1. Introduction

Mode-locked solid-state lasers emitting sub-100-fs pulses in the 2-µm spectral range featuring relatively high average output powers (above 100 mW) at high repetition rates (about 100 MHz) and Fourier-transform limited pulses with sideband-free spectra are very suitable for applications as frequency combs in high resolution molecular spectroscopy [1] as well as for seeding/pumping of parametric nonlinear frequency down-conversion [2] and ultrafast (chirped-pulse) regenerative laser amplifiers [3]. Typically, solid-state laser emission at ∼2 µm is achieved using thulium (Tm³⁺) or holmium (Ho³⁺) ions. Recently, significant efforts were applied towards exploring and developing novel laser materials featuring broad and smooth spectral gain profiles naturally extending beyond 2 µm which is desirable to avoid the detrimental water vapor absorption/dispersion in the atmosphere.

Typically, Tm lasers tend to operate slightly below 2 µm (on the ³F₄ → ³H₆ electronic transition), which requires a special spectrally selective element to red-shift the oscillation wavelength above 2 µm for generating femtosecond pulses from mode-locked (ML) lasers [4]. Obviously, such a spectrally selective element will limit the achievable emission bandwidth and, thus, the minimum pulse duration. In order to overcome this limitation, few crystalline matrices have been identified, either featuring strong crystal fields for the Tm³⁺ ions causing to a large total Stark splitting of the ground-state (³H₆) or structural/compositional disorder leading to significant inhomogeneous spectral broadening resulting in extremely broad and flat gain profiles extending up to 2.1 µm. Large crystal field splitting combined with disorder is characteristic of some families of isotropic materials, such as the cubic multicomponent garnets (e.g. Ca₃Nb_1.5Ga_3.5O₁₂-type) [5,6], and the mixed cubic rare-earth sesquioxides A₂O₃ (where A is a combination of Sc, Y and Lu) [7–10].

Alternatively, by doping with Ho³⁺ instead of Tm³⁺ ions, one can ensure laser oscillation wavelengths above 2 µm on the ⁵I₇ → ⁵I₈ transition independent of the host material, together with higher gain cross-sections in this spectral range. However, Ho³⁺-doped crystalline laser gain media exhibit narrower and structured gain profiles which limits the achievable spectral bandwidth in femtosecond ML lasers. With respect to direct diode pumping, AlGaAs-based laser diodes emitting near 0.8 µm for Tm-doped materials are well developed and widely commercially available whereas the required InP-based laser diodes with emission around 1.9 µm for Ho pumping have not yet reached a mature level. Besides, high-brightness tunable continuous-wave (CW) pump sources for Ho lasers are still not well developed. Tm³⁺, Ho³⁺-codoped gain media provide a certain trade-off in terms of spectroscopic properties given the advantages and limitations of the two dopants. In a codoped material, the composite gain profile depends on the individual emission and reabsorption cross-sections and the corresponding inversion rates. Consequently, Tm,Ho-codoped laser materials are expected to support extremely broad spectra (i.e., corresponding to few optical-cycle pulses). Inhomogeneous spectral broadening in disordered host materials can be exploited also in the case of codoping. The first sub-100 fs pulse generation using a codoped material was reported in 2018. A Tm,Ho-codoped disordered tetragonal CaYAlO₄ crystal was employed as a gain medium and 87-fs pulses at ∼2043 nm with an average output power of 27 mW were generated using a GaSb-based SEmiconductor Saturable Absorber Mirror (SESAM) [11]. Even shorter pulse duration of 52 fs was achieved from a SESAM ML isostructural Tm,Ho:CaGdAlO₄ laser with an average output power of 376 mW at 2015 nm [12]. Finally, pulses as short as 46 fs were emitted from a SESAM ML Tm,Ho:Ca(Gd,Lu)AlO₄ laser at 2033 nm with an average output power of 121 mW, combining structural and compositional disorder [13].

The cubic multicomponent garnets have already been employed as disordered host crystals for generation of ultrashort pulses from ML lasers based on Nd³⁺, Yb³⁺ and Tm³⁺ [14–16]. Among them, the above-mentioned calcium niobium gallium garnets (abbreviated CNGG) attract significant attention because they exhibit a considerable inhomogeneous spectral line broadening for the rare-earth (RE³⁺) dopant ions due to the local structural disorder originating from the random distribution of Nb⁵⁺ and Ga³⁺ cations over two non-equivalent lattice sites. The actual composition of CNGG-type crystals deviates from the stoichiometry and monovalent cations such as Na⁺ or Li⁺ are added (the host crystals are then abbreviated as CNNGG and CLNGG, respectively) to minimize vacancies on the structure and/or to increase the segregation coefficient of the active ion [17]. Codoping with Tm³⁺ and Ho³⁺ ions of such crystals for obtaining broadband emission properties has been described in [18]. The first sub-100 fs Tm,Ho:CNGG laser, ML by a single-walled carbon nanotube saturable absorber (SWCNT-SA), was demonstrated also in 2018. It generated 76 fs pulses at 2081 nm with an average output power of 67 mW [19]. A shorter pulse duration of 67 fs at 2083 nm was obtained from a Tm,Ho:CLNGG laser ML by the same SA [20].

A novel Tm³⁺,Ho³⁺-codoped CNGG-type disordered cubic multicomponent crystal containing La³⁺ and Li⁺ ions both serving for local charge compensation (abbreviated: Tm,Ho:LCLNGG) was recently grown at the Institute of Chemical Materials, China Academy of Engineering Physics. In this work, we explore its ultrashort pulse generation potential in the sub-100 fs time domain.

2. Crystal characterization

Lanthanum calcium lithium niobium gallium garnet codoped with Tm³⁺ and Ho³⁺ ions was grown by the Czochralski (Cz) method in argon atmosphere using an iridium crucible; the seed was oriented along the [111] axis. The starting reagents [CaCO₃ (purity: 4N), Nb₂O₅ (4N), Ga₂O₃ (5N) and RE₂O₃ (RE = Tm, Ho, La, 5N)] were taken according to the formula (Tm₃Ga₅O₁₂)_0.03(Ho₃Ga₅O₁₂)_0.005(Ca_2.4La_0.6Li_1.22Nb_1.82Ga_2.36O₁₂)_0.965. The La³⁺ and Li⁺ cations were introduced for local charge compensation in heterovalent doping (as the trivalent RE³⁺ ions are expected to replace divalent Ca²⁺ host-forming cations), improvement of the material crystallinity and elimination of unwanted cationic vacancies causing color center formation. The as-grown crystal of high optical quality was yellow colored. To improve its transparency, it was annealed in air. The annealed crystal had a very weak residual yellowish coloration.

The actual concentrations of RE³⁺ ions in the crystal were determined by the inductively coupled plasma mass spectrometry (ICP – MS) method to be 2.02 at.% Tm³⁺, 0.36 at.% Ho³⁺ and 9.87 at.% La³⁺ (all defined with respect to Ca²⁺). The ion densities of laser-active dopants in the crystal were N_Tm = 2.47 × 10²⁰ at/cm³ and N_Ho = 0.438 × 10²⁰ at/cm³.

The crystal structure was determined by X-ray diffraction. Tm,Ho:LCLNGG belongs to the cubic class (sp. gr. Ia$\bar{3}$d – $O_h^{10}$, a = 12.5292(8) Å, V = 1966.88 ų, Z = 8). The general chemical formula of multicomponent garnets reads {A}[B]₂(C)₃O₁₂, where {A}, [B] and (C) designate dodecahedral (Wyckoff symbol: 24c), octahedral (16a), and tetrahedral (24d) sites whose coordination numbers with oxygen, C.N. are VIII, VI and IV, respectively. The Ca²⁺|RE³⁺ cations occupy the {A} sites, the Nb⁵⁺ and Ga³⁺ ones are distributed over both the [B] and (C) sites, while Li⁺ incorporation takes place only at the (C) sites. This determines the structure disorder leading to inhomogeneous spectral broadening for the active ions. The Rietveld refinement of the crystal structure indicates a very low content of cationic vacancies □ in the {A} and (C) sites (about 0.4%) which is an evidence for the positive role of charge compensators.

Let us describe briefly the spectroscopic properties of the Tm,Ho:LCLNGG crystal. Firstly, the transmission spectra of several Tm,Ho:CNGG-type crystals grown under identical conditions with similar doping (unmodified, containing only Li⁺ cations and containing both La³⁺ and Li⁺ cations) were measured in the visible, Fig. 1(a). The thickness of the studied samples was the same. For the last crystal, the broad absorption band underlying the bands due to RE³⁺ ions and originating from color centers has the lowest intensity. This indicates the positive role of introducing both the La³⁺ and Li⁺ charge compensators.

 

Fig. 1. Optical spectroscopy of the Tm,Ho:LCLNGG crystal: (a) transmission spectrum in the visible, the spectra for Tm,Ho:CNGG and Tm:CLNGG crystals are given for comparison; (b) absorption cross-section, σ_abs, corresponding to the ³H₆ → ³H₄ Tm³⁺ transition; (c) luminescence spectrum at ∼2 µm, λ_exc = 802 nm; (d) luminescence decay curves for Tm³⁺ (1800nm) and Ho³⁺ (2070nm) emissions, λ_exc = 1615 nm.

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The Li⁺ cations reduce the vacancies only at the tetrahedral sites (C) which they occupy. As for the La³⁺ cations, together with other two RE³⁺ (Tm³⁺, Ho³⁺) ions they substitute for the Ca²⁺ ions in the dodecahedral sites (A). This substitution is expected to reduce the lattice tension and vacancies in the (A) sites. The ionic radii of laser-active Tm³⁺ and Ho³⁺ dopants for VIII-fold oxygen coordination (R_Tm = 0.994 Å and R_Ho = 1.015 Å) are smaller than that of the host-forming Ca²⁺ cations (R_Ca = 1.12 Å). A substitution of 1Ca²⁺ by 1Tm³⁺|Ho³⁺ requires a vacancy □ and causes a significant lattice tension. The La³⁺ ions are relatively big (R_La = 1.16 Å), so that during the substitution, e.g., of 3Ca²⁺ by 1La³⁺ and 1Tm³⁺, the lattice tension is reduced and no vacancy is involved. Thus, the introduction of Li⁺ and La³⁺ decreases the vacancies in the (C) and (A) sites, respectively, thus improving the material crystallinity and its optical quality.

Figure 1(b) shows the absorption band related to the ³H₆ → ³H₄ transition of Tm³⁺ ions in LCLNGG. The maximum absorption cross-section σ_abs is 0.92 × 10⁻²⁰ cm² at 801.0 nm and the absorption bandwidth is ∼27 nm. This indicates the suitability of this crystal for pumping with AlGaAs-based diode lasers. The emission spectrum of the Tm,Ho:LCLNGG crystal at ∼2 µm is presented in Fig. 1(c). The composite luminescence is due to the spectrally overlapping ³F₄ → ³H₆ Tm³⁺ and ⁵I₇ → ⁵I₈ Ho³⁺ transitions. The spectrum is smooth and broad spanning up to ∼2.15 µm. In the long-wave part of the emission spectrum where laser operation is expected (considering the quasi-three-level laser schemes), a broad peak centered at ∼2.07 µm is observed. Such emission properties are attractive for the design of ML lasers.

The luminescence decay from both ions was studied under resonant excitation of the Tm³⁺ ions, Fig. 1(d). The decay curves reveal an efficient and predominantly unidirectional Tm³⁺ → Ho³⁺ energy transfer. The thermal equilibrium decay time τ₀ for both the ³F₄ Tm³⁺ and ⁵I₇ Ho³⁺ multiplets is 5.5 ± 0.2 ms.

3. Experimental configuration

A scheme of the Tm,Ho:LCLNGG laser is shown in Fig. 2. An X-shaped astigmatically compensated linear cavity was employed for evaluating both the CW and passively ML laser performance. The rectangular active element was cut from the 2.02 at.% Tm³⁺, 0.36 at.% Ho³⁺:LCLNGG crystal along the crystallographic [111] direction. It had an aperture of 3 mm × 3 mm and a thickness of 3 mm. The active element was polished to laser quality from both sides and left uncoated. It was mounted in a water-cooled Cu holder (coolant temperature: 14°C) and placed at Brewster’s angle between two dichroic folding mirrors M₁ and M₂ (radius of curvature: RoC = −100 mm). The pump source was a CW Ti:Sapphire laser tuned to the absorption maximum. It was focused into the crystal with a spherical focusing lens (f = 70 mm) yielding an estimated waist radius of ∼30 µm × 57 µm in the sagittal and tangential planes, respectively. A Lyot filter (3.2-mm thick quartz plate) was inserted at Brewster’s angle close to the output coupler (OC) for wavelength tuning in the CW regime.

 

Fig. 2. Scheme of the Tm,Ho:LCLNGG laser: L: spherical focusing lens (f = 70 mm); M₁-M₂: concave mirrors (RoC = −100 mm), M₃: flat rear mirror for CW operation; M₄: concave mirror (RoC = −100 mm); M₅: concave mirror (RoC = −50 mm); OC: output coupler; SWCNT-SA: single-walled carbon nanotube saturable absorber.

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A transmission-type SWCNT-SA was used in the mode-locking experiments to initiate and stabilize the soliton pulse shaping. It was inserted in the second beam waist formed by the concave M₄ (RoC = −100 mm) and M₅ (RoC = −50 mm) mirrors. The SA comprised an uncoated ∼1 mm-thick quartz substrate with a SWCNT/PMMA composite film on it deposited by spin coating. The diameters of the purified SWCNTs synthesized by the dried arc-discharge method were selected to provide a broad absorption band spanning from 1.9 to 2.1 µm due to the first fundamental transition of the semiconducting nanotubes, E₁₁. The absorption saturation properties for normal incidence were the following: a modulation depth <0.5%, a non-saturable loss of 1% and a saturation fluence about 10 µJ/cm². The recovery time of the initial absorption at ∼2 µm was ∼1 ps [21].The intracavity group delay dispersion (GDD) was managed by broadband dispersive mirrors (DMs) exhibiting negative GDD of −125 fs² per bounce and more than 300 nm reflectivity bandwidth from 1850 to 2150 nm.

4. Experimental results

4.1 CW laser operation

The CW laser performance of the Tm,Ho:LCLNGG crystal was first investigated with a four-mirror laser cavity including a plane rear reflector M₃ and a plane-wedged OC (without the SA). Four OCs with transmission T_OC in the range of 0.2% - 3% were used. The radius of the laser mode in the crystal was estimated using the ABCD formalism yielding 23 µm × 46 µm in the sagittal and tangential planes, respectively. The measured single-pass pump absorption under lasing conditions was dependent on the output coupling and amounted to 48.2% for 1.5% OC, revealing some absorption bleaching.

A maximum CW output power of 350 mW was obtained at 2080.5 nm for an absorbed pump power of 1.54 W, corresponding to a laser threshold of 92.8 mW and a slope efficiency of 23.8% with respect to the pump power absorbed in the crystal (T_OC = 1.5%), see Fig. 3(a). The laser threshold gradually increased with the output coupling, from 70.2 mW for 0.2% OC to 108.8 mW for 3% OC. The emission wavelength experienced a blue-shift with T_OC, from 2085.4 nm for 0.2% OC to 2075.1 nm for 3% OC. This behavior is due to the quasi-three-level nature of the ⁵I₇ → ⁵I₈ Ho³⁺ transition. The laser operated solely on the Ho³⁺ laser transition, no Tm³⁺ co-lasing was detected. The Lyot filter was inserted for wavelength tuning in the CW regime. With the 0.5% OC, a relatively broad range of continuous wavelength tuning, ∼210 nm (1904.1–2114.1 nm) was achieved at an absorbed pump power of 1.04 W, see Fig. 3(b). The maximum output power was obtained at the wavelength of 2085.4 nm.

 

Fig. 3. CW Tm,Ho:LCLNGG laser: (a) input-output dependences for different OCs, η - slope efficiency; (b) spectral tuning range obtained with a Lyot filter, P_abs = 1.04 W, T_OC = 0.5%; (c) evaluation of the passive losses using the Caird approach.

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The Caird analysis [22] was applied to estimate the total passive losses δ (including cavity and laser crystal but excluding the reabsorption effect) and the intrinsic slope efficiency η₀ through fitting the measured laser slope efficiency as a function of the reflectivity of the OC, R_OC = 1 – T_OC. The best fit gave round trip cavity losses of δ = 0.3 ± 0.1% and an intrinsic slope efficiency of η₀ = 27.4%, see Fig. 3(c).

4.2 Soliton ML operation

For mode-locking, the SWCNT-SA was placed in the second beam waist created by the M₄ and M₅ mirrors and inclined at Brewster’s angle. The beam radius at the SA was estimated by the ABCD formalism to be 149 µm × 214 µm in the sagittal and tangential planes, respectively. To balance the self-phase modulation (SPM) inducing a positive frequency chirp and to ensure efficient soliton pulse shaping, the M₄ mirror was replaced by a concave DM₁ (RoC = −100 mm, GDD = −125 fs² per bounce) resulting in a total round-trip GDD of −250 fs², see Fig. 2. Firstly, by applying the 1.5% OC, self-starting ML operation was achieved. The measured spectrum and the fringe-resolved autocorrelation trace gave a pulse duration of 96 fs at a central wavelength of 2067.6 nm and a spectral bandwidth (determined at full width at half maximum, FWHM) of 46.3 nm assuming sech²-shaped spectral and temporal profiles, see Fig. 4. The resulting time-bandwidth product (TBP) was 0.318, very close to the Fourier-transform limit for sech²-shaped soliton pulses. The average output power from the ML laser amounted to 121 mW at an absorbed pump power of 1.59 W and the pulse repetition rate was ∼102.5 MHz. Excellent sech²-shaped spectral and temporal profiles of the generated pulses indicated efficient soliton ML operation of the Tm,Ho:LCLNGG laser.

 

Fig. 4. ML Tm,Ho:LCLNGG laser with T_OC = 1.5%: (a) optical spectrum; (b) interferometric autocorrelation trace.

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The shortest pulse duration was achieved by employing a lower OC of 0.5%. The measured spectrum of the ML laser was centered at 2072.7 nm spanning from 1928 to 2234 nm, see Fig. 5(a). After external linear chirp compensation with a 3-mm thick ZnS ceramic plate, pulses as short as 63 fs were confirmed by an autocorrelation trace measurement. Note that the pulse duration of 63 fs was ∼17% above the Fourier limit. The maximum average output power for the shortest pulses amounted to 63 mW at an absorbed pump power of 1.59 W with a pulse repetition rate of ∼102.5 MHz.

 

Fig. 5. ML Tm,Ho:LCLNGG laser with T_OC = 0.5%. (a) optical spectrum; (b) interferometric autocorrelation trace.

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The pulse train from the Tm,Ho:LCLNGG laser was characterized by a radio-frequency (RF) spectrum analyzer. The fundamental beat note was located at ∼102.5 MHz (recorded with a resolution bandwidth, RBW = 100 Hz) and exhibited high extinction ratio of >82 dBc above the noise level, see Fig. 6(a). The measured uniform harmonic beat notes in a 2-GHz frequency span (RBW: 100 kHz) revealed highly stable steady-state CW mode-locking without any unwanted Q-switching or multi-pulsing instabilities, see Fig. 6(b).

 

Fig. 6. RF spectra of the ML Tm,Ho:LCLNGG laser: (a) fundamental beat note and (b) 2-GHz span. RBW: resolution bandwidth.

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5. Conclusion

To conclude, we have demonstrated the first passively ML Tm,Ho:LCLNGG laser with pulse durations in the sub-100 fs time domain. A transmission-type SWCNT-SA was implemented for initiating and stabilizing the soliton pulse shaping. Pulses as short as 63 fs were achieved at 2072.7 nm with an average output power of 63 mW at a pulse repetition rate of ∼102.5 MHz. This result represents the shortest pulse ever achieved from a ML laser at ∼2 µm based on Tm³⁺,Ho³⁺-codoped cubic multicomponent garnets. The introduction of Li⁺ and La³⁺ in the structure reduces the vacancies and mosaicity in the crystal improving its quality and providing better laser performance. Higher average output power of 121 mW was obtained at the cost of longer pulse duration of 96 fs at 2067.6 nm. The relevant spectroscopic properties of this novel codoped CNGG-type garnet crystal, as well as the results of the present work, i.e., the broad tunability range and the generation of sub-100-fs pulses, indicate the potential of Tm,Ho:LCLNGG for the design of ultrafast (few optical cycle) power-scalable oscillators emitting at ∼2 µm, pumped by commercial high-power diode lasers at ∼800 nm.