b) without feedback (Balakshy,Mantsevich,

2009) and our system containing collinear AO cell

and feedback (figure 7c). Three curves were

calculated for each case for three pairs of optical

wavelengths: curve 1 - λ

=654 nm, λ

=656 nm, Δλ=

2 nm; curve 2 - λ

=654.25 nm, , λ

=655.75 nm,

Δλ=1.5 nm; curve 3 - λ

=654.335 nm, λ

=655.665

nm, Δλ=1.33 nm.

Figure 7a represents the dependence of diffracted

light intensity on optical wavelength for the

conventional collinear AO filter. These curves have

two main maxima that correspond to the incident

optical radiation wavelengths. The examined

collinear AO filter with 4cm AO interaction length

resolve light spectrum components well for all three

cases but it doesn’t provide high spectral contrast.

The transmission functions intersect at levels 1.5%,

11,1% and 25.5% from maximal value for curves

(a)

(b)

(c)

Figure 7: AO collinear cell spectral response on incident

light with two spectral components. a – conventional AO

cell; b - AO cell with specific polarizer orientation; c –

AO cell with feedback, Γ

= π/200, μ=4. curve 1 - Δλ=2

nm; curve 2 - Δλ=1.5 nm; curve 3 - Δλ=1.33 nm.

Acousto-optic Spectrum Analyzer - The New Type of Optoelectronic Device

241

1-3 correspondingly (central minimum of the

dependences). If we simulate the same dependences

for the same AO cell but with special polarizer and

analyzer orientation the significant differences could

be observed. Firstly, the spectral contrast is worse

than for conventional collinear AO filter. Secondly,

the deterioration of spectral resolution occurs, the

value Δ=1.33 (curve 3 at figure 7b) is marginal

for this case.

The situation changes significantly if we

introduce the feedback circuit. The results of

calculations for the collinear AO cell with feedback

(Γ

= π/200 , =4) are presented at figure 7c. The

side lobes of transmission function are suppressed

hence the spectral contrast increases in comparison

with the traditional geometry. Transmission

functions overlap at the level 0.4% and 4% from

maximal for curves 1 and 2 correspondingly. It is

possible to enhance the spectral contrast by reducing

and increasing  values. Nevertheless the spectral

resolution of the system decreases, it will be set by

the dependences at figure 7b as exactly these curves

are transformed under the action of the feedback.

That is why the system is not able to select two

spectral lines separated by spectral interval Δ=

1.33 nm (curve 3). But the spectral lines displaced at

wider intervals Δ will be selected well without

overlapping.

The theoretical simulations presented at figure 7

were verified in experiment. The results of the

experimental investigation are presented at figure 8.

Here the spectral response of the conventional

collinear AO filter (figure 8a) and AO system with

feedback (figure 8b) for the optical radiation (near

655nm) containing two components with spectral

interval Δ=1.4 nm are presented. Both figures

have the same scale.

(a)

(b)

Figure 8: AO collinear cell spectral response for incident

optical radiation with two spectral components.

a – conventional AO cell; b – AO cell with feedback,

Δλ=1.4 nm.

The deviation of diffracted light intensity in the

centre of the conventional collinear AO filter

spectral response curve is approximately 15%. The

feedback appearance strongly sharpens the spectral

response of the system and the spectral components

became clearly distinguishable.

4.3 Nonlinear effects in the system

The examined optoelectronic system, as the most

part of the electronic systems with feedback, is

nonlinear. The nonlinearity is one of the main

constraints and appears as the diffraction efficiency

dependence on the incident optical radiation

intensity 



in this case.

The nonlinearity causes the distortion of system

spectral response, when optical spectral components

pass through the system with varied amplification.

Let’s define the coefficient of diffraction efficiency

amplification ψ as the ratio of diffraction efficiency

for the system with feedback to the diffraction

efficiency I





⁄

without feedback. The results of







evaluations for the HF generator acoustic

power Γ

= π/100 and various feedback circuit

amplification values are presented at figure 9. These

dependences have evidently nonlinear shape. The

growth of feedback circuit amplification μ causes

the shift of ψ







dependences to the left and

nonlinearity may appear for lower values of incident

light intensity. The magnitude of diffraction

efficiency amplification is in the range between 1

and 25 for Γ

= π/100 , this mean that some spectral

components of light will pass through the system

PHOTOPTICS 2017 - 5th International Conference on Photonics, Optics and Laser Technology

242

(a)

(b)

(c)

Figure 9: AO collinear cell with feedback nonlinearity.

a - diffraction efficiency amplification ψ







evaluations,

= π/100 , λ=655 nm; curve 1 - μ=4.5, curve 2 - μ=

5.5, curve 3 - μ=6.5; b - experimentally measured

conventional collinear AO filter spectral response; c –

experimentally measured collinear AO filter with feedback

spectral response

without any amplification and some other will be

amplified in 25 times.

The experimental verification of nonlinearity

existence was carried in the following way. Optical

radiation containing two spectral components with

diverse intensity (20% difference) is applied to the

system optical input. The spectral response on such

signal was registered by conventional AO filter

(figure 9b, AO filter is the linear system by light)

and by the system with feedback (figure 9c).

Comparing the oscillograms figures 9b and 9c it can

be seen that the difference between diffracted

radiation intensities is much lower for the

conventional AO filter (20% difference) than for the

AO system with feedback (46% difference).

4.4 The continuous input optical

spectrum case

The examined AO system nonlinearity has both

positive and negative influence. On one hand the

nonlinearity disturbs the spectral response of the

system, and on the other hand it enhances the light

spectrum contrast.

AO tunable filters are widely used for spectral

analysis to date (Mazur et.al, 1996; Mantsevich

et.al., 2015). In this application the incident light has

continuous spectrum with some peculiarities, for

example, absorption bands of gases.

Let’s treat the case when incident optical

radiation has continuous spectrum 









shown by

curve 1 at figure 10.

Figure 10: AO optical spectrum analyzer operation. Curve

1 – spectrum on the input I







, curve 2 – light spectrum

on the output of conventional collinear AO filter Γ=π,

curve 3 – light spectrum on the output of AO system with

feedback

= π/100

, μ=5.5.

It is possible to simulate the spectrum of optical

radiation on the output of conventional collinear AO

Acousto-optic Spectrum Analyzer - The New Type of Optoelectronic Device

243

filter (curve 2 figure 10) and on the output of

collinear AO cell with feedback (curve 3 figure 10),

for the curve 3 the parameters AO interaction

parameters were: Γ

= π/100, =5.5.

Curve 2 differs much from the curve 1. The

reason of this difference is that the conventional

collinear AO filter transmission function has side

lobes that let pass the undesirable spectral

components and cause the smoothing of diffracted

light spectrum peculiarities and significantly distort

its shape.

Thereby the real spectral resolution of the AO

filter is much lower than the filter transmission

function passband (approximately in 10 times).

If we use the AO system with feedback the high

spectral contrast gives the possibility to dispose the

side lobes and to let pass only the spectral

components that fit the passband. Consequently the

shape of curve 3 at figure 10 is much closer to the

shape of curve 1, except the spectrum contrast. The

growth of light spectrum contrast is caused by the

AO system nonlinearity, but this distortion could be

corrected using the dependences presented at figure

9 and calibrations.

5 CONCLUSIONS

In this paper, we have analyzed the functioning of

the optoelectronic system containing the collinear

AO filter and electronic feedback. This feedback is

implemented due to a special geometry of AO

interaction in the collinear cell, when light

diffraction by a traveling acoustic wave is

accompanied by light intensity modulation at the

acoustic frequency f. Due to this peculiarity, the

output signal of the photodetector contains the

component that could feed the cell transducer

together with the RF generator. The feedback action

results in narrowing the system spectral passband

and, consequently, increasing the accuracy of optical

wavelength measurement. The main advantage of

the examined system is that the shape of the filter

transmission function can be controlled through the

gain factor of the feedback amplifier. It can be used

for conversion of the optical spectrum into the

electrical one.

The system spectral resolution is limited by the

AO collinear filter passband without feedback.

The examined system may be considered as a

new type of spectrum analyzer but with taking into

consideration the feedback nonlinearity. This

nonlinearity can be taken into account at computer

processing of the output signal and calibrations.

ACKNOWLEDGEMENTS

The work has been supported by the Russian

Science Foundation (RSF), project 14-22-00042.

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