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Abstract
We have recently experimentally demonstrated that a novel liquid crystal-based photonic transducer for sensing systems could be utilized as an active Q-switch in a miniaturised and integrated waveguide laser system. In this paper, we now present a comprehensive numerical modelling study of this novel laser architecture by deriving a set of equations that accurately describe the temporal optical response of the liquid crystal cell as a function of applied voltage and by combining this theoretical model with laser-rate equations. We validate the accuracy of this model by comparing the results with previously obtained data and find them in excellent agreement. This enables us to predict that under realistic conditions and moderate pump power levels of 500 mW, the laser system should be capable of generating peak power levels in excess of 1.1 kW with pulse widths of about 20 ns, corresponding to pulse energies > 20 μJ. We believe that such a low-cost and ultra-compact laser source could find applications ranging from trace gas sensing and LIDAR to material processing.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
After the principle of Q-Switching was first introduced by R. W. Hellwarth and F. J. McClung in 1962 [1], classical solid-state bulk lasers became the dominant type of Q-Switched lasers, owing to their good energy storage capacity. A few decades later, classical bulk lasers were gradually replaced by guided-wave lasers [2]. In 1998, H. Suche reported the first efficient Q-switched Ti:Er:LiNbO3 waveguide laser [3], in which a compact and rugged laser design was introduced with a monolithically integrated folded Mach-Zehnder type modulator of high extinction ratio to generate Q-Switched laser pulses with a duration of 4.3 ns and a peak power of up to 1.44 kW at a repetition frequency of 1 kHz. Since then, femtosecond laser direct-writing (FLDW) has evolved into a major technology for the fabrication of optical waveguides within bulk glasses [4]. Integrated continuous-wave (cw) waveguide lasers with and without incorporating Bragg gratings have been demonstrated using this technique [5,6].
In this paper, we will introduce a comprehensive numerical model for actively Q-switched waveguide lasers that are based on a novel liquid crystal transducer cell. Unlike passively Q-Switched lasers, in which the laser repetition rate is determined by the properties of the laser gain medium and the saturable absorber material [7], the repetition rate of actively Q-switched waveguide lasers can be controlled by the frequency of modulation signals applied to the modulator. Active devices used for Q-Switching are usually either acousto-optic modulators (AOMs) and electro-optic modulators (EOMs). Both types are rather large, bulky and require either high Radio-Frequency power and/or high voltage amplifiers [8]. To circumvent these limitations, we have recently demonstrated that a novel liquid crystal-based photonic transducer cell that was developed for optical sensing networks [9] and biomedical devices [10], could also be utilized as an active Q-switch that is fully compatible with a miniaturised and integrated waveguide laser architecture [11]. This cell is filled with a ferroelectric liquid crystal mixture and exhibits a strong electric field-controlled birefringence that can be translated into an electric field-controlled cavity loss with high modulation depth and high speed. In initial experiments, the device exhibited a modulation depth of around 80% under 60 V of applied voltage and could work under modulation frequencies of up to 1 MHz. In our proof-of-principle experiments, slope efficiencies of up to 22% accompanied with pulse durations below 40 ns and peak power level in excess of 50 W were demonstrated. In this paper we now introduce a new comprehensive numerical model for actively Q-switched waveguide lasers based on liquid crystal transducers with the aim of investigating the full potential of this novel actively Q-switched waveguide laser architecture. We derive a set of equations that accurately describe the temporal optical response of the deformed-helix ferroelectric liquid crystal cell as a function of applied voltage and combine this theoretical framework with a laser rate-equation model to simulate the behaviour of the overall laser system. We then validate the accuracy of this newly developed model by comparing its outcomes with previously obtained experimental results and find them in excellent agreement. This further enables us to predict the expected performance of the laser system after careful optimization. We show that a miniaturized and fully monolithic setup driven by an 80 V peak-to-peak voltage signal has the potential to generate laser pulses with a width of 17.00 ns and a peak power in excess of 1.1 kW, if the optical losses are reduced to 10.00% by optimizing the design of the liquid crystal transducer, the waveguide chip is pumped by 500 mW and the operation temperature is increased to 55 °C.
2. Liquid crystal cell design and characterization
The deformed-helix ferroelectric (DHF) liquid crystal cell presented here is shown in Fig. 1. and has been described in great detail in our previous papers [12].
Fig. 1: (a) The liquid crystal cell used in experiments, width=length=2 cm, thickness=4 mm. (b) The layered structure of the active area in a liquid crystal cell.
The entire liquid crystal cell consists of one gold layer, two glass layers, two Indium Tin Oxide (ITO) layers and two thin polyimide alignment layers. The middle layer is filled with the ferroelectric liquid crystal mixture FLC-576A developed in P. N. Lebedev Physical Institute of Russian Academy of Sciences, in which the birefringence is controlled by the applied electric field [13]. To align the helix axis of the liquid crystal layer, the liquid crystals are sandwiched between two thin polyimide layers with anti-parallel rubbing, giving rise to a homogeneous alignment where the helix axis of the smectic-C* phase is parallel to the cell’s surface [14]. To generate an electric field in the liquid crystal layer, two ITO layers are deposited on top of the polyimide layers. Owing to its high optical transmittance in the visible and near-infrared combined with its low electrical resistivity, ITO is a suitable electrode material [15]. Additionally, a gold mirror is deposited on the back of the liquid crystal cell to provide broadband reflection. The directors of the molecules and the helical structure in the ferroelectric liquid crystal (FLC) layer with Smectic-C* phase are shown in Fig. 2(a).
Fig. 2: (a) Coordinates and orientations of molecules in the liquid crystal layer with Smectic-C* phase. (b) Setup of crossed polarizer/analyzer for liquid crystal cell. (PBS: Polarizing Beam Splitter)
This particular class of liquid crystals is made of rod-shaped chiral molecules and a dimensionless unit vector, called the director d⃗, can be introduced to represent the direction of the preferred orientation of these molecules in the neighbourhood of any point. In the Smectic-C* phase, the molecules form smectic layers, in which all the directors are parallel and in which the molecules have a nematic-like order along the director, d⃗. Successive layers show a precession of the director around a uniform twist axis perpendicular to the smectic layers (z-axis). This gives rise to a helical structure with a pitch p0 and a tilt angle θt. We define φ as the azimuthal angle of rotation of the director in the smectic layer plane with respect to the x-axis, while P⃗s is defined as the spontaneous polarization of molecules, which is perpendicular to the director d⃗ in the x–y plane. If an electric field is applied between the ITO layers, i.e. along the y-axis, it will cause a reorientation of the directors which can be described by the so called “soft” and “Goldstone” modes. In the following sections, we will focus on the Goldstone mode which is the dominant relaxation mechanism for the liquid crystal cells described in this paper. The dynamic behavior of the FLC director under an applied electric field along the y-axis can be described by the double sine-Gordon equation [12]:
where the left-hand side represents the viscoelastic torque and the right-hand side refers to the elastic and ferroelectric torques respectively. In Eq. (1), p0 is the helix pitch in the liquid crystal layer, τc is the elastic relaxation time, which depends on the material composition and the temperature but is independent of the applied electric field, and Ecrit is the critical unwinding electric field at zero frequency. According to the double sine-Gordon equation shown in Eq. (1), the external electric field could change the azimuthal rotation angle φ, which means that the helical structure of liquid crystal is deformed by an external electric field. At a macroscopic level, the deformation of the helical structure caused by an electric field is translated into a change of birefringence Δn(E) and the optical axes rotation angle Ω(E) of the liquid crystal cell [16–18]. After propagation through a liquid crystal cell with an applied electric field E, two orthogonal polarizations of linearly polarized light experience a phase difference of , which depends on the electric field intensity. Simultaneously, the optical axes of the liquid crystal cell is rotated by an electric field dependent angle Ω(E). To translate these modulations into voltage-controlled optical transmissions, a crossed polarizer/analyzer setup as shown in Fig. 2(b) is used, and a polarizing beam splitter cube separates the s- and p-polarization components. The reflectance of this configuration can be expressed as [19] where λ is the wavelength of the incident light, d is the thickness of the liquid crystal layer in the cell (typically a few micrometers), Δn(E) is the effective birefringence which can be controlled by the electric field intensity, β is the angle between the polarization of the incident light and the helix axis without the electric field, and Ω(E) is the rotation of the optical axes in the liquid crystal cell which can also be controlled by an electric field that is applied to the LC cell.For practical considerations, it is difficult to adjust the angle β by rotating the liquid crystal cell without affecting the propagation path of the light beam within the liquid crystal cell. Instead, a half-wave plate is added into the setup to adjust the angle between the polarization of the incident light and the helix axis. In addition, in order to fine-tune the phase difference between the polarizations of the incident and reflected waves, and thus to maximize the change in reflectance for a given step in applied voltage, a quarter-wave plate is inserted between the half-wave plate and liquid crystal cell. Using the analytical 4×4 transfer matrix algorithm introduced by Schubert in 1996 [20], the expression of the crossed reflectance then becomes
Throughout this paper, we define the angle between the helix axis of liquid crystal cell and the fast axis of the quarter-wave plate (half-wave plate) as θwpq (θwph). From Eq. (3), the crossed reflectance as a function of half-wave plate and quarter-wave plate angles, θwph and θwpq, respectively, is shown in Fig. 3(a).
Fig. 3: (a) The crossed reflectance as a function of half-wave and quarter-wave plate angles and (b) crossed reflectance as a function of half-wave plate angle without (grey) / with a quarter-wave plate rotated by θwpq = 45° (red) for the 9.0 μm thick liquid crystal cell.
It can be seen that without the quarter-wave plate, the crossed reflectance R⊥ can oscillate only in the range from 0 to 59%, whereas in the setup that contains a quarter-wave plate at an angle of θwpq = 45°, the crossed reflectance, R′⊥, could have the full range from 0 to 100%. In this paper, the experimental and theoretical results presented in the following sections are all based on this optimal configuration. The crossed reflectance at optimal configuration can be expressed as
As a first step, the properties of the liquid crystal transducer that are important for its intended use as an active intracavity Q-Switch modulator were characterized in a cross-polarized setup as shown in Fig. 4(a). The modulation depth was investigated under a periodical electrical signal of constant amplitude and varying modulation frequencies and the results are shown in Fig. 4(b). With a periodical electrical signal with a constant amplitude of 60V, the modulation depth was 30% at 198 kHz and still 6% at 914 kHz, showing that the liquid crystal cell has an ultrafast response and can be used under a very wide frequency range of up to 1 MHz. In addition to the fast response, the liquid crystal cell is capable of providing a large modulation depth of 97% at a low frequency (<1 kHz), even if the amplitude of the externally applied voltage is as low as 12 V (see Fig. 5).
Fig. 4: (a) Schematic of the controlled optical loss measurement and (b) under the square wave signals with the constant amplitude of 60V, modulation depths are 30% at 198 kHz, 18% at 326 kHz and 6% at 914 kHz.
Fig. 5: (a) The square wave signals with the frequency of 5 Hz and the duty cycle of 50% are applied on the liquid crystal cell and (b) corresponding optical loss controlled by the electrical signals, in which the modulation depth is around 97% (close to 100%).
3. Numerical simulation and analysis
In this section, we introduce an comprehensive numerical modelling to simulate the behaviour of waveguide lasers that are Q-Switched utilizing the liquid crystal transducers that have been described above. From the double sine-Gordon equation shown in Eq. (1), it is evident that the external electric field E can deform the helical structure of the liquid crystals by varying the azimuthal angle φ. The electric field-controlled deformation changes the birefringence Δn(E) and the orientation of the optical axes Ω(E) of the liquid crystal cell. To calculate the birefringence Δn(E) and the orientation angle of the optical axes Ω(E) under a time-varying electric field, our analytical model uses the effective dielectric tensor, which can be expressed as [20]
In the case of an electric field which is much smaller than the critical unwinding electric field (E ≪ Ecrit) and when the electric field change is on a much slower timescale than the relaxation time of liquid crystals, τc, the dynamic response of the azimuthal angle φ(z, t) can be expressed as
where q0 = 2π/p0 and αE is defined as the ratio of the applied electric field to the critical unwinding electric field, αE = E/Ecrit. Based on the assumption that αE ≪ 1, the effective dielectric tensor elements shown in Eq. (5) can be calculated by the approach introduced by us in [21]: where , , , and θt is the tilt angle of liquid crystals. In experiments, square-wave signals with a pulse duration of tp and an amplitude of V = E0d were applied to the liquid crystal cell. In this case, the time-dependent factor αE(t) can be calculated as where Eeff is defined as the effective electric field experienced by the liquid crystal cell, which can be expressed asIn the above equation, the relaxation time constant τc of the liquid crystal cell indicates how fast the modulator can respond to varying electric signals. It is worth noting that even though, in our experiments, the applied electric field is larger than the critical unwinding electric field Ecrit, the effective electric field Eeff is still below the critical unwinding electric field Ecrit, due to its short pulse duration (tp = 2μs), which means the assumption of this model is valid. Based on the effective dielectric tensor shown in Eq. (5), the birefringence Δn(t) and the rotation of the optical axes Ω(t) can be approximated by
where and are two elements of the effective dielectric tensor shown in Eq. (5). is the value of without an applied voltage and can be calculated by .The full numerical model uses rate equations for the population inversion density n and the photon flux ϕ to simulate the generated Q-Switched laser pulses within the cavity [22]. The overall laser system includes spontaneous emission, stimulated emission and absorption. Radial and longitudinal variations within the gain medium are neglected. The rate equations of the population inversion density n and the photon flux ϕ within the cavity can be expressed as
where σemi is the stimulated emission cross section, which depends on the gain medium used in experiments. c is the speed of light within the medium, τf is the fluorescence lifetime, Wp is the pump rate and ntot is the total number of active laser ions within the system. S describes the spontaneous emission rate, τd is the decay time of photons and δ describes the combined cavity losses, which can be found in Table 1. R⊥ is the crossed reflectance at the optimal configuration, which can be calculated by substituting Eq. (8) into Eqs. (10) and (11), and then into Eq. (4).
Table 1:. Optical and Physical Parameters in the Numerical Model
4. Setup design and experiments
The setup for our experiments is shown in Fig. 6(a). The active gain medium is a heavy-metal fluoride glass (ZBLAN - ZrF4, BaF4, LaF4, AlF3, NaF3) doped with 2.5 mol% ytterbium (Yb). The length of the Yb:ZBLAN chip and the embedded waveguides is 10 mm. The fluorescence lifetime of Yb doped into ZBLAN is τf = 1.81 ms and the emission cross section is σemi = 0.46×10−20cm2 [24]. The longer the fluorescence lifetime τf and the smaller the emission cross-section σem, the longer the build-up time of laser pulses, which is more suitable for a slow Q-switch. The depressed cladding waveguide was inscribed using femtosecond lasers from Ti:sapphire extended-cavity oscillator [25]. The pulse energy on target was 80 nJ which resulted in a refractive index change of Δn = −1.2 × 10−3 to form a depressed cladding region. The inscribed waveguides have core diameters ranging from 6 μm to 14 μm ; further details can be found in [26]. For the following experiments, the 8 μm diameter waveguide as shown in Fig. 6(b) was used, as it resulted in the highest output power. The waveguide is pumped by a 976 nm fibre-coupled laser diode that can deliver a maximum pump power of 360 mW. The pump beam is focused into the waveguide through an input-coupling mirror via an aspheric focusing lens (f = 15.4 mm). The input-coupling mirror is a shortpass dichroic mirror with a cutoff wavelength of 1000 nm and has high transmission (> 99.8%) at 976 nm and high reflectance (> 99.99%) at a wavelength between 1010 nm and 1200 nm. Inside the laser cavity, the beam is collimated using another aspheric lens (f = 18.4 mm, anti-reflection coated 650 nm to 1050 nm). The diameter of collimated beam is approximately 3 mm and exhibits negligible angular divergence. It is then directed onto a polarizing beam splitter followed by a zero-order half- and a zero-order quarter-wave plate, and finally the liquid crystal cell. As described earlier, the half- and the quarter-wave plate were introduced into the setup for two reasons: (i) To maintain the light propagation path in the liquid crystal cell, the half-wave plate can be used to adjust the relative angle of the polarization with respect to the optical, instead of rotating the liquid crystal cell itself; (ii) the quarter-wave plate can be used to optimize the modulation depth though changing the polarization state of the light incident on the liquid crystal cell as has been shown in Fig. 3. In order to investigate the performance of liquid crystal cells with varying thicknesses, 3.3 μm and 9.0 μm thick liquid crystal cells are tested and compared. The total length of the laser cavity is 250 mm which is mainly limited by the size of off-the-shelf optical mounts used in the setup. Square wave electrical signals with a pulse duration of 2 μs and varying amplitudes are applied to both liquid crystal cells (3.3 μm and 9.0 μm thick) to control the crossed reflectance R⊥. A small negative offset voltage is also added to keep the mean value of the electrical signals to be zero, as non-zero DC voltage could potentially damage the liquid crystal cell. The repetition rate of the electrical pulses frep is set to 5 kHz. The intensity of the generated Q-Switched laser pulses is measured and recorded by a photo-detector. Additionally, the angle β between the polarization of the incident light and the LC helix axis without an applied electric field is β = 45°. The cavity losses δ include waveguide propagation losses, Fresnel losses and losses from the polarizing beam splitter and the liquid crystal cell. The overall cavity losses in the setup are estimated to be 70.1% for a 3.3 μm thick liquid crystal cell and 72.5% for a 9.0 μm thick liquid crystal cell.
Fig. 6: (a) Schematic of the laser setup. In this setup, the pump light is coupled to a waveguide through a dichroic in-coupling mirror. Additionally, the polarizing beam splitter combined with waveplates and liquid crystal cell acts as a actively-controlled variable output-coupling mirror. (b) Cross-section of the depressed-cladding waveguides.
Optical and physical parameters of experimental setup and microscopic parameters of LC mixture (FLC-576A) have been summarized in Table 1. For liquid crystal cells used in experiments, the ordinary (extraordinary) refractive index is no = 1.5 (ne = 1.72), the tile angle is θt = 32° and the helix pitch p0 is 0.2 μm at the room temperature [23]. The thickness of two liquid crystal cells used in our experiments are 16 times and 45 times larger than the helix pitch, respectively, so the helix will be retained within boundaries [13]. Based on the schematic shown in Fig. 4(a), both 3.3 μm and 9.0 μm thick liquid crystal cells are tested under electrical signals with varying waveforms, frequencies and amplitudes. It is worth noting that two important parameters of the model, namely the elastic relaxation time τc and critical unwinding electric fields Ecrit, depend on the specific properties of the cell, particularly its thickness and the type of alignment layer. In our case, we measured unwinding electric fields Ecrit and elastic relaxation times τc of two liquid crystal cells by applying sine wave voltage with varying amplitudes and rotating a half-wave plate. Experimental results shows that the 9.0 μm thick liquid crystal cell has a smaller elastic relaxation time τc and a larger critical unwinding electric field Ecrit than the 3.3 μm thick liquid crystal cell. It is because the thickness of the 3.3 μm liquid crystal cell approaches the critical thickness of the liquid crystal material. In this case, the effects of boundary surfaces on the helical structure of a ferroelectric smectic-C* liquid crystal (FLC) cannot be neglected. Indeed, solid surfaces bounding the FLC layer could induce the deformation and untwisting of the helix, when the thickness of the cell approaches a critical thickness dc [27]. The critical thickness dc of the cell can be calculated as , where W is the anchoring energy on LC-substrate surfaces, kφ is the elastic constant and q0 = 2π/p0. For DHFLC cells in the Smectic-C* phase with the helix pitch of 0.2 – 1.0 μm, we can use typical values W = 1 × 10−2J/m2 [28] and kφ = 1 × 10−11N [29]. When the helix pitch of DHFLC cells p0 is 0.2 μm at room temperature, the estimated value of critical thickness dc is 0.8 μm. Because the thickness of the thinner liquid crystal cell (3.3 μm) is only 4 times larger than the critical thickness, its boundary surfaces can affect the helical structure and lead to a smaller unwinding electric field Ecrit and a larger elastic relaxation time τc. Pozhidaev et al. [30] evaluated the electrically controlled birefringence via ellipticity measurements. In their experiments, the ferroelectric smectic-C* liquid crystal (FLC) material with the helix pitch po of 0.33 μm was used, and two planar cells with different FLC layer thicknesses (16 and 44 μm) were assembled with the same configuration as we introduced. Their measurements proved that the thicker liquid crystal cell has a larger critical unwinding electric field Ecrit and a larger elastic constant kφ, even through the thickness of the thinner FLC layer is 7 times larger than the critical thickness dc = 2.24 μm.
5. Results and discussion
In this section, we reported the experimental results and interpret them by using the model presented in the previous sections. Based on electro-optical parameters shown in Table 1, the experimental and numerical simulation results for the crossed reflectance for 3.3 μm and 9.0 μm thick liquid crystal cells subject to a single voltage pulse are shown in Fig. 7.
Fig. 7: The crossed reflectance of the 3.3 μm (a) (b) and the 9.0 μm (c) (d) thick liquid crystal cells as a function of time under varying electric signals. The grey line represents experimental measurement results, while the red line represents the corresponding numerical simulation results.
From the above figure, it can be concluded that the numerical model can accurately reproduce the crossed reflectance R⊥ of liquid crystal cells under fast changing applied voltages. It is evident that from both, experimental and simulation results for two liquid crystal cells, a stronger electric field can lead to a larger modulation depth. Compared with the 3.3 μm thick liquid crystal cell, the 9.0 μm thick liquid crystal cell can give rise to a larger modulation depth under the same electric field intensity. To characterize the properties of generated Q-Switched laser pulses, pulse width and peak power are the two most crucial performance parameters. Since it can be seen that the 9.0 μm thick liquid crystal cell can provide a larger modulation depth and can withstand applied voltages with larger amplitude, experimental and simulation results based on the 9.0 μm thick liquid crystal cell will mainly be analyzed and discussed. In experiments, with the 9.0 μm thick liquid crystal cell, the square wave electric signal had a constant pulse duration of 2 μs with an amplitude range from 35 V to 90 V. The pulse width and peak power of the resulting laser pulses are shown in Fig. 8. When the applied voltage changes from 30 V to 90 V, the pulse width decreases from 70 ns down to 40 ns, and the peak power increases from 10 W to 50 W. However, when the amplitude of the applied voltage is larger than 70 V, both the pulse width and peak power start to saturate. The numerical simulation model also shows the same dependence of pulse width and peak power on the applied voltage, and all simulation results are in very good agreement with the experimental results.
Fig. 8: (a) Experimental (red circles) and simulation results (grey squares) of pulse width and (b) peak power as a function of the applied voltage for the 9.0μm thick cell.
In addition to the mentioned properties of Q-Switched laser pulses, the conversion efficiency η is another important characteristic. It is defined as the fraction of pump power that can be converted into Q-Switched laser pulses, and it can be calculated by η = Pavg/Ppump, in which Pavg is average output power and Ppump is absorbed pump power. The simulation and experimental results of the average output power Pavg as a function of absorbed pump power Ppump are shown in Fig. 9(a). It can be seen that the threshold absorbed pump power Pth is 70 mW. When the absorbed pump power is larger than Pth, the average output power Pavg starts to increase linearly with the absorbed pump power Ppump. The slope of this linear relationship dictates the conversion efficiency η and it is around 7.9%. To investigate the impact of higher repetition rates on the output laser performance, the simulation results for peak power and pulse width as a function of repetition rate are shown in Fig. 9(b). In this section, the theoretical model was characterized from different aspects, including the cross-polarized reflectance as well as pulse width, peak power and average output power of the generated Q-Switched lasers. The excellent agreement with the experimental results validates our theoretical model which means that this model can be used to optimize the performance and explore the limitations of our technology.
Fig. 9: (a) Experimental results (red squares) and simulation results (grey squares) of average output power as a function of absorbed pump power and (b) simulation results of pulse width and peak power as a function of repetition rate.
6. Optimization
To improve the performance of Q-Switched waveguide lasers based on this approach, some specific physical parameters can be adjusted for optimization purposes, including pump power, optical losses and operation temperature. As mentioned earlier, this specific type of liquid crystal cell was developed as a transducer for sensing applications, which means it hasn’t been optimized for its use in a laser setup. From measurements of optical losses summarized in Table 1, the total optical losses in the setup are around 72.52%, which means that only 27.48% of light remains after one round trip within the laser cavity. High optical losses and low available pump power are two critical limitations of the initial proof-of-principle setup. Increasing the absorbed pump power Ppump is straightforward by using commercial pump laser diodes with higher pump power levels. To reduce the optical losses, the bottom ITO layer could be removed from the liquid crystal cell as the bottom reflecting gold layer could also be used as an electrode. Additionally, the other ITO layer could be replaced by an Index-Matched Indium Tin Oxide (IMITO) layer [31], which has an average transmittance of 95%. With this, it would be possible to reduce the optical losses from 72.52% to at least 10.00%. Based on the numerical model introduced in the last section, when the optical losses are reduced to 10.00% and the pump power is increased from 200 mW to 400 mW, the predicted pulse width and peak power of the generated Q-Switched laser pulses based on a 9 μm liquid crystal cell are shown in Table 2.
Table 2:. Prediction of Q-Switched Lasers with Low Optical Losses and/or High Pump Power
The impacts of lower optical losses and higher pump power on the pulse width and peak power of Q-Switched lasers are further investigated separately. If the applied voltage is 36.99 V and the pump power is increased to 400 mW, the pulse width decreases dramatically from 58.30 ns to 23.06 ns, and the peak power increases from 19.73 W to 147.90 W, respectively. In contrast, if the applied voltage is still 36.99 V, but the optical losses are reduced from 72.52% to 10.00%, the peak power increases from 19.73 W to 38.30 W, but the pulse width decreases to 52.25 ns slightly. Moreover, if the applied voltage is increased to 88.05 V and the pump power is maintained at 400 mW, the pulse width can be shortened to 20.00 ns, and the peak power can reach 277.66 W. Therefore, a higher pump power not only leads to a higher peak power, but also shortens the pulse width significantly. However, lowering the optical losses only improves the peak power but does not affect the pulse width. If optical losses and pump power are optimized at the same time, the pulse width can be 20.25 ns and the peak power can be up to 650.94 W. If the repetition rate is increased to 20 kHz, the pulse width of generated lasers is longer, and thus their peak power is lower. These optimized Q-Switched laser pulses are shown in Fig. 10.
Fig. 10: (a) Q-Switched laser pulses with a repetition rate of 5 kHz from the simulation model and (b) the shortest Q-Switched laser pulses from the model with a pulse width of 20 ns and a peak power of 650.94 W. It could be achieved, when the amplitude of applied voltage is 88.05 V, the pump power is 400 mW and the optical losses is reduced to 10.00%.
As has been shown by Pozhidaev et al., the azimuthal rotational viscosity of a ferroelectric liquid crystal (FLC) is dependent on the operation temperature; and it is lower at higher temperatures resulting in faster responses and shorter relaxation times τc [17]. Thus, because the response time of the liquid crystal cell varies under different temperatures, even if the applied voltage is constant, the pulse width and peak power of the generated Q-Switched laser pulses can be further optimized by adjusting the operation temperature. In experiments, we also measured the elastic relaxation time τc of the 9 μm liquid crystal cell under varying temperatures. The experimental results show that the operation bandwidth of the liquid crystal cell varies with temperature and that the widest bandwidth can be achieved at a temperature of 55 °C, which means that the liquid crystal cell has its fastest response and the smallest elastic relaxation time τc at 55 °C. Therefore, when the temperature is adjusted to 55 °C, the elastic relaxation time τc of the 9 μm liquid crystal cell can be reduced from 15.2 μs to 7.6 μs, and the generated Q-Switched laser pulses can be optimized further. The predicted pulse width and peak power of Q-Switched laser pulses at a temperature of 55 °C are shown in Table 3.
Table 3:. Prediction of Q-Switched Lasers at the Temperature of 55 °C
At the optimal temperature of 55°C, a modulation depth of 100% can be achieved at an applied voltage of 53.7V. In this case, assuming a pump power of 400 mW and optical losses of 10.00%, the pulse width of the generated Q-Switched laser pulses is as short as 20.50 ns and the peak power is increased from 394.90 W to 711.83 W. Comparing the pulse width and peak power at 25°C and 55°C, it is worth noting that a temperature of 55°C does not lead to a shorter pulse width, but it results in a larger modulation depth and a higher peak power. If the pump power is further increased to 500 mW and temperature, applied voltage and optical losses are maintained at the values given above, the peak power of the generated laser pulses can be increased to 1.15 kW and the width of laser pulses can be shortened to 17.00 ns.
7. Conclusion
In this paper, we have demonstrated a novel approach to generate actively Q-switched laser pulses based on an integrated waveguide chip and a liquid crystal cell in the deformed helix ferroelectric (DHF) mode. In this approach, a liquid crystal cell can behave like an active Q-Switch modulator under a wide range of repetition frequencies. Experimental results show that the pulse duration of generated Q-Switched lasers is well below 40 ns, which is much shorter than the typical response time of liquid crystal. These surprising results have been reproduced and confirmed by numerical simulations that accurately reproduce pulse width, peak power and average output power for various operating conditions. Based on our numerical model, the impacts of lower optical losses and higher pump power on the optimization of Q-Switched lasers have been investigated and discussed. It was shown that lower optical losses can increase the peak power of laser pulses, but do not lead to shorter pulse widths. In contrast, higher pump power levels can increase the peak power and shorten the pulse width of the generated laser pulses simultaneously. From the prediction of optimization based on our numerical simulation model, the shortest pulse width can be as low as 17.00 ns and the highest peak power can be as high as 1.15 kW, when the temperature is optimized and other parameters are optimized simultaneously. To achieve these performance values, the optical losses can be reduced by removing the bottom ITO layer from the liquid crystal cell, and the top ITO layer can be replaced with a conductive coating with better transparency, such as Index-Matched ITO with an average transmittance of 95%. Besides, the liquid crystal cell can directly be integrated onto the waveguide chip to avoid Fresnel losses. Moreover, the maximum absorbed pump power in experiments was limited to 200 mW in our previous experiments, and increasing the pump power is straightforward. Based on experimental results and our theoretical model, it is possible to generate actively Q-Switched laser pulses with a pulse width of 17.00 ns and a peak power in excess of 1 kW from a fully monolithic laser setup whose total length is in the order of only 1 cm.
Funding
Cooperative Research Centres Projects Program, Australian Government Department of Industry (CRC-P-49); Australian Research Council Discovery Projects (DP160104625); Australian National Fabrication Facility (ANFF) (OptoFab Node and UNSW Node, NCRIS).
Acknowledgments
We would like to acknowledge the support from Zedelef Pty Ltd for providing the LC transducer cells used in this work.
References
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