#
Comparative Performance Analysis of Femtosecond-Laser-Written Diode-Pumped Pr:LiLuF_{4} Visible Waveguide Lasers

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{4}, LLF), obtaining laser emissions from waveguides of different design at four distinct wavelengths: 604 $\mathrm{n}$$\mathrm{m}$, 645 $\mathrm{n}$$\mathrm{m}$, 698 $\mathrm{n}$$\mathrm{m}$ and 721 $\mathrm{n}$$\mathrm{m}$. This is also the first demonstration of a praseodymium-based waveguide laser operating at 645 $\mathrm{n}$$\mathrm{m}$.

## 2. Materials and Methods

_{4}(YLF), being a tetragonal crystal with the structure of the scheelite (CaWO

_{4}). Its lattice constants are $a=5.124\AA $ and $c=10.54\AA $ [20]. It was preferred over YLF due to its better thermomechanical properties [21]. In this host, praseodymium absorption transition ${}^{3}{\mathrm{H}}_{4}\to \phantom{\rule{-0.166667em}{0ex}}{\phantom{\rule{-0.166667em}{0ex}}}^{3}{\mathrm{P}}_{2}$ is located at 444 $\mathrm{n}$$\mathrm{m}$ and its absorption cross section is about $1.0\times {10}^{-19}\phantom{\rule{0.166667em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}$, allowing efficient diode-based optical pumping [2]. Its fluorescence spectrum in the 600–750 $\mathrm{n}$$\mathrm{m}$ is composed by four main transitions. The one with the greater emission cross section is the ${}^{3}{\mathrm{P}}_{0}\to \phantom{\rule{-0.166667em}{0ex}}{\phantom{\rule{-0.166667em}{0ex}}}^{3}{\mathrm{F}}_{2}$, corresponding to an emission wavelength of 640 $\mathrm{n}$$\mathrm{m}$ in $\sigma $ polarization (E//a). At the same wavelength, two peaks of low intensity (639 $\mathrm{n}$$\mathrm{m}$ and 645 $\mathrm{n}$$\mathrm{m}$) are present for $\pi $ polarization (E//c). For $\pi $ polarization, three other peaks are present: ${}^{3}{\mathrm{P}}_{0}\to \phantom{\rule{-0.166667em}{0ex}}{\phantom{\rule{-0.166667em}{0ex}}}^{3}{\mathrm{H}}_{6}$ (604 $\mathrm{n}$$\mathrm{m}$), ${}^{3}{\mathrm{P}}_{0}\to \phantom{\rule{-0.166667em}{0ex}}{\phantom{\rule{-0.166667em}{0ex}}}^{3}{\mathrm{F}}_{3}$ (698 $\mathrm{n}$$\mathrm{m}$), ${}^{3}{\mathrm{P}}_{0}\to \phantom{\rule{-0.166667em}{0ex}}{\phantom{\rule{-0.166667em}{0ex}}}^{3}{\mathrm{F}}_{4}$ (721 $\mathrm{n}$$\mathrm{m}$). For sigma polarization, a strong emission is present at 607 $\mathrm{n}$$\mathrm{m}$${(}^{3}{\mathrm{P}}_{0}\to \phantom{\rule{0.166667em}{0ex}}{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{H}}_{6})$ and minor peaks are present in correspondence of the other transitions listed before. Polarized absorption and fluorescence spectra are reported in Figure 1.

_{3}and PrF

_{3}powders from AC materials, Tarpon Springs, FL, USA), by a Czochralski furnace at the University of Pisa. The dopant concentration in the melt was of 1%. Using X-ray diffraction [3], the crystallographic axes have been identified and the boule oriented. Subsequently, two oriented samples have been carved from the boule. A known effect in growing Pr:LLF is dopant segregation [3]. This reflects in lower concentrations of Pr

^{3+}ions in the grown material with respect to the nominal doping in the melt. The real dopant concentration has been estimated from absorption measurements, realized with a CARY 5000 spectrophotometer, by knowing the absorption cross section [2]. The Pr

^{3+}concentration results equal to 0.2% for both samples. This value is in agreement with the one obtained by ICP analysis in [3]. Samples have been polished to obtain laser quality facets. The final dimensions of the samples are 4 $\mathrm{m}$$\mathrm{m}$(a) × 4 $\mathrm{m}$$\mathrm{m}$(c) × 8 $\mathrm{m}$$\mathrm{m}$(a) for sample 1 and 4 $\mathrm{m}$$\mathrm{m}$(a) × 4 $\mathrm{m}$$\mathrm{m}$(c) × 9 $\mathrm{m}$$\mathrm{m}$(a) for sample 2. The waveguides were written parallel to an a-axis in both samples, resulting in a 8 $\mathrm{m}$$\mathrm{m}$ long waveguide for sample 1 and 9 $\mathrm{m}$$\mathrm{m}$ long for sample 2.

#### 2.1. Waveguide Fabrication

- Circular cladding (CC): this waveguide type consists of a cladding with a reduced refractive index that is produced by multiple parallel laser damage tracks following the desired circular geometry [8]. The scanning velocity was varied between 600 $\mathsf{\mu}$$\mathrm{m}$/$\mathrm{s}$ and 1200 $\mathsf{\mu}$$\mathrm{m}$/$\mathrm{s}$, the pulse energy between 70 $\mathrm{n}$$\mathrm{J}$ and 100 $\mathrm{n}$$\mathrm{J}$ and the separation between adjacent tracks was set to 2 $\mathsf{\mu}$$\mathrm{m}$. With these parameters CCs were inscribed with different radius.
- Circular cladding “with ears” (CC-E): in certain circumstances, propagation loss of CC waveguides is reduced by designing a more complex structure of damage tracks at the side of the claddings (“ears”) that may minimize leakage from the waveguide [10]. Same parameters as CC were tested for CC-E waveguide fabrication.
- Hexagonal cladding (HC): cladding waveguides with a hexagonal geometry [23]. The separation between tracks of the cladding was set to 7 $\mathsf{\mu}$$\mathrm{m}$, and the pulse energy and scanning velocity were varied as for CC waveguides.
- Stress-induced double-line (DL): stress-induced waveguides make use of the compressive stress created at the side of the damage tracks to produce a region with increased refractive index [24]. Our design consisted of two parallel tracks with a separation of 3 $\mathsf{\mu}$$\mathrm{m}$, and two other identical tracks with a separation of 14, 16 or 20 $\mathsf{\mu}$$\mathrm{m}$. The pulse energy was varied between 90–120 $\mathrm{n}$$\mathrm{J}$ and the scanning velocity was set to 100 $\mathsf{\mu}$$\mathrm{m}$/$\mathrm{s}$.
- Stress-induced double-line with rhombic cladding (DL-RC): same structure as DL but adding some tracks above or below the waveguide region to improve confinement [14]. DL tracks were fabricated with the same parameters as DLs and the cladding tracks with a pulse energy of 100 $\mathrm{n}$$\mathrm{J}$ and a scanning velocity of 100 or 500 $\mathsf{\mu}$$\mathrm{m}$/$\mathrm{s}$.
- Single line (SL): it consists of a single laser scan that acts as waveguide in the cases where a refractive index increase could be produced at the damage track [24]. We have tested these structures in Pr:LLF with pulse energies between 50 and 100 $\mathrm{n}$$\mathrm{J}$, and scanning velocities between 150 and 500 $\mathsf{\mu}$$\mathrm{m}$/$\mathrm{s}$.

#### 2.2. Waveguide Analysis

_{3}[25]. In this case, the multiple tracks that compose the waveguide act as a set of parallel waveguides (see Figure 3c), coupling a total power comparable or greater than the one confined in the core, but with a modal profile that resembles the cladding shape, which is not useful for the construction of a laser device. The waveguide design which demonstrates the lower propagation losses is the CC-E design. Except for WG10 of sample 1, those waveguides possess propagation losses lower than $0.4$ $\mathrm{d}$$\mathrm{B}$/$\mathrm{c}$$\mathrm{m}$ for $\pi $-polarization, a value lower than those previously reported for femtosecond-laser-written waveguides on fluorides [14,15]. In particular, waveguide WG8 of sample 1 shows an upper limit for the propagation losses of $0.12$ $\mathrm{d}$$\mathrm{B}$/$\mathrm{c}$$\mathrm{m}$, a value comparable to the one observed for ultra-large area waveguides realized by helical inscription technique [16].

^{3+}ions. A collimation lens was used to collect the beam exiting from the laser diode and then a couple of cylindrical lenses (Schäfter+Kirchhoff 5 AN-3-V-35) was used to reduce the beam astigmatism. Since the laser diode emission is mainly polarized, a half wavelength plate and a polarizing beam splitter were used to control the pump power, keeping constant the emission wavelength of the diode. A second half wavelength plate was employed to control the beam polarization, in order to study both $\sigma $ and $\pi $ polarization at this wavelength. The maximum available power before the focusing lens was about $1.7$ $\mathrm{W}$. The best performance has been observed employing as coupling lens the same achromatic lens of 30 $\mathrm{m}$$\mathrm{m}$ focal length employed for the $632.8$ $\mathrm{n}$$\mathrm{m}$ wavelength. The focused beam has been studied with the BP. The beam had a diameter of 60 $\mathsf{\mu}$$\mathrm{m}$ with a corresponding value of ${\mathrm{M}}_{\mathrm{x}}^{2}$ of 20 in the horizontal direction and a diameter of 40 $\mathsf{\mu}$$\mathrm{m}$ with an ${\mathrm{M}}_{\mathrm{y}}^{2}$ of 1.7 for the vertical direction. The definition of ${\mathrm{M}}_{\mathrm{x}}^{2}$ and ${\mathrm{M}}_{\mathrm{y}}^{2}$ is the one reported in the ISO 11146-1:2021 standard. The choice of a pump beam wider than the average dimension of the waveguide is due to the numerical aperture of the waveguides (about 0.04), which limits the divergence of the input beam. The chosen lens was found to be the best compromise between beam diameter and divergence.

#### 2.3. Cavity Design

^{−5}for $630\mathrm{n}\mathrm{m}\lambda 740\mathrm{n}\mathrm{m}$, covering all the red and deep red emission of Pr

^{3+}ions. Four different output couplers were employed for the laser experiments and their characteristics are reported in Table 5:

## 3. Results

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

SSL | Solid State Laser |

ST | Single Track |

DL | Stress-induced double-line |

DL-RC | Stress-induced double-line with rhombic cladding |

CC | Circular cladding |

CC-E | Circular cladding with "ear-like" structures |

HC | Hexagonal cladding |

## Appendix A. Model Derivation

## Appendix B. Summary of the Results for All the Waveguides

**Table A1.**Writing parameters, type of guided modes and upper limit for the propagation losses for sample 1. SM means single mode waveguide, MM stands for multimodal waveguide, CL is for a mode confined in the cladding and not in the core while - is a non-confined polarization. The upper limit for the losses is reported only when the radiation is confined in the core of the waveguide.

WG | Description | E [nJ] | V [$\mathsf{\mu}$m/s] | T [$\mathsf{\mu}$m] | Modes | $\mathit{\alpha}$ [dB/cm] | ||
---|---|---|---|---|---|---|---|---|

$\mathit{\pi}$ | $\mathit{\sigma}$ | $\mathit{\pi}$ | $\mathit{\sigma}$ | |||||

1 | CC 8 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | SM | CL | 2.8 | - |

2 | CC 9 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | SM | CL | 2.8 | - |

3 | CC 10 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | SM | CL | 1.3 | - |

4 | CC 8 $\mathsf{\mu}\mathrm{m}$ rad. | 78 | 1200 | 2 | SM | CL | 3.5 | - |

5 | CC 9 $\mathsf{\mu}\mathrm{m}$ rad. | 78 | 1200 | 2 | SM | CL | 1.8 | - |

6 | CC 10 $\mathsf{\mu}\mathrm{m}$ rad. | 78 | 1200 | 2 | SM | CL | 1.5 | - |

7 | CC-E 18 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | MM | CL | 0.22 | - |

8 | CC-E 20 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | MM | CL | 0.12 | - |

9 | CC-E 18 $\mathsf{\mu}\mathrm{m}$ rad. | 78 | 1200 | 2 | MM | CL | 0.41 | - |

10 | CC-E 20 $\mathsf{\mu}\mathrm{m}$ rad. | 78 | 1200 | 2 | MM | CL | 1.2 | - |

11 | HC 14 $\mathsf{\mu}\mathrm{m}$ core | 90 | 750 | 7 | SM | CL | 3.2 | - |

12 | HC 14 $\mathsf{\mu}\mathrm{m}$ core | 101 | 750 | 7 | SM | CL | 2.5 | - |

13 | HC 14 $\mathsf{\mu}\mathrm{m}$ core | 90 | 750 | 7 | SM | CL | 3.3 | - |

14 | HC 14 $\mathsf{\mu}\mathrm{m}$ core | 101 | 750 | 7 | SM | CL | 3.9 | - |

15 | DL 14 $\mathsf{\mu}\mathrm{m}$ sep. | 90 | 100 | 14 | - | - | - | - |

16 | DL 16 $\mathsf{\mu}\mathrm{m}$ sep. | 90 | 100 | 16 | - | - | - | - |

17 | DL 20 $\mathsf{\mu}\mathrm{m}$ sep. | 90 | 100 | 20 | - | - | - | - |

18 | DL 14 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 100 | 14 | - | - | - | - |

19 | DL 16 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 100 | 16 | - | - | - | - |

20 | DL 20 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 100 | 20 | - | - | - | - |

21 | DL-RC 14 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 500/100 | 7 | - | - | - | - |

22 | DL-RC 16 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 500/100 | 7 | - | - | - | - |

23 | DL-RC 14 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 500/100 | 7 | SM | - | 7.7 | - |

24 | DL-RC 16 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 500/100 | 7 | SM | - | 5.7 | - |

25 | CC 6 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | SM | CL | 11 | - |

26 | CC 7 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | SM | CL | 10 | - |

27 | CC 6 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | SM | CL | 5.2 | - |

28 | CC 7 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | SM | CL | 2.8 | - |

29 | CC 8 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | SM | CL | 2.3 | - |

30 | DL-RC 14 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 500/100 | 7 | SM | CL | 4.7 | - |

31 | DL-RC 14 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 500/100 | 7 | SM | CL | 9.3 | - |

32 | HC 14 $\mathsf{\mu}\mathrm{m}$ core | 90 | 750/100 | 7 | SM | CL | 13 | - |

**Table A2.**Writing parameters, type of guided modes and upper limit for the propagation losses for sample 2. The facet used for the waveguide inscription is specified nearby the number of the waveguide. Abbreviations are the same of Table A1.

WG | Description | E [nJ] | V [$\mathsf{\mu}$m/s] | T [$\mathsf{\mu}$m] | Modes | $\mathit{\alpha}$ [dB/cm] | ||
---|---|---|---|---|---|---|---|---|

$\mathit{\pi}$ | $\mathit{\sigma}$ | $\mathit{\pi}$ | $\mathit{\sigma}$ | |||||

1(a) | CC 8 $\mathsf{\mu}\mathrm{m}$ rad. | 90 | 600 | 2 | SM | CL | 6.8 | - |

2(a) | CC 9 $\mathsf{\mu}\mathrm{m}$ rad. | 90 | 600 | 2 | SM | CL | 4.1 | - |

3(a) | CC 10 $\mathsf{\mu}\mathrm{m}$ rad. | 90 | 600 | 2 | SM | CL | 2.2 | - |

4(a) | CC 8 $\mathsf{\mu}\mathrm{m}$ rad. | 106 | 1200 | 2 | SM | CL | 7.2 | - |

5(a) | CC 9 $\mathsf{\mu}\mathrm{m}$ rad. | 106 | 1200 | 2 | SM | CL | 5.5 | - |

6(a) | CC 10 $\mathsf{\mu}\mathrm{m}$ rad. | 106 | 1200 | 2 | SM | CL | 2.3 | - |

7(a) | CC-E 18 $\mathsf{\mu}\mathrm{m}$ rad. | 90 | 600 | 2 | MM | CL | 0.38 | - |

8(a) | CC-E 20 $\mathsf{\mu}\mathrm{m}$ rad. | 90 | 600 | 2 | MM | CL | 0.19 | - |

9(a) | CC-E 18 $\mathsf{\mu}\mathrm{m}$ rad. | 106 | 1200 | 2 | MM | CL | 0.30 | - |

10(a) | CC-E 20 $\mathsf{\mu}\mathrm{m}$ rad. | 106 | 1200 | 2 | MM | CL | 0.19 | - |

11(a) | HC 14 $\mathsf{\mu}\mathrm{m}$ core | 115 | 750/100 | 7 | SM | CL | 3.0 | - |

12(a) | HC 14 $\mathsf{\mu}\mathrm{m}$ core | 115 | 750/100 | 7 | SM | CL | 2.5 | - |

13(a) | DL-RC 14 $\mathsf{\mu}\mathrm{m}$ sep. | 115 | 750/100 | 7 | SM | - | 3.9 | - |

14(a) | DL-RC 16 $\mathsf{\mu}\mathrm{m}$ sep. | 115 | 750/100 | 7 | SM | - | 4.7 | - |

15(a) | SL | 98 | 500 | - | - | SM | - | 8.7 |

16(a) | SL | 98 | 150 | - | - | - | - | - |

17(a) | SL | 90 | 500 | - | - | SM | - | 6.9 |

18(a) | SL | 98 | 150 | - | - | SM | - | 10 |

19(a) | SL | 80 | 500 | - | - | SM | - | 5.3 |

20(a) | SL | 80 | 150 | - | - | SM | - | 7.2 |

1(c) | CC 8 $\mathsf{\mu}\mathrm{m}$ rad. | 78 | 600 | 2 | SM | CL | 5.3 | - |

2(c) | CC 9 $\mathsf{\mu}\mathrm{m}$ rad. | 78 | 600 | 2 | SM | CL | 4.3 | - |

3(c) | CC 10 $\mathsf{\mu}\mathrm{m}$ rad. | 78 | 600 | 2 | SM | CL | 4.4 | - |

4(c) | CC 8 $\mathsf{\mu}\mathrm{m}$ rad. | 92 | 1200 | 2 | SM | CL | 9.6 | - |

5(c) | CC 9 $\mathsf{\mu}\mathrm{m}$ rad. | 92 | 1200 | 2 | SM | CL | 3.8 | - |

6(c) | CC 10 $\mathsf{\mu}\mathrm{m}$ rad. | 92 | 1200 | 2 | SM | CL | 3.7 | - |

7(c) | CC-E 18 $\mathsf{\mu}\mathrm{m}$ rad. | 92 | 1200 | 2 | MM | CL | 0.38 | - |

8(c) | CC-E 20 $\mathsf{\mu}\mathrm{m}$ rad. | 92 | 1200 | 2 | MM | CL | 0.34 | - |

9(c) | HC 14 $\mathsf{\mu}\mathrm{m}$ core | 101 | 750 | 7 | SM | CL | 4.2 | - |

10(c) | HC 14 $\mathsf{\mu}\mathrm{m}$ core | 101 | 750 | 7 | SM | CL | 3.9 | - |

11(c) | DL-RC 14 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 750 | 7 | SM | - | 4.9 | - |

12(c) | DL-RC 16 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 750 | 7 | SM | - | 5.5 | - |

13(c) | SL | 84 | 500 | - | - | SM | - | 6.2 |

14(c) | SL | 84 | 150 | - | - | SM | - | 16 |

15(c) | SL | 73 | 500 | - | - | SM | - | 5.7 |

16(c) | SL | 73 | 150 | - | - | SM | - | 7.3 |

17(c) | SL | 62 | 500 | - | - | - | - | - |

18(c) | SL | 62 | 150 | - | - | - | - | - |

19(c) | SL | 50 | 500 | - | - | - | - | - |

20(c) | SL | 50 | 150 | - | - | - | - | - |

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**Figure 1.**Polarized absorption (

**left**) and fluorescence (

**right**) spectra of Pr:LLF. The fluorescence spectrum for all the visible range is reported in [3]. The spectral bandwidth of the light employed for absorption measurements was $0.09$ $\mathrm{n}$$\mathrm{m}$ while the resolution of the fluorescence spectra is $0.13$ $\mathrm{n}$$\mathrm{m}$.

**Figure 2.**Optical microscope pictures of the different waveguide types fabricated in Pr:LLF, taken in transmission mode with white light illumination. The scale bar corresponds to 10 $\mathsf{\mu}$$\mathrm{m}$ and it is common to all figures. (

**a**) Circular cladding (CC), (

**b**) circular cladding “with ears” (CC-E), (

**c**) hexagonal cladding (HC), (

**d**) stress-induced double-line (DL), (

**e**) stress-induced double-line with rhombic cladding (DL-RC) and (

**f**) single line (SL).

**Figure 3.**Microscope images of the end facets of the waveguides (

**a**,

**d**) and near-field pictures for WG7 (

**b**,

**c**) and WG8 (

**e**,

**f**) of sample 1. The orientation of crystallographic axes reported in the figure (

**b**) is common to all pictures. Near-field profiles have been registered adjusting the position of the input beam in order to obtain the maximum output power.

**Figure 4.**(

**a**–

**c**) Transmission data and best fit for the three waveguide analyzed. (

**d**) Linear fit of the ${P}_{S}$ best fit parameters for the three waveguides.

**Figure 5.**Schematic representation of the setup employed for the experiments (

**above**) and a picture of the laser cavity (

**below**). The waveguide is visible due to the fluorescence emitted under blue light pumping. Abbreviations: FL: focusing lens, IC: input coupler, CRYS: crystal, OC: output coupler, CLL: collection lens, LP: long pass dielectric filter, DET: power meter.

**Figure 6.**Data and best fit 698 $\mathrm{n}$$\mathrm{m}$ laser emission. For each point, the dimension of the marker corresponds to the relative error bar.

**Figure 9.**Intensity profiles of the laser emission at various wavelengths. The intensity profiles were taken at maximum output power.

**Table 1.**Writing parameters, type of guided modes, and upper limit for the propagation losses for sample 1. WG is the waveguide number, E is the pulse energy on the sample, V is the scan velocity and T is the track separation. SM means single mode waveguide, MM stands for multimodal waveguide, CL is for a mode confined in the cladding and not in the core while - denotes a non-confined polarization. The upper limit for the losses is reported only when the radiation is confined in the core of the waveguide.

WG | Description | E [nJ] | V [$\mathsf{\mu}$m/s] | T [$\mathsf{\mu}$m] | Modes | $\mathit{\alpha}$ [dB/cm] | ||
---|---|---|---|---|---|---|---|---|

$\mathit{\pi}$ | $\mathit{\sigma}$ | $\mathit{\pi}$ | $\mathit{\sigma}$ | |||||

1 | CC 8 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | SM | CL | 2.8 | - |

3 | CC 10 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | SM | CL | 1.3 | - |

5 | CC 9 $\mathsf{\mu}\mathrm{m}$ rad. | 78 | 1200 | 2 | SM | CL | 1.8 | - |

7 | CC-E 18 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | MM | CL | 0.22 | - |

8 | CC-E 20 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | MM | CL | 0.12 | - |

11 | HC 14 $\mathsf{\mu}\mathrm{m}$ core | 90 | 750 | 7 | SM | CL | 3.2 | - |

12 | HC 14 $\mathsf{\mu}\mathrm{m}$ core | 101 | 750 | 7 | SM | CL | 2.5 | - |

18 | DL 14 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 100 | 14 | - | - | - | - |

19 | DL 16 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 100 | 16 | - | - | - | - |

20 | DL 20 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 100 | 20 | - | - | - | - |

23 | DL-RC 14 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 500/100 | 7 | SM | - | 7.7 | - |

24 | DL-RC 16 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 500/100 | 7 | SM | - | 5.7 | - |

27 | CC 6 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | SM | CL | 5.2 | - |

28 | CC 7 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | SM | CL | 2.8 | - |

29 | CC 8 $\mathsf{\mu}\mathrm{m}$ rad. | 70 | 600 | 2 | SM | CL | 2.3 | - |

30 | DL-RC 14 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 500/100 | 7 | SM | CL | 4.7 | - |

31 | DL-RC 14 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 500/100 | 7 | SM | CL | 9.3 | - |

**Table 2.**Writing parameters, type of guided modes and upper limit for the propagation losses for sample 2. The facet used for the waveguide inscription is specified in brackets together with the waveguide number. Abbreviations are the same of Table 1.

WG | Description | E [nJ] | V [$\mathsf{\mu}$m/s] | T [$\mathsf{\mu}$m] | Modes | $\mathit{\alpha}$ [dB/cm] | ||
---|---|---|---|---|---|---|---|---|

$\mathit{\pi}$ | $\mathit{\sigma}$ | $\mathit{\pi}$ | $\mathit{\sigma}$ | |||||

1(a) | CC 8 $\mathsf{\mu}\mathrm{m}$ rad. | 90 | 600 | 2 | SM | CL | 6.8 | - |

2(a) | CC 9 $\mathsf{\mu}\mathrm{m}$ rad. | 90 | 600 | 2 | SM | CL | 4.1 | - |

3(a) | CC 10 $\mathsf{\mu}\mathrm{m}$ rad. | 90 | 600 | 2 | SM | CL | 2.2 | - |

8(a) | CC-E 20 $\mathsf{\mu}\mathrm{m}$ rad. | 90 | 600 | 2 | MM | CL | 0.19 | - |

9(a) | CC-E 18 $\mathsf{\mu}\mathrm{m}$ rad. | 106 | 1200 | 2 | MM | CL | 0.30 | - |

12(a) | HC 14 $\mathsf{\mu}\mathrm{m}$ core | 115 | 750/100 | 7 | SM | CL | 2.5 | - |

13(a) | DL-RC 14 $\mathsf{\mu}\mathrm{m}$ sep. | 115 | 750/100 | 7 | SM | - | 3.9 | - |

14(a) | DL-RC 16 $\mathsf{\mu}\mathrm{m}$ sep. | 115 | 750/100 | 7 | SM | - | 4.7 | - |

19(a) | SL | 80 | 500 | - | - | SM | - | 5.3 |

1(c) | CC 8 $\mathsf{\mu}\mathrm{m}$ rad. | 78 | 600 | 2 | SM | CL | 5.3 | - |

5(c) | CC 9 $\mathsf{\mu}\mathrm{m}$ rad. | 92 | 1200 | 2 | SM | CL | 3.8 | - |

6(c) | CC 10 $\mathsf{\mu}\mathrm{m}$ rad. | 92 | 1200 | 2 | SM | CL | 3.7 | - |

7(c) | CC-E 18 $\mathsf{\mu}\mathrm{m}$ rad. | 92 | 1200 | 2 | MM | CL | 0.38 | - |

8(c) | CC-E 20 $\mathsf{\mu}\mathrm{m}$ rad. | 92 | 1200 | 2 | MM | CL | 0.34 | - |

10(c) | HC 14 $\mathsf{\mu}\mathrm{m}$ core | 101 | 750 | 7 | SM | CL | 3.9 | - |

11(c) | DL-RC 14 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 750 | 7 | SM | - | 4.9 | - |

12(c) | DL-RC 16 $\mathsf{\mu}\mathrm{m}$ sep. | 101 | 750 | 7 | SM | - | 5.5 | - |

15(c) | SL | 73 | 500 | - | - | SM | - | 5.7 |

**Table 3.**Transmission efficiency for $\pi $ polarized radiation at 444 $\mathrm{n}$$\mathrm{m}$ for the circular cladding waveguides “with ears”.

Sample | WG | Radius [$\mathsf{\mu}$m] | ${\mathit{T}}_{\mathit{\pi}}[\%]$ |
---|---|---|---|

1 | 7 | 18 | 34 |

8 | 20 | 42 | |

9 | 18 | 29 | |

10 | 20 | 36 | |

2 | 7 a-cut | 18 | 27 |

8 a-cut | 20 | 35 | |

9 a-cut | 18 | 25 | |

10 a-cut | 20 | 32 | |

7 c-cut | 18 | 32 | |

8 c-cut | 20 | 35 |

WG | ${\mathit{P}}_{\mathit{S}}$ [W] | ${\mathit{\eta}}_{\mathbf{CL}}$ [%] |
---|---|---|

3 | $0.09$ | 12 |

7 | $0.40$ | 35 |

8 | $0.56$ | 44 |

**Table 5.**Summary of the characteristics of the employed mirrors. The transmittance values were measured with the CARY 5000 spectrophotometer.

Mirror | R [mm] | Transmittance [%] at $\mathit{\lambda}$ [nm] | |||
---|---|---|---|---|---|

604 | 645 | 698 | 721 | ||

1 | plane | 77 | 0.8 | 0.03 | 0.05 |

2 | plane | 16 | 96 | 58 | 71 |

3 | plane | 96 | 74 | 69 | 46 |

4 | 50 | 75 | 7 | 0.9 | 0.8 |

**Table 6.**Summary of laser obtained with the waveguides with the ears using as output coupler mirror 1.

Sample | WG | Radius [$\mathsf{\mu}$m] | $\mathit{\lambda}$ [nm] | ${\mathit{T}}_{\mathbf{OC}}\phantom{\rule{3.33333pt}{0ex}}[\%]$ | ${\mathit{P}}_{\mathbf{OUT}}$ [mW] |
---|---|---|---|---|---|

1 | 7 | 18 | 604 | 77 | 63 |

8 | 20 | 698 | $0.03$ | $3.0$ | |

9 | 18 | 604 | 77 | 50 | |

10 | 20 | 721 | $0.05$ | $1.0$ | |

2 | 7 a-cut | 18 | 721 | $0.05$ | $1.0$ |

8 a-cut | 20 | 721 | $0.05$ | $1.5$ | |

9 a-cut | 18 | 721 | $0.05$ | $0.9$ | |

10 a-cut | 20 | 721 | $0.05$ | $1.0$ | |

7 c-cut | 18 | 721 | $0.05$ | $1.0$ | |

8 c-cut | 20 | 721 | $0.05$ | $1.2$ |

**Table 7.**Comparison between the best laser result obtained in each sample. The best overall results for each wavelength are shown in bold.

$\mathit{\lambda}$ [nm] | WG | ${\mathit{T}}_{\mathbf{OC}}$ [%] | ${\mathit{\eta}}_{\mathit{c}}\phantom{\rule{3.33333pt}{0ex}}[\%]$ | ${\mathit{P}}_{\mathbf{THR}}\phantom{\rule{3.33333pt}{0ex}}\left[\mathbf{mW}\right]$ | ${\mathit{P}}_{\mathbf{MAX}}\phantom{\rule{3.33333pt}{0ex}}\left[\mathbf{mW}\right]$ |
---|---|---|---|---|---|

604 | WG8(1) | 16 | 16 | 100 | $\mathbf{86}$ |

WG8 (2 a-cut) | 16 | 14 | 140 | 56 | |

WG7(1) | 77 | $\mathbf{26}$ | 310 | 63 | |

721 | WG8(1) | 46 | 14 | 280 | 60 |

WG8 (2 a-cut) | 46 | $\mathbf{18}$ | 150 | $\mathbf{70}$ |

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## Share and Cite

**MDPI and ACS Style**

Baiocco, D.; Lopez-Quintas, I.; R. Vázquez de Aldana, J.; Tonelli, M.; Tredicucci, A.
Comparative Performance Analysis of Femtosecond-Laser-Written Diode-Pumped Pr:LiLuF_{4} Visible Waveguide Lasers. *Photonics* **2023**, *10*, 377.
https://doi.org/10.3390/photonics10040377

**AMA Style**

Baiocco D, Lopez-Quintas I, R. Vázquez de Aldana J, Tonelli M, Tredicucci A.
Comparative Performance Analysis of Femtosecond-Laser-Written Diode-Pumped Pr:LiLuF_{4} Visible Waveguide Lasers. *Photonics*. 2023; 10(4):377.
https://doi.org/10.3390/photonics10040377

**Chicago/Turabian Style**

Baiocco, Davide, Ignacio Lopez-Quintas, Javier R. Vázquez de Aldana, Mauro Tonelli, and Alessandro Tredicucci.
2023. "Comparative Performance Analysis of Femtosecond-Laser-Written Diode-Pumped Pr:LiLuF_{4} Visible Waveguide Lasers" *Photonics* 10, no. 4: 377.
https://doi.org/10.3390/photonics10040377