Potassium tantaloniobate crystal and low-voltage electro-optic phase modulator using the same

CN115976641BActive Publication Date: 2026-10-27NEW MATERIAL INST OF SHANDONG ACADEMY OF SCI
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Patent Information

Application Number
CN202211684294.5
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-12-27
Publication Date
2026-10-27
Estimated Expiration
2042-12-27

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Benefits of technology

[0021]与现有技术相比,本发明的优点和积极效果在于:本发明采用Li+掺杂技术来调控钽铌酸钾晶体的居里温度,可以在Nb组分较低的情况下得到居里点在室温附近的晶体,减小了高Nb含量钽铌酸钾晶体生长的困难;

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Abstract

The application belongs to the field of body-type electro-optical modulation devices, and particularly relates to a potassium tantalum niobate crystal and a low-voltage electro-optical phase modulator using the same. 1‑x Nb x O3, wherein 0.1<=X<=0.3, a cubic phase, and the potassium tantalum niobate crystal is co-doped with Cu 2+ , Li + two ions, and the molar content of the two elements in the crystal after doping is Cu: 0.001-0.01%, Li: 1-3%, the potassium tantalum niobate crystal is located in the middle, further comprising a first electrode located on the upper surface of the potassium tantalum niobate crystal and a second electrode located on the lower surface, the upper surface is further provided with an incident hole, and the lower surface is provided with an exit hole; the crystal with a Curie point near room temperature can be obtained under the condition of a low Nb component, the difficulty of growing the potassium tantalum niobate crystal with a high Nb content is reduced, the electro-optical coefficient of the potassium tantalum niobate crystal is increased by 2-3 times, the driving voltage of the final component is greatly reduced, a larger incident angle tolerance is obtained, and the demand of free space optical communication application can be better met.
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Description

Technical Field

[0001] This invention belongs to the field of bulk electro-optic modulation devices, and particularly relates to a potassium tantalate niobate crystal and a low-voltage electro-optic phase modulator using the same. Background Technology

[0002] Electro-optic modulators are devices that utilize the electro-optic effect of crystals to control the phase, amplitude, and polarization state of light. Based on their structure, electro-optic modulators can be divided into waveguide-type electro-optic modulators (integrated optical modulators) and bulk electro-optic modulators. Waveguide-type electro-optic modulators, because they apply an electric field to only a very small area, typically have a driving voltage one to two orders of magnitude smaller than bulk modulators, making them particularly suitable for fabricating low-power, compact devices. They have been widely used in fiber optic communication. For example, lithium niobate crystals possess physical properties such as femtosecond-level response speeds, linear electro-optic effects, and wide transparent windows, making them one of the most popular electro-optic modulation materials. Waveguide-type modulators based on lithium niobate crystals were commercialized thirty years ago, demonstrating excellent performance.

[0003] However, in the field of free-space optical communication, bulk modulators are indispensable components. Because the electro-optic coefficients of existing electro-optic crystal materials are relatively small, a very strong external electric field must be applied to change the optical properties of the entire crystal, thereby achieving the purpose of modulating the light waves within the crystal. A drawback of bulk electro-optic modulators is the relatively high modulation voltage, typically requiring hundreds or even thousands of volts. Therefore, finding materials with larger electro-optic coefficients and designing and developing electro-optic modulators with lower modulation voltages are currently urgent technical challenges to be solved in the field of bulk electro-optic modulation. Summary of the Invention

[0004] To address the aforementioned technical problems in the prior art, this invention proposes a potassium tantalate niobate crystal with a high electro-optic coefficient, and a low-voltage electro-optic phase modulation element using the potassium tantalate niobate crystal. This low-voltage electro-optic phase modulation element is a volume modulator and is applied in the field of free-space optical communication.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A potassium tantalate niobate crystal, characterized by having the chemical formula KTa. 1-x Nb x O3, wherein 0.1 ≤ X ≤ 0.3, is a cubic phase, and the potassium tantalate niobate crystal is made of Cu. 2+ Li + The two ions are co-doped, and the molar content of the two elements in the crystal after doping is Cu: 0.001-0.01% and Li: 1-3%.

[0007] A low-voltage electro-optic phase modulator using the aforementioned potassium tantalate niobate crystal, wherein the potassium tantalate niobate crystal is located in the middle, and the modulator also includes a first electrode located on the upper surface of the potassium tantalate niobate crystal and a second electrode located on the lower surface. The upper surface is also provided with an entrance hole, and the lower surface is provided with an exit hole.

[0008] The light beam enters through the entrance hole on the upper surface, and after multiple reflections, exits through the exit hole on the lower surface. During the transmission of the light beam inside the potassium tantalate niobate crystal, under the action of an applied voltage, the refractive index of the crystal is changed by the secondary electro-optic effect of the potassium tantalate niobate crystal, thereby achieving modulation of the phase of the light beam.

[0009] Preferably, the first electrode and the second electrode are one of the metal films Al, Ag, and Au, and the metal film serves as both a reflective film and an electrode.

[0010] Preferably, the potassium tantalate niobate crystal needs to be optically polished before electrode plating, and the roughness of the upper surface and the lower surface is ≤0.5nm to ensure the reflectivity of the subsequent coating.

[0011] Preferably, both the entrance aperture and the exit aperture are coated with transparent ITO electrodes. Since the first electrode and the second electrode are both metal electrodes, the entrance aperture and the exit aperture are positioned with transparent ITO electrodes to ensure light transmission and to ensure that the light beam is always in a uniform electric field throughout the crystal.

[0012] Preferably, in order to reduce beam distortion caused by inherent compositional fringes within the potassium tantalate niobate crystal, the normal direction of the plane containing the first electrode and the second electrode is aligned with the growth direction of the potassium tantalate niobate crystal.

[0013] Preferably, the incident light of the low-voltage electro-optic phase modulator is linearly polarized light, and the polarization direction is parallel to the plane where the first electrode is located, with an incident angle ranging from 15° to 45°.

[0014] Preferably, when the low-voltage electro-optic phase modulator is working, the temperature of the potassium tantalate niobate crystal is controlled at 5-10°C above the Curie temperature and kept constant, with a temperature control accuracy of ±0.1°C.

[0015] Preferably, the phase difference ΔΦ generated by the electro-optic effect in the low-voltage electro-optic phase modulator can be expressed as:

[0016]

[0017] Where λ is the incident light wavelength; n0 is the refractive index of the potassium tantalate niobate crystal when no voltage is applied; S 12V is the second electro-optic coefficient of the potassium tantalate niobate crystal; L is the voltage applied to the potassium tantalate niobate crystal; l is the light transmission length within the potassium tantalate niobate crystal; and d is the thickness of the potassium tantalate niobate crystal in the direction of the electric field.

[0018] Preferably, the half-wave voltage of the low-voltage electro-optic phase modulator is expressed as:

[0019]

[0020] Where λ is the incident light wavelength; n0 is the refractive index of the potassium tantalate niobate crystal when no voltage is applied; S 12 V is the second electro-optic coefficient of the potassium tantalate niobate crystal; L is the voltage applied to the potassium tantalate niobate crystal; l is the light transmission length within the potassium tantalate niobate crystal; and d is the thickness of the potassium tantalate niobate crystal in the direction of the electric field.

[0021] Compared with the prior art, the advantages and positive effects of the present invention are as follows: The present invention uses Li + Doping techniques can be used to control the Curie temperature of potassium tantalate niobate crystals, which can produce crystals with a Curie point near room temperature even with low Nb content, thus reducing the difficulty of growing high Nb content potassium tantalate niobate crystals.

[0022] The electro-optic coefficient of potassium tantalate niobate crystal is 1 to 2 orders of magnitude higher than that of widely commercially available lithium niobate crystal. This invention uses Cu... 2+ Doping technology further increases the electro-optic coefficient of potassium tantalate niobate by 2 to 3 times, which can significantly reduce the driving voltage of the final components.

[0023] Since the half-wave voltage of the electro-optic modulation device is proportional to the wafer thickness in the electric field direction and inversely proportional to the light transmission length, this invention reduces the wafer thickness while increasing the light transmission length through multiple reflections, thereby further reducing the half-wave voltage.

[0024] Cubic potassium tantalate niobate crystal, as an isotropic secondary electro-optic crystal material, has a greater incident angle tolerance than linear electro-optic crystals, and is better able to meet the needs of free-space optical communication applications. Attached Figure Description

[0025] Figure 1 An electro-optic phase modulator based on a cubic potassium tantalate niobate crystal prepared according to an embodiment of the present invention;

[0026] Figure 2 Comparative Example 1Li of the present invention + A schematic diagram illustrating the effect of doping technology on the Curie temperature of a crystal;

[0027] Figure 3 Potassium tantalate niobate crystals prepared in Example 1 of this invention are in Cu 2+Secondary electro-optic coefficients s before and after doping 12 The contrast;

[0028] Figure 4 It is the half-wave voltage of the electro-optic phase modulator prepared in Embodiment 1 of the present invention when laser light is incident at different wavelengths;

[0029] Figure 5 It is the half-wave voltage of the electro-optic phase modulator prepared in Embodiment 2 of the present invention when laser light of different wavelengths is incident;

[0030] Figure 6 It is the half-wave voltage of the electro-optic phase modulator prepared in Embodiment 3 of the present invention when laser light of different wavelengths is incident;

[0031] Figure 7 An electro-optic phase modulator for the potassium tantalate niobate crystal prepared in Comparative Example 2;

[0032] Figure 8 The half-wave voltage of the electro-optic phase modulator of the potassium tantalate niobate crystal prepared in Comparative Example 2 under different wavelength laser incident conditions.

[0033] Among them, 10 is potassium tantalate niobate crystal; 11 is the upper surface; 111 is the first electrode; 112 is the entrance hole; 12 is the lower surface; 121 is the second electrode; and 122 is the exit hole. Detailed Implementation

[0034] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] Example 1

[0036] A potassium tantalate niobate crystal, using Cu 2+ Li + Prepared by co-doping with two ions, composition is KTa 0.9 Nb 0.1 The molar content of doped elements in the O3 crystal is: Cu: 0.001%, Li: 3%, and it is a cubic phase.

[0037] The potassium tantalate niobate crystal 10 prepared in Example 1 was used as a low-voltage electro-optic phase modulation element in free space. It was fabricated into a 3mm × 6mm × 5mm cuboid, and the upper surface 11 and lower surface 12 of the 3mm × 6mm crystal were optically polished to a roughness of 0.5nm. The normal directions of the upper surface 11 and lower surface 12 were both crystal growth directions. The polished surfaces of the upper surface 11 and lower surface 12 retained the entrance aperture 112 and exit aperture 122, respectively. Other areas were coated with Al films using magnetron sputtering as the first electrode 111 and the second electrode 121. Then, ITO transparent electrodes were deposited in the entrance aperture 112 and exit aperture 122 areas. Since the first electrode 111 and the second electrode 121 are both metal electrodes, the transparent ITO electrodes at the entrance aperture 112 and exit aperture 122 positions ensure light transmission, guaranteeing that the light beam propagates in a uniform electric field throughout the crystal.

[0038] The dielectric temperature spectrum of potassium tantalate niobate crystal 10 was measured, revealing its Curie point to be 20.4℃. The temperature of the potassium tantalate niobate crystal 10 was kept constant at 25.4℃ with a temperature control accuracy of ±0.1℃. The secondary electro-optic coefficient s at this temperature was determined. 12 =2.1×10 -14 m 2 / V 2 .

[0039] Commercial electro-optic modulation devices, such as lithium niobate, utilize the linear electro-optic effect of crystals. Crystals that produce this effect are typically anisotropic crystals without a center of symmetry. Correspondingly, electro-optic devices usually require perpendicular incident light. Cubic potassium tantalate niobate crystals, as isotropic secondary electro-optic crystal materials, offer greater incident angle tolerance compared to linear electro-optic crystals, better meeting the needs of free-space optical communication applications. Linearly polarized light with its polarization direction parallel to the surface of the potassium tantalate niobate crystal 10 is incident at a 15° angle through the incident aperture, undergoes four reflections within the crystal, and exits through the exit aperture.

[0040] During the propagation of the light beam inside the crystal, applying a voltage to the potassium tantalate niobate crystal 10 allows for modulation of the beam's phase using the crystal's secondary electro-optic effect. The modulation law follows the formula...

[0041]

[0042] The half-wave voltage corresponding to incident light of different wavelengths can be obtained from the formula.

[0043]

[0044] The calculations show that the pattern is as follows: Figure 4 As shown, from Figure 4As can be seen, within the commonly used frequency band, its half-wave voltage is controlled at around 41 to 81V. Compared with the bulk electro-optic modulators on the market that are usually several hundred volts or even thousands of volts, the half-wave voltage is significantly reduced.

[0045] Figure 3 Potassium tantalate niobate crystals of Example 1 in Cu 2+ Secondary electro-optic coefficients s before and after doping 12 In comparison, the electro-optic coefficient of potassium tantalate niobate crystals is 1 to 2 orders of magnitude higher than that of lithium niobate crystals, which are currently widely used in the market. This is achieved using Cu... 2+ Doping technology further increases the electro-optic coefficient of potassium tantalate niobate by 2 to 3 times, which can significantly reduce the driving voltage of the final components.

[0046] Example 2

[0047] A potassium tantalate niobate crystal using Cu 2+ Li + Prepared by co-doping with two ions, composition is KTa 0.8 Nb 0.2 The molar content of doped elements in the O3 crystal is: Cu: 0.005%, Li: 2%, and it is a cubic phase.

[0048] The potassium tantalate niobate crystal 10 prepared in Example 2 was used as a low-voltage electro-optic phase modulation element in free space. It was fabricated into a 2mm × 5mm × 3mm cuboid, and the upper surface 11 and lower surface 12 of the 2mm × 5mm crystal were optically polished to a roughness of 0.4nm. The normal directions of the upper surface 11 and lower surface 12 were aligned with the crystal growth direction. The polished surfaces of the upper surface 11 and lower surface 12 retained the entrance aperture 112 and exit aperture 122, respectively. Au films were deposited in other areas using magnetron sputtering as the first electrode 111 and the second electrode 121. Then, ITO transparent electrodes were deposited in the entrance aperture 112 and exit aperture 122 areas.

[0049] The dielectric temperature spectrum of potassium tantalate niobate crystal 10 was measured, revealing its Curie point to be 23.2℃. The temperature of the potassium tantalate niobate crystal 10 was kept constant at 30.4℃ with a temperature control accuracy of ±0.1℃. The secondary electro-optic coefficient s at this temperature was determined. 12 =1.79×10 -14 m 2 / V 2 Linearly polarized light, with its polarization direction parallel to the surface of the potassium tantalate niobate crystal 10, is incident on the crystal through the entrance aperture at an angle of 30°. After undergoing six reflections inside the crystal, it exits through the exit aperture.

[0050] During the propagation of the light beam inside the crystal, applying a voltage to the potassium tantalate niobate crystal 10 allows for modulation of the beam's phase using the crystal's secondary electro-optic effect. The modulation law follows the formula...

[0051]

[0052] The half-wave voltage corresponding to incident light of different wavelengths can be obtained from the formula.

[0053]

[0054] The calculations show that the pattern is as follows: Figure 5 As shown, from Figure 5 As can be seen, within the commonly used frequency band, its half-wave voltage is controlled at around 29 to 57V. Compared with the bulk electro-optic modulators on the market that are usually several hundred volts or even thousands of volts, the half-wave voltage is significantly reduced.

[0055] Example 3

[0056] A potassium tantalate niobate crystal using Cu 2+ Li + Prepared by co-doping with two ions, composition is KTa 0.7 Nb 0.3 The molar content of doped elements in the O3 crystal is: Cu: 0.01%, Li: 1%, and it is a cubic phase.

[0057] The potassium tantalate niobate crystal 10 prepared in Example 3 was used as a low-voltage electro-optic phase modulation element in free space. It was fabricated into a 2.5mm × 3mm × 2mm cuboid, and the upper surface 11 and lower surface 12 of the 2.5mm × 3mm were optically polished to a roughness of 0.4nm. The normal directions of the upper surface 11 and lower surface 12 were aligned with the crystal growth direction. The upper surface 11 and lower surface 12 retained an entrance aperture 112 and an exit aperture 122, respectively. Other areas were coated with Ag films using magnetron sputtering as the first electrode 111 and the second electrode 121. Then, ITO transparent electrodes were deposited in the areas of the entrance aperture 112 and the exit aperture 122.

[0058] The dielectric temperature spectrum of potassium tantalate niobate crystal 10 was measured, revealing its Curie point to be 18.5℃. The temperature of the potassium tantalate niobate crystal 10 was kept constant at 28.5℃ with a temperature control accuracy of ±0.1℃. The secondary electro-optic coefficient s at this temperature was determined. 12 =1.4×10 -14 m 2 / V 2 Linearly polarized light with its polarization direction parallel to the surface of potassium tantalate niobate crystal 10 is incident into the crystal through the entrance hole at an angle of 45°. After four reflections inside the crystal, it exits through the exit hole.

[0059] During the propagation of the light beam inside the crystal, applying a voltage to the potassium tantalate niobate crystal 10 allows for modulation of the beam's phase using the crystal's secondary electro-optic effect. The modulation law follows the formula...

[0060]

[0061] The half-wave voltage corresponding to incident light of different wavelengths can be obtained from the formula.

[0062]

[0063] The calculations show that the pattern is as follows: Figure 6 As shown, from Figure 6 As can be seen, within the commonly used frequency band, its half-wave voltage is controlled at around 27 to 53V. Compared with the bulk electro-optic modulators on the market that are usually several hundred volts or even thousands of volts, the half-wave voltage is significantly reduced.

[0064] Since the half-wave voltage of the final component is proportional to the wafer thickness in the electric field direction and inversely proportional to the light transmission length, this invention reduces the wafer thickness while increasing the light transmission length through multiple reflections, thereby further reducing the half-wave voltage.

[0065] Comparative Example 1

[0066] Since the difficulty of growing potassium tantalate niobate crystals increases with the increase of Nb content, Examples 1-3 of this invention use Li + Doping techniques can be used to control the Curie temperature of potassium tantalate niobate crystals, allowing crystals with a Curie point near room temperature to be obtained even with low Nb content, thus reducing the difficulty of growing high Nb content potassium tantalate niobate crystals.

[0067] To prove Li + To investigate the effect of doping on the Curie point of potassium tantalate niobate crystals, we prepared two types of crystals using the Czochralski method: one was pure KTa without any doping. 0.71 Nb 0.29 O3 crystals, another type is only Li + Doped KTa 0.71 Nb 0.29 O3 crystals with a Li molar content of 1.1% and identical Ta / Nb compositions were used. Both crystals were processed to the same size, optically polished to the same precision, and then Ag electrodes were deposited on their surfaces. The dielectric temperature spectra of both crystals were measured. Figure 2 As shown, through Li + Doping adjusted the Curie point of potassium tantalate niobate crystals from -42.5℃ to room temperature (25.1℃), indicating that Li... + Doping has a significant regulatory effect on the Curie point of potassium tantalate niobate crystals.

[0068] Comparative Example 2

[0069] Examples 1-3 all used Cu 2+A phase modulation device with low half-wave voltage is obtained by doping KTN crystals and combining them with multiple reflection techniques. In contrast, a device using only Li-doped crystals... + The potassium tantalate niobate crystals, with the same Ta / Nb ratio and Li content as in Example 1, i.e., a composition of KTa. 0.9 Nb 0.1 The O3 and Li elements have a molar content of 3%. The crystal is processed into a 3mm×6mm×5mm cuboid, and the two 3mm×6mm surfaces are optically polished to a roughness of 0.5nm. The normal direction of the surface is the crystal growth direction. ITO transparent electrodes are deposited on the two polished surfaces.

[0070] Measuring KTa 0.9 Nb 0.1 The dielectric temperature spectrum of O3 yielded a Curie point of 20.4℃, which controlled the KTa... 0.9 Nb 0.1 The temperature of the O3 crystal was kept constant at 25.4℃ with a temperature control accuracy of ±0.1℃. The secondary electro-optic coefficient s at this temperature... 12 =0.8×10 -14 m 2 / V 2 .

[0071] With the polarization direction parallel to KTa 0.9 Nb 0.1 Linearly polarized light from the O3 crystal surface is incident perpendicularly to the electrode surface. The beam passes through the crystal and exits directly from the other side, such as... Figure 7 As shown.

[0072] By applying a voltage to the two electrode surfaces, the phase of the light beam can be modulated using the secondary electro-optic effect of the crystal, following a formula.

[0073]

[0074] The half-wave voltage corresponding to incident light of different wavelengths can be given by the formula:

[0075]

[0076] The calculations show that the pattern is as follows: Figure 8 As shown.

[0077] Attachment Figure 4 The half-wave voltage of Example 1 shown is compared with that of the comparative example. Figure 8 In comparison, using Cu 2+ The doping and multiple reflection techniques significantly reduce the half-wave voltage.

Claims

1. A potassium tantalate niobate crystal, characterized in that, Its chemical formula is KTa 1-x Nb x O3, wherein 0.1 ≤ X ≤ 0.3, is a cubic phase, and the potassium tantalate niobate crystal is made of Cu. 2+ Li + Two ions are co-doped, and the molar content of the two elements in the crystal after doping is Cu: 0.001~0.01%, Li: 1~3%; the Curie temperature of the potassium tantalate niobate crystal is 18.5-23.2℃, and the second electro-optic coefficient S 12 (1.4×10) -14 )-(2.1×10 -14 )m 2 / V 2 .

2. A low-voltage electro-optic phase modulator, using the potassium tantalate-niobate crystal of claim 1, characterized in that, The potassium tantalate niobate crystal is located in the middle, and the device also includes a first electrode located on the upper surface of the potassium tantalate niobate crystal and a second electrode located on the lower surface. The upper surface is also provided with an entrance hole, and the lower surface is provided with an exit hole. The light beam enters through the entrance hole on the upper surface, and after multiple reflections, exits through the exit hole on the lower surface. During the transmission of the light beam inside the potassium tantalate niobate crystal, under the action of an applied voltage, the refractive index of the crystal is changed by the secondary electro-optic effect of the potassium tantalate niobate crystal, thereby achieving modulation of the phase of the light beam.

3. The low-voltage electro-optic phase modulator according to claim 2, characterized in that, The first electrode and the second electrode are metal films of Al, Ag, and Au.

4. The low-voltage electro-optic phase modulator according to claim 3, characterized in that: The potassium tantalate niobate crystal needs to be optically polished before electrode plating, and the roughness of both the upper and lower surfaces is ≤0.5nm.

5. The low-voltage electro-optic phase modulator according to claim 4, characterized in that: Both the entrance hole and the exit hole are coated with transparent ITO electrodes.

6. The low-voltage electro-optic phase modulator according to claim 2, characterized in that, The normal direction of the plane containing the first electrode and the second electrode is consistent with the growth direction of the potassium tantalate niobate crystal.

7. The low-voltage electro-optic phase modulator according to claim 4, characterized in that, The incident light of the low-voltage electro-optic phase modulator is linearly polarized light, and the polarization direction is parallel to the plane where the first electrode is located, with an incident angle ranging from 15° to 45°.

8. The low-voltage electro-optic phase modulator according to claim 7, characterized in that, When the low-voltage electro-optic phase modulator is working, the temperature of the potassium tantalate niobate crystal is controlled at 5~10℃ above the Curie temperature and kept constant, with a temperature control accuracy of ±0.1℃.

9. The low-voltage electro-optic phase modulator according to claim 4, characterized in that, The phase difference ΔΦ generated by the electro-optic effect in the low-voltage electro-optic phase modulator is expressed as: Where λ is the incident light wavelength; n0 is the refractive index of the potassium tantalate niobate crystal when no voltage is applied; S 12 V is the second electro-optic coefficient of the potassium tantalate niobate crystal; L is the voltage applied to the potassium tantalate niobate crystal; l is the light transmission length within the potassium tantalate niobate crystal; and d is the thickness of the potassium tantalate niobate crystal in the direction of the electric field.

10. The low-voltage electro-optic phase modulator according to claim 9, characterized in that, The half-wave voltage of the low-voltage electro-optic phase modulator is expressed as follows: Where λ is the incident light wavelength; n0 is the refractive index of the potassium tantalate niobate crystal when no voltage is applied; S 12 V is the second electro-optic coefficient of the potassium tantalate niobate crystal; L is the voltage applied to the potassium tantalate niobate crystal; l is the light transmission length within the potassium tantalate niobate crystal; and d is the thickness of the potassium tantalate niobate crystal in the direction of the electric field.

Citation Information

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