Diode pumped compact single frequency cw ruby laser

Investigations on 405 nm diode-pumped cw ruby lasers operated in less than 3 mm plane-parallel resonators are reported. With 2.5 mm long ruby crystals TEM00 emission with output powers up to 40 mW are achieved. With an uncoated thin etalon of 0.13 mm thickness, single frequency emission on both ruby lines R1 and R2 is possible. With the piezoelectric shifting of one resonator mirror and corresponding tilting of the etalon, single frequency tuning of up to 400 GHz has been achieved. Details of the laser system are presented, and potential applications will be discussed.


Introduction
In some recently published papers [1][2][3], cw ruby laser operation, pumped by 405 nm laser diodes, has been reported. The achieved data and the ease of operation suggest that more than 60 years after the first realization of a laser, a flash lamp pumped pulsed ruby laser [4], diode laser pumped cw ruby lasers will become an exciting tool for applications in metrology or as simple to use efficient and low cost all solid-state lasers in the visible spectral range. In papers [1,2], semi-concentric spherical resonators of typically 50 mm in length have been used and investigated in detail, yielding thresholds as low as 100 mW and output powers up to 120 mW. This semiconcentric laser configuration is easy to operate and insensitive to misalignment, but due to this may also oscillate on transversal modes. In [3] cw operation in a bow tie ring resonator was first demonstrated, and clean TEM 00 single-frequency emission could be achieved for the unidirectional operation of the ring resonator by using an internal Faraday rotator. However, such a scheme is more complex and probably only suited for specific scientific applications. To achieve single frequency operation in a linear cavity, short laser cavities and/or additional internal frequency selection elements like Fabry-Perot etalons may be used, as successfully applied for many laser systems [5], p. 236. Considering the good gain achieved from ruby crystals of 5 mm length, it appears well feasible to operate short cavity ruby lasers using plane-parallel resonators. In fact, the very first realized cw ruby lasers, pumped with mercury arc lamps [6,7] and argon ion lasers at liquid nitrogen temperature [8], already used plane-parallel resonators. In this contribution, we will present the first experiments of 405 nm diode laser-pumped cw ruby lasers using ruby crystals of 2.5 mm thickness within planeparallel resonators of less than 3 mm in length. The longitudinal mode spectrum is analyzed, and single frequency emission is demonstrated using an uncoated internal solid glass etalon of 0.13 mm thickness.

Experimental
The experimental setup is given in figure 1. The 405 nm diode laser radiation is collimated (beam radius 2 mm divergence 0.33 mrad) and focused through mirror M1 by a focusing lens (f = 50 mm) into the c-cut ruby crystal (diameter 9 mm, length 2.5 mm, Cr 2 O 3 concentration 0.05 %), forming a thin parallel fluorescence channel (beam radius ω P 16.5 μ m, Rayleigh length about 3.7 mm within the ruby crystal. The mirror M1 is directly coated to the ruby crystal (coating: high transmission for 405 nm, high reflectivity for 694 nm). In addition, the opposite crystal surface (M * ) is coated for high transmission for 694 nm and high reflectivity for 405 nm to Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. return the non-absorbed pump power into the crystal. At the same time, the separate mirror M2 serves as an output coupler with various transmission values.

Output coupling and laser power
The output power of the ruby laser has been measured (figure 2) for different output coupling ratios. The optimum output coupling of the mirror M2 has been determined to be 2.6 % (figure 2).
The largest output power is achieved for the shortest possible cavity length of about 2.55 mm. With increasing cavity length, the threshold increases, and the output power decreases, as shown in figure 3. The linearity, of course, will allow higher diode pump power. The slope may be increased by a longer crystal, by another focusing lens, and by using a pump diode with a better beam profile. This is partly shown in the preceding work [1][2][3].
Laser operation for a cavity length well above 7 mm was impossible for the given pump condition, even when decreasing the output coupling. Obviously, a stability limit is reached. To understand this, one should remember that the plane-parallel resonator is potentially unstable as it operates at the border of the stability diagram for optical resonators [5], p. 206. However, it is well known that for solid-state lasers, the absorption of the pump radiation within the laser crystal generates a thermal lens that stabilizes a plane-parallel resonator and allows  stable TEM 00 emission [5,7]. Direct attempts to measure this thermal lens f th for the ruby laser used here have failed so far. To get an estimate for our experimental conditions, we followed the calculations given in [5], p. 468, using the equation (1) f K P e where K c is the thermal conductivity of the laser material, dn dt the change of the refractive index with temperature, ω P the pump beam radius, P H the fraction of pump power which is absorbed, α the absorption coefficient and l the length of the laser crystal (data and units given in table 1). We first repeated the calculation given in [5] for an Nd:YAG rod (curve C in figure 4) using the properties of the Nd:YAG material as given in table 1. With the same equation but with the crystal properties of the ruby material used here (see table 1), curve B (figure 4) is calculated. In addition, curve A is calculated for Nd:YAG material, however, with the same crystal length and focus as for the ruby rod. It appears that the thermal lensing of the ruby is close to that of the Nd:YAG material.
According to this calculation, the focal length of the thermal lens of the ruby is about 10 mm at a typical pump power of 1 W. Since the diameter of the lens is of the order of the pump beam diameter of about 33 μm, it is hard to measure it with a probe laser.
A plane-parallel resonator with a thin thermal lens f placed close to one mirror, which roughly corresponds to the here given situation, is stable for a resonator length L opt f [5], p. 211. Thus the measurements of figure 3, yielding a maximum optical resonator length of about 10mm, agree quite well with the above-given estimate for the thermal lens. Under all operation conditions, the ruby laser emits a good TEM 00 mode, as shown in figure 5.

Frequency spectrum and single frequency operation
The ruby fluorescence spectrum consists of two strong lines (R 1 and R 2 ) (see figure 10 in 2.3) which are homogeneously broadened [9], having a spectral FWHM (Full Width at Half Maximum) at room temperature of about 0.7 nm (R1) and 0.6 nm (R2). The homogeneous broadening favors the oscillation of only a few longitudinal modes. We may expect oscillation on a single longitudinal mode for very short cavity lengths of the ruby laser. For the laser considered here, the free spectral range FSR is given by [5], p. 238:   c is the speed of light, L c the length of the ruby crystal, n c the ruby index of refraction (1.77), L the geometrical cavity length and n air the refractive index of air between the ruby crystal and the cavity mirror M 2 (see figure 1). For the minimum cavity length L = 2.55 mm (0.5 mm air spacing), we obtain a free spectral range of FSR = 33.5 GHz. To measure, control, and manipulate the mode spectrum of the ruby laser, the setup shown in figure 6 is used. For the laser itself, the mirror M2 is attached to a piezoelectric transducer (PZT) to allow a finetuning of the optical cavity length, and the air spacing between the ruby crystal and the mirror M2 is enlarged to about 2 mm, to allow the insertion of a thin solid-state etalon. To measure the fluorescence spectrum and to see whether laser oscillation occurs on R1 or R2 line, a grating spectrometer (HR4000 Ocean Optics) with an optical fiber is used. A Fabry-Perot with a free spectral range FSR of about 5-6 times larger than the laser mode spacing is required for the mode spectrum. We use a plane-parallel scanning Fabry-Perot (SFP) with 0.5 mm mirror spacing, having a free spectral range of 300 GHz. With conventional λ/10 laser mirrors, having a reflectivity of 95% at the ruby wavelength, an experimental finesse of 40 is easily obtained ( figure 7). Figure 7 shows a typical mode spectrum for the laser without internal etalon at the shortest possible cavity length of 2.55 mm (FSR 33.5 GHz). The emission, here of the R1 line, consists of up to five longitudinal modes covering a spectral range of about 135 GHz, which corresponds to about 30% of the spectral width of the R1 line of 420 GHz. Superimposed (dashed line (G)) is a Gaussian curve that corresponds to the upper part of the R1 line in figure 10.
With the insertion of an 0.13 mm uncoated solid glass etalon (refractive index 1.46, FSR = 790 GHz) at a slightly increased cavity length of 2.65 mm, single frequency oscillation is easily achieved (figure 8). From figure 8, an instrument-limited emission width of the mode of about 5.5 GHz can be estimated. A spherical scanning Fabry-Perot is used to obtain a higher spectral resolution. It consists of two identical mirrors (reflectivity 96%) with a radius of curvature of 50 mm (confocal geometry), resulting in a free spectral range (FSR) of 1.5 GHz. A corresponding oscilloscope trace is shown in figure 9 for the single-mode laser, yielding now an instrument-limited spectral width of 25 MHz.

Single mode tuning
As can be seen from the fluorescence curve (A) of figure 10 and the SFP trace of figure 7, tuning of the ruby laser over extended parts of the spectrum should be possible. For the R1 line (see figure 10(A)), a range of 420 GHz (0.7 nm) is expected, which is in the range of the fiber-coupled spectrometer, having a resolution of 0.1 nm. While monitoring the single-mode operation with the high-resolution Fabry-Perot, the tuning of the ruby laser is achieved by tilting the etalon inside the cavity. Already a few arc minutes of tilting tunes the entire range. To avoid mode hopping, the mirror M2 is shifted with the PZT to set the optimum cavity length. For each tilt of the etalon, the emission spectrum is taken, and the ruby laser intensity is plotted against the wavelength read out of the spectrometer. In this way, the tuning curve (B) of figure 10 is obtained, showing for the R1 line a tuning range of 405 GHz and 112 GHz for the R2 line. As soon as the losses due to the etalon increase for either the R1 or R2 line, the laser jumps to the line with lower losses.

Summary and conclusions
For the first time, a 405 nm diode laser pumped cw ruby laser with a very short plane-parallel resonator is demonstrated and investigated in detail. With a 2.5 mm long ruby crystal within a cavity of only 3 mm length, more than 40 mW output power at a pump power of 1W is achieved in a clean TEM 00 mode. With an internal solid state etalon and one laser mirror attached to a PZT, single frequency emission with more than 20 mW output power is obtained, tunable over more than 400 GHz for the R2 line.
Measurement with a spherical scanning Fabry-Perot yields a line width of fewer than 25 MHz, limited by the instrumental resolution. Due to the long lifetime of the upper laser level of the ruby laser and the compact noiseimmune setup, a linewidth in the kHz range or even less will be expected.
The combination of the relatively high output, the excellent coherence properties, and the possibility to realize a very compact and stable system make this laser attractive for application in high-precision metrology.  Compared to the He-Ne laser often used for this purpose, the ruby laser offers superior power, lower power consumption, and lower operating voltage, enabling a much more rigid and compact construction.
Finally, considering the low threshold of the 2.5 mm ruby laser, it is expected that even a 0.5 mm ruby crystal will be sufficient for laser operation. In this case, single-frequency oscillation without an internal etalon is expected due to the increased mode spacing of 170 GHz. This should allow an extremely compact, fully integrated laser system.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).