Open Access
Add to BibSonomy
Abstract
We report on the first injection-seeded nanosecond Ti:Sapphire laser that demonstrates a stable single-longitudinal-mode operation with no feedback loop for active cavity stabilization. The short cavity generates 6-mJ transform-limited pulses at a wavelength of 807 nm and with a slope efficiency of 43%. An intracavity dispersive prism makes a novel cavity design for injection-seeded lasers and provides pre-selection of the emission wavelength. In support of these experiments, we perform numerical simulations that include extra cavity losses. The simulation results are in good agreement with the outcome of the experiment and reveal the formation scenario of the laser mode.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Pulsed laser sources characterized by narrow single-longitudinal-mode spectral bandwidth, broad wavelength tuning capability, and both relatively high pulse energy and good beam quality are particularly useful in high-resolution laser spectroscopy. Additionally, molecular spectroscopy applications require such laser sources to operate in the near infrared spectral domain. Optically pumped injection-seeded tunable solid state lasers often fulfill these technical needs. Overall, modern injection-seeded laser systems demonstrate reliable operation and satisfactory performance. At the same time, they remain bulky, overly complicated, high maintenance, sensitive to the environment, and expensive. As these factors limit the usage of the injection seeding technology to a well-equipped facility, any design improvements, particularly simplification, are to increase availability and affordability of injection-seeded lasers. Bio-medical research in particular would reap important benefits from such improvements.
Likely, the first demonstration of injection seeding [1] on a ruby laser was made in 1967 and extended to a Nd:YaG crystal in 1985 [2] and a Ti:Sapphire (Ti:S) crystal in 1986 [3]. Further research found that this technique provides an experimentally feasible and highly efficient way to control spectral properties of intense nanosecond pulses via control of a relatively weak seed wave. Later, this technique became viewed as more technically advanced as compared to other approaches, particularly those that handle spectral properties of intense laser pulses [4]. This article presents the detailed theory that sets the requirements for a seed signal and covers many other important laser parameters for solid state lasers. Merits of this technology facilitated the development of many custom pulsed laser sources, allowing to address the custom needs of various applications of high resolution laser spectroscopy and beyond. Some laboratory injection-seeded Ti:S lasers enable experiments on electromagnetically induced transparency [5], frequency conversion [6], population transfer in molecules by a STIRAP scheme [7], and four-wave mixing [8]. The latter laser source has a short ring cavity, but employs a pulsed seeding source. Remote water vapor concentration measurements by Differential Absorption LIDAR also benefit from the injection-seeded single-mode Ti:S lasers [9–11]. Wagner et al. provides the comprehensive performance modeling for both stable and unstable resonators with emphasis on output spectral purity [11]. To date, the publication record on injection-seeding technology is vast.
Low-power single-mode CW lasers provide seeding signal to most of the injection-seeded lasers, including those with a Ti:S crystal. With various performance parameters, they exploit the same design feature – a feedback loop to provide active cavity stabilization by making some length adjustments to the slave cavity in order to maintain it in resonance to a seed wave frequency. Techniques developed to implement stabilization include the minimizing built-up time [2] and ramp-and-fire [6,12] techniques. Another improved technique combines both of these methods [10]. A different approach [13–15] utilizes a Q-switched slave laser and requires no synchronization because of a regenerative amplification in an extra-long cavity of the slave laser. To the best of our knowledge, no other major innovations into the injection-seeded laser design or seeding techniques have been reported to date. The cavity stabilization loop remains a source of the significant technical complications to injection-seeded lasers.
The first distinct feature of the suggested laser design is the lack of active cavity stabilization. A short-length cavity offers considerably improved mechanical stability when compared to a longer one, supporting stable operation with no cavity length adjustments. Substantial output energy under short cavity length constitutes the second distinct feature of our laser. We opted for a standing-wave cavity because it allows for a large roundtrip gain. This large gain, combined with a small roundtrip time and a large output coupling is to result in the output pulse of a short duration. The standing-wave cavity arrangement is usually avoided in such type of lasers, since spatial hole burning can prevent single-mode operation. However, a large output coupling along with a low pumping level above the threshold provide an opportunity to minimalize this unwanted effect enough in order to enable a pulsed single-longitudinal-mode operation. Besides, a standing-wave cavity solution provides better handling in an experiment than a ring cavity scheme. Our laser cavity also features an intracavity dispersive prism that narrows down unwanted-but-amplifiable spontaneous emission spectrum. This cavity configuration is novel to injection-seeded lasers. In the past, a dispersion prism was used in the same fashion in the amplifier section of the single-mode dye laser [16] and the Ti:S injection-seeded laser with a ring cavity [6]. Overall, the combination of a short linear cavity, the use of a dispersion prism, and no need for stabilization is the novel design idea for the injection-seeded laser systems.
Our motivation for this work stems from the possibility to study and exploit coherent transient phenomena in atomic and molecular gases, and in particular the opportunity to explore broad-band generation by molecular modulation [17]. Specifically, a combination of narrow-linewidth laser pulses with a shorter duration than the dephasing time can establish large atomic/molecular coherence in transient regime [18]. Since the collisional decoherence rate often limits the dephasing of a dipole-forbidden transition (being in turn proportional to gas pressure), shorter pulses of sufficiently high energy allow engaging with larger ensemble densities.
In this paper, we demonstrate the injection-seeded single-longitudinal-mode Ti:S laser, optimized for the generation of few-nanosecond transform-limited pulses. Its operation starts with gain switching by an external pumping. Injection-seeding by a continuous-wave single-mode diode laser sets the operating wavelength, and along with initial cavity tuning, determines its single-longitudinal-mode pulsed operation at 807-nm wavelength (about 12 nm off Ti:S gain peak [19]), as required by experiments similar to the one conducted by Sokolov et al. [20]. Our experiment is supported with a numerical model that includes the additional losses for scattering and demonstrates the cavity mode evolution.
2. Experimental setup and measured laser performance
The schematic layout of the injection-seeded laser setup, depicted in Fig. 1(a), consists of two parts: the slave laser cavity and the seeding line. The photo in Fig. 1(b) shows the top view of the slave cavity while its schematic layout, Fig. 1(a), mimics the cavity components arrangement. The cavity consists of the Ti:S crystal rod, an angular dispersive prism, and two mirrors. The Ti:S crystal rod itself, which measures 3-cm in length and 9 mm in diameter, is doped for 2.5 cm-1 absorption at a wavelength of 490 nm with the figure of merit value of 250. The side faces are cut at a Brewster angle to prevent reflection losses of p-polarized light circulating in the cavity (the plane of polarization lies in the plane of Fig. 1(a)). The Ti:S crystal rod’s C-axis is parallel to the seed wave polarization. The back cavity mirror MB has a reflectivity of 100% and the front coupler MF has a reflectivity of 70% at 800 nm. Both mirrors are flat and transparent to the pump wavelength. A 66.7°-apex angle dispersion prism made of BK7 is set between the crystal and mirror MB. The prism is introduced to favor an oscillating wavelength that matches the seed wavelength. The prism has no antireflection coating; neither could it be set at an exact Brewster angle, thus allowing small losses to occur during lasing. The physical length of the cavity is 66.5 mm; its double optical length 2L equals about 178.6 mm. The proposed short linear cavity design, which consists of only four components including the prism, has never before been reported for these types of lasers.
Fig. 1. (a) Experimental schematic of the linear-cavity injection-seeded Ti:S laser with an intra-cavity dispersive prism is shown. The solid black and grey dashed lines show the seed and pump beams pathways respectively; the dashed black line represents the generated pulse path. The seed and generated beams, shown separately for clarity, overlap completely inside the cavity and all the way through the Faraday Rotator. (b) The top view of the laser cavity is shown. The Ti:S crystal is enclosed in the rectangular copper box; the prism is to its left.
Assembly of the Ti:S laser, excluding the seed and pump lasers, takes place on a separate optical bench placed on top of a vibration-isolated optical table, in a temperature-controlled laser room. The slave laser cavity features an exceedingly rigid design where all four cavity components are mounted on a 4-inch long stainless steel bar with a 1-inch square cross-section to ensure high stability and to minimize cavity length fluctuations. The end mirror mounts are equipped with high-precision translating actuators to tune the cavity manually. The slave laser cavity base, the prism holder, and the crystal holder and its base were fabricated in the machine shop.
The seed line starts with the external-cavity diode laser in the Littman configuration (Sacher-Laser Model TEC 500) as a source of CW single-mode beam. Its lasing wavelength can be tuned mechanically over 25-nm bandwidth centered at 822 nm, and by means of a piezoelectric transducer within 0.6 nm. We set the wavelength at 807 nm; its measured output power was in the range of few mW. The beam travels though optical Isolator 1 and becomes coupled/uncoupled into a single-mode fiber by the corresponding lenses LC/LU. Subsequently, it passes through Isolator 2 and Isolator 3, composed of the Faraday Rotator and Polarizers 1&2. The beam then becomes polarized in the horizontal plane (setup plane) after passing half-wave plate (λ/2). It passes the dichroic long-wave-pass mirror MP with no attenuation, and finally is incident onto the front cavity mirror MF. By this point, it becomes a seed beam with a power of 0.5 mW. As measured, the beam is slightly divergent after lens LU which resulted in its diameter increasing to 2.0 mm at a distance of 20 cm from mirror MF. The Ti:S laser pulse generated in the slave cavity traces the seed beam path back as shown with a dashed black line in Fig. 1(a). Polarizer 1 reflects the pulse out of the seed beam pathway due to the turning of its polarization plane by the Faraday Rotator. The isolators serve as fuses to avoid damaging the seed laser and optical fiber by the intense output pulse generated in the slave cavity. The optical fiber serves as both an extra fuse and a spatial mode filter that produces the Gaussian seed beam. Overall, our Ti:S laser was assembled using regular commercial off-the-shelf components available from many vendors.
Second harmonic emission of the Q-switched Nd:YaG laser (Quanta-Ray 6350) is used to pump the Ti:S crystal to switch gain in the slave cavity. The laser generates 8-ns pulses with transversal Gaussian intensity distribution at a repetition rate of 10 Hz and a wavelength of 532 nm. The dichroic long-wave-pass mirror MP deflects this pulsed beam (dashed gray line, Fig. 1), which measures about 8 mm in diameter at the laser output, onto the Ti:S crystal. The lens L (focal length f = 75 сm) then focuses it into a 2.0-mm diameter spot on the crystal’s front surface, with the focal point behind the cavity. The pump and seed beams overlap on the front surface of the Ti:S crystal. Both beams are incident onto the crystal’s surface at 60.5 degrees, which equals the Brewster angle for the pump beam. However, the beams refract at slightly different angles within the crystal, their paths parting slightly. Its effect on the generated laser pulse is discussed in greater detail in the Discussion and Summary section.
Figure 2 shows the dependence of the generated pulses energy on the pump energy. Lasing onset in a seeded regime occurs when the pump level reaches 11 mJ/pulse. The output energy reaches its highest value of 6 mJ/pulse at 25 mJ/pulse pumping, or 2.4 times the threshold. It delivers a slope efficiency of 43%, as shown in Fig. 2(a). The higher pumping rate results in the breakdown of the pulse. This breakdown limits the pumping to 25 mJ. The maximum seed signal power of 0.5 mW, or an even slightly smaller value, provides stable seeded lasing within the whole range of pumping rates. However, a seeded lasing could not be achieved without the dispersive prism. In addition, increasing both the pump and seed beam size in an attempt to generate a greater output in the seeded regime failed to provide a stable lasing. An unseeded regime demonstrates the same laser performance values, see Fig. 2(b): lasing onset tops 10 mJ/pulse and the slope efficiency equals 42% (these values remain exactly same as those in the seeded case if the pumping range to consider is limited to 25 mJ/pulse). Additionally, no breakdown occurs enabling the higher pumping rate, as shown in Fig. 2(b). However, all generated pulses in both operating regimes have an elliptical footprint (see the Fig. S1 in Supplement 1), not circular as initially expected from the cavity geometry. The output energy measurements below the lasing onset returned zero and are excluded from the graphs.
Fig. 2. The dependence of the generated output pulse energy vs pump energy is shown for the seeded and unseeded regimes of the laser operation. Seeded (a) and unseeded (b) slope efficiencies equal 43% and 42% respectively.
The temporal profiles of the generated laser pulses were measured with a fast home-made photodiode detector connected to 1-GHz (5 GS) Tektronix TDS 684C oscilloscope. For a seeded regime, the oscilloscope screen snapshot, Fig. 3(a), and the solid curve on the Fig. 3(c) show the typical pulse profile with the duration of 4.9 ns FWHM. The build-up time, measured as the time interval between the peaks of the pump and generated pulses is 25 ns. When the seeding signal is switched off, the output laser pulse of equal duration, Fig. 3(b), builds up 6.1 ns later, as shown by the dashed curve depicted in Fig. 3(c). This temporal delay serves as an alternative mark of a seeded generation – a single-longitudinal-mode laser operating regime as it is shown in the next paragraph. No additional signal spikes were observed. The build-up time delay exceeding the pulse duration itself indicates the high spectral purity of the generated pulse and is subject to further research. Both pulses have bell-shaped profiles featuring a slightly steeper front slope and a temporal lag that exceeds their duration. The generation remains stable in both regimes, and we observed no stable side “ripples”. Visualization 1 comprises the video of the running generation process that contains hundreds of pulse profiles. The horizontal time scale equals 10 ns per division for all graphs, as well as the video.
Fig. 3. The seeded (a) and unseeded (b) laser pulse profiles are shown as oscilloscope snapshots. Graph (c) demonstrates both profiles and their relative lag of 6.1 ns on a single plot. The time origin offset is arbitrary. The horizontal time scale equals 10 ns per division for all graphs. Visualization 1 contains the short video of the laser generation with hundreds of generated pulse profiles.
We use a scanning confocal Fabry-Perot interferometer (Burleigh) with a free spectral range (FSR) of 2 GHz, a finesse of 300, and a resolution of 6.7 MHz to measure the spectrum of seeded pulsed Ti:S generation. Its FSR is larger than the laser cavity, FSR = c/2L = c/178.6 mm = 1.68 GHz, where c is the speed of light. The interferometer cavity scanned continuously while the output pulse energy was measured. Figure 4 displays these measurements. Each diamond-shaped data point represents one laser pulse. Spectra (a) and (b) are independent measurements taken under the same operating conditions for the whole laser setup. The graphs demonstrate reproducible measurements indicating stable seeded single-longitudinal-mode lasing with the linewidth of about 100 MHz. No side spectral spikes and no elevated background were detected. Without the seed signal, the generated spectrum width broadens to about 6 nm, as measured with a diffraction grating.
Fig. 4. The spectrum of a seeded generation is measured with a continuous scanning confocal Fabry-Perot interferometer. (a) and (b) spectra represent two independent measurements. Each point on the graphs corresponds to a single laser pulse. The solid curves imposed on the spectrum data are the Fourier transform of the temporal pulse shape shown in Fig. 3.
We performed Fourier transformation of the temporal profile of the seeded pulse shown in Fig. 3 and placed it as a solid curve on both graphs in Fig. 4 in order to compare it with the measured spectral data. We found that closely matches the experimental data. Based on this Fourier profile, the spectral width of the oscillating pulse mode equals 87 MHz at FWHM. For comparison, we calculated the spectral width of the measured temporal pulse profile from Fig. 3, assuming it has a Gaussian profile. According to the equation $\Delta v = {{2\ln 2} / {(\pi {\kern 1pt} \Delta t}})$, where Δt is the pulse duration at FWHM, a 90-MHz spectrum width for a 4.9-ns pulse is obtained. Therefore, we conclude that the experimentally measured laser pulses are near transform-limited and their temporal profiles close to Gaussian distribution.
The seed diode laser can only be tuned within a 25-nm range according to its specification, thus limiting the tunability of the Ti:S laser to the same range. The following explains our procedure of tuning the slave cavity to a new seed wavelength. We aligned the back cavity mirror manually each time in order to make a geometrically closed pathway for a circulating intracavity wave. Then, the synchronization of seed frequency to slave cavity resonance frequency was achieved in two steps. First, we gradually changed the cavity length in relatively large increments by manually rotating the 100-thread-per-inch actuators (the cavity mirror holders are equipped with 3 actuators each as shown in Fig. 1(b)). The sensitive photo-detector placed behind the back cavity mirror monitored the cavity transmission. The process is performed on a “cold” cavity and discontinued when the maximum signal is achieved. The second step repeats the first step on a “hot” cavity. This time, the oscilloscope monitors the pulse built-up time with the goal of minimizing it, as suggested by Rahn [2]. The geometrical relationship allows controllable cavity length adjustment by ΔL = 0.36 um for each degree of the actuator knob rotation, which matches the actuator sensitivity limit according to the manufacturer specification. We tested and achieved subdegree manual rotation that happens to be both feasible and efficient (but tedious) in matching a seed wavelength to a cavity mode. We used the described procedure to tune the laser cavity to 807 nm. Probably, fine-tuning was possible to perform on the “hot” cavity only as, by estimation, it is characterized by few-times-smaller finesse than “cold” one. Alternatively and much more easily, cavity mode matching was achieved by fine-tuning the seed wavelength.
The initial alignment and tuning of the Ti:S cavity enabled the slave laser to operate in single-mode regime at 807-nm wavelength for up to 30 minutes. As observed, the seeded single-mode generation continued running for as long as the seed laser maintained its stable operation. This regime eventually discontinued solely due to the uncontrollable seed wavelength drift. This demonstrates no need in controllable cavity length adjustments and signifies that the inherent cavity length fluctuations of both of mechanical and thermal origin were small enough to break the single-mode regime. We believe the mechanical vibrations were relatively small (dampened) due to the solid base design of the cavity. The temperature fluctuations of the cavity base in the temperature-controlled ambient lab environment had limited effect due to its short length. At the same time, its bulkiness smoothed out the effect of any temperature fluctuations caused by an ambient lab environment. As the thermal (see the section 3.2) and vibration effects have much shorter development time, 30 minutes is a sufficiently long interval to establish the unbiased seeded single-longitudinal-mode operation of the slave laser under the conditions of the stable seeding signal and no cavity synchronization. However, the demonstrated stability effect requires further research. The generation in an unseeded regime ran for hours.
When tested with burn paper, the transverse intensity distribution of the laser pulses revealed an oval-shaped beam profile, as seen in Fig. S1 in Supplement 1. For our application, the laser beam quality is not a primary concern as the beam will be focused onto a relatively large spot.
3. Numerical simulation
Given a small cavity length of 66.5 mm and no intracavity aperture or curved mirrors, our laser features a relatively large spot size of the pump beam, equal to 1.0 mm, which suggests significant changes to the mode profile during the pulse build up process. We found modeling the laser operation using the equations derived for Gaussian beams inadequate, so we simulated the laser operation by calculating intracavity wave transformation at each oscillation. The numerical simulation presented below investigates the pulse build-up processes in the Ti:S laser cavity with the goal of revealing the mode formation scenario and obtaining laser performance characteristics.
3.1 Ti:S cavity partition
As shown in Fig. 5, the original laser cavity depicted in Fig. 1 is divided into six parts in order to illustrate the calculation steps. The part marked (1) is plane of the front (pumped) face of the Ti:S crystal. This part includes the thermal lens with focal distance fp induced by the pump beam in the crystal and instant inverted medium Gain Aperture that is equal to the transversal profile of cumulative single-pass cavity gain. Parts (2), (3), and (6) comprise the crystal length lC and the distance lB between the back face of the crystal and the back mirror MB, and the distance lA between the front face of the crystal and front mirror MF, respectively. The back MB mirror and front coupler MF are marked as parts (4) and (5), correspondingly. The schematic cavity excludes the prism because the prism serves to select wavelength and should not affect spatial parameters of the cavity mode.
Fig. 5. Schematics of the cavity partition. Horizontal arrows trace out the calculation steps. The numbers (1) through (6) mark cavity domains where the circulating light wave experiences transformations.
3.2 Thermal lens estimation
Before calculating the intracavity wave profile, we estimated the focal length fp of the introduced thermal lens. This lens is formed due to heat deposition in the laser rod caused by the absorption of the pump beam: the created spatial temperature gradient modulates the refraction index. Due to its dynamic property, this gradient eventually diminishes. According to [21], temperature relaxation in the rod depends on the thermal time constant, τT, of the rod and the associated dimensionless parameter AT that characterizes the cooling conditions. By its meaning and value, the AT factor has a greater value for a higher heat extraction capability. For a side (not end) pumped crystal geometry, these factors are defined as the following:
According to Fig. 3 in [21], initial uniform temperature distribution across the rod created by a uniform pumping transforms into a radial bell-shaped distribution due to the external side cooling in about 0.04 or 0.05 units of the normalized time t/τT. Afterwards, this bell-shaped temperature distribution gradually vanishes over time at a rate proportional to the applied cooling. This distribution roughly preserves its shape throughout the process, enabling it to be characterized at any given time by a single parameter – its amplitude.
The obtained parameter values enable the usage of the scenario of temperature relaxation in side-pumping geometry in order to estimate the temperature relaxation of the Ti:S rod in an end-pumping setting. In contrast to side-pumping geometry, Gaussian profile of the pump beam in the end-pumping geometry immediately induces a Gaussian thermal profile across the Ti:S rod. In addition, its temporal evolution is to follow approximately the evolution of the bell-shaped profile described by Koechner in [21], but with no temporal offset to form a bell-shaped temperature profile because the pump beam creates such a profile already. Using Koechner's Fig. 1 [21] and applying AT = 2 and the pulse interval tP = 0.1 sec. normalized by τT = 1.9 sec, an 8% decrease in the amplitude of the temperature profile before the next pulse arrives can be deduced. (Subsequent numerical simulation verifies the negligible effect of such a small variation on the cavity mode.) Furthermore, in a repetitively pumped crystal, such temperature oscillating behavior is reached after about 15 pulses [21]. Therefore, the small temperature amplitude variation during the interval between pump pulses allows the consideration of the previously formed thermal lens in the preheated crystal as a lens with a fixed focal length. We consider the 8-ns pump pulse followed by a 25-ns offset and a 4.9-ns generated pulse as a single instantaneous event much shorter than a 0.1-sec interval between pump pulses. Consequently, a 10-Hz pump repetition rate can be considered as CW pumping for the purpose of evaluating the thermal lens.
The analytical solution for a fixed focal length of the induced thermal lens, due to temperature-induced refractive index changes for the case of CW end-pumping geometry and steady-state cooling conditions, is given by the following equation [23]:
3.3 Laser generation: numerical simulation method
One roundtrip of light circulating in the cavity is calculated numerically in the following order according to the cavity partition shown in Fig. 5:
At the plane (1), the circulation starts with the Gaussian seed signal US :The pump pulse creates an inversion population η that replicates its intensity distribution:
In this simulation, the pumped Ti:S rod is viewed as a combination of an instantaneous gain factor G and a thin lens factor ΦS both attributed to the plane (1). To calculate G, we use the solution for a square pulse to experience upon traversing an inverted medium [24]:
Equation (6) gives the factor ΦS associated with the thermal lens:
3.4 Additional losses
The intracavity wave circulations calculated by means of Eq. (7) initially led to redundant laser performance characteristics. In particular, the lasing threshold happened to be considerably lower than the one obtained experimentally. At the same time, the focal length of the thermal lens and the cavity partition order had no significant effect on the laser performance characteristics. Altogether, these factors suggest a more complicated lasing mechanism. We suppose that the two-wave mixing occurring in the Ti:S crystal between the oscillating wave – fundamental cavity mode – and spontaneous radiation leads to formation of dynamic diffraction gratings that self-enhance as the generating wave builds up. These gratings facilitate the power depletion of the fundamental mode. Experimental and theoretical investigation into such effect was reported in [25], where generation of free carrier charges induced a nonlinear index of refraction in CdTe crystal and made efficient grating formation possible. Similar effect reported by Arutyunov et al. [26] exploited a thermally induced nonlinear refractive index; the total power depletion described as scattering amounted to 10%.
Large refractive-index change occurs in a Nd:YaG laser crystal during the pumping and amplification of an optical beam [27,28]. The effect is attributed to a large difference in the polarizability of excited and unexcited Nd3+ ions [28]. Similar refractive-index changes were observed with Cr3+ based laser crystal [29]. At this time, limited knowledge of electron refractive-index changes of laser crystals in an inverted state does not allow for proper estimation for those changes in each particular case [28].
In the case considered, we hypothesize the formation of efficient phase diffraction gratings in the Ti:S crystal. This might be possible due to large nonlinear refractive-index changes in the inverted crystal, and should result in additional power losses to the oscillating fundamental mode. To account for the expected power depletion, we increased the total losses used in the numerical simulation by 18.5% to match the lasing threshold measured in the experiment. Therefore, the total effective losses adjust to 30% + 18.5% = 48.5%, where 30% is the transmission of the output coupler R.
3.5 Numerical simulation results
Figure 6(a) depicts the temporal evolution of the total instant population inversion along with the laser output energy profile with green and red dots correspondingly. Any such dot – a data point – characterizes the laser parameters that are one oscillation ahead or behind to the adjacent data points. The lasing threshold energy serves to normalize the data point values of both graphs. The cavity oscillation number “j” represents the temporal scale, with its unity equaling the cavity roundtrip time of 0.6 ns. The shapes of both profiles correspond to the laser rate equations solution [30,31], while the gain Eq. (5) is the solution to these equations modified for an amplifier [24]. Our calculations result in the output pulse with an energy of 10-mJ, a buildup time of 12.5 ns, and a pulse duration of 3.6 ns. The modeled build up process starts with an instant gain switching.
Fig. 6. Graph (a) depicts the temporal profiles of the total population inversion and output energy. Graphs (b) through (d) show both radial-cuts of the instant and instant time-integrated energy distribution profiles of the oscillating intracavity wave at plane (1) for a certain oscillation number j. The tallest green bell-shaped curve, which represents the pump beam profile, serves as a reference. All profiles except the residual transversal population inversion density distribution have been normalized to unity. The colorful label below the graphs indentifies the curves. Visualization 2 in supplementary materials demonstrates the comprehensive oscillation-by-oscillation evolution of the laser pulse.
The dashed red curve in Figs. 6(b)-(d) shows the transversal energy distributions of the oscillating intracavity wave at plane (1) corresponding to a certain oscillation, represented by “j”. Integrating all these instant distributions starting from the gain-on moment till a particular oscillation number j produces the instant time-integrated energy distribution depicted by the solid blue curves. The transversal distribution of the pump beam, represented by the tallest green bell-shaped curve, and the transversal dependence of the instant population inversion, shown by a dashed green curve are added for reference on each picture thereafter. All of the distributions have been normalized to unity except for the instant population inversion curve.
After cavity gain is turned on, the seed beam size contracts and preserves its size until the gain begins saturating. j = 17: the population inversion profile demonstrates slight sagging, as seen in Fig. 6(b). The simulations show that the instant beam size remains unchanged when the focal length of the thermal lens equals 92 meters; stronger focus leads to a varying beam size during the unsaturated amplification phase. This is the reason why the instant beam profile and the instant time-integrated energy profiles remain overlapped. As the oscillation progresses, the instant pulse profile gradually spreads and demonstrates sagging when its instant intensity reaches maximum, as seen in Fig. 6(с) and Fig. 6(a) at j = 21. Furthermore, this profiles’ shape follows the gradually sagging instant inversion population profile during the remaining part of the saturated amplification phase as shown in Fig. 6(d) (the oscillating wave intensity has vanished). The solid blue curve mimics the pump beam profile at the end, as seen in Fig. 6(d), providing a circularly symmetric transversal fingerprint of the output beam of the ideally aligned laser cavity that is measurable in experiment. Our experiment demonstrated the deviation from the simulated shape. The next section discusses this deviation.
Figures 6(b)-(d) show only three key points of laser generation. Visualization 2 presents the complete oscillation-by-oscillation pulse build-up evolution. Finally, the modeled build-up evolution for an unseeded pulse starts with 40 photons in the mode and follows up the seeded pulse evolution with a 6.8-ns delay.
Table 1 summarizes the laser performance characteristics for both the experiment and modeling. A good agreement between the experimental and calculated data was obtained. However, there exists a noticeable discrepancy between the modeling and experiment in build-up time and pulse duration, which is discussed in the next section.
Table 1. The experimental and simulated performance characteristics of the Ti:S laser.
4. Discussion and summary
- 1. The additional losses of 18.5% due to diffraction on the dynamic gratings discussed in the section 3.4 should contribute proportionally to the output coupling losses (30%), as the diffraction grating efficiency grows proportionally to the intensity of the recording wave [28]. In the considered case, that wave is the oscillating intracavity wave. Therefore, 10-mJ output pulse energy can be considered as a sum of 6.2 and 3.8 mJ attributed to output coupling losses and additional losses respectively. The first summand matches the measured energy, as seen in Table 1. However, no diffracted radiation related to the additional losses was detected in our experiment, though it can be measured according to Arutyunov et al. [28]. ]. As the diffraction diverts a fraction of the intracavity beam, relative to the oscillating wave pathway, by a small angle (2° [26] or 10−2 rad [25,28]), the numerous apertures, as seen in Fig. 1, stop the diverted beam on its way to the photo detector. Unfortunately, no appropriate arrangements were done at the time of experiment; further investigation is required.
- 2. In our simulations we did not account for spatial hole burning effect. We expect this effect to have a negligible influence, as the measured output energy happens to be equal for both the seeded single-mode and the unseeded multi-mode (bandwidth of about 5-6 nm) regimes. This energy equality demonstrates that no significant fraction of the pump energy is lost in residual inversion population due to single-mode regime. The combination of high cavity losses, low pumping rate, and significant intracavity beam size variation during the saturated phase amplification may account for the diminished effect of spatial hole burning. Overall, the good agreement between the measured and calculated performance values demonstrates a proper choice of the simulation model and its utility to the laser design.
- 3. In contrast to the calculated transversal energy distribution of the generated pulse that leaves a circular footprint, the laser pulses generated in the experiment demonstrated an oval footprint elongated in the plane of angular dispersion of the intracavity prism. Fig. S1 in Supplement 1 provides examples of such an elongated footprint. We attribute this shape discrepancy in the footprints to non-matching propagation directions of the pump and seed beams in the bulk of the Ti:S crystal, that gives rise to a transversal elongation. Upon incident on the Ti:S crystal surface at the very angles of 60.53 degrees and on the same exact spot, the pump and seed beams refract at slightly different angles (difference of 0.18 degrees) due to the refractive index dispersion. Due to the laser cavity’s alignment to match the laser mode to the seed beam, the gain profile happens to be diverted slightly off the seed beam. During the pulse build-up phase, the laser mode expands in the plane of the angular dispersion, which imparts the output pulse with extra divergence (less than 0.18 degrees for each circulation) in the same plane. The divergence increases as the divergence angle accrues with every oscillation, which in turn results in the oval footprint of the pulse.
The transversal expansion of the circulating wave may affect the temporal characteristics of the output pulse by extending both the build-up time and pulse duration; modeling would provide accurate values. However, a slight correction of the incidence angle of the pump beam to make both beams refract at the same angle into the Ti:S crystal should eliminate the unwanted transversal expansion of the output beam and improve the pulse duration and the build-up time. The current arrangement of angle, often used for long cavity lasers with Brewster-cut crystals, may not be the right arrangement for our short cavity laser.
For the first time since the invention of injection seeding technology, we have demonstrated a gain-switched pulsed Ti:Sapphire laser that operates in single-longitudinal-mode with no active cavity stabilization. Sturdy cavity construction and a temperature-stable laboratory environment along with the large free spectral range and low cavity finesse facilitate self-sustaining single-longitudinal-mode laser generation at a given seeded wavelength. Such a generation lasts as long as the seed wavelength remains stable, 30-minutes maximum interval with the seed laser we used. The transition process of the single-mode formation is subject to further research. The proposed cavity design, featuring a dispersive prism, is novel to injection-seeded lasers. A low-power single-mode CW diode laser seeds the Ti:S laser that generates a substantial energy output for its small cavity and demonstrates the slope efficiency that nearly matches the efficiency of many stabilized seeded ring-cavity lasers. Its simple design and decreased cost would make our laser the preferable solution for small labs. The proposed numerical model of the laser’s operation with additional losses demonstrates a good agreement to the experiment, which can prove useful in subsequent laser designs. Future research will reveal more insights into the origin of stable single-mode lasing with no cavity stabilization and will aid in choosing optimal laser parameters for maximum energy output.
Funding
Welch Foundation (A-1547).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
See Supplement 1 for supporting content.
References
1. A. N. Bondarenko, K. G. Folin, V. A. Smirnov, and V. V. Antsiferov, “Generation induced in a Q-switch ruby laser by an external signal,” JEPT Lett. 6, 178–180 (1967).
2. L. A. Rahn, “Feedback stabilization of an Injection-Seeded Nd:YAG Laser,” Appl. Opt. 24(7), 940 (1985). [CrossRef]
3. P. Brockman, C. H. Bair, J. C. Barnes, R. V. Hess, and E. V. Browell, “Pulsed injection control of a tiatium doped sapphire laser,” Opt. Lett. 11(11), 712–713 (1986). [CrossRef]
4. N. P. Barnes and J. C. Barnes, “Injection Seeding (: Theory,” IEEE J. Quantum Electron. 29(10), 2670–2683 (1993). [CrossRef]
5. A. Kasapi, G. Y. Yin, and M. Jain, “Pulsed Ti:sapphire laser seeded off the gain peak,” Appl. Opt. 35(12), 1999 (1996). [CrossRef]
6. T. Walther, M. P. Larsen, and E. S. Fry, “Generation of Fourier-transform-limited 35-ns pulses with a ramp-hold-fire seeding technique in a Ti:sapphire laser,” Appl. Opt. 40(18), 3046 (2001). [CrossRef]
7. L. Cabaret and C. Drag, “Highly scannable injection seeded nanosecond Ti:sapphire ring laser,” Eur. Phys. J.: Appl. Phys. 51(2), 20702 (2010). [CrossRef]
8. C. E. Hamilton, “Single-frequency, injection-seeded Ti:Sapphire ring laser with high temporal precision,” Opt. Lett. 17(10), 728 (1992). [CrossRef]
9. G. Wagner, A. Behrendt, V. Wulfmeyer, F. Späth, and M. Schiller, “High-power Ti:sapphire laser at 820 nm for scanning ground-based water-vapor differential absorption Lidar,” Appl. Opt. 52(11), 2454 (2013). [CrossRef]
10. K. Ertel, H. Linné, and J. Bösenberg, “Injection-seeded pulsed Ti:sapphire laser with novel stabilization scheme and capability of dual-wavelength operation,” Appl. Opt. 44(24), 5120 (2005). [CrossRef]
11. G. Wagner, V. Wulfmeyer, and A. Behrendt, “Detailed performance modeling of a pulsed high-power single-frequency T:S laser,” Appl. Opt. 50(31), 5921 (2011). [CrossRef]
12. S. W. Hendersen, E. H. Yuen, and E. S. Fry, “Fast resonance-detection technique for single-frequency operation of injection-seeded Nd-YAG lasers,” Opt. Lett. 11(11), 715 (1986). [CrossRef]
13. A. Khizhnyak, V. Markov, and F. Wu, “Injection seeded Nd:YaG ring laser generating 200 mJ Q-switched pulses,” Proc. SPIE 6871, 687107 (2008). [CrossRef]
14. C. Tian, T. Walther, R. Nicolaescu, X. Pan, Y. Liao, and E. Fry, “Synchronous, dual-wavelength, injection-seeded amplification of 5-ns pulses in a flash-lamp-pumped Ti:sapphire laser,” Opt. Lett. 24(21), 1496 (1999). [CrossRef]
15. V. Talluto, T. Blochowicz, and T. Walther, “A nanosecond regenerative Ti:Sapphire amplifier for the simultaneous generation of 940 nm and of 320 nm pulses,” Appl. Phys. B 122(5), 132 (2016). [CrossRef]
16. J. Pinard and S. Liberman, “A frequency locked, Single Mode Pulsed Dye Laser. Application to single frequency tunable UV generation,” Opt. Commun. 20(3), 344–346 (1977). [CrossRef]
17. A. V. Sokolov and S. E. Harris, “Ultrashort Pulse Generation by Molecular Modulation,” J. Opt. B: Quantum Semiclassical Opt. 5(1), R1–R26 (2003). [CrossRef]
18. M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, “Efficient Nonlinear Frequency Conversion with Maximal Atomic Coherence,” Phys. Rev. Lett. 77(21), 4326–4329 (1996). [CrossRef]
19. P. F. Moulton, “Spectroscopic and laser characteristics of Ti:Al2O3,” J. Opt. Soc. Am. B 3(1), 125 (1986). [CrossRef]
20. A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, “Raman Generation by Phased and Antiphased Molecular States,” Phys. Rev. Lett. 85(3), 562–565 (2000). [CrossRef]
21. W. Koechner, “Transient thermal profile in optically pumped laser rods,” J. Appl. Phys. 44(7), 3162–3170 (1973). [CrossRef]
22. G. Wagner, M. Shiler, and V. Wulfmeyer, “Simulations of thermal lensing of a Ti:Sapphire crystal end-pumped with high average power,” Opt. Express 13(20), 8045 (2005). [CrossRef]
23. M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990). [CrossRef]
24. L. M. Frantz and J. S. Nodvik, “Theory of Pulse Propagation in a Laser Amplifier,” J. Appl. Phys. 34(8), 2346–2349 (1963). [CrossRef]
25. S. G. Odulov, S. S. Slyusarenko, M. S. Soskin, and A. Khizhnyak, “Mirrorless Four-Wave Parametric Oscillation in CdTe Crystals,” Quant. Electr. 15(8), 1564 (1988).
26. Y. A. Arutyunov, A. A. Bagan, V. B. Gerasimov, A. V. Golyanov, V. E. Ogluzdin, V. A. Sugrobov, and A. I. Khizhnyak, “Nonstationary Stimulated Thermal Scattering in the Field of Quasi-Planar Counterpropagating Pumping Beams,” Quant. Electr. 17(4), 456 (1990).
27. O. I. Antipov, A. S. Kuzhelev, and D. V. Chausov, “Nondegenerate four-wave-mixing measurements of a resonanatly induced refractive-index grating in a Nd:YaG amplifier,” Opt. Lett. 23(6), 448 (1998). [CrossRef]
28. O. I. Antipov, A. S. Kuzhelev, D. V. Chausov, and A. P. Zinovev, “Dynamics of refractive-index changes in a Nd:YaG laser crystal under excitation of Nd3+ ions,” J. Opt. Soc. Am. B 16(7), 1072 (1999). [CrossRef]
29. T. Catunda and J. C. Castro, “Phase conjugation in GdAlO3:Cr3+ and ruby,” Opt. Commun. 63(3), 185–190 (1987). [CrossRef]
30. A. E. Siegman, Lasers (University Science, Mill Valley, California1986).
31. Кондилеко И.И., Коротков П.А., Хижняк А.И., Физика Лазеров (Вища Школа, Киев, 1984).
