Compact low-voltage electro-optic Q-switch made of LiNbO<sub>3</sub>

Jifang Shang; Jifang Shang; Jinfeng Yang; Jinfeng Yang; Jinfeng Yang; Jinfeng Yang; Haoshan Hao; Haoshan Hao; Haoshan Hao; Qinglian Li; Ling Zhang; Jun Sun

doi:10.1364/OE.393958

1. Introduction

Electro-optic (EO) Q-switching technology is a common method to achieve pulse lasers that have been extensively applied in the fields of laser ranging, remote sensing, laser machining, environmental monitoring, medicine, etc. [1–5]. It relies on the changes to optical anisotropy that occur under electric fields. Compared with other Q-switching technologies, e.g., acousto-optic Q-switching and passive Q-switching [6,7], EO Q-switching has the advantages of a faster switching rate, better hold-off ability, and low temporal jitter at the repetition rate [8], all of which enable the generation of stable and energetic short laser pulses.

Up to now, EO crystals used for EO Q-switching have mainly included KD₂PO₄ (DKDP), LiNbO₃ (LN), RbTiOPO₄ (RTP), KTiOPO₄ (KTP), La₃Ga₅SiO₁₄ (LGS), β-BaB₂O₄ (BBO), etc. [9]. The EO cells are usually made of their so-called direct cuts being fabricated in a shape of rectangular prisms with the faces that are perpendicular to the principal crystallographic axes [10–15]. For such a cell geometry, a quarter-wave plate (QWP) or an analyzer is usually required when the EO switch operates in pulse-on mode, this is disadvantageous for the compactness and reliability of Q-switched lasers which are of great interest for engineering applications [16]. In pulse-off mode, no QWP or analyzer is needed, the resonant cavity is more compact, lossless and stable than the pulse-on one, but the continuous application of a high voltage would shorten the lifetime of the Q-switch due to electro-chemical degradation effects [17]. Additionally, the Q-switching performance may be severely affected by piezoelectric and elastic-optic effects [18,19].

In our previous paper [20], a compact LN EO Q-switch, which integrates the advantages of the pulse-on and pulse-off mode, had been developed and successfully used in a pulse-on cavity without using a QWP or analyzer. It was fabricated in a shape of a rectangular prism with the faces that are oriented to certain crystallographic directions, not to the principal ones. With this cell geometry, the LN crystal was used both as a QWP and a pockels cell (PC) by taking advantage of its natural birefringence and EO effects. In the previous design, we neglected the high-order terms in the expression for calculating the birefringence in any direction in LN crystals when an electric field is applied. The results showed a set of proper crystal orientations with the same quarter-wave voltage (QWV). However, as will be determined in the present work, the high-order terms have a significant effect on the QWVs in different directions in LN crystals. The difference of QWVs in the four directions defined by the angles φ = ±45°, ±135° with the same angle θ in principal crystallophysical system is as high as about 1 kV. As we all know, a low driving voltage is of great importance for engineering applications because of low electromagnetic interference and easy fabrication of EO drivers [21]. Therefore, this finding is encouraging, we expect to develop a compact LN EO Q-switch with lower driving voltage.

In this work, we conduct an accurate analysis of the birefringence in any direction in LN crystals when an electric field is applied. Combined with the theory of EO Q-switching, we determine the proper crystal orientations and the QWVs for each orientation. The results are further confirmed by measuring the dynamic QWVs in a Nd:YAG laser. Based on the results, we obtain the optimized cell geometries. A set of compact LN EO Q-switches with various cell geometries were prepared and investigated in the Nd:YAG laser. For comparison, we also employ two commercial Z-cut LN Q-switch with a QWP in the laser.

2. Methods

2.1 Theoretical analysis

The birefringence in any direction in LN crystals when an electric field is applied is first analyzed. When an electric field E is applied to the X direction of LN, the index ellipsoid will change due to the EO effect. The optical impermeability tensor matrix β may be written as [22]

(1)$$\left( {\begin{array}{ccc} {\frac{1}{{n_o^2}}}&{ - {\gamma_{22}}E}&{{\gamma_{51}}E}\\ { - {\gamma_{22}}E}&{\frac{1}{{n_o^2}}}&0\\ {{\gamma_{51}}E}&0&{\frac{1}{{n_e^2}}} \end{array}} \right)$$

where γ₂₂ and γ₅₁ are EO coefficients, n_o and n_e are ordinary and extraordinary refractive indices. By using the expression given by Mason for calculating the birefringence in any direction in a crystal of lowest symmetry [23] and the terms in Matrix (1), the birefringence Δn in any direction can be expressed as

(2)$$\Delta n = \frac{{n_o^3}}{2}\sqrt {{K_2}}$$

(3)$$\begin{array}{l} {K_2} = {({{\beta_{33}} - {\beta_{22}}} )^2}{\sin ^4}\theta \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} + 2({{\beta_{33}} - {\beta_{22}}} ){\sin ^2}\theta [{{\beta_{12}}\sin 2\varphi ({1 + {{\cos }^2}\theta } )- {\beta_{13}}\sin 2\theta \cos \varphi } ]\\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} + {({2{\beta_{12}}} )^2}({{{\sin }^4}\theta {{\sin }^2}\varphi {{\cos }^2}\varphi + {{\cos }^2}\theta } )\\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} - 4{\beta _{12}}{\beta _{13}}{\sin ^2}\theta \sin \varphi [{{{\cos }^2}\theta {{\cos }^2}\varphi + {{\sin }^2}\varphi } ]\\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} + {({2{\beta_{13}}} )^2}{\sin ^2}\theta ({{{\cos }^2}\theta {{\cos }^2}\varphi + {{\sin }^2}\varphi } )\end{array}$$

where β_ij (i, j = 1, 2 or 3) are the optical impermeability tensor components, θ represents the angle between the optic axis and the wave normal, φ is the azimuthal angle of the wave normal. One eigen polarization direction of the wave in the crystal is at an angle of ψ to the principal plane, and the other polarization direction is perpendicular to this one, as shown in Fig. 1. The angle ψ can be derived as

(4)$$\tan 2\psi = \frac{{2{\beta _{12}}\cos \theta \cos 2\varphi + 2{\beta _{13}}\sin \theta \sin \varphi }}{\begin{array}{l} {\beta _{11}}[{{{\cos }^2}\theta {{\cos }^2}\varphi - {{\sin }^2}\varphi } ]+ {\beta _{12}}({1 + {{\cos }^2}\theta } )\sin 2\varphi \\ - {\beta _{13}}{\sin ^2}\theta \cos \varphi + {\beta _{22}}({{{\cos }^2}\theta {{\sin }^2}\varphi - {{\cos }^2}\varphi } )+ {\beta _{33}}{\sin ^2}\theta \end{array}}$$

When no voltage is applied, the LN crystal is expected to act as a QWP by taking advantage of its natural birefringence. It is known that in the pulse-on cavity the fast and slow axes of QWP should be held 45° with respect to the polarization direction of the light [24]. As the eigen polarization directions of natural birefringence are parallel or perpendicular to the principal plane [25], the angle φ should be taken as ±45°, ±135° when the transmission direction of the polarizer is along the X or Y axis of LN, and the angle θ should be derived from the equation

(5)$${\Gamma _0} = \frac{{l\Delta n_o^3{{\sin }^2}\theta }}{2} = \frac{\lambda }{4} + k\frac{\lambda }{2}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} k = 0, \pm 1, \pm 2 \ldots$$

where Γ₀ represents the optical path difference (OPD) induced by natural birefringence [25], $\Delta = {1 / {n_e^2}} - {1 / {n_o^2}}$, l is the optical path length, λ is laser wavelength. It is important to note that the transmission direction of the polarizer is not necessary to be along the X or Y axis, and thus the other values of angle φ are also available.

Fig. 1. Eigen polarization directions of the wave in crystal for an electrical field applied. X, Y, and Z axes along each crystallographic axis respectively, k represents wave normal direction, P₁ and P₂ are eigen polarization directions.

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When high voltage is applied, the optical anisotropy and thus the phase retardation will change. To achieve the hold-on state, the phase retardation should be kπ (k=0, ±1, ±2…). According to Eq. (2), the QWV can be calculated from the equation

(6)$${\Gamma _1}\textrm{ = }\frac{{n_o^3\sqrt {{K_2}} l}}{2} = k^{\prime}\frac{\lambda }{2}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} k^{\prime} = 0, \pm 1, \pm 2 \ldots$$

where Γ₁ represents the OPD when an electric field is applied. In the previous work [20], the terms containing β₁₃ and the terms (2β₁₂)²sin4θsin2φcos2φ in Eq. (3) were neglected as contributing only secondary effects, which resulted in the same QWVs in all the proper directions. However, when these terms are considered, the linear terms of cosφ and sinφ will undoubtedly cause the difference of the QWVs in different directions. Even for the same angle θ, the QWVs in the four directions defined by the angles φ = ±45°, ±135° will be different, and the difference will be larger with the increasing angle θ.

Utilizing Eqs. (1), (3) and (6), we calculated the QWVs in various proper directions at λ=1064 nm, where the refractive indices and EO coefficients of LN were taken from the literature [26], the dimensions of LN crystal are 9 mm×9 mm×18.8 mm (X × Y×Z), the angle θ was calculated from Eq. (5) by taking the value of k as 2, the results are listed in Table 1. Note that Γ₁ is λ/4 smaller than Γ₀ (i.e. k′=k) for the angles φ = 45°, -135° and is λ/4 larger than Γ₀ (i.e. k′=k+1) for the angles φ = -45°, 135° when QWV is applied to the + X direction, and it is contrary when the voltage polarity is reversed.

Table 1. Theoretical and experimental QWVs in different directions in LN crystals.

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2.2 Measurement of dynamic QWVs

For experimental verification, the dynamic QWVs in different directions in LN crystals were measured in a Nd:YAG laser, the configuration is shown in Fig. 2. A plano-plano cavity was employed, a Nd:YAG crystal was chosen as the laser crystal which was side-pumped by a pulsed Xe-lamp. The polarizer was a quartz plate oriented along the Brewster angle. Two commercial Z-cut LN PCs with dimensions of 9 mm×9 mm×18.8 mm (X × Y×Z) were used, they were labeled as LN₁ and LN₂. By rotating the LN crystal about the X-axis and Y-axis by an angle of $\pm {{\sqrt 2 {n_o}\theta } / 2}$, respectively, the laser can travel in the desired direction in the crystal. The voltage was supplied with a homemade EO Q-switch driver with a rise time of 7 ns. The output energy was measured by a laser energy meter.

Fig. 2. Experimental setup of the Nd:YAG laser for measuring dynamic QWVs in LN crystals.

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When no voltage is applied, the Q-switches can reach hold-off state and no energy was detected. When the Q-switch driver is on, giant laser pulses were achieved. The output energy is found to vary with the Q-switching voltage in a sine form, thus the voltage corresponding to the maximum output energy is defined as dynamic quarter-wave voltage. Table 1 lists the experimental results of dynamic QWVs in different directions in the two LN PCs.

2.3 Preparation and application of compact LN EO Q-switches

Based on the above results, the crystal orientations with lower and higher QWV were derived, and compact LN Q-switches with various cell geometries were prepared and used in the Nd:YAG laser. The LN crystals were $({\textrm{XZtw}} )- \frac{\theta }{{\sqrt 2 }}/\frac{\theta }{{\sqrt 2 }}$ or $({\textrm{XZtw}} )\frac{\theta }{{\sqrt 2 }}/{-} \frac{\theta }{{\sqrt 2 }}$ cut with dimensions of 9 mm×9 mm×18.8 mm and 9 mm×9 mm×25 mm, the notation of cut type is defined in the IEEE standard [27]. Figure 3 illustrates the $({\textrm{XZtw}} )- \frac{\theta }{{\sqrt 2 }}/\frac{\theta }{{\sqrt 2 }}$ cut LN crystals. The angles θ were calculated from Eq. (5) by taking the different values of k. Each face of the crystals was finely ground, the transmission surface was precisely polished and anti-reflection (AR) coated at 1064 nm. The near-X surface was plated with gold and chrome.

Fig. 3. Illustration of the $({\textrm{XZtw}} )- \frac{\theta }{{\sqrt 2 }}/\frac{\theta }{{\sqrt 2 }}$ cut LN crystals.

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We first measured the dynamic extinction ratios of the Q-switches, the configuration is shown in Fig. 4. A pulsed laser with a wavelength of 1064 nm, a pulse width of 10 ns and a repetition rate of 1 Hz was used, the beam diameter is 5 mm, the laser divergence angle is 5 mrad, the energy jitter is less than 3%. The extinction ratio of the system was first measured, the transmission direction of the analyzer was adjusted to parallel or perpendicular to that of the polarizer respectively, thus the maximum and minimum transmitted energy were obtained through rotating the QWP, the ratio is the extinction ratio of the system. Then the dynamic extinction ratios of the Q-switches were measured. The transmission directions of the polarizer and analyzer were kept parallel, the fast and slow axes of QWP were held 45° to the transmission direction of the polarizer. When no voltage is applied, the polarization plane of the transmitted light is rotated by 90° so that the transmitted energy is minimum. When half-wave voltage is applied to the Q-switches, the maximum transmitted energy can be obtained. The ratio of the maximum and minimum transmitted energy is defined as dynamic extinction ratio.

Fig. 4. Experimental setup for measuring dynamic extinction ratio of compact LN Q-switches.

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The Q-switching performances were investigated in the Nd:YAG laser. The Q-switches were used in the cavity with the transmission surface perpendicular to the optical axis of the laser. The mentioned EO Q-switch driver and an adjustable high-voltage DC power supply were used, the voltage was applied along the + X direction of the LN crystals. The output energy was measured by the laser energy meter. The temporal pulse behavior of the Q-switched laser was detected using an InGaAs photodetector connected to a digital oscilloscope, the high voltage pulses were also recorded by a high voltage probe connected to the same oscilloscope.

3. Results and discussion

3.1 Dependence of QWV on the directions of light propagation

As shown in Table 1, the difference in QWVs in different directions reaches the kilovolt level. The QWVs of the two LN PCs have the same dependence on the directions of light propagation as well as the direction of the applied electric field, the maximum difference in QWVs in the same direction is no more than 2.5%. The dependencies are consistent with the theoretical results, the differences between the theoretical and experimental values are thought to be due to the deviation of the EO coefficients and refractive indices.

When voltage is applied to the + X direction, the minimum magnitude of QWV appears along the direction defined by the angles θ = 1.81° (φ = 45°) or θ = 178.19° (φ = -135°). The QWV in the direction defined by the angles θ = 1.81° (φ = 135°) or θ = 178.19° (φ = -45°) is a little larger than this one. When the electric field is reversed, the QWVs in these two directions change with each other, i.e., the direction with minimum QWV is closely related to the applied voltage polarity.

The QWVs for different angles θ that are corresponding to different values of k in Eq. (5) were also investigated. For comparison, another Z-cut LN PC with dimensions of 9 mm×9 mm×25 mm (X × Y×Z) was also used. For simplicity, Table 2 lists only the QWVs in the directions with an acute angle θ when the voltage is applied to + X direction. Clearly, the dependencies of QWVs on the directions of light propagation are consistent in the two LN PCs with different lengths. The QWVs in the directions with different angles θ exhibit a similar dependence on the angle φ. In the directions with lower QWV, the QWV decreases with the increase of angle θ, conversely, the QWV increases with the increase of angle θ in the directions with higher QWV. Therefore, we can achieve lower QWV by choosing a larger angle θ. Additionally, it is noticed that the difference of QWVs in the directions with different angles φ is larger for the crystals with smaller aspect ratio, and the variation of QWVs is more significant with the increase of angle θ.

Table 2. Dynamic QWVs in various directions with different angles θ.

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Based on the above analysis, the optimized cell geometries and corresponding directions of applied voltage are determined. The LN crystal should be $({\textrm{XZtw}} )- \frac{\theta }{{\sqrt 2 }}/\frac{\theta }{{\sqrt 2 }}$ cut when the electric field is applied along + X direction and should be $({\textrm{XZtw}} )- \frac{\theta }{{\sqrt 2 }}/{-} \frac{\theta }{{\sqrt 2 }}$ cut when the electric field is reversed.

3.2 Q-switched laser outputs

We have prepared a set of compact LN EO Q-switches. For the crystals with a length of 18.8 mm, the angles θ are 1.4°, 1.81°, and 2.14° respectively, which are derived from Eq. (5) by taking the value of k as 1, 2, and 3. The Q-switches corresponding to θ = 1.4°, 2.14° were $({\textrm{XZtw}} )- \frac{\theta }{{\sqrt 2 }}/\frac{\theta }{{\sqrt 2 }}$ cut for the sake of low QWV. For comparison, the other one was $({\textrm{XZtw}} )\frac{\theta }{{\sqrt 2 }}/{-} \frac{\theta }{{\sqrt 2 }}$ cut, which is corresponding to the direction with maximum QWV when the electric field is applied along + X direction. The crystals with a length of 25 mm were both $({\textrm{XZtw}} )- \frac{\theta }{{\sqrt 2 }}/\frac{\theta }{{\sqrt 2 }}$ and $({\textrm{XZtw}} )\frac{\theta }{{\sqrt 2 }}/{-} \frac{\theta }{{\sqrt 2 }}$ cut with an angle θ of 2.32° which is corresponding to k = 5.

The dynamic extinction ratios of the compact Q-switches are shown in Table 3. Considering the laser energy jitter, we averaged the energy of ten pulses. For comparison, we also measured the extinction ratios of two conventional Z-cut LN Q-switches with lengths of 18.8 mm and 25 mm. The extinction ratio of the system was measured to be 946:1. There are certain differences between the extinction ratios of these Q-switches. The extinction ratio of the (XZtw)-0.99°/0.99° cut LN Q-switch is higher than that of others, while the extinction ratio of the (XZtw)-1.51°/1.51° cut LN Q-switch is worst. The extinction ratio is largely determined by the minimum transmitted energy which reflects the hold-off capability of the Q-switches. The differences are thought to be caused by the differences in optical quality of crystals and processing deviation.

Table 3. Dynamic extinction ratios of the LN EO Q-switches.

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We investigated the performances of these LN Q-switches in the Nd:YAG laser. The static energy when there was only a polarizer in the cavity was approximately 200 mJ, the energy jitter is less than 3%. For each measurement, we take the average energy of ten laser pulses to ensure higher accuracy. When the Q-switch is inserted into the cavity and the Q-switch driver is off, the output energy E₁ was measured. The adjustable high DC voltage was applied to the Q-switch, the maximum output energy E₂ and corresponding voltage U₁ (static QWV) were recorded. When the Q-switch works and the repetition rate is 10 Hz, the maximum output energy E₃ and the optimum Q-switching voltage U₂ (dynamic QWV) were measured. Besides, the pulse width τ was obtained from the pulse shape. The results are shown in Table 4, a pulse shape is shown in Fig. 5. For the sake of contrast, we also measured the performances of two commercial Z-cut LN Q-switch, a QWP was used in this regime to realize the pulse-on Q-switching operation.

Fig. 5. Pulse shape of the compact LN EO Q-switched laser.

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Table 4. Output results of the compact LN EO Q-switched Nd:YAG lasers.

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Clearly, the compact LN Q-switches show comparable performances to the commercial Z-cut LN Q-switch. When no voltage is applied, the laser can be completely hold-off, which demonstrates that the compact Q-switches had successfully worked as a QWP. When proper voltage is applied, the outputs for all the Q-switched laser are equivalent within a reasonable error range. The maximum difference in the dynamic output energy E₃ is only 3.5%, and that of the output energy E₂ is only 4.8%. The laser outputs fit well with the results of the dynamic extinction ratio. Besides, it is noticed that the maximum output energy E₂ when static QWV is applied is lower than the dynamic output energy E₃, this may be due to the electro-optic inhomogeneity caused by the continuous application of a high voltage [28], which results in larger depolarization loss. Based on the dynamic output results, we estimated the insertion loss of the Q-switches to be between 1.5% and 3.5%.

More importantly, the QWVs of the $({\textrm{XZtw}} )- \frac{\theta }{{\sqrt 2 }}/\frac{\theta }{{\sqrt 2 }}$ cut LN Q-switches are substantially reduced. With the same dimensions, the (XZtw)-1.51°/1.51° cut LN Q-switch possesses a dynamic QWV 600 V lower than that of the Z-cut LN Q-switch and 1300V lower than that of the (XZtw)1.28°/-1.28° cut LN Q-switch. Even with the same angle θ, the dynamic QWV of the (XZtw)-1.64°/1.64° cut LN Q-switch is 700 V lower than that of the (XZtw)1.64°/-1.64° cut LN Q-switch. Moreover, it is clear that the QWVs decrease with the increasing angle θ for the $({\textrm{XZtw}} )- \frac{\theta }{{\sqrt 2 }}/\frac{\theta }{{\sqrt 2 }}$ cut LN Q-switches.

Additionally, it is noticed that the decline in QWV is larger for the compact Q-switch with smaller aspect ratio, this is valuable because the conventional LN Q-switches with small aspect ratio usually possess a large caliber or a high extinction ratio which is favorable for high peak power lasers, but they are limited in many applications because of the high driving voltage. Foreseeably, the compact Q-switches with appropriate cut are more beneficial to engineering applications.

4. Conclusions

We have successfully designed and demonstrated a set of compact LN EO Q-switches with lower driving voltage than conventional ones. The LN crystals were used both as a QWP and a PC by taking advantage of optical anisotropy and EO effects. Through theoretical calculations and experiments, a set of proper crystal orientations were determined, the QWVs were found to vary with the crystal orientations and voltage polarity. Based on the results, we obtained the optimized cell geometries and corresponding directions of applied voltage and prepared a series of compact LN EO Q-switches. They had successfully operated in the pulse-on Q-switching mode without using a QWP or analyzer, and the Q-switched laser outputs are comparable to those obtained by employing a conventional Z-cut LN Q-switch and a QWP. More importantly, the QWVs of the $({\textrm{XZtw}} )- \frac{\theta }{{\sqrt 2 }}/\frac{\theta }{{\sqrt 2 }}$ cut LN Q-switches are significantly reduced, and the QWV can be further reduced by increasing the angle θ. Furthermore, the reduction of QWV is larger for the Q-switch with a smaller aspect ratio. The compact LN Q-switches with lower QWV are of more importance for engineering applications.

Funding

National Natural Science Foundation of China (51902087, 61705059); Science and Technology Department of Henan Province (202102210023).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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Voltage direction	Direction of light propagation		Quarter-wave voltage (V)
	θ=1.81°	θ=178.19°	Theoretical values	Experimental values
	θ=1.81°	θ=178.19°	Theoretical values	LN₁	LN₂
+X	φ=+45°	φ=-135°	2768	3100	3050
	φ=+135°	φ=-45°	2906	3150	3200
	φ=-45°	φ=+135°	3942	4050	4000
	φ=-135°	φ=+45°	4491	4200	4200
-X	φ=+45°	φ=-135°	2906	3200	3200
	φ=+135°	φ=-45°	2768	3100	3150
	φ=-45°	φ=+135°	4491	4250	4150
	φ=-135°	φ=+45°	3942	4100	4000

Crystal length (mm)	k	θ	Dynamic quarter-wave voltage (V)
Crystal length (mm)	k	θ	φ = +45°	φ = +135°	φ = -45°	φ = -135°
18.8	0	0.81°	3250	3450	3600	4000
	1	1.4°	3150	3300	3800	4150
	2	1.81°	3100	3200	4000	4200
	3	2.14°	3000	3100	4200	4300
25	1	1.21°	2380	2500	2700	2880
	3	1.85°	2320	2460	2840	3000
	5	2.32°	2300	2420	2940	3080

Crystal length (mm)	Cell geometry	Minimum energy (mJ)	Maximum energy (mJ)	Extinction ratio
18.8	(XZtw)-0.99°/0.99° cut	0.807	188	233:1
	(XZtw)1.28°/-1.28° cut	1.213	184	152:1
	(XZtw)-1.51°/1.51° cut	1.606	181	113:1
	Z cut	0.932	186	200:1
25	(XZtw)-1.64°/1.64° cut	0.984	185	188:1
	(XZtw)1.64°/-1.64° cut	1.176	184	156:1
	Z cut	0.856	188	220:1

Crystal length (mm)	Cell geometry	E₂ (mJ)	U₁ (V)	E₃ (mJ)	τ (ns)	U₂ (V)
18.8	(XZtw)-0.99°/0.99° cut	189	2000	197	6.2	3300
	(XZtw)1.28°/-1.28° cut	182	2600	193	6.2	4300
	(XZtw)-1.51°/1.51° cut	181	1950	193	6.2	3000
	Z cut	186	2200	194	6.2	3600
25	(XZtw)-1.64°/1.64° cut	185	1260	194	6.2	2300
	(XZtw)1.64°/-1.64° cut	183	1700	193	6.2	3000
	Z cut	188	1520	196	6.2	2700

Voltage direction	Direction of light propagation		Quarter-wave voltage (V)
	θ=1.81°	θ=178.19°	Theoretical values	Experimental values
	θ=1.81°	θ=178.19°	Theoretical values	LN₁	LN₂
+X	φ=+45°	φ=-135°	2768	3100	3050
	φ=+135°	φ=-45°	2906	3150	3200
	φ=-45°	φ=+135°	3942	4050	4000
	φ=-135°	φ=+45°	4491	4200	4200
-X	φ=+45°	φ=-135°	2906	3200	3200
	φ=+135°	φ=-45°	2768	3100	3150
	φ=-45°	φ=+135°	4491	4250	4150
	φ=-135°	φ=+45°	3942	4100	4000

Compact low-voltage electro-optic Q-switch made of LiNbO₃

Abstract

1. Introduction

2. Methods

2.1 Theoretical analysis

2.2 Measurement of dynamic QWVs

2.3 Preparation and application of compact LN EO Q-switches

3. Results and discussion

3.1 Dependence of QWV on the directions of light propagation

3.2 Q-switched laser outputs

4. Conclusions

Funding

Disclosures

References

Cited By

Figures (5)

Tables (4)

Equations (6)

Optics Express