Compound Cavity Passively Q-Switched Single-Longitudinal-Mode Diode-Pumped Laser

Introduction

In recent years, lasers with different spectral and time-domain characteristics have been widely used in spectral detection, space exploration, manufacturing, etc. [1–4]. Across the domains of coherent optical communications, sodium guide star technology, gravitational wave detection, and non-linear optics, solid-state single-longitudinal-mode (SLM) laser sources with a narrow spectral bandwidth are attracting significant interest [5–10]. These lasers, which often also carry additional characteristics such as broad wavelength tuning capability, high pulse energy, and good beam quality, are enabling a host of new techniques and methodologies. SLM laser sources that operate in the near-infrared spectral region are also gaining traction as the ideal laser sources for molecular spectroscopy [11].

From a practical standpoint, lasers which operate with a SLM must have an effective means of eliminating the spikes created by the beat frequency of adjoining longitudinal modes; this is because these spikes are the most common source of damage to laser system components [12–14]. A number of methods have been used to produce SLM output from solid-state lasers include twisted-mode cavities (TMC) [15], ring cavities [16], the application of etalons or gratings [17–19], microchip lasers [15, 16], and seed injection lasers [20, 21]. However, it should be noted that many of these approaches yield laser outputs with quite low SLM ratio (herein defined as the ratio of the number of single longitudinal mode pulses to the total number of pulses in a certain time). This is due to the wide gain bandwidth and narrow longitudinal mode spacing which is a common characteristic of solid-state lasers. Recent demonstrations (circa 2016–2020) of SLM output from a number of different solid-state laser designs are summarized in Table 1. Here the summary focusses on advancements in cavity design and mode-selecting/isolating capability.

TABLE 1

TABLE 1. Summary of recently reported SLM lasers.

The prior literature shows that the primary approaches to generating SLM output are based on threshold regulation and mode competition enhancement [18–24]. In comparison to ring cavities, it is commonly shown that standing wave cavities can generate higher energy pulses with narrower pulse width and with minor beam distortion. A standing-wave cavity is also more desirable from a practical standpoint as it is often more robust and easier to handle in comparison to a ring cavity design. Additionally, standing wave cavities may quite easily integrate with mode selection devices/approaches such as injection-seeding and Fabry-Perrot (F-P) etalons to produce SLM output [19, 25]. It should be noted that the emission from SLM lasers which make use of passive mode selection techniques (TMC and three-plane resonant reflector) typically exhibit inferior SLM ratio unless multiple intracavity components are used [15]. In this case, the insertion of multiple components (such as F-P etalons) increases the loss within the cavity and limits energy output [19, 26]. Injection-seeding can be used to achieve a high SLM ratio; however, it is a bulky, costly, and complicated approach which also typically requires high maintenance. Cavity-stabilization loops are also a source of significant technical complications for injection-seeded lasers [25, 27]. There is, hence, a need for new and novel approaches which may improve the simplicity, robustness, and affordability of high SLM ratio lasers.

One such approach which may address this need is to utilize a mode selection strategy based on a compound cavity combined with a TMC. Here, a compound cavity comprising two distinct cavities is used for longitudinal mode selection, replacing conventional devices such as etalons or gratings. The application of a compound cavity increases mode competition within the laser and also acts as a frequency-selector, suppressing numerous longitudinal and transverse modes. The above feature is the main difference between the compound cavity and the three-plane resonant reflector. In the three-plane resonant reflector, the inserted mirror is coupled with the output mirror for use as the output mirror. In this work, a compound cavity was integrated into a passively Q-switched, standing wave cavity which provided significant round-trip gain. The long transit time of the laser field within the passively Q-switched cavity was beneficial in limiting the generation of multiple-longitudinal-modes. The considerable laser gain combined with small initial transmittance of the passive Q-switch was conducive to obtaining laser pulses with a short pulse duration and high peak power. The TMC (formed using quarter wave plates) was integrated into the laser as a means of limiting the effect of spatial hole burning; this further improved the laser’s single-mode operation. The laser was capable of operating with output pulse frequencies from 1 to 10 Hz with high energy stability (the root mean square energy fluctuation was <1%).

Experimental Setup and Numerical Analysis

The setup of the compound cavity, passively Q-switched SLM diode-pumped laser device is shown in Figure 1. The physical length of the cavity was 420 mm. The back cavity mirror M₃ and the resonant mirror M₂ constituted a resonant sub-cavity. Quarter-wave plates (QWPs) were used to form a TMC which limited the spatial hole burning in the laser gain medium. The front cavity mirror M₁ had a reflectivity of 60% at 1,064 nm. The resonant mirror M₂ had a reflectivity of 10% at 1,064 nm on the side facing mirror M₃, and was anti-reflection coated (for 1,064 nm) on the side facing mirror M₁. The back cavity mirror M₃ had a reflectivity of more than 99.5% at 1,064 nm. The laser gain medium was an Nd:YAG (Φ 3 × 78 mm) crystal with a 1% Nd³⁺ doping concentration; both faces of the crystal were coated anti-reflecting at 1,064 nm. A diode pump laser with a repetition rate of 10 Hz and a pulse duration of 250 µs was used in a side-pumping configuration (this was done so as to minimize thermal loading within the laser crystal). The laser was passively Q-switched by a saturable absorber Cr⁴⁺:YAG crystal (Φ 6 × 3.25 mm), which had an initial transmittance of 12.23%. The laser produced Q-switched output when the pump energy was ∼0.5 J. The laser was p-polarized via the inclusion of a thin-film polarizer (TFP); a 2 mm pinhole (PH) was used to control the intracavity transverse modes.

FIGURE 1

FIGURE 1. Schematic diagram of the compound cavity passively Q-switched single-longitudinal-mode diode-pumped laser. QWP, quarter-wave plate; PH, pinhole; TFP, thin-film polarizer. (Illustration: resonant mirror frequency selector.)

In Figure 1, the resonant mirror (M₂) is used to induce frequency selection within the laser. The means by which this is achieved can be modeled theoretically using thin-film analysis methods in combination with laser signal build-up times. Such an analysis is presented below. We start by calculating the transmission matrix. As outlined in Figure 1, for a plate of thickness d₁, and plate separation of d₂, the transmission matrix is given by [28]:

$M_j=\left[\begin{array}{cc}\cos {\delta }_j& -\frac{i}{n_j}\sin {\delta }_j\\ -i{n}_j\sin {\delta }_j& \cos {\delta }_j\end{array}\right](1)$

where δ_j is the phase delay of light passing through the medium. The expression of δ_j is given by:

${\delta }_j=\frac{2\pi }{\lambda }{n}_j{d}_j\cos {\theta }_j(2)$

where n and d are the refractive index and thickness of the jth media, respectively. λ and θ are the incident wavelength and angle of incidence, respectively. The total transmission matrix is expressed as:

$M={\displaystyle {\prod }_i}{M}_i=\left[\begin{array}{ll}{m}_{11}\hfill & i{m}_{12}\hfill \\ i{m}_{21}\hfill & m_{22}\hfill \end{array}\right](3)$

The combined reflectivity of the compound frequency selector system as a function of wavelength is then given by:

$R\left(\lambda \right)=\frac{{\left(m_{11}{P}_0-m_{22}{P}_1\right)}^2+{\left(m_{12}{P}_1·P_0-m_{21}\right)}^2}{{\left(m_{11}{P}_0+m_{22}{P}_1\right)}^2+{\left(m_{12}{P}_1{P}_0+m_{21}\right)}^2}(4)$

where P₀ and P_l are the parameters which depend on the medium in which both ends of the resonant reflector system are placed. If placed in air, then P₀ = P_l = cos θ₀.

In this work, the thickness of the resonant mirror M₂ is d₁ = 6.35 mm, and the refractive index is 1.51. The distance between M₂ and M₃ is d₂ = 5 cm. From this, one can calculate the combined reflectivity of the system, as a function of wavelength. This was done for the wavelength range 1,063.8–1,064.4 nm in 0.01 pm steps, and this is shown as the blue plot in Figure 2A. The envelope period of the reflectivity depends on d₁, and the period of the fine structure depends on d₂. When the separation distance is greater than the thickness, such a structure has a peak reflection of 40%. When this occurs, the reflectivity of M₂ is less than M₁, and M₂ becomes the output mirror of the sub-resonant cavity.

FIGURE 2

FIGURE 2. (A) Gain spectrum (green trace) and the reflectivity of the resonant mirror (blue trace) as a function of laser wavelength; (B) modeled laser spectrum as a function of wavelength for q = 5 transits; (C) modeled laser spectrum as a function of wavelength for q = 50 transits; and (D) modeled laser spectrum as a function of wavelength for q = 500 transits.

When the laser is operating in a low gain state, the round-trip gain is [15]:

$G=R{\left(T_0{T}_p{T}_d\right)}^2\exp \left[2g_{0}l\frac{{(\mathrm{\Delta }\lambda /2)}^2}{{\left(\lambda -{\lambda }_0\right)}^2+{(\mathrm{\Delta }\lambda /2)}^2}\right](5)$

where T₀, T_p and T_d are the initial transmittance of the Cr⁴⁺: YAG, the transmittance of the TFP, and the transmittance of the PH, respectively. Δλ is the fluorescence linewidth of the gain medium, and g₀ is the small-signal gain coefficient at the laser center wavelength. l is the length of the gain medium, and R is the reflectivity of the resonant mirror frequency selector (as detailed above).

In a standing wave cavity, the number of longitudinal modes of oscillation in the resonant cavity is determined by the gain linewidth Δυ of the gain medium and the longitudinal mode interval Δυ_q of the resonant cavity. The gain linewidth of Nd:YAG is Δυ₀ = 200 GHz, and the longitudinal mode interval of the resonant cavity is Δυ_q = c/2L, where c is the speed of light and L is the optical length of the resonant cavity. Note also that in a compound cavity laser design, longitudinal modes of the resonant cavity must also be supported within the compound cavity if they are to oscillate.

The net gain difference between two adjacent longitudinal modes is proportional to the transit time. Therefore, as the transit time increases, the desired signal gradually accumulates from noise, while at the same time suppressing other longitudinal modes [29]. For passively Q-switched lasers, the laser field build-up process typically requires hundreds to thousands of transits, and this is conducive to the accumulation of laser gain and energy within a SLM, with a high SLM ratio [30]. The number of loop transits (or round trips) that a laser field undertakes during its build-up from noise to typical output power levels is given by q [28, 31]. It has been calculated that passively Q-switched systems typically require q > 500 before the field is output.

In a practical laser, the difference in gain between two adjacent longitudinal modes can be a mere 0.5%. Nevertheless, this minor difference in gain is significant in the context of laser systems wherein laser modes build from noise to megawatt power levels; here the laser modes with the lowest losses emerge as the dominant modes. This effect can be demonstrated through modeling of the laser spectrum. The theoretical spectrum of the laser in this work was modeled for increasing numbers of transits (q) and the resultant spectra are shown in Figures 2B–D. It can be seen from the figures that as the number of transits increase, there is a progressive decrease in the number of gain regions that are present in the spectrum. In the case of q = 500 transits, the difference in intensity between the primary gain region and its adjacent neighbor is more than an order of magnitude.

Experimental Results and Discussion

As this system does not require the use of additional external components (such as piezoelectric transducers and external circuits) to actively adjust cavity mirrors, and does not need injection seeding, the laser system is inherently simple, low cost, and easy to maintain.

The experimental results showed that the insertion angle of the resonant mirror (M₂) had a significant effect on the output characteristics of the laser. When the insertion angle was large (>1°), the insertion of a resonant mirror would lead to significant loss and poor energy stability, resulting in an increase in the laser threshold and linear jitter of the output beam. The spatial characteristics of the output beam were recorded with a laser beam profiler (DataRay WinCamd-LCM). Images of the near-field spatial profiles of the laser output for a range of mirror M₂ insertion angles (<0.1°) are shown in Figure 3A. The plots show that a near-perfect Gaussian-like output spot is generated when mirror M₂ is aligned perfectly parallel with the primary laser cavity (formed by mirrors M₁ and M₃). Angular deviation of M₂ led to the formation of two distinct cavities within the laser system. This resulted in undesired oscillation of transverse modes and mode competition. The end result was a reduction in output energy and stability, and deterioration of the mode profile. The system also exhibited some sensitivity to fluctuations in the ambient temperature and the temperature of the water used to cool the laser gain crystal. These fluctuations in the range of ±1°C had the effect of changing the length of the laser cavity and drove mode jumps and occasionally multi-longitudinal mode operation [25]. It is anticipated that this sensitivity can be overcome through simple engineering to improve the temperature-stability of the system.

FIGURE 3

FIGURE 3. (A) Near-field intensity distribution of the laser output for different M₂ insertion angles from 0.1 to 0° (left-to-right); (B) plot of a typical laser output pulse at maximum pulse energy; (C) plot of the laser output linewidth as determined using a Fabry-Perot interferometer (inset: typical interferogram from the Fabry-Perot interferometer); and (D) plot of the laser beam propagation characteristics and fits used for determination of the beam quality factor.

The output energy was measured using a laser energy meter (OPHIR PE50BB-DIF-C and OPHIR NOVA II). The average pulse energy was 14.81 mJ (at a pump energy of about 0.5 J), and the pulse energy fluctuation was 0.82% over 10,000 shots (taken over a period of ∼1 h). The temporal waveform of the output was detected using a fast photodetector (THORLABS DET08C) and was recorded on an oscilloscope (Tektronix MSO64). The pulse shape of the output is shown in Figure 3B. The average pulse width was 10.18 ns. Due to the long time required for passive Q-switching to turn off completely when operating at high pump energy, there is a slight tail in the output pulse. It was observed that the TMC had the effect of removing secondary emission peaks in the output when operating at high pump energies.

A home-made Fabry-Perot interferometer with a 7.5 GHz free spectral range and 144 MHz bandwidth was used to examine the spectral properties of the laser output. The emission spectrum of the laser output is shown in Figure 3C; also shown inset is an interferogram of the output. The single ring in each interference order indicates that the laser operates with a SLM. The spectrum shows that the laser output linewidth is 254.3 MHz. We believe that this relatively broad linewidth is the result of the length of the laser cavity and the time required for the passive Q-switched to establish oscillation. The SLM ratio of the laser was determined in real-time by examining the output waveform and looking for the presence of any beat frequency components (using the oscilloscope). The measured SLM ratio was ∼99.6% over 3,000 shots. Under the same experimental conditions, when TMC is used without a compound cavity, the output waveform is unstable, and it is difficult to achieve SLM ratios greater than 95%.

The beam quality factor of the output was measured, as shown in Figure 3D. Standard Gaussian beam propagation fits were used to determine beam quality factors in the x and y directions of 1.12 and 1.14, respectively. We believe that the significantly better beam quality in this work in comparison to the work summarized in Table 1 results from the PH and the resonant mirror controlling the transverse modes within the cavity. Future work is focused on reducing the overall cavity length, improving the cavity engineering to achieve stable SLM output without mode hopping, and to investigate methods of further increasing energy output.

Conclusion

In conclusion, a pulsed laser utilizing a compound cavity, which operates in SLM with no active cavity stabilization, has been demonstrated. The output has a SLM ratio of 99.6% and a linewidth of 253.4 MHz at a repetition rate of 10 Hz. The pulse width was 10.18 ns, and the average beam quality factor was 1.13. The average pulse energy was 14.81 mJ, with 0.82% pulse energy fluctuations as measured over a 1-h stability test. The compound cavity proposed in this paper has the advantages of a high SLM ratio, high single pulse energy, high energy stability, low cost, compact structure, and is comparatively low maintenance.

Data Availability Statement

The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.

Author Contributions

BC: design of the study, investigation, data curation, writing—original draft. ZB: methodology, writing—review and editing, and supervision. GZ: methodology, data curation, and investigation. YZ: methodology, data curation, and investigation. BY: investigation, writing—original draft, and writing—review and editing. YQ: investigation, and writing—review and editing. JD: investigation, and writing—review and editing. KW: methodology, and supervision. YW: conceptualization, methodology, and supervision. ZL: conceptualization, methodology, supervision, and funding acquisition. All authors contributed to the article and approved the submitted version.

Funding

This work was supported by the National Natural Science Foundation of China (No. 61927815).

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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