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Abstract
The high efficiency acousto-optic modulators become indispensable in photonics and optoelectronics for the pulse generation and signal modulation in optical display and telecommunications. In this paper, the validity and feasibility of the biaxial crystals as acousto-optic mediums have been theoretically analyzed and confirmed by experiments using a biaxial crystal of β-BaTeMo2O9. The diffraction angle and diffraction efficiency of the β-BaTeMo2O9 acousto-optic Q-switch are determined to be 1.420° and 78.1%, which are comparable with that of TeO2 acousto-optic modulator at the identical operating wavelength of 1064 nm and 100 MHz, respectively. The minimum of the modulated pulse width can be achieved to be 6 ns at 5 kHz with Nd:YVO4 as the gain medium. The results not only provide an excellent acousto-optic medium, but also explore the field of biaxial acousto-optic medium for device fabrications.
© 2017 Optical Society of America
1. Introduction
Acousto-optic (A/O) modulation is an essential operation in optoelectronics and photonics, such as optical interconnection, environment monitoring, bio-sensing, medicine and security applications [1–6]. Right now, SiO2 glass, PbMoO4, and TeO2 crystals are widely used mediums for A/O devices [7–9]. SiO2 glass, in general, affords practically important amorphous media for the ease in fabrication, and the availability in large size and arbitrary shape. But the radio frequencies applicable to glass are limited to 100 MHz because of its large acoustic attenuation [10]. The large figure of merit, M2 = 36 × 10−18 s3/g, as well as low acoustic loss, make PbMoO4 crystals very useful for practical A/O devices [5, 10]. However, PbMoO4 is a leaded compound and has a completed cleavage normal to c axis. TeO2 is the most wide-ranging crystalline medium because of its low acoustic velocity, large figure of merit, and low attenuation along [110] [11, 12]. However, TeO2 is grown by Czochralski or Bridgeman method, and crystals with high quality are difficult to obtain [13]. It is obviously that the widely used A/O crystals are usually uniaxial crystals. Although the light propagation in biaxial is more complex than that in uniaxial crystal, the biaxial crystals are still promising for A/O devices due to their excellent A/O properties. However, rare report on biaxial crystal prisms was found.
To design A/O devices with high diffraction efficiency, the crucial factor is a medium with excellent A/O properties. Furthermore, figure of the merit for fully evaluating the A/O properties of materials is, where n, p, ρ and ν are the refractive index, photo-elastic constant, density and acoustic velocity of the materials, respectively. Since the parameters of p, ρ and ν exhibit no extreme variations from one material to the next, the advantage usually lies with mediums having large refractive index in combination with good quality and acoustical quality. Guidelines, simultaneously, were established which directed this search to relatively soft yet dense materials having heavy cations [14].
The biaxial crystal β-BaTeMo2O9 (β-BTM) was a novel photoelectric material which was first grown using the top-seeded solution growth (TSSG) method by our group [15–17]. It crystallizes in the noncentrosymmetric system, space group P21 (no. 4), with β = 90.897°. β-BTM crystal exhibits wide transmission (0.5-5.0 μm), large refractive index (2.15@1064nm), suitable hardness (mohs~4.8), no cleavage [18,19]. Its growth habit shows that it can be easily obtained with large size and high quality. All these mentioned above are benefit for the high quality A/O devices. Thus, the A/O devices based on the β-BTM is of high interest, though it is a biaxial crystal.
In this letter, the feasibility and validity of the biaxial crystals as A/O medium have been theoretically analyzed and investigated by experiments using the biaxial crystal of β-BTM for the first time. The β-BTM A/O Q-switch exhibits the diffraction angle and diffraction efficiency to be 1.420° and 78.1%. The minimum of the modulated pulse width can be achieved to be 6 ns at the PRR of 5 kHz with Nd:YVO4 as the gain medium.
2. The operation principles of A/O interaction in biaxial crystal
Different from the uniaxial crystal, the A/O interaction in biaxial crystal is more complicated. Figure 1 shows the schematic diagram of A/O interaction in biaxial A/O devices. The operating principle of an A/O modulator is that, high-frequency sound wave in the megahertz range is generated by the driver, then applied to a piezo transducer. The presence of the acoustic waves causes a periodical optical index profile through the photo-elastic effect, which can be viewed as a dynamic optical phase grating with adjustable wavelength and amplitude introduced in A/O medium [20], the schematic diagram of A/O interaction is shown in Fig. 1, accordingly. Regarding the refractive-index ellipsoid, the originally spherical surface is stretched or compressed under the A/O interaction [21]. Since TeO2 and PbMoO4 belong to uniaxial crystal [5, 11], the polarization characteristic would be more intricate here in biaxial crystal. Figure 2(a) clearly shows the variation of the refractive-index ellipsoid with the uploading ultrasonic wave in the biaxial crystal, and the refractive index ellipsoid equation of biaxial crystal considering the stiffness matrix can be expressed as [19]:
Where nx, ny and nz are the refractive index of the optical axes, Δnx, Δny and Δnz are the variation of the refractive index affected by A/O interaction along X, Y, and Z axis, respectively.
Fig. 1 The principle diagram of the A/O interaction in the A/O modulator. 1. Electrode Layer. 2, Piezoelectric Transducer. 3, Electrode Layer. 4, Bonding Layer. 5, Electrode Layer. 6, Acousto-optic material.
Fig. 2 a, The refractive-index ellipsoid of the biaxial crystal. b, The refractive-index ellipse with light propagating along one axis for the biaxial crystal. c, The refractive-index ellipsoid of the uniaxial crystal. d, The refractive-index ellipse with light propagating along one axis for the uniaxial crystal.
Since β-BTM crystal exhibits excellent piezoelectric properties (d34 = 30.25 pC/N, S44 = 36.46 pm2/N), to avoid the influence of the piezoelectric effect of this β-BTM crystal on the A/O interaction, the propagation of acoustic wave along X axis is selected for the poorest piezoelectricity according to the matrix of piezoelectric constant [22]. Moreover, the incident light are propagating along Y axis, which are parallel to the crystallographic b axis in this piezo-coordinate system. The Eq. (1) can be simplified if the incident light propagates along one of axes, as shown in Fig. 2(b). The refractive index ellipsoid can be simplified as an ellipse with Z = 0 taking the light propagation along optic Z axis, which can be expressed as:
Where p13 and p23 are the effective A/O coefficients of this β-BTM A/O medium, S3 is the strain vector element along Z axis.The simplified equations were also suit for uniaxial crystal, as shown in Figs. 2(c) and 2(d), which means that biaxial crystals can also be used as A/O mediums when the incident light propagates along one axis. Since the A/O interaction in β-BTM crystal can be treated as that in uniaxial crystal in this condition, the principle of the normal Bragg diffraction can be applied equally to the biaxial crystal with the longitudinal wave propagating along the Z axis.
3. The architectures of the A/O modulator based on the β-BTM crystal
The architectures of the β-BTM A/O modulator including an A/O modulator element and driver electronics unit were shown in Figs. 3(b) and 3(c), respectively. The β-BTM A/O modulator element was mainly fabricated with piezoelectric transducer, the A/O medium, and impendence-matching network, followed by electrode layer, bonding layer and acoustic absorber, as shown in Figs. 3(a) and 3(c), respectively. The 36°-Y cut LiNbO3 with dimensions of 14 × 4 × 0.035 mm3 operating at 100 MHz was used as a piezoelectric transducer. The β-BTM crystal with a size of 14 × 10 × 5 mm3 was cut with light propagating along Y-axis and acoustic wave along X axis as A/O medium. Both the Y- and X-planes were polished, while the Y-planes with no coating. Au of a thickness of 2.52 μm was used to the electrode layers, and the thickness of piezoelectric transducers and the tin banding layer are 35 μm and 4.93 μm, respectively. The impendence-matching network was determined to be 50 Ω, which was used to inhibit the emission of the electric power. Then the β-BTM A/O modulator was packaged as shown in Fig. 3(b). The driver electronics unit was shown in Fig. 2 with the TTL (Transistor-Transistor Logic) modulation signal, and the operating voltage was designed to be + 24 V DC. The driving power and the modulated bandwidth was determined to be 1.80 W and more than 1 MHz, respectively. Simultaneously, 78.1% of the diffraction efficiency was obtained on this β-BTM A/O modulator, which was comparable with that of TeO2 with the same transducer, impendence-matching network, and the testing conditions. Then, the systemically measurements on this β-BTM A/O modulator were performed to characterize its modulation properties.
Fig. 3 The completed A/O device made by β-BTM. a, The internal structure diagram of the A/O modulator element. b, The packaged A/O modulator element. c, The driver electronics unit of the β-BTM A/O modulator.
4. The A/O properties of the β-BTM A/O modulator
The β-BTM A/O device was used in Nd:YVO4 and Nd:YAG Q-switch laser output. The experimental configurations are shown in Fig. 4. The pump source was a fiber-coupled continuous-wave (CW) LD emitting at 808 nm with a radius of 400 μm. The laser cavity was made up of an input mirror M1, a Nd:YAG or Nd:YVO4 crystal, the β-BTM A/O Q-switching device, and an output mirror M2. M1 was a plano-concave mirror with a curvature radius of 100 mm. The plane was anti-reflection coated at 808 nm (AR, R<0.2%); the concave face was coated for high transmission at 808 nm (HT, T>95%) and high reflection (HR, R>99.5%) at 1064 nm. A 1.0 at.% Nd-doped YAG crystal with the size of 3 × 3 × 3 mm3, and an a-cut 0.3 at.% Nd-doped YVO4 crystal with the size of 3 × 3 × 10 mm3 were AR coated at 808 nm and 1064 nm on both sides. The output mirror is a flat mirror, and was HR coated at 808 nm, with 10% transmission at 1064 nm. The laser crystals of Nd:YAG and Nd:YVO4 were wrapped with indium foil and mounted in a copper block cooled by water at a temperature of 18 °C. The β-BTM A/O modulator was located beside the gain medium. The overall fundamental cavity length was about 40 mm. The temporal behaviors of the modulated pulse were recorded by a digital oscilloscope (Tektronix, DPO7104) and a photodetector (EOT, model ET5000A).
5. Discussion
As a new kind of biaxial mediums for A/O devices, Fig. 4 shows the experimental configuration of this β-BTM A/O modulator. Firstly, the average pulse width verse pump power at the pulse repetition rate (PRR) of 5 kHz, 10 kHz and 15 kHz, and the narrowest pulse with Nd:YAG as gain medium, were shown in Figs. 5(a) and 5(b), respectively. The modulation pulse width decreased as the input power increased, and 16 ns of pulse width was obtained with the input power of 1.07 W. The minimum pulse width in our experiments was 6 ns with the incident pump power of 1.15 W and the PRR of 15 kHz under the configuration of Nd:YVO4 as gain medium, as shown in Fig. 6(b). Each point of the modulation pulse width was obtained by averaging arbitrary 8 pulse-width values obtained from the oscilloscope. Next, the effects of the light polarization on the average modulation pulse width and typical pulse were investigated with Nd:YVO4 as gain medium, as shown in Fig. 6. Figures 6(a) and 6(c) presented the modulation pulse width verse the pump power at the PRR of 5, 10, and 15 kHz, and with the incident light in horizontal polarization and in vertical polarization with Nd:YVO4 as gain medium, respectively. The typical narrowest pulse consistent with the incident light in horizontal and vertical polarization were 6 ns and 17 ns with the pump power of 3.5 W, corresponding to the PRR of 5 kHz and 15 kHz, as shown in Figs. 6(b) and 6(d), respectively. The modulation pulse width with continuous-wave laser operated by Nd:YVO4 in horizontal polarization was much narrower than that in vertical polarization, which might illustrate that the polarization of the incident light played a very important role on the variation of the modulation pulse-width. Figure 7 depicted the pulse trains at the incident pump power of 3 W and at the PRR of 5 kHz, which were relatively stable and uniform with no noise, and it could satisfy the requirements of laboratory. Simultaneously, the variation of diffraction angle via polarization of the incident light was investigated with Nd:YVO4 as gain medium. The diffraction angles varied from 1.420° in horizontal polarization to 1.386° in vertical polarization with the β-BTM A/O modulator. The possible reasons for the variation of the diffraction angles were the asymmetry and the strong piezoelectric properties of β-BTM crystal. It had reported that β-BTM single crystal exhibited excellent piezoelectric properties [22], and the distortions destroy the superposition of the positive and negative charge centers in the cell, resulting in electric dipoles in the crystal. Consequently, the direction of the acoustic wave was selected to be corresponding to the weakest piezoelectricity.
Fig. 5 β-BTM A/O modulation pulse width and the minimum pulses with Nd:YAG as gain medium. a) The modulation pulse width of continuous-wave laser. b) The typical modulation pulse of continuous-wave laser operated.
Fig. 6 β-BTM A/O modulation pulse width and the typical minimum pulse with Nd:YVO4 as gain medium. a) The modulation pulse width versus input power with continuous-wave laser operated in horizontal polarization. b). The modulation pulse of continuous-wave laser operated by Nd:YVO4 in horizontal polarization. c) The modulation pulse width versus input power with continuous-wave laser operated in vertical polarization. d) The typical modulation pulse of continuous-wave laser in vertical polarization.
The sensitivity to the polarization of the β-BTM A/O modulator had put forward to the higher requirement for the crystal fabrication or the operating laser sources. Correspondingly, the acoustic velocity was calculated to be 4269 m/s and 4392 m/s at 100 MHz in horizontal polarization and vertical polarization by the equation of , respectively, where θB is the diffraction angle, λ is the wavelength, f is radio-frequency, V is the sound velocity. Then the corresponding acoustic impendences were 2.338 × 107 kg/(m2·s) and 2.406 × 107 kg/(m2·s), which were calculated by multiplying the density and the sound velocity of the β-BTM under 100 MHz.
Since the diffraction angle, diffraction efficiency, and modulation pulses are insufficient to completely characterize the properties of the β-BTM A/O modulator, some other technical parameters have been investigated to fully evaluate the β-BTM A/O Q-switch, including pulse rise time τr, pulse fall time τf, electrical power consumption P, driving power, and effective light aperture D. The temporal behaviors of the modulation pulse were recorded on the oscilloscope with the impendence of 50 Ω settled. Then the experimental value of the pulse rise time was about 56 ns, which was in agreement with the calculated value of 53 ns using the equation of , where d is the beam waist diameter of the Guassian beam, and V is the sound velocity of the β-BTM crystal under the radio-frequency of 100 MHz. Correspondingly, the pulse down time was about 100 ns. The driving power PD operating on the transducer was 1.80 W, the effective light aperture D was investigated to be 0.5 mm by evaluating the diffraction efficiency, and the electrical power consumption P was measured to be 480 W. The above measurements indicate that this biaxial crystal, β-BTM, can be used for the A/O device, and the A/O interaction on the refractive index are almost the same when the light propagates along one of the axes. This work can overcome the limitation of the A/O crystalline materials in traditional uniaxial crystal and provide new functionality for biaxial crystal as the A/O medium.
Table 1 lists the properties of the most widely used material of TeO2 and β-BTM for A/O modulators. Limited by the transmission bands and the quality of the single crystals, TeO2 were generally applied in the small dimensions of A/O devices, while an obvious absorption peak in the transmission band of 3-5 μm limits their application in mid-infrared band. Compared to TeO2, β-BTM crystal exhibits a good transmittance from 0.5 to 5.0 μm with no absorption. The refractive index of this crystal in its transmission ranges can be comparable with that of TeO2. The diffraction efficiency of 78.1% and the diffraction angle of 1.42° were comparable with those of TeO2 in the same transducer, impendence-matching network, and the driving power. Since the β-BTM A/O modulator is designed for 1064 nm, and the diffraction efficiency and diffraction angle were the priority for the application, which suggests that β-BTM crystal can be an excellent candidate for A/O modulator in a wide wavelength region.
Table 1. Properties of widely used materials for A/O modulator
6. Conclusion
In conclusion, the theoretical analysis of A/O interaction on biaxial crystals has demonstrated that biaxial crystals can be used as A/O materials when the incident light propagates along one of the axes, which has been made a breakthrough in terms of A/O materials. The biaxial β-BTM A/O modulator with diffraction angle of 1.420° and diffraction efficiency of 78.1% has been fabricated with the operating wavelength of 1064 nm and the radio-frequency at 100 MHz. The minimum of the modulated pulse width can be achieved to be 6 ns with Nd:YVO4 as the gain medium. The systematically investigations on the β-BTM A/O Q-switch indicates that β-BTM is an excellent A/O medium, though it is a biaxial crystal. Moreover, since its high transmission in 0.5-5 μm, β-BTM would be a strong competitive A/O material in the 3-5 μm range.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51321091, 51202128, 51227002, 51323002 and 61405073), National key Research and Development Program of China (Grant No. 2016YFB1102201), and the Program of Introducing Talents of Disciplines to Universities in China (111 Program No. b06015).
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