Kovacs effect enhanced broadband large field of view electro-optic modulators in nanodisordered KTN crystals

Yun-Ching Chang; Chao Wang; Shizhuo Yin; Robert C. Hoffman; Andrew G. Mott

doi:10.1364/OE.21.017760

1. Introduction

Although 40 + GHz waveguide based electro-optic (EO) modulators have become commercially available and have been successfully deployed in broadband fiber optic communication networks, they are not suitable for some other applications such as modulating retro reflectors (MRR) for broadband free space optical communication, high- speed large aperture optical shutters, laser pulse shaping, and laser Q-switches, which demand not only high modulation speed (~GHz) but also large optical throughput (mm - cm range aperture) and large field of view (e.g., +/−30 deg). Thus, there is a continuous effort to develop non-waveguide based, broadband, large field of view EO modulators in the past four decades. Due to the existence of birefringence in linear EO crystals such as lithium niobate (LiNbO₃), they are not suitable for large field-of-view electro-optic modulators. Thus, quadratic EO materials (crystals and ceramics) are preferred for this application. Among the different types of quadratic EO materials available, the EO ceramic lead lanthanum zirconatetitanate (PLZT) was intensively investigated for the application of large aperture and large field of view electro-optic modulators and shutters [1, 2]. Although PLZT based electro-optic modulators can have a large aperture and large field of view, the speed is limited in the MHz range due to the existence of multiple domains in the ceramic material. It is extremely challenging to increase the speed of PLZT ceramic based modulator in the GHz range due to the slow domain wall movement.

On the other hand, EO potassium tantalate niobate [KTa_1-xNb_xO₃ (KTN)] crystals also have a large quadratic EO coefficient and have been studied for more than four decades [3, 4]. However, high quality, sizable KTN -crystals suitable for device fabrication have only become commercially available in the past several years, which allow us to investigate KTN modulator from the practical device point of view [5]. One of the key factors that affect the practical usage of electro-optic modulators is the driving energy and driving power that is proportional to the quadratic electro-optic efficient. Even with the large quadratic electro-optic coefficient of KTN crystal, the driving energy still increases rapidly as the aperture size increases. Thus, there is a critical need to further increase the EO coefficient, in particular for the large aperture and high speed electro-optic modulator because the driving power is driving energy divided by the modulation speed. For example, a one-nanosecond modulation speed will require a 1 megawatt (MW) driving power even with a 1 mJ driving energy. Such a large driving power is not preferred from the device point of view.

Recently, nanodisordered KTN crystals, created by super-cooling, were investigated [6–8]. There were polar-nano regions (PNR) in the nanodisordered KTN crystal and the crystal was in the non-thermal-equilibrium state. The unique physical effect-Kovacs effect (i.e., system state depending on the thermal cycling history) exists in such kind of nanodisordered KTN crystals. It was found out that the light field induced refractive index change (optical Kerr effect) could be enhanced in nanodisordered KTN crystals via the super-cooling process. The diffractionless optical transmission was successfully realized in nanodisordered KTN crystals [6]. To take advantage the unique feature of nanodisordered KTN crystal (i.e., the existence of PNR), in this paper, instead of investigating the application of enhanced optical Kerr effect for diffractionless optical transmission, we conducted a quantitative study on the enhanced electro-optic effect in nanodisordered KTN crystal by the Kovacs effect and its application to broadband large field of view EO modulators. We determined that the EO coefficient can be substantially enhanced (a 3.5 fold increase) due to the existence of Kovacs effect in nanodisordered KTN crystals and the half-wave driving voltage can be correspondingly reduced from 1500 V to 800 V in a nanodisordered KTN crystal based electro-optic modulator. This will be greatly beneficial for the construction of a broadband large field- of-view EO modulator due to the reduced driving energy and driving power.

2. Kovacs effect enhanced electro-optic modulation in nanodisordered KTN crystal

The Kovacs effect refers to the phenomenon that irreversibly deformed glassy materials can remember their deformation history [9]. Thus, at a given temperature and pressure, the system behavior can be different at the nonequilibrium state, depending on the thermal cycling history. For a relaxor ferroelectric such as KTN, it can become a nanodisordered crystal, containing PNR, via the supercooling process [6–8]. In this case, the KTN is in the deformed glassy state. One of the key features of the nanodisordered KTN is that one can substantially increase the electric susceptibility without increasing the optical scattering. For the conventional KTN crystal, although the electric susceptibility, $χ$ , increases as the temperature approaches the phase transition temperature, $T_{c}$ , as given by

χ \propto \frac{1}{{(T - T_{c})}^{δ}},

where

δ

is a critical parameter, the correlation length,

r_{c}

, also correspondingly increases, as given by

r_{c} \propto \frac{1}{{(T - T_{c})}^{δ / 2}} .

Since the physical meaning of correlation length, $r_{c}$ , in Eq. (2) is related to the average size of ferroelectric clusters in the paraelectric matrix, it limits the maximum achievable value of $χ$ by simply making T close to $T_{c}$ due to the potential scattering effect.

However, the temperature dependent bond between $χ$ and $r_{c}$ is broken for the nanodisordered KTN crystal. The correlation length will be limited by the dimension of PNR, which is much smaller than the optical wavelength. Thus, one can substantially increase $χ$ by employing proper thermal cycling without suffering the limitation of optical scattering, as illustrated in Fig. 1. It can be seen that the electric susceptibility of point A is much higher than that of point B although they are at the same temperature because they have different temperature histories (i.e., Kovacs effect) [10]. To illustrate the advantage of applying this larger electric susceptibility to electro-optic modulator, in this section, we will derive a quantitative relationship between the electrical driving energy/power and the electric susceptibility for the nanodisordered KTN crystal based EO modulator. It can be seen that such an enlarged electric susceptibility cannot only enhance the refractive index modulation but also reduce the switching energy/power although it is also proportional to the electric susceptibility [10].

Fig. 1 A conceptual illustration of electric susceptibility as a function of temperature for a nanodisordered KTN crystal with different temperature cycling histories. Solid curve: reduce decreasing temperature, dashed curve: increase increasing temperature [10].

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Figure 2 is a conceptual illustration of a large aperture KTN based transversal electro-optic modulator, where $w, L, and t$ denote the gap between two electrodes, the length of the electrode, and the thickness of the crystal, respectively. For the purpose of simplicity, we consider the case of $w, L ≫ t$ , which is a realistic case. In this case, we can assume that the electric field is uniformly distributed within the crystal and along the vertical (y) direction, as illustrated in Fig. 2.The stored electric energy, $U$ , is then given by

\begin{array}{l} U = \frac{1}{2} ε \int_{V} {| E |}^{2} d V \\ = \frac{1}{2} ε_{0} ε_{r} E^{2} L \times w \times t \approx \frac{1}{2} ε_{0} χ E^{2} L \times w \times t, \end{array}

where

ε 0

is the dielectric constant in vacuum,

ε_{r}

is the relative dielectric constant and approximately equals to

χ

when

χ ≫ 1

for the case of nanodisordered KTN crystal, and

E

is the magnitude of the applied electric field. The electric field induced refractive index difference between the horizontal (x) and vertical (y) polarized light,

Δ n

, is expressed as [3]

Δ n \approx \frac{1}{2} n_{0}^{3} ε_{0}^{2} χ^{2} (g_{11} - g_{12}) E^{2},

where

n_{0}

is the refractive index without external electric field, and

g_{11}

and

g_{12}

are the quadratic electro-optic coefficient. The quadratic electro-optic coefficient

g_{i k}

instead of

s_{i k}

is used in Eq. (4) because

g_{i k}

is the proportional coefficient between the optical impermeability tensor and electric polarization density, which does not depend on electric susceptibility,

χ

. On the other hand,

s_{i k} = ε_{0}^{2} χ^{2} g_{i k}

is the proportional coefficient between the optical impermeability tensor and electric field, which does depend on electric susceptibility [11]. This was confirmed by the experimental results of [5]. Figure 6 and Fig. 7 in [5] depicted the experimentally measured relative dielectric constant (~approximately equal to electric susceptibility

χ

) and

s_{11}

as a function of temperature, respectively. It can be clearly seen that the slope of

s_{11}

is higher than that of

χ

, which indirectly confirms that

s \propto χ^{2}

. Based on Eq. (4), the required half-wave switching electric field,

E_{π}

, which changes the polarization state of the light in phase of

π

(

Δ n \times t = λ / 2

) for a Kerr electro-optic modulator, as depicted in Fig. 2 can be derived as

E_{π} = \sqrt{\frac{λ}{n_{0}^{3} ε_{0}^{2} χ^{2} (g_{11} - g_{12}) t}},

where

λ

is the wavelength of the light. Substituting Eq. (5) into Eq. (3), the required half-wave electric switching energy,

U_{π}

, is obtained as

U_{π} \approx \frac{1}{2} ε_{0} χ E^{2} L \times w \times t = \frac{λ L \times w}{2 n_{0}^{3} ε_{0}^{} χ (g_{11} - g_{12})} .

Since

U_{π}

is inversely proportional to

χ

, the increased electric susceptibility for the nanodisordered KTN can reduce the required switching energy.

Fig. 2 A conceptual illustration of a transversal large aperture nanodisordered KTN crystal based electro-optic modulator.

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3. Experiments and discussions

To experimentally confirm that the switching energy/power can be reduced by employing nanodisordered KTN crystal, we conducted following experiments: first, we fabricated a transverse KTN based EO modulator, as shown in Figs. 3(a) and 3(b), respectively. The KTN crystal used in the transverse EO modulator had a composition of KTa_0.65Nb_0.35O₃ and a dimension of 10 mm x 10 mm x 0.5 mm. Gold electrodes with a width of 1.75 mm were coated on both top and bottom surfaces, as illustrated in Fig. 3(a). After the electrode coating, the optical aperture dimension of the modulator became $L = 10 mm$ , $w = 6.5 mm$ , and $t = 0.5 mm$ . Since both L and w were much larger than t, the electric field was quite uniform within the crystal.

Fig. 3 (a) A schematic sketch of transverse EO modulator; (b) picture of fabricated transverse EO modulator.

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Second, we measured the half wave switching voltages, $V_{π}$ , at the same temperature but with different thermal history. Since the half wave switching voltage is inversely proportional to electric susceptibility, as given by

V_{π} = E_{π} w = \sqrt{\frac{λ w^{2}}{n_{0}^{3} ε_{0}^{2} χ^{2} (g_{11} - g_{12}) t}},

one should see a reduced half wave voltage if there is a Kovacs effect enhanced

χ

. In the experiment, half wave voltages were measured at different temperatures and with different temperature history. One sample was measured during the temperature increasing process, corresponding to point B of Fig. 1. The other one sample was measured during the temperature decreasing process, corresponding to point A of Fig. 1. The temperature changing rate was 0.1°C/s. The Curie temperature of the KTN sample was −4°C. Since there could be condensed water on the crystal surface when temperature closed to the dew point ( = 1.9°C when relative humidity, RH = 30% at an air temperature of 20°C), the measurement was conducted within a temperature range >2°C that minimized the frost. The half wave voltage was determined by measuring the optical transmission as a function of applied driving voltage. Then,

s_{11} - s_{12}

value was determined from the measured half wave voltage, as given by

s_{11} - s_{12} = ε_{0}^{2} χ^{2} (g_{11} - g_{12}) = \frac{λ w^{2}}{n_{0}^{3} t} \times \frac{1}{V_{π}^{2}} .

Figure 4 shows the experimentally measured quadratic electro-optic coefficients $s_{11} - s_{12}$ as a function of temperature for different temperature cycling histories. The circle and square lines denote the temperature decreasing and temperature increasing processes, respectively. One can clearly see that the quadratic EO coefficients $s_{11} - s_{12}$ were larger when the sample had a decreased temperature cycling history due to the formation of a nanodisordered KTN crystal. Also, the difference of EO coefficient between the decreasing and increasing temperature cycling histories become larger and larger when the temperature approaches the Curie point. For example, $s_{11} - s_{12} = 5.78 \times 10^{- 15} m^{2} {/V}^{2}$ with a decreasing temperature history at 2.5°C. On the other hand, $s_{11} - s_{12} = 1.64 \times 10^{- 15} m^{2} {/V}^{2}$ with an increasing temperature history at the same 2.5°C measurement temperature. Thus, there is a 3.5 fold increase in quadratic EO coefficient, which results in a factor of 1.87 reduction in required driving voltage. An even larger increase in electro-optic coefficient is anticipated when the measurement temperature approaches the Curie temperature −4°C which will be investigated in the future. It should be noted that as the temperature closes to the paraelectric (PE) - ferroelectric (FE) phase transition temperature, the optical depolarization may happen due to scattering from the FE clusters embedded in the PE matrix and decrease the EO effect [12]. However, this adverse effect is substantially alleviated due to the reduced cluster size (i.e. from micro-clusters to nano-clusters) by the supercooling process. In other words, since the dimension of nano-clusters is much smaller than that of optical wavelength, the adverse optical depolarization effect becomes smaller, this allows the operation temperature to be close to the phase transition temperature.

Fig. 4 The experimentally measured transmission quadratic EO coefficient as a function of temperature. Circle line: decreasing temperature history; Square line: increasing temperature history.

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Also, it is known that the Curie temperature and EO coefficient of KTa_1-xNb_xO₃ crystal depend on the composition parameter x. They can have very different values when the value of x changes, which can affect the enhancement factor of Kovacs effect. Thus, it is possible to achieve an even larger enhancement factor (i.e., >3.5) for a KTN crystal with other composition parameter x (e.g., x = 0.4), which will be further investigated in the future.

To ensure that the nanodisordered KTN crystal based EO modulator was a broadband electro-optic modulator, the response time of the modulator was measured by using the experimental setup, as depicted in Fig. 2. A high voltage pulsed voltage power supply with a maximum output voltage 10,000V, a rise time 1 ns, and a 50 Ω impedance was used to drive the EO cell. A high speed photodetector with a <1 ns response time was used to detect the output optical pulse. To minimize the influence from the capacitance of EO modulator, the length of the electrode was reduced from L = 10 mm to L = 2 mm while maintaining the same gap, w = 6.5 mm. Figure 5 shows the experimentally detected output signal as a function of time when a square pulse (corresponding to the half wave voltage of the modulator) was applied on the modulator. It can be seen that the rise time, defined as the time from 10% to 90%, closes to 1 ns. Thus, the developed modulator is indeed a broadband modulator with a GHz bandwidth. It should be noted that the rising time is mainly limited by the RC time constant rather than the quadratic EO effect itself. It should also be mentioned that as the temperature approaches to the phase transition temperature, the dielectric constant $ε$ increases, which can increase the capacitance and rise time if all the other parameters remain the same. However, since the electro-optic effect induced refractive index change is approximately proportion to the square of dielectric constant, as given by Eq. (4), one can maintain the same capacitance by using a wider electrode gap, W, as illustrated in Fig. 3(a), to compensate the increase of dielectric constant without increasing the half-wave voltage so that the overall capacitance maintains the same. In practice, since the driving energy is inversely proportional to dielectric constant, as given by Eq. (6), a higher dielectric constant is preferred. Furthermore, we also measured the field of view of the EO modulator by measuring the extinction ratio as a function of incident angle. In the experimental measurement, the EO modulator was rotated by a precise rotating stage. The transmittances were measured at both the ON state (i.e., the transmission state with the half wave voltage) and OFF state (i.e., blocking state without the applied voltage) for a set of incident angles within the range of +/− 30 deg. Mathematically, the extinction ratio is defined as $E_{r} = \log (T_{o n} / T_{o f f})$ and in units of OD. The blue line of Fig. 6 shows the experimentally measured extinction ratio. It can be seen that the extinction changes slowly as the incident angle increases. For the purpose of comparison, the extinction ratio as a function of rotation angle for the linear LiNbO₃ based EO modulator with the same transverse configuration was also measured, as depicted in red line of Fig. 6. By comparing two plots, one can clearly observe that the presented EO modulator indeed has a larger field of view than the conventional linear EO modulator.

Fig. 5 The experimentally measured response time of the nanodisordered KTN crystal based quadratic EO modulator.

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Fig. 6 The experimentally measured extinction ratio as a function of incident angle. Solid line: the result for nanodisordered KTN crystal based quadratic EO modulator; dashed line: the result for lithium niobate based EO modulator.

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4. Conclusion

A lower driving energy/power EO modulator based on nanodisordered KTN crystal was developed. First, a transvere KTN crystal-based EO modulator was built. Second, the nanodisordered KTN crystal was created by the supercooling process. The major advantage of nanodisordered KTN crystal was the increased electric susceptibility by the Kovacs effect. In this paper, we theoretically predicted and experimentally verified that the driving energy/power could be substantially reduced (almost by half in terms of half-wave voltage) by applying Kovacs effect because the driving energy was inversely proportional to the electric susceptibility. This was particularly beneficial for the large aperture EO modulator because the driving energy/power was also proportional to the aperture size. A reduction in driving energy could be very helpful for increasing the aperture size. Furthermore, we also experimentally demonstrated that this kind of EO modulator was also broadband (GHz range) and had a large (+/−30 deg) field of view. Since the KTN crystal is highly transparent within 400 nm to 4000 nm spectral range [13] and the optical attenuation except the Fresnel surface reflection loss is less than a couple of percent, the modulation bandwidth could be further increased by taking advantage the broad transmittance of KTN crystal (400 nm – 4000 nm) such as via wavelength division multiplexing (WDM) technology [13]. The presented EO modulator could play an important role in a variety of applications such as modulating retro reflectors for broadband free space optical communications, laser Q-switches, laser pulse shaping, and high-speed optical shutters.

Acknowledgments

Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-09-2-0016. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation heron.

References and links

1. J. Cutchen, “PLZT thermal/flash protective goggles: device concept and constraints,” Ferroelectrics 27(1), 173–178 (1980). [CrossRef]

2. G. H. Haertling, “PLZT electrooptic materials and applications - a review,” Ferroelectrics 75(1), 25–55 (1987). [CrossRef]

3. F. S. Chen, J. E. Geusic, S. K. Kurtz, J. Skinner, and S. H. Wemple, “Light modulation and beam deflection with potassium tantalate-niobate crystals,” J. Appl. Phys. 37(1), 388–398 (1966). [CrossRef]

4. J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, “Electro-optic properties of ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964). [CrossRef]

5. T. Imai, M. Sasaura, K. Nakamura, and K. Fujiura, “Crystal growth and electro-optic properties of KTa1-xNbxO3,” NTT Tech. Rev. 5(9), 1–8 (2007).

6. E. DelRe, E. Spinozzi, J. Agranat, and C. Conti, “Scale free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5(1), 39–42 (2011). [CrossRef]

7. J. Parravicini, A. Agranat, C. Conti, and E. Delre, “Equalizing disordered ferroelectrics for diffraction cancellation,” Appl. Phys. Lett. 101(11), 111104 (2012). [CrossRef]

8. J. Parravicini, C. Conti, A. J. Agranat, and E. DelRe, “Rejuvenation in scale-free optics and enhanced diffraction cancellation life-time,” Opt. Express 20(24), 27382–27387 (2012). [CrossRef] [PubMed]

9. E. Bouchbinder and J. Langer, “Nonequilibrium thermodynamics of the Kovacs effect,” Soft Matter 6(13), 3065–3073 (2010). [CrossRef]

10. E. DelRe and C. Conti, Nonlinear Photonics and Novel Optical Phenomena (Springer, 2012), Chap. 8.

11. A. Yariv and P. Yeh, Optical Waves in Crystals (John Wiley & Sons, 1984), pp. 221.

12. A. Gumennik, Y. Kurzweil-Segev, and A. J. Agranat, “Electrooptical effects in glass forming liquids of dipolar nano-clusters embedded in a paraelectric environment,” Opt. Mater. Express 1(3), 332–343 (2011). [CrossRef]

13. X. Wang, J. Wang, and B. Liu, “Growth and properties of cubic potassium tantalate niobate crystals,” Adv. Mat. Res 306–307, 352–357 (2011). [CrossRef]

Kovacs effect enhanced broadband large field of view electro-optic modulators in nanodisordered KTN crystals

Abstract

1. Introduction

2. Kovacs effect enhanced electro-optic modulation in nanodisordered KTN crystal

3. Experiments and discussions

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (6)

Equations (8)

Optics Express