1. Introduction

High repetition-rate femtosecond lasers are widely applied in physics, biology, optical communication and other fields owing to their short pulse width, high peak power, and strong focus capacity [1–3]. In addition, due to the high-resolution characteristics of femtosecond lasers, it also has irreplaceable advantages in the medical field, such as lesions diagnosis, medical imaging, and biological detection, etc. [4–7]. Especially, femtosecond lasers around 750 nm are important as the optimal excitation source for a variety of widely used fluorophores in the multiphoton microscopy [8].

Alexandrite (Cr³⁺: BeAl₂O₄) is a tunable laser gain medium with superior performances, with a broadband wavelength tuning range from 701 to 858 nm. Although Ti:Sapphire lasers are currently widely used and the tuning range covers alexandrite, alexandrite has many outstanding advantages. Alexandrite has a longer fluorescence lifetime (262 µs at room temperature), which is more favorable for energy storage and low-threshold laser oscillation. Alexandrite crystals also have a wide absorption band in the visible range, so it can be pumped with red LDs, which has the advantages of high quantum efficiency, compact structure, and low cost. In addition, the alexandrite laser has a unique temperature characteristic that it can work well at room temperature, and the effective gain cross-section of the alexandrite crystal increases with the increase of the crystal temperature, which is beneficial to the laser output [9,10]. Therefore, alexandrite-based femtosecond lasers with high repetition rate and ultrashort pulse width may be a potential candidate for excitation sources used in multiphoton microscopy. Since 2013, benefitting from the rapid development of high-power laser diode (LD) technology around 640 nm [11], highly efficient and miniaturized alexandrite femtosecond lasers gradually became a hot topic in the field of advanced solid-state lasers. To date, studies have demonstrated mode-locking, Q-switching and continuous-wave (CW) lasing with high power and wavelength tuning capability of alexandrite lasers [12–16]. In 2018, C. Cihan et al. reported the current shortest passive mode-locking laser of alexandrite crystal with a pulse width of 65 fs, with a pulse repetition rate of 5.56 MHz [12]. In 2021, we demonstrated LD-pumped alexandrite pulsed laser with high repetition rate up to 7.5 GHz by Kerr-lens mode-locking (KLM). Pulse width of 201 fs was achieved [13]. Current research is focused on further shorten the pulse width under high repetition rate.

For femtosecond pulses, short pulse durations corresponding to a wide spectrum bandwidth in the frequency domain. Self-phase modulation produced by the nonlinear effect when ultrafast laser passes through a transparent medium can broaden the laser spectrum [17,18]. However, self-phase modulation (SPM) from nonlinear media is often small under GHz repetition rate and large cavity mode size. Alternatively, inserting spectral modulating components in cavity, such as Fabry-Perot (F-P) etalons and birefringent filters, to shape the net gain profile of the spectrum, can also lead to a broader spectrum and possibly lead to a short pulse duration [19].

Here, we demonstrated a LD pumped alexandrite self-pulsed laser using a compact plano-concave cavity. A broadband ultrafast laser at the center wavelength of 765 nm with approximately 20 nm full width at half maximum (FWHM) was obtained by inserting a 0.5 mm-thick quartz plate modulator. This simple resonator produced pulse duration as short as 36 fs with a high repetition rate of 2.48 GHz, under the pump power of 17 W. To the best of our knowledge, this is the shortest pulse generated with alexandrite laser so far.

2. Experimental setup

The experimental setup was shown in Fig. 1, which consisted of pump source, focus system and simple plano-concave cavity. A commercial fiber-coupled 638 nm LD with core diameter of 200 µm and numerical aperture of 0.22 was employed as the pump source. Through the focus system with a 2:1 compression ratio and 50 mm focal length, pump beam was focused into the crystal. A c-cut 3 × 3 × 10 mm³ (a × b × c) alexandrite crystal doped with 0.2 at.% of Cr³⁺ was used as gain medium. Both end surfaces were polished and antireflection coated (AR) at 750 nm. The crystal was wrapped in indium foil and held in a copper holder cooled by water at 25 °C. The plane pump mirror M1 was coated with high transmission (HT) coating at the wavelength range of 550-665 nm, and high reflection (HR) coating at the wavelength range of 700-900 nm. The plano-concave mirror M2 as output coupler, has a radius of curvature of 50 mm and transmittance of 1% at the wavelength range of 700-900 nm. A quartz birefringent plate with a thickness of 0.5 mm and optical axis within the plate was insert into the cavity for spectral broadening. Due to the limitation of cavity length for operation at GHz repetition rate, the quartz plate was not placed at Brewster angle but tilted only about 1∼2 degree to the beam. Laser emission spectrum was broadened by rotating the plate along the incident axis perpendicular to the surface of the plate.

 

Fig. 1. Schematic of the alexandrite self-pulse laser.

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3. Results and discussion

For referencing, we first performed the pulse laser experiment without inserting quartz plate. In the experiment, the alexandrite crystal was slightly titled to control the F-P effect. According to the calculation method in our previous work [13], the realization of pulse self-starting should satisfy ${L_{nl}} > \pi {T_R}\Delta v/\ln (m )$, where L_nl is the nonlinear loss modulation, T_R is the round-trip time in the cavity, Δν is the 3-dB width of the first beat note of the axial mode, and m is the number of modes initially oscillating. Therefore, the self-starting threshold was calculated to be approximately 10⁻⁶. The round-trip diffraction loss introduced by the Kerr-lens of alexandrite crystal was about 10⁻⁵, so the self-pulsing laser can be achieved by self-starting. By carefully optimizing the length of cavity, the stable self-pulsed laser was realized with an average output power of 190 mW at a pump power of ∼13 W. Average output power as a function of pump power was shown in Fig. 2(a). Detailed pulses characteristics measuring at pump power of 16 W were shown in Fig. 2(b)-(d), which detected by a fast photodetector (New Focus, 818-BB-45F), and recorded by digital oscilloscope (Tektronix, MSO 72504DX). Pulse trains under the time range of 5 ns and 10 µs were displayed in Fig. 2(b), showing that the self-pulsing was stable and no Q-switching was observed within the long scanning range. During more than thirty minutes of observation, we found that the pulse was stable. From radio frequency (RF) spectrum as shown in Fig. 2(c)–2(d), the repetition rate was measured to be ∼2.6 GHz, which was in good agreement with the effective length of the cavity. The signal-to-noise ratio (SNR) of the fundamental beat notes was 59 dB, suggesting a stable operation without Q-switching instabilities. The autocorrelation trace of the single pulse was 213 fs assuming a sech²-shaped pulses as shown in Fig. 2(e), which measured by commercial intensity autocorrelator (APE, Pulse Check). Since the autocorrelator only receives light polarized in the horizontal direction, and alexandrite can directly generate polarized light due to its strong birefringence. Therefore, in the preliminary experiments, the polarization direction of the laser was ensured to be consistent with the requirement of autocorrelator by changing the crystal placement. In addition, GHz pulses were difficult to measure by autocorrelator due to their small single-pulse energy of only ∼0.1 nJ, which resulted in a lower SNR. The corresponding laser spectrum was centered at 770 nm, with a FWHM of 3.4 nm as shown in Fig. 2(f), which measured by spectrometer (Ocean Optics, HR4000). With an average output power of 281 mW at pump power of 16 W, the corresponding peak power was calculated to be 0.51 kW.

 

Fig. 2. Characterization of the self-pulsed laser without quartz plate. (a) Average output power versus pump power in self-pulsed laser; (b) Typical pulses train at the time scale of 5 ns and 10 µs; Detailed pulse characteristic at 16 W pump power: (c) Fundamental RF beat note at ∼2.6 GHz with a span of 800 MHz (RBW: resolution bandwidth); (d) RF spectrum with span of 16 GHz; (e) Autocorrelation trace; (f) Optical spectrum.

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To further compress the pulse width, 0.5-mm thick quartz birefringent plate was inserted into the cavity. Due to the limitation of the cavity length, the quartz plate was only tilted about 1°∼2° and not placed at the Brewster angle, which will introduce some insertion loss. The laser spectrum broadening was achieved by rotating the quartz plate around the axis perpendicular to the surface of the plate.

The spectrum broadening can attribute to different modulation mechanisms of inserted quartz plate. By rotating the quartz plate, we first observed an unstable intermediate state with spectrum modulations as shown in Fig. 3(a).

 

Fig. 3. (a) Measured unstable intermediate state laser spectrum and transmittance of quartz filter calculated with A = 45° and θ=1.03°; (b) Measured optical spectrum of the stable self-pulse laser and transmittance of the quartz plate calculated with A = 9° and θ=1.1°.

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We performed the following theoretical calculations to explain the intermediate state. Polarized light passes through the filter and can be decomposed into ordinary and extraordinary light due to the birefringence. The phase delay can be expressed as [20]

For the filter with the optical axis within the plane, its transmission can be given by [20]

With the principle of space analytic geometry, cos γ=cos A × cos θ, where A is the tuning angle. The calculated transmittance of the quartz filter with A = 45° and θ=1.03° was also shown in Fig. 3(a), which was in good agreement with the measured modulated spectrum, indicating that the quartz plate has a filtering effect on the gain spectrum.

Then by carefully rotating the quartz plate to optimize the angle and fine-adjusting the output mirror M2, stable ultrashort self-pulsed laser was generated when A = 9° and θ=1.1°. The emission spectrum centered at ∼765 nm has approximately 20 nm FWHM bandwidth as shown in Fig. 3(b). Using the above formulas (1) and (2), with A = 9° and θ=1.1°, the transmittance of the quartz plate was calculated as well and shown in Fig. 3(b). It can be noticed that by rotating the quartz plate to correct angle, the reflection loss at the center wavelength was greater than that on both sides of the spectrum, resulting in a reshaping of its gain profile and further broadening of the spectrum.

We further characterized the pulses at pump power of 17 W. Autocorrelation trace was shown in Fig. 4(a). Pulse width as short as 36 fs was achieved assuming a sech² profile, which is the shortest pulse obtained in the alexandrite crystal so far. The inset was a long-delay autocorrelation trace with a scan range of 13 ps, and no double-pulse phenomenon was observed during the measurement, which further clarified that was stable single-pulse operation. Meanwhile, to further verify the self-pulsing operation, the second-harmonic generation (SHG) signal strength was measured by zero scan of the autocorrelator, which the distance between the two interference arms was fixed and equal. It was found that its strength of SHG signal was about 8 times that of the CW, which was sufficient to demonstrate the stable operation of self-pulsing.

 

Fig. 4. (a) Autocorrelation trace of the single pulse (Inset: 13 ps scan range); (b) Pulses train record with oscilloscope at time scales of 5 ns and 4 µs, respectively; (c) Fundamental RF beat note at 2.48 GHz with a span of 1 GHz; (d) RF spectrum with a span of 13 GHz (RBW: resolution bandwidth).

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To check the stability of the self-pulsed operation, pulses train at different time scales was shown in Fig. 4(b), which indicating that the self-pulsed operation was stable without Q-switching instabilities. Laser was maintained stable within 30-minutes operations. From different span RF spectrum shown in Fig. 4(c)–4(d), we can see that the repetition rate and the SNR of the pulse were 2.48 GHz and 57 dB, respectively. The average output power was measured to be 153 mW at pump power of 17 W, which leads to a peak power of 1.71 kW.

The positive group delay dispersion (GDD) in this resonator is mainly produced by alexandrite crystal. According to the Sellmeier equation of the alexandrite [21], the group velocity dispersion (GVD) of the alexandrite is calculated to be ∼58 fs²/mm (at 765 nm, for E ‖ b). Therefore, for 10 mm length alexandrite, the round-trip (RT) GDD introduced is ∼1160 fs². For soliton mode-locking according to the calculation [22], we could calculate from the experiment results that a total RT GDD of −1230 fs² is required to balance the SPM and material dispersion introduced by the alexandrite under the pulse width of 36 fs. By comparing the present results with and without the birefringent plate (pulse width of 213 fs and 36 fs), we can clearly get that the negative GDD is generated by the quartz birefringent plate related to the birefringence, which has been reported previously [23]. The generation mechanism of negative GDD should be based on the detailed measurement of the anisotropic linear and nonlinear optical properties of the present quartz birefringent plate, which will be finished in the near future.

Table 1 summarizes the ultrafast laser research results of alexandrite crystal as a gain medium. To our best knowledge, the pulse width achieved in our work is the shortest among all the alexandrite ultrashort pulse lasers. Moreover, it is worth noting that current result was demonstrated with LD pumping with a compact linear cavity, not only achieved ultrashort pulse laser, but also taken into account the high repetition rate, which is on the order of GHz.

Table 1. Summary of ultrafast laser experiment results with alexandrite crystal as gain medium

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4. Conclusion

In conclusion, we demonstrated a diode pumped GHz femtosecond alexandrite laser. In the experiment, a 0.5 mm quartz birefringent filter as spectral modulation component was used to broadening the laser spectrum to nearly 20 nm at the wavelength of ∼765 nm. Pulse as short as 36 fs with the repetition rate of 2.48 GHz was obtained. To the best of our knowledge, this is the shortest pulse achieved with alexandrite crystal so far. Our research only uses a compact linear cavity to achieve both ultrashort pulses and high repetition rates, which provides the possibility for the use of miniaturized, portable femtosecond light sources in many fields, such as material processing, ultrafast spectroscopy, medical treatment, etc.