## Abstract

A cascaded system of two acousto-optical cells is proposed for equalization of multichannel optical signal satisfying coarse wavelength-division multiplexing standard. Two similar acousto-optical modulators for unpolarized light on the basis of 10°-cut paratellurite crystals were used in a free-space gap of a fiber line. The system controlled intensity of several optical carriers in the spectral range from 1200 to 1700 nm. The device was tested in a four-channel regime of operation in the range 1510–1570 nm. Overall optical insertion losses did not exceed -2 dB and less than 1 W electric power per channel was necessary for -20 dB intensity attenuation of the signal in a continuous operation mode. Compensation for birefringence in paratellurite provided diffraction regime that was insensitive to polarization of light. Interchannel crosstalk was less than -10 dB.

©2009 Optical Society of America

## 1. Introduction

Development of optical communication networks with the use of wavelength-division multiplexing (WDM) technology required new types of spectral devices for control of multichannel light beams. One of the problems in optical communications with multiple carriers is amplitude equalization of channels. Many factors result in variations of the optical power in a line: wide optical bandwidth, laser diode drifts, non-flatness of gain characteristics of optical amplifiers [1]. Acousto-optical (AO) modulators are good candidates for spectral equalization in WDM systems because they can operate in a multifrequency mode: different optical channels are independently controlled by corresponding ultrasonic waves in the same crystal. These devices are compact and reliable and they provide a high operation rate and a low power consumption [2, 3]. Acousto-optical tunable filters (AOTFs) may not be directly used in Dense WDM networks because their passband is wider than the channel spacing. Nevertheless, noncollinear AOTFs have a suitable passband for operating in Coarse WDM (CWDM) networks with a 20 nm interchannel spacing [4]. The narrowest passband in paratellurite 0.2 nm at the wavelength 1550 nm was achieved using a quasi-collinear AOTF with a big interaction length [5].

It is known that an optical wave transmitted through the fiber is depolarized and direction of polarization is rotated due to fiber curvature and intermodal dispersion [1]. Therefore, optical devices for control of transmitted light should be insensitive to polarization of waves. Traditional AO devices that are based on anisotropic Bragg diffraction of light do not satisfy this requirement [2, 3]. Special schemes of AO diffraction are applied for processing unpolarized light [6]. We used a filtering configuration of anisotropic diffraction with polarization splitting in a modulator for unpolarized light [7]. Former analysis of this scheme did not take into consideration inevitable splitting of the transmitted beam because of birefingence of the material. We improved the scheme of AO modulator of unpolarized light by means of using a cascade of two AO cells. Thus, the problem of birefringence was solved and additionally the driving power per cell was decreased.

The paper briefly discusses the general principles of AO modulation of unpolarized light (Section 2). Sections 3 and 4 are devoted to design of the filters and characterization of the system for monochromatic light input. Performance of the developed device for multicarrier CWDM applications is discussed in Section 5.

## 2. Principle of operation

It is a common knowledge that Bragg diffraction of light by ultrasonic waves in birefringent crystals is more complicated than that in isotropic materials [2, 3]. Existence of two optical modes in a birefringent crystal and stimulated light conversion from one mode to another provide new regimes of diffraction absent in glasses and cubic crystals. One of the specific geometries of AO interaction in anisotropic media is characterized by a simultaneous diffraction of ordinary and extraordinary beams into opposite diffraction orders [7]. An angle between the facet of a piezoelectric transducer (PT) and an optical axis of a material *α* is usually defined as *cut angle* of the crystal. This regime of diffraction may be used for modulation and filtering of optical beams with arbitrary direction of polarization. The design of the cells is based on a specific geometry of AO interaction as described below.

The phenomenon of AO diffraction may be illustrated by means of wave vector diagrams that correspond to a momentum-conservation law during the interaction. Figure 1 depicts wave vector diagrams of AO interaction in the case of a simultaneous up- and down-shifted diffraction of beam components with different polarizations. A crystalline plane (110) of paratellurite was used in the further analysis because it provides the best AO properties of the crystal in the regime of anisotropic diffraction. This material is also highly gyrotropic around the optical axis. However for the interaction considered here, the light beams propagate far from the optical axis, hence optical activity can be neglected. For an extraordinarily polarized optical beam with the wave vector *k*⃗^{(e)}
_{i}, the phase matching condition is described by the equation

where *k*⃗^{(o)}
_{d} is the wave vector of the diffracted beam and *K*⃗ is the wave vector of ultrasound. Moreover, the extraordinarily polarized beam has a group vector *s*⃗^{(e)}
_{i} and propagates with a walk-off angle *β*. Simultaneously, the ordinarily polarized beam with the wave vector *k*⃗^{(o)}
_{i} may be diffracted by the same acoustic wave into the -1 order. Correspondent vector condition will be the following:

Here *k*⃗^{(e)}
_{d} is the wave vector of extraordinarily polarized diffracted light. Incidence and diffraction angles *θ*
^{(o)}
_{i}, *θ*
^{(e)}
_{i}, *θ*
^{(o)}
_{d}, and *θ*
^{(e)}
_{d} are measured relatively to the wave front of ultrasound.

In both vector triangles presented in Figure 1, the following relations between incidence and diffraction angles are valid:

and

where *V* is the phase velocity of ultrasound, λ is the optical wavelength in air, *n*
_{o} is an ordinary refractive index of the crystal, and *n*
_{e} is a direction-dependent refractive index for the extraordinarily polarized wave. Application of Eqs. (2) and (3) together with (1a) provides functions *θ*
^{(o)}
_{i} (*θ*
^{(e)}
_{d}) and *f*(*θ*
^{(e)}
_{d}), while a vector triangle (1b) gives relations *θ*
^{(o)}
_{d} (*θ*
^{(e)}
_{i}) and *f*(*θ*
^{(e)}
_{i}). Hence, a condition of simultaneous up- and down-shifted diffraction is expressed as a system of equations with unknown quantities *θ*
^{(e)}
_{i} and *θ*
^{(e)}
_{d}:

Solution of this system gives values of parameters *θ**_{i} and *f**=*f*(*θ**_{i}) that provide diffraction of unpolarized light.

Analysis shows that both *θ**_{i} and *f** are functions of the crystal cut angle *α*. Meanwhile, the magnitude of optimal Bragg angle *θ**_{i} is practically independent of the optical wavelength λ. Permanency of light incidence angle onto a crystal is an important advantage of this interaction geometry because it eliminates misadjustment of the cells while varying the wavelength of the optical carrier.

Tuning the ultrasonic frequency results in adjusting the wavelength of transmitted light. If the ultrasonic frequency *f** corresponds to the wavelength λ of one of the carriers of the WDM grid, modulation of this channel is provided. Variation of driving power is used for control of transmitted light intensity [7]. Application of several harmonic electrical signals to the PT provides the possibility of modulation of corresponding optical carriers independently.

The general scheme of beam traces and orientation of the cells is presented in Figure 2. In the first cell, the arbitrary polarized incident beam was split into two adjacent beams with orthogonal polarization even at a switched off ultrasound. The second AO cell compensated birefringence in the first crystal because it was placed symmetrically to the first one. Thus, an extraordinarily polarized beam was deflected by the second crystal to the same distance as by the first crystal but in the opposite direction. At a switched on ultrasound, diffracted beams of +1 and -1 orders (dashed lines) appear at the output of both cells. These beams were stopped by the shields as shown in the figure.

## 3. Design of the AO cells

In order to obtain both a high diffraction efficiency and good spectral resolution, we designed paratellurite-based AO cells with the cut angle *α*=10°. Calculations via Eq. (4) gives the magnitude of Bragg angle *θ**_{i}=12.1°. Usage of the filter as a modulator of light in the zeroth diffraction order determined configuration of the cells: both input and output optical facets were cut orthogonally to the beam, and antireflection coatings were fabricated on the crystals. Maximum reflectivity per surface in the cells was less than 0.3% in the range of wavelength from 1250 to 1550 nm with the minimum magnitude 0.11% for AO cell no. 1 and 0.13% for AO cell no. 2 at λ=1340 nm. Generation of ultrasound with the efficiency 50% and higher was provided in the range of radio frequency (RF) signals from 41 to 78 MHz in the first AOTF and from 37 to 79 MHz in the second AOTF. This corresponds to a near-infrared (NIR) spectral operation range of the AOTFs from 900 to 1700 nm. Thus, the system was capable of processing WDM signals in both 1260–1360 and 1530–1565 nm transmission windows that are widely used in optical networks [1].

Requirements of WDM standards restrict the performance of the filters because their passband should be narrower than the period of the optical grid. It is known that FWHM spectral bandwidth Δλ of a noncollinear AOTFs may be calculated as follows [8]:

where *l* is the length of the PT and *ψ* is the walk-off angle of ultrasound. The phase velocity of a slow shear acoustic wave in the chosen geometry of interaction equals to *V*≈710 m/s and the walk-off angle is as wide as 54° [9, 10]. Thus, it becomes possible to calculate the bandwidth of the filter on the basis of Eq. (5). The designed filters had the PT length *l*=12 mm and their passband was equal to Δλ=7.7 nm at λ=1310 nm and Δλ=10.8 nm at λ=1550 nm. Therefore, the AOTFs of the proposed configuration were capable of processingCWDMsignals with a 20 nm channel spacing over the entire band (1270–1610 nm) [4].

A requirement of precise compensation for birefringence demanded similarity of optical properties of both AO cells. To provide this, the cells were produced from a single bulk crystal of paratellurite after cutting the optical facets and welding the PT onto the crystal. The optical walk-off angle of an extraordinarily polarized wave in the crystal was equal to *β*=2.4°, so at the output of the first cell, the distance between the axes of the adjacent beams was equal to 1.1 mm. This magnitude is comparable with the width of the beams, therefore extraordinarily polarized component of the incident light may be lost if the shift was not compensated.

It may be shown that maximum diffraction efficiency, i.e. the ratio of intensities of incident and diffracted light, is obtained when the driving RF power equals to [8]:

where *M*
_{2} is the AO figure of merit of the medium in the chosen geometry of interaction [2, 3], and *b* is the width of the PT. For the designed cells with *b*=6 mm, the computation showed that driving power that was necessary for providing diffraction efficiency *T* >95% was equal to approximately 2.0 W for the longest wavelength of the tuning range. For a shorter wavelength the optimal driving power was lower due to a *P*
_{0}~λ^{2} dependence.

## 4. System layout

Basic experiments and testing of the system were done with a set of laser diodes in the wavelength range 1510–1570 nm. Corresponding frequency *f** was varied from 43.6 to 45.6 MHz. Electronic RF matching of both cells provided over 80% of conversion efficiency of electric power into the ultrasonic wave. Four independent laser diodes with the wavelengths λ_{1}=1510 nm, λ_{2}=1530 nm, λ_{3}=1550 nm, and λ_{4}=1570 nm were used as sources of optical carriers. Signals from the lasers were multiplexed and passed through the filtering module. A spectrum analyzer was used for measuring the parameters of the transmitted light.

The main filtering module of the system is presented in Fig. 3. Two similar gradient index lenses (1) were used to provide efficient input and output of light from the fiber pigtails. Since the Bragg angle *θ** is approximately constant in a wide range of optical wavelength, it was possible to carry out primary adjustment of the system using visible light of a He-Ne laser. For this purpose, an additional mirror (2) was used. The direction of the optical beam between the lenses was fixed with the help of two irises (3). Orthogonal incidence of the beam onto the facets of AO cells (4) was adjusted. After the primary adjustment, the visible channel with λ=633 nm was disabled and fine tuning was carried out with NIR radiation.

The measurement demonstrated that total insertion losses in the system were equal to -2 dB. The magnitude of losses was not dependent on the polarization of light. A driving RF signal was independently provided for each AO cell. Maximum attenuation of the optical signal was equal to -20 dB in each filter that corresponds to the diffraction efficiency *T*=99%. Diffraction efficiencies for the ordinarily and the extraordinarily polarized light were equal, therefore the same efficiency 99% was provided for a beam with arbitrary polarization. A simultaneous application of two identical electrical signals to both cells yielded a -36 dB attenuation of a correspondent carrier.

## 5. Multichannel operation

The main goal of the experiment was to test the setup in a multiwavelength regime of operation that is typical forWDMnetworks [1]. A traditional problem of applying AO devices in fiber optics is diffraction of different optical carriers on the side lobes of a spectral transfer function of the AOTF [11]. This phenomenon causes interchannel crosstalk and provides basic restriction for wide application of AO devices in optical communications. However, as the interchannel spacing in CWDM networks is relatively large (20 nm), these constraints become much less severe. Another problem of multichannel devices that are driven by several RF signals is presence of intermodulation and acoustic crosstalk [12]. In the cascaded system described here, these phenomena are significantly reduced because the operating frequencies are distributed among two cells instead of a single one as presented usually.

General theory of AO interaction demonstrates that the diffraction efficiency may be calculated as function of the Raman-Nath parameter *A* and dimensionless mismatch parameter *H*:

The Raman-Nath parameter *A* is proportional to the amplitude of the acoustic wave, while the mismatch parameter characterizes violation of phase matching conditions (1). Equation (7) gives two important consequences for the analysis of the multichannel operation of AOTFs. Evidently, absolute maximum diffraction efficiency *T*=1 is obtained in the case of phase matching (*H*=0) when the optimal driving power *P*
_{0} is applied to the filter. The equation for *T* in this case is the following:

This relation shows, that a driving power equal to 0.5*P*
_{0} if *A*≈0.7 provides approximately 80% diffraction efficiency. It means that operation of the device as an equalizer does not require more than 1Wfor a controlled channel. Distribution of four channels over two cells limited the driving power per cell to the tolerable magnitude of 2 W.

Another implication of (7) is obtained if the optimal driving power *P*
_{0} is applied to the AO cell, i.e. *A*=1. Then the diffraction efficiency can be considered as a function of the mismatch parameter *H*:

At a fixed ultrasonic frequency *f*=*f**, the magnitude of the mismatch *H* is proportional to a variation *δ*λ of the optical wavelength λ. A detailed analysis of the phase matching conditions (1) shows that *H*=1.6*δ*λ/Δλ, where the passband Δλ is described by Eq. (5). Equation (8b) describes a typical oscillating transfer function of an AOTF with a first side lobe *T*≈0.11 at *H*=±√8. This function determines the shape of the central maximum of the transfer function and also transmission of the filter outside the passband.

Diffraction efficiency in the AO cells was measured separately at the frequencies *f*
_{1}=45.4 MHz, *f*
_{2}=44.8 MHz, *f*
_{3}=44.2 MHz, and *f*
_{4}=43.6 MHz that correspond to the wavelengths of the lasers. The obtained spectrograms are presented in Fig. 4 with solid curves for the first AO cell and dashed curves for the second AO cell. The plot shows that the maximum of the first side lobe of the transfer function is situated near the central wavelength of the adjacent channel. This disadvantage of the device could be decreased, if the system was used in another spectral range. For example, for the wavelength λ=1310 nm, the mismatch for an adjacent channel with *δ*λ=20 nm equals to *H*=3.7. Therefore, the diffraction efficiency in the nearby channels does not exceed 0.5%.

Another factor that reduces amplitude of the side lobes is limitation of driving power. Analysis of Eq. (7) shows that a normalized magnitude of the first side lobe is reduced with the decrease of the driving power. For example, at *A*=1, the diffraction efficiency in the first side lobe equals to 11%. Meanwhile, if *A* tends to zero, the magnitude of the first side lobe equals to 5% of the central maximum. Usually a typical operation regime of an equalizer does not require diffraction efficiency higher than *T*≈0.3 [11]. It means that the first side lobe does not exceed 6% of the main maximum at the appropriate level of the driving power.

Basic characteristics of the developed AO cells are summarized for the carriers of CWDM standard in Table 1. The total range of nominal wavelengths from 1271 to 1611 nm includes 18 channels. One can see in the table that maximum driving power per channel varies from 1.2 to 2.0 W. Therefore, in practical cases where signals have to be reduced in several channels, total driving power is higher than 2W. Meanwhile, it is known that a stable operation of an AO cell is possible if the power of ultrasonic wave does not exceed 2 W [2]. One of the possibilities to decrease RF power consumption is optimization of parameters of the cells. For example, using an AOTF with a narrow PT (*b*≪*l*) gives a sufficient decrease in the magnitude of *P*
_{0}. In practice, the lower limit of the PT width is determined by the diameter of the optical ray. Another way of reducing the magnitude of *P*
_{0} is choosing a smaller cut angle of the crystal [8]. For example, a similar system on the basis of 6.5°-cut cell with *b*=2 mm and *l*=15 mm would demand maximum driving power *P*
_{0}=0.3 W per channel at λ=1610 nm and the level of crosstalk would not exceed -12 dB.

Experimental measurement of the interchannel crosstalks was carried out for the first (*f*
_{1}=45.4 MHz) and the second (f2=44.8 MHz) channels. The results are presented in Figure 5 together with theoretical predictions. Solid curves correspond to theoretical dependencies of central maximum and the first side lobe intensities on the Raman-Nath parameter. Experimental plots are given for the crosstalks both to a next (empty circles) and previous (filled squares) adjacent channels. Data presented by filled circles and empty square plots are in a good accordance with Eq. (8a) for the first and the second channel correspondingly. Analysis of the obtained data shows that at a low diffraction efficiency (*A*<0.5), the level of crosstalk does not exceed a statistical error during the measurement. At greater driving power, the diffraction on the side lobes was observed, but it was lower than that predicted by theory because the maximum of the side lobe was not exactly coincident with the wavelength of a nearby carrier.

## 6. Conclusion

We developed a prototype of an AO equalizer for CWDM optical networks. A cascade of two similar modulators was capable of simultaneous independent filtering and modulation of several optical carriers. Overall optical insertion losses did not exceed -2 dB, while a -20 dB suppression of the signal required less than 2 W of RF power. The advantages of the developed system are the simplicity and the small size of the setup. The system is universal and may be applied in any transmission window that is used in fiber-optical communications. The speed of response of AO modulators is about 10^{-5} sec. That is quite enough for compensation for laser drifts. At the same time, variations of transmission coefficient are much slower than the rate of data transfer. Therefore, usage of the equalizer does not influence information flow through the fiber.

The AOTFs that were used in the system possessed a passband Δλ≈11 nm at λ=1550 nm and were tested in a four-channel operation mode. Operation of the system with a greater number of carriers was not possible because of a high power consumption of the device. Never-theless, this restriction is not crucial and it may be avoided by a proper design of the cells. The advantages of the proposed method of equalization of optical carriers is that the same filtering module may be used for processing any set of channels within the tuning range of the filter. An increase of the number of equalized channels does not require any complication of the optical module of the system due to a flexible configuration of the filters.

## Dedication

The paper is dedicated to the memory of our colleague Alexander Tchernyatin who contributed to the research and tragically died in a road accident.

## References and links

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