Acousto-optic laser chopper based on light diffraction by hypersonic standing waves in lithium niobate single crystal

Optics Communications 294 (2013) 1–7

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Acousto-optic laser chopper based on light diffraction by hypersonic standing waves in lithium niobate single crystal Erik Blomme a, Piotr Kwiek b, Bogumil Linde b,n, Vitaly B. Voloshinov c a

Katholieke Hogeschool Zuid-West-Vlaanderen (KATHO), K.U. Leuven Association, B-8500 Kortrijk, Belgium University of Gdansk, Institute of Experimental Physics, 80-952 Gdansk, Poland c Department of Physics, M.V. Lomonosov Moscow State University, 119991 Moscow, Russia b

a r t i c l e i n f o

abstract

Article history: Received 22 February 2012 Received in revised form 20 October 2012 Accepted 23 October 2012 Available online 12 November 2012

The paper presents results on the theoretical and experimental investigations of an acousto-optic modulator based on single crystal lithium niobate. The modulator uses a regime of operation with a standing longitudinal acoustic wave generated in the material along the axis X. The optimum cut in the LiNbO3 crystal has been calculated and it is shown that the highest figure of merit can be obtained in the YZ-plane of the crystal if light propagates not along the crystalline axis Z or Y but at an angle of 371 with respect to the axis Y. Application to the instrument of a harmonic driving electric signal at a frequency included in the range 450–550 MHz resulted in modulation of light intensity and generation of a sequence of laser pulses having repetition frequencies 0.9–1.1 GHz. The efficiency of light diffraction in the examined laser chopper was equal to 7–10% depending on frequency and power at a driving electric power of 1.0 W or higher and a wavelength of light equal to 532 nm. The possibilities to develop a similar acousto-optic modulator but with repetition frequencies up to 10 GHz are discussed. & 2013 Published by Elsevier B.V.

Keywords: Acousto-optics Acousto-optic modulator Diffraction efficiency Hypersonic frequencies Laser pulses Repetition frequency

1. Introduction It is known that modern optical communication lines and high-speed optical information processing networks use short pulses of laser radiation. It is evident that repetition rate and duration of the pulses are the basic factors to determine operation parameters of optical communication systems and information processing systems [1–5]. The generation of short laser pulses is also required for the illumination of fast changing processes, where the pulses serve as short snapshots in time. In particular stroboscopic illumination in the gigahertz frequency range could be useful for the visualization of instantaneous density profiles produced by a hypersonic wave. In many biological investigations it is not possible to expose tissues to continuous laser radiation simply because it would be harmful. In the majority of practical cases, actively mode-locked lasers are used to generate very short optical pulses at a high repetition frequency [1–6]. In the actively locked quantum generators, the required mode locking is obtained by inducing a periodic gain or a periodic loss in a laser cavity. However modulation of gain by a direct control of pump current is problematic, especially in gas and solid state lasers. As for semiconductor devices, control of the driving current is not so

n

Corresponding author. E-mail address: fi[email protected] (B. Linde).

0030-4018/$ - see front matter & 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.optcom.2012.10.059

difficult but it has limitations on modulation frequency and driving power [1,2]. A more simple and convenient method to obtain a modelocking regime consists in usage of electro-optical amplitude or phase modulators in a laser cavity [1–6]. For example, application of the modulators of Mach–Zehnder type provides pulse regimes of laser operation with repetition rates of the order 10 GHz. Moreover, the best reported result obtained with the help of a Mach–Zehnder lithium niobate (LiNbO3) modulator is even a few times better [7]. In this respect, the electro-optic modulators are advantageous in comparison with devices of other classes, e.g., acousto-optic modulators. On the other hand, acousto-optic instruments of laser beam control are probably the most commonly used devices in optics and laser technology [8–10]. The acousto-optic devices are capable of regulation of amplitude, frequency, phase, polarization and direction of propagation of a laser beam. At present, acoustooptic modulators, deflectors and filters have found many applications in science and technology because of their flexibility of operation, reliability, small size and many other advantages. One of these advantages is related to much lower driving power requirements as compared to electro-optic modulators. The voltage applied to the electrodes positioned on opposite facets of the crystals dramatically increases with the modulation frequency. At gigahertz frequencies it results in a driving electric energy of about dozens of watts. In AO modulators, however,

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lower driving power is needed and this driving power does not depend on the modulation frequency. Therefore, the higher the frequency of modulation, the more evident the advantage of an AO modulator with respect to those of the electro-optic devices. However, there are problems originating from practical requirements that may hardly be solved by application of acousto-optic instruments. The major disadvantage of acousto-optic devices consists in low quick-action and high rise time of optical pulses as measured by a detector at the output of a modulator. This time may not be shorter than the transit time of an acoustic wave front over the cross section of a laser beam. The drawback originates from relatively low magnitudes of acoustic velocities in acoustooptic crystals [8–11]. For example, the transit time t of ultrasound over a laser beam cross section is determined by the ratio t ¼a/Vs, where a is the beam aperture and Vs is the phase velocity of ultrasound. In a commonly used acousto-optic material, e.g., crystal quartz, the velocity of sound is equal to Vs ¼ 6  105 cm/s [8–11]. Therefore, the transit time of sound over a laser beam aperture a ¼0.3 cm equals t ¼0.5 ms. This optical rise time corresponds to frequencies of light modulation limited to about F¼1/ t ¼2 MHz. Hence in order to obtain fast modulation of diffracted light, it would not be useful to apply a periodically varying voltage to the transducer element. However, applying a constant voltage to the transducer in order to generate a progressive sound wave with constant amplitude, modulation of the diffracted light intensities is not possible as the intensities remain time independent. In order to establish higher modulation frequencies, e.g., on the order of 100 MHz or higher, they may be obtained only by means of a special modulator design and by an accurate focusing of laser radiation. Fortunately, acousto-optics provides a relatively simple method to increase modulation frequency of light to a few hundreds of megahertz and even higher. The modulation may be obtained in both the intracavity and extracavity regimes of laser operation [1–7]. Light diffraction by a standing acoustic wave formed by contra propagating acoustic waves in a crystal may be used for the purpose. As known, the frequency F of optical intensity modulation in a standing wave regime is equal to doubled frequency f of sound, i.e. F¼2f [9,10]. In this paper, we examined a possibility to extend the modulation frequency in an acousto-optic modulator to the gigahertz region. To a certain extent, the developed modulator may be defined as a fast ‘‘laser chopper’’ having continuous laser radiation as an input and forming optical pulses at the output of the device, as illustrated by Fig. 1. In the chopper, we intended to obtain a pulse regime of laser radiation with repetition frequencies of the order F Z1.0 GHz. Lithium niobate single crystals were used because the material demonstrates relatively low attenuation of acoustic waves at the hypersonic frequencies and also tolerable magnitudes of the acousto-optic figure of merit, as compared to the known materials [8–14].

Fig. 1. Designed AO modulator may act as a laser chopper extracting fast optical pulses from continuous laser radiation.

The present paper is structured as follows. In Section 2, problems related to the selection of an optimal cut in the LiNbO3 crystal, the figure of merit of the crystal and regular trends of the photoelastic effect in the material are discussed [7]. Section 3 of the manuscript is devoted to a theoretical analysis of the modulation problem, while in Section 4, a prototype modulator operating at the repetition frequencies FZ1.0 GHz is described. Finally, in Section 5, we discuss the possibility to increase the repetition frequency of laser pulses in the laser chopper up to 10 GHz.

2. Selection of the optimal crystal cut in lithium niobate As will be demonstrated in Section 3, high repetition rates of optical pulses at the output of acousto-optic modulators may be obtained if the instruments operate at very high acoustic frequencies f. In order to achieve this it is clear that only acousto-optic materials with low attenuation of hypersound in the gigahertz frequency range should be considered. The carried out analysis proves that the crystals of sapphire (a-Al2O3), gallium phosphate (GaP), rutile (TiO2) and lithium niobate (LiNbO3) are possible candidates for the application in fast modulators [5–7]. On the other hand, not only the attenuation of hypersound but also the figure of merit of a material should be taken into consideration in the design of the instruments [8,9]. In this respect, the single crystal of lithium niobate is advantageous, as compared to the other listed crystalline materials. Therefore, in this research, we selected the trigonal LiNbO3 crystal to obtain the required chopper regime of laser operation. It is known that generation of pure acoustic modes by piezoelectric transducers is more effective in comparison with quasilongitudinal and quasi-shear waves, especially with respect to the transformation of electric energy into elastic energy. Moreover, propagation of pure longitudinal waves in a crystal is accompanied by lower losses of elastic energy, as compared to pure shear waves [11]. As for the lithium niobate crystal, the pure longitudinal modes propagate along the axes Z and X of the material (see Fig. 2 for the reference system). That is why one of the acousto-optic interaction geometries in the lithium niobate crystal that were considered for use in a laser chopper was based on the application of a longitudinal acoustic wave propagating along

Fig. 2. Reference system of the AO configuration. A standing sound wave is established by two contra-propagating waves of the same frequency O. In case the second wave is the reflected wave of the other, transducer T2 can be omitted.

E. Blomme et al. / Optics Communications 294 (2013) 1–7

the axis Z of the material. The acoustic phase velocity and acoustic attenuation coefficient of the crystal for this acoustic mode are, respectively, equal to Vl ¼ 7.3  105 cm/s and a ¼0.3 dB/cm GHz2 [8–14]. The analysis proved that if light is sent along the axis X and an optical beam is polarized along the axis Y then the acoustooptic figure of merit of the crystal M 2 ¼ p2ef f n6o =rV 3l reaches the magnitude 1.45  10–18 s3/g. In the material, the effective photoelastic coefficient has the value peff ¼p13 ¼0.133, the index of refraction for the ordinary polarized beam equals no ¼ 2.286 and the crystal density r ¼4.6 g/cm3 [8–10]. For a light beam polarized along the axis Z, the index of refraction, the effective photoelastic coefficient and the figure of merit are respectively equal to ne ¼2.2, p33 ¼0.071 and 0.33  10–18 s3/g. It is clear that the obtained magnitudes of the figure of merit in the examined cut of lithium niobate do not exceed the figure of merit M2 ¼1.51  10–18 s3/g in fused silica. Therefore, it may be concluded that the acousto-optic efficiency of the examined cut in the crystal is low, while the interaction geometry is not promising for the application. On the other hand, the carried out analysis proved that a longitudinal acoustic wave propagating along the axis X of the crystal might also be used in the modulator. Moreover, application of this wave was advantageous in comparison with an acoustic wave along the optical axis. The acoustic phase velocity and the attenuation coefficient of hypersound in the chosen direction of the acoustic propagation are correspondingly equal to Vl ¼6.6  105 cm/s and a ¼0.4 dB/(cm GHz2) respectively, [10–14]. In order to evaluate diffracted light intensity in the crystal and calculate its figure of merit, it is necessary to consider the photoelastic effect in lithium niobate in more detail [8–10]. The effect describes variations of the refractive index n in the material under influence of applied acoustic strain. In particular, one has the following relation:

DBi ¼ pij Sj ,

ð1Þ

where DBi is the acoustically induced variation of this component, pij is the photoelastic coefficient and Sj is the strain component. In Eq. (1), the indexes i and j take the values 1,2,y,6 [10]. It is known that a pure longitudinal acoustic wave propagating along the axis X in a trigonal crystal is described by the deformation component corresponding to j ¼1 so that Sj ¼S1 [11]. In order to find the induced changes of the indicatrix coefficients, using Eq. (1), we carried out the following multiplication of the matrices: 0

p11 Bp B 12 B B p31 DBi ¼ pij Sj ¼ B B B p41 B B 0 @ 0

p12 p11

p13 p13

p14 p14

0 0

p31 p41 0 0

p33 0 0 0

0 p44 0 0

0 0 p44 p14

10 1 0 1 0 p11 S1 S1 C C B B 0 C B 0 C B p12 S1 C C CB C B C 0 C 0 C B p31 S1 C CB C, C¼B CB C B 0 CB 0 C B p41 S1 C C CB C C B B p41 C A A @0 A @0 p66 0 0

ð2Þ where the photoelastic matrix pij in lithium niobate was found in Ref. [10]. Consequently, the general equation for the acoustically disturbed indicatrix in the lithium niobate crystal is as follows:       x2 1= n2o þ p11 S1 þ y2 1=n2o þp12 S1 þ z2 1= n2e þp31 S1 þ2p41 S1 yz ¼ 1 ð3Þ On the basis of Eq. (3), one can easily calculate the figure of merit of the crystal M2. For example, if light propagates along the axis Z then for z¼0, we obtain peff ¼p11 ¼ 0.026 and M2 ¼0.07  10  18 s3/g for a light beam polarized along the axis X. On the other hand, the photoelastic coefficient and the figure of merit are correspondingly peff ¼p12 ¼0.09 and M2 ¼0.88  10  18 s3/g for an optical beam polarized along the axis Y. If a laser beam propagates along the axis Y then at y¼ 0, one has peff ¼p11 ¼  0.026 and M2 ¼0.046  10  18 s3/g, for the radiation

3

polarized along the axis X. However, for a laser beam polarized along the axis Z, one has peff ¼p31 ¼0.179 and M2 ¼2.79  10  18 s3/g. It is seen that this magnitude of the figure of merit exceeds the acousto-optic figure of merit in fused silica by about a factor of 2. It means that the latter interaction geometry is superior relative to the acousto-optic interaction geometry with hypersound propagating along the optical axis. On the other hand, our analysis proved that even higher figure of merit values might be obtained in the YZ-plane of lithium niobate crystal if light propagates not along the crystalline axis Z or Y but at an angle j with respect to them. In order to examine the far-off-axis propagation of light and to find the optimal geometry of light diffraction characterized by the maximal figure of merit value, it is necessary to calculate the effective photoelastic coefficient in the material versus the propagation angle j. The calculation made it possible to determine the magnitude of the maximal figure of merit in the crystal. In order to examine the cross section of the indicatrix by a plane orthogonal to the direction of light propagation, we introduced a new system of coordinates with axes rotated by an angle f with respect to the crystalline axes. Executing the rotation, we evaluated the optical propagation angle f relatively to the axis Y. The following transformation of the system of coordinates was made for the purpose y ¼ u cosfv sinf z ¼ u sinf þ v cosf

ð4Þ

Using Eqs. (3) and (4), we obtained the expression for the indicatrix in the new u and v coordinates:    2 x2 1=n2o þ p11 S1 þ ðu cosfv sinfÞ 1=n2o þp12 S1   2 þ ðu sinf þ v cosfÞ 1=n2e þp31 S1 þ 2p41 S1 ðu cos fv sinfÞðu sinf þ v cosfÞ ¼ 1

ð5Þ

Since light is sent along the axis U, i.e. at the angle f with respect the axis Y, intersection with the plane u¼ 0 gives the ellipse    1 1 1 2 2 x2 2 þ p11 S1 þ v2 2 sin f þ 2 cos2 f þ p12 S1 sin f þ p31 S1 cos2 f no no ne p41 S1 sin2 f ¼ 1:

ð6Þ

It is seen in Eq. (6) that the effective photoelastic coefficient is equal to p11 ¼  0.026 for a light beam polarized along the axis X. As for the diffracted optical beams polarized along the axis Z, they are characterized by the following effective photoelastic coefficient: pef f ¼ p12 sin2 f þp31 cos2 fp41 sin2 f

ð7Þ

Taking into account that p12 ¼0.09, p31 ¼0.179 and p41 ¼  0.075 [10], we found that the maximum effective photoelastic coefficient in the examined cut of the crystal is equal to peff ¼0.292. The maximal magnitude may be obtained at the optical propagation angle f ¼ 371. Analysis also proves that the refraction index for the extraordinary polarized radiation is equal to ni ¼2.225. The acousto-optic figure of merit of the crystal in the optimal case is written as M 2 ¼ p2ef f n6i = rV 3l . Substituting in this expression, the magnitudes of the refractive index ni ¼2.225, the effective photoelastic coefficient peff ¼ 0.292, the acoustic velocity Vl ¼6.6  105 cm/s and the density r ¼4.6 g/cm3, we obtained the maximal magnitude of the figure of merit in the YZ-plane of the crystal M2 ¼7.9  10  18 s3/g. This figure of merit value is a few times higher as compared to the magnitudes M2 along directions coinciding with the crystalline axes of the lithium niobate. Therefore, we designed the laser modulator according to the above presented conclusions of the theoretical examination. In particular, we sent the longitudinal acoustic wave along the axis X of lithium niobate and the optic beam at the angle f ¼371 with respect to

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Table 1 Summary of the investigated AO configurations. Propagation direction of sound

Propagation direction of light

Polarization direction of light

Figure of merit M2 (s3/g)

Z (Vl ¼ 7300 m/s)

X

X (Vl ¼6600 m/s)

Z

Y Z X Y X Z 371 with respect to Z in YZ-plane

1.45  10  18 0.33  10  18 0.07  10  18 0.88  10  18 0.046  10  18 2.79  10  18 7.9  10  18

Y 371 with respect to Y in YZ-plane

the axis Y of the crystal making a Bragg angle with respect to the acoustic wave front. Due to the Bragg angle, light does not propagate parallel to the YZ-plane of the crystal but at an angle yB with respect to the YZ-plane. It can be shown that this reduces the figure of merit M2 only by a factor cos yB which in the present case is close to 1 (in Fig. 2 the Bragg angle is not shown). Table 1 shows a summary of the analysis.

3. Theoretical analysis of acousto-optic light modulation by standing acoustic waves In order to simulate the AO light modulation by a standing acoustic wave, we consider two superposed antiparallel longitudinal ultrasonic waves of frequency O and wave number K propagating in the X direction (see Fig. 2). The two waves either can be launched by separate transducers with their active surfaces directed to each other, or the second wave can be considered as a reflected replica of the first one. In both configurations it is assumed that the distance between the opposite sides of the crystal in the X direction is a multiple of half the wavelength L of the antiparallel sound waves, in order to establish a pure standing wave. The variation of the refractive index n under influence of the applied acoustic strain can then be described by nðx,t Þ ¼ n0 þ Dn þ sinðOtKxÞDn sinðOt þ KxÞ

ð8Þ

where n0 is the refractive index of the non-disturbed crystal along the chosen axis X, and Dn þ and Dn  are the maximum variations induced by the upward respectively downward sound beam. In case the downward component is a reflected replica of the upward component, Dn  in general is smaller than Dn þ due to hypersound absorption in the crystal, especially at frequencies in the gigahertz range. It should be noted that multiple reflections (echoes) from the opposite surfaces of the crystal are not taken into account in the present theoretical model. For light propagating along the axis U, the complex amplitudes Cp (p being an integer indicating the order of diffraction) of the diffracted light waves at the border u ¼L of the sound column can be calculated from a system of coupled wave equations [15] which can be written in the form   dC p  2q C p1 exp ðjOt ÞC p þ 1 exp ðjOtÞ du  gq  Q C p1 exp ðjOtÞC p þ 1 exp ðjOt Þ ¼ jpðpbÞ C p :  ð9Þ 2 2L The system is subject to the boundary conditions C0(0)¼1 and Cp(0) ¼0 for pa0. In these equations, q ¼ 2p Dn þ =l cosy is a coupling coefficient related to the upward acoustic component, y being the light incidence angle, l the wavelength of light, and g ¼ Dn  /Dn þ is the reflection coefficient. Next, Q¼K2L/n0k is the Klein–Cook parameter, k being the wavenumber of light. Finally, b

represents the angle at which the light beam impinges on the acoustic wavefronts, expressed in units of the Bragg angle yB defined by 9sin yB9¼K/2k. At hypersound frequencies the optimum diffraction efficiency is to be expected if the Bragg condition is fulfilled, i.e. b ¼1. In the neighborhood of the Bragg angle, the diffracted light is distributed among the orders p ¼0 and p ¼1 and it can be assumed that Cp ¼0 for all other orders. Then the infinite system (9) reduces to a system of only two equations 8   < dC 0 þ q C 1 exp ðjOtÞ þ g exp ðjOt Þ ¼ 0 2 du   ð10Þ Q 1 : dC  2q C 0 exp ðjOt Þ þ g exp ðjOtÞ ¼ jð1bÞ 2L C1 du which can be solved analytically. Straightforward calculations lead to the expressions for the diffracted light intensities in the zero and Bragg order:

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  s2 þAðtÞcos2 s2 þ AðtÞ z 2 ð11Þ I0 ðt Þ ¼ 9C 0 9 ¼ s2 þ AðtÞ 2

I1 ðt Þ ¼ 9C 1 9 ¼

AðtÞsin2

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  s2 þ AðtÞ B

s2 þAðtÞ

ð12Þ

In these expressions, z ¼qL¼2pDn þ L/lcosy is the Raman–Nath parameter. At moderate acoustic power this parameter mainly determines the efficiency of the light diffraction and in practice it takes values between 0 and p. Next, s is a system parameter defined by

s¼

Q Db 4B

ð13Þ

Hence s depends on both the Klein–Cook parameter Q and the Raman–Nath parameter z, and also on the deviation Db ¼1 b from the Bragg angle in units of the latter. The time dependency of I0 and I1 is introduced by the function A(t) defined as Aðt Þ ¼

 1 1 þ g2 þ 2g cos2Ot 4

ð14Þ

Note that A(t) depends on the SWR of the antiparallel acoustic waves and that at any time A(t) Z0. Due to the presence of 2O, it is clear that the diffracted light intensity is modulated in time by twice the hypersound frequency which was to be expected in view of the standing wave character of the resulting sound wave. The highest acousto-optic coupling is established at pure Bragg incidence (Db ¼ 0). In that case s ¼ 0 and Eqs. (4) and (5) reduce to

pffiffiffiffiffiffiffiffi  AðtÞ B I0 ¼ cos2 ð15Þ I1 ¼ sin2

pffiffiffiffiffiffiffiffi  AðtÞ B

ð16Þ

Note that these expressions are independent of the Klein–Cook parameter Q. In order to obtain the best modulation contrast in combination with optimum diffraction efficiency, the Bragg angle condition is crucial as one can see from Fig. 3. The simulation shows the Bragg order intensity modulation over two ultrasonic periods for a more or less moderate value of the RN-parameter (z ¼ 0.32; this value was chosen in order to get 10% efficiency of modulation which was close to preliminary experimental observations). Note that the repetition frequency of the produced pulses is twice the hypersound frequency. At 5% deviation from the Bragg angle, the efficiency of the diffraction is already halved, and for a deviation of 10%, the modulation and the diffraction have almost disappeared. Once the Bragg angle condition is fulfilled, the modulation effects completely depend on the reflection coefficient g and the RN parameter z. As in any other AO interaction, the RN parameter is an important indicator for the established diffraction efficiency and hence for the amount of optical energy which is pumped into

E. Blomme et al. / Optics Communications 294 (2013) 1–7

Fig. 3. Diffracted light intensity modulation over two ultrasonic periods in a LiNbO3 cell for z ¼ 0.32 at a sound frequency of 0.5 GHz and 0%, 5% and 10% deviation of the angle of incidence from the Bragg angle.

the pulses. The higher the figure of merit, the higher the z-value obtained at equal voltage applied to the transducer, as can be seen from the relationship rffiffiffiffiffiffiffiffiffiffiffiffiffiffi p 2M 2 Pl ð17Þ B¼ d l cosyB where P represents the acoustic driving power and l and d are the length and width, respectively, of the driving electrode of the transducer (which are usually equal to the dimensions of the acoustic column). Unfortunately, in practice only small to moderate z-values can be achieved at high ultrasonic frequencies without introducing acoustic non-linearities or without damaging the transducer. Finally an extremely important parameter is the reflection coefficient g. In order to establish the chopper regime, g should be either equal to 1 or as close as possible to 1. In a configuration whereby a standing wave is constructed by superposing 2 contrapropagating waves with the same frequency and amplitude, g can be considered as being 1. However, if the downward hypersound wave is the reflected wave of the upward component—which in practice is the most convenient configuration—the resulting wave in general is not a pure stationary wave but a standing wave with g o1 because of the sound attenuation. The stronger the acoustic attenuation and the thicker the AO cell, the smaller the reflection coefficient g. This can be disastrous for the chopping effect, as one can see from Fig. 4 where g is decreased from 1 to 0.25. Not only is there a decrease of the peak value of the generated pulses, but also more important is the appearance of a pedestal, a non-zero base level, which should be avoided to let the AO modulator act as a chopper. Taking into account the rather low z-values that can be established at hypersound frequencies, and the fact that the time function A(t)40 at any time whenever g o1, it is easily seen from Eq. (16) that a non-zero base level cannot be avoided. This explains once more the importance of selecting an AO material like LiNbO3 with a rather low acoustic attenuation in the direction of propagation of the acoustic wave. Only then the reflection coefficient can be kept reasonably close to 1.

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the opposite facet of the crystal cell and propagated in back direction with respect to the generated wave. In this way, a standing wave regime of the modulator operation was obtained. Actually, after the RF-signal is applied to the cell, the acoustic wave goes back and forth a few times in the crystal until a stable standing wave regime is obtained. The AO device has been used only in this regime and not during the transient process preceeding it. A linearly polarized laser beam was sent at Bragg angle yB E lf/2nV1 ¼0.521 with respect to the acoustic wave front. The cell was cut in the form of a rectangular parallelepiped with linear dimensions 0.5 cm along the axes X and U. The size of the fabricated cell along the axis V is 0.4 cm. The acoustic waves were generated by a piezoelectric ZnO transducer with dimensions l ¼0.3 cm along the direction of light propagation and d ¼0.2 cm in the orthogonal direction. The transducer was evaporated on the crystal facet and divided into three sections electrically connected in series to provide better matching of electric impedances of the transducer and a driving RF generator. The transducer was capable of operation in the frequency range from f¼450 to 550 MHz. The acoustic facets of the crystal were fabricated with a slight misalignment in order to avoid extreme sensitivity of the modulator to heating of the crystal by absorbed acoustic power. The block scheme of the experimental setup is shown in Fig. 5. We used a diode-pump frequency-doubled CW laser (Spectra Physics Millennia Pro) radiating 2.5 W of optical power at the wavelength l ¼532 nm. The optical radiation was directed to the cell by an optic fiber with a beam expander at its end. The cross section and the angular divergence of the laser beam illuminating the cell were correspondingly equal to 0.1 cm and 0.5 mrad, respectively. An electric driving signal formed by the signal synthesizer 6062A (Fluke Model) and the RF amplifier (Model 525 ENI) was directed to the modulator. The continuous RF driving power applied to the transducer was limited to 1.0 W. The diffracted light in the Bragg diffraction order (in the figures labeled order 1) was directed to the PIN GaAs photodetector (ET-400 Electro-Optic Technology) by means of the focusing lens and the fiber. The rise time of the detector was less than 35 ps. Next, the electric signal from the detector was sent to the digital oscilloscope (PM 3340 Philips) characterized by a sampling frequency 2 GHz, a rise time 275 ps and a frequency bandwidth 2 GHz. It was found experimentally that the developed system of optical registration provided reliable records of light intensity every 2.5 ps. The oscilloscope was working in the so called ‘‘sampling scope’’ or ‘‘stroboscopic’’ regime, i.e. that in contrast

4. Description of modulator and experimental investigation of the chopper regime According to the conclusions of Section 2, we fabricated a laser modulator based on a lithium niobate crystal in which a longitudinal acoustic wave was generated in forward direction along the X-axis of the material. This acoustic wave was reflected from

Fig. 4. Diffracted light intensity modulation over two ultrasonic periods in a LiNbO3 cell for three selected values of the reflection coefficient g (1, 0.5 and 0.25) at Bragg incidence and z ¼ 0.32.

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E. Blomme et al. / Optics Communications 294 (2013) 1–7 1.2

6062A

1 0.8

525 lens

au

0.6

1 LASER 0

GaAs

PM 3340 DSO

fiber optic connection US cell

0.4 0.2

0 -0.2

Fig. 5. Scheme of apparatus for measurement of modulation of the laser beam by ultrasonic wave (0—zero diffraction order; 1—first diffraction order; laser—Millennia Pro, Spectra Physics; 6062A—Synthesized FR signal generator; 525—LA, ENI, power amplifier; GaAs—PIN detector, ET 4000F, Electro-Optic Tech.; PM 3340, DSO—2 GHz digitalizing oscilloscope; US cell— ultrasonic cell).

to the real scope the input signal is sampled once per trigger. The next time the scope is triggered, a small delay is added and another sample is taken. For the used oscilloscope which was operating in recurrent mode, the experimental data could be collected every 2.5 ps. The application of a driving electric signal to the transducer terminal resulted in the desired modulation of the laser intensity, as shown in Fig. 6. The data presented in the figure were obtained at the electric frequency f¼500.012 MHz. The diffracted light efficiency at the output of the device was equal to approximately 7% at this frequency which is lower than what theory predicts (20%). The discrepancy may be explained by losses in the electric matching network of the modulator and also by losses in the optical system responsible for the delivery of the diffracted radiation to the detector. As for the regime of the modulator operation, the data in Fig. 6 prove that the instrument indeed operated in the chopper mode. In other words, the device was capable of generating distinct laser pulses at the repetition frequency F¼1.00 GHz. A similar result was obtained at other driving frequencies between 450 MHz and 550 MHz, i.e. all over the frequency band of the transducer. Consequently, the repetition frequencies of pulses belong to the range F¼900 MHz–1.1 GHz.

5. Possibilities of modulation frequency growth The experimental investigation of the developed laser modulator proved that the device demonstrated a reliable operation resulting in the required generation of a sequence of laser pulses at the repetition frequencies up to F¼1.1 GHz. It should be noted that the carried out research is only the first step in a program of investigations related to the development of fast acousto-optic modulators. Therefore, the examined device should be considered as a prototype instrument, while the final goal of the research consists in the development of a laser chopper providing laser pulses with the repetition rate of a few gigahertz. Our analysis demonstrates that the major factor limiting operation of the device at the extremely high acoustic frequencies is the attenuation of hypersound in the crystal. The attenuation coefficient for the longitudinal acoustic wave along the axis X of lithium niobate is approximately equal to a ¼0.4 dB/cm GHz2. This means that the acoustic wave in a crystal with a length of 1.0 cm is attenuated at the acoustic frequency f¼10 GHz to about  40 dB. It is evident that this magnitude of the hypersonic attenuation is not tolerable for the majority of acousto-optic applications. On the other hand, in the standing wave regime of the modulator operation, the optical repetition frequency F¼10 GHz is obtained by application of a driving signal with the electric frequency twice as low, i.e. equal to f¼5.0 GHz. Hence, the acoustic absorption in the

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

time [ns]

Fig. 6. Observation of laser beam modulation by a hypersonic wave (f¼ 0.50 GHz, F¼ 1.00 GHz). The background level line refers to the signal obtained without sound.

standing wave regime becomes 4 times lower because of the square dependence of the attenuation coefficient on the acoustic frequency apf2 [8]. In other words, it is reasonable to expect a decrease in the acoustic loss from  40 dB to 10 dB. This attenuation is still too high but not so dramatically, as compared to the case with the driving frequency f¼10 GHz. Designing a laser chopper, it is possible to shorten the AO cell thickness and make it equal to the diameter of a laser beam, e.g., to about 0.2–0.3 cm. Hence, a round-trip path of a hypersonic wave in a crystal may be limited to 0.4 cm so that the total acoustic attenuation in the crystal becomes not equal to  10 dB but to  4 dB. Focusing of a laser beam makes it possible to decrease the crystal size further on, resulting in total acoustic losses less than  3 dB. In general, the predicted 3 dB acoustic loss may be considered as tolerable and suitable for the applications in a laser chopper. On the other hand, the proposed acousto-optic method of light beam modulation at the repetition frequencies F ¼10 GHz has evident disadvantages. Since the forward and reflected acoustic waves propagate in a crystal over different distances from the piezoelectric transducer, the reflected wave is always weaker than the forward propagating wave because of the acoustic energy attenuation. This results in a non-zero intensity of the standing acoustic wave at the time interval when intensities of the two waves are subtracted and should compensate for each other. Therefore, it may be predicted that in general the optical signal will be observed in the form of pulses but on a pedestal, i.e. a non-zero base level. Consequently, the depth of the intensity modulation at the output of the modulator, i.e. the difference between the maximum and the minimum optical signal power in the device, will become relatively low. As for the developed chopper, the pedestal is practically absent, as proved by the data presented in Fig. 7. The reason for the effect consists in a very low attenuation of hypersound a ¼0.1 dB/cm at the acoustic frequency f¼500 MHz. The effect of the appearance of a non-zero base level may be negligible at acoustic frequencies o1 GHz, it can no longer be ignored at acoustic frequencies beyond 1 GHz and may become problematic in the frequency range 43 GHz if no special precautions are taken. The theoretical simulation in Fig. 7 shows what happens if the acoustic frequency is raised from 0.5 GHz (i.e. the frequency applied in the experiment) to 5.5 GHz for an arbitrarily chosen RN parameter. The reflection coefficient g can be calculated from the acoustic attenuation of 0.4 dB/cm GHz2, in accordance with the measurements of Spencer and Lenzo [13]. The dashed lines refer to a cell thickness of 1 cm. The upper curve represents the peak intensity while the lower curve represents the base level intensity. It is seen that up to 1.5 GHz the base level of the modulation is equal to zero which enables chopping frequencies up to 3 GHz with reasonable peak levels of approximately 20% of

E. Blomme et al. / Optics Communications 294 (2013) 1–7

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of laser light intensity at frequencies as high as 1 GHz. It is shown that a standing wave regime of acousto-optic modulation may be recommended for generation of relatively short optical pulses out of continuous laser radiation incident on a modulator. It was demonstrated that repetition frequencies of pulses at the output of the developed lithium niobate acousto-optic modulator exceeded 1 GHz. In general, the repetition frequencies in the examined devices may approach a few gigahertz. Therefore, the developed type of a modulator may be defined as a fast laser chopper. It is evident that the chopper may be recommended for various applications in optical communication and laser technology.

Acknowledgment

Fig. 7. Base and peak level of light diffracted in a LiNbO3 cell with thickness 10 mm, 5 mm and 3 mm for z ¼ 0.32 and hypersound frequencies varying from 0.5 to 5.5 GHz.

initial light intensity. However, performances strongly depend on the thickness of the AO cell. Decreasing the cell thickness to 5 mm, an almost zero base level is obtained up to approximately 2 GHz which enables repetition frequencies up to 4 GHz. In that case it is easily calculated that a ¼0.8 dB. Further reducing the cell thickness to 3 mm, the base level is seen to remain negligible up to at least 3 GHz which makes it possible to establish repetition frequencies to at least 6 GHz. Consequently, it may be predicted that the required chopper regime of the modulator operation may be obtained by rather simple methods. For example, by application of a relatively short lithium niobate crystal or by focusing of a laser beam in a crystalline sample. On the other hand, it is reasonable to expect an additional improvement in the operation of the device at very high driving frequencies f if one does not use a single piezoelectric transducer but a pair of piezoelectric transducers radiating from opposite acoustic facets of a crystal. In that case the requirement g ¼ 1 is automatically satisfied. It is evident that the transducers should be activated at identical frequencies f but propagate in opposite directions with respect to each other. There is one more disadvantage of the modulation method examined in this paper which should be mentioned here. Since the driving acoustic energy is absorbed in a crystal, the acoustooptic interaction medium is inevitably heated by hypersound. Consequently, in order to avoid drifts of operation parameters in the device, careful thermal stabilization of the modulator becomes absolutely necessary and this has not been applied in the present experimental cell.

6. Conclusion The carried out theoretical and experimental analysis proves a principal possibility to use acousto-optic interaction for modulation

The paper is dedicated to the memory of Professor Yury A. Zyuryukin from Saratov State Technical University, Russia, who carried out the major part of job in design and fabrication of the acousto-optic device. The research was supported by the University of Gdansk IFD 5200-4-0024-12. One of the authors, P. Kwiek would like to thank the National Science Centre for supporting the experimental part by the research grant N 0855/B/H03/2011/40.

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