# Low-Loss Coupling of Quantum Cascade Lasers into Hollow-Core Waveguides with Single-Mode Output in the 3.7–7.6 μm Spectral Range

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## Abstract

**:**

## 1. Introduction

_{00}mode, and essentially diffraction-limited low beam divergence with M

^{2}values in the range 1.0–1.3 [1,2,3]. Commercial laser sources are often packaged with internal optics providing collimated output beams, which define and stabilize the output laser mode. These are typically designed and optimized to provide beam divergence of a few milliradians. However, the beam profile often does not result in a single-mode Gaussian-like shape, and typically exhibits an elliptical profile. Spatial defects, such as beam tails, can be easily removed by means of a pinhole. The most common beam collimating system is composed of an aspheric lens, which focuses the laser beam through a pinhole, and collimating optics, which collects the light passing through the pinhole [4,5]. If the laser beam contains higher-order modes, a modal filter for beam cleaning is essential. The ideal modal filter rejects all input field components that have no overlap with the fundamental mode of the filter, without attenuation of this mode [6]. Chalcogenide glass fibers are the most used single-mode solid-core optical waveguides in the infrared spectral range. They have a broad infrared wavelength transmission window between 1.5 and 11 μm. They are usually based on a step-index configuration and are designed to be single mode for wavelengths above a selected cut-off wavelength value. The coupling efficiency has a maximum at a specific wavelength and drops rapidly in the remaining operational spectral range. In the chalcogenide glass family, those based on As-S-Se exhibit single-mode delivery in the near infrared region (<5.5 µm) with and a minimum transmission loss of approximately 0.1 dB/m but suffering a coupling efficiency as low as 60%–70% [7]. For the infrared spectral range >5 μm, photonic crystal fibers have been used to provide single-mode delivery at 3.39 μm, 9.3 μm, and 10.6 μm [8], with losses around 2 dB/m at 10.6 μm [9].

## 2. Experimental Setup

^{2}. The AgI coating was designed to provide low propagation losses in the mid-infrared spectral range from 3.5 µm to 12 µm, as confirmed by the absorbance profile shown in Figure 1.

## 3. Optical Coupling Conditions

_{0}, y

_{0}) are the spatial coordinates of the center, and σ

_{0,x}and σ

_{0,y}are the x and y spreads at the waveguide entrance, respectively. When the 2D laser beam enters the fiber, it transforms into a composition of the fiber modes. Hence, a coupling efficiency can be calculated for each n-th guided mode as:

_{n}(x,y) is the n-th waveguide mode represented by a Bessel function. The lowest-order guided mode E

_{1}(x,y) has a Gaussian spatial profile with circular symmetry. As stated previously, to achieve the optimum coupling conditions, as much of the available laser beam power as possible must be coupled in the lowest-order mode. Higher-order modes suffer increased losses, and the power coupled into these modes is rapidly dissipated as the beam propagates through the waveguide. If the HWC fiber is long enough, only the E

_{1}(x,y) mode survives, and a single-mode output at the waveguide exit is obtained [20]. Numerical calculations have shown that coupling efficiencies η

_{1}higher than 0.89 can be obtained when both the ratios w

_{0,x}/d and w

_{0},

_{y}/d are in the 0.5–0.75 range, where w

_{0,x}= 2σ

_{0,x}and w

_{0,y}= 2σ

_{0,y}are the beam diameters at the waveguide entrance. In our case, this implies that the laser beam at the waveguide entrance must have both w

_{0,x}and w

_{0,y}in the range 100–150 μm. Hence, a coupling lens with an adequate focal length must be selected to achieve this condition. Measurements of beam diameters as small as 100 μm cannot be resolved by available infrared cameras. Therefore, the beam widths w

_{0,x}and w

_{0,y}of the focused laser beam at the waveguide entrance was estimated by measuring the diameters w

_{x}and w

_{y}of the laser beam at the coupling lens using the following expression:

_{x}and w

_{y}can be extracted by evaluating the second-order moments of the beam intensity distribution, as reported in [11].

## 4. Beam Profiles and Related Spatial Quality

_{x}and w

_{y}beam diameters and the calculated w

_{0,x}and w

_{0,y}values obtained using Equation (3), based on the coupling lens selected for each QCL source.

_{0,x}and w

_{0,y}dimensions falling in the range 96–144 µm, nearly identical to the optimal one, as described above. We coupled the QCL beams into the waveguide by positioning the focusing lens 7 cm from the QCL output. The best coupling conditions were obtained by maximizing the HCW output power. Figure 3e–m show the beam profiles obtained at the exit of a 15-cm- and 30-cm-long HCWs in straight positions for the QCL emitting at 7.3 μm (Figure 3e,k), at 4.9 μm (Figure 3f,j), 4.5 μm (Figure 3g,l), and 3.7 μm (Figure 3h,m). To collect the beam profile, we positioned the pyro-camera ~2 cm far from the waveguide exit.

_{1}(x,y) guided mode, as shown by the circular-symmetric beam output [21]. Similar single-mode results were obtained for the 50-cm-long HCW. For the shorter wavelength QCL emitting at 3.7 μm, the acquired profiles show a Gaussian-like pattern with small tails. However, only <3% of the total power is contained in the beam tails, which can be removed using a pinhole. A similar profile was also observed for the 50-cm-long fiber.

^{2}which compares the laser beam angular divergence in the two transverse directions with a diffraction-limited Gaussian beam, which has M

^{2}= 1. For the beam exiting from the QCLs, the M

^{2}value can be defined as:

_{i}) is the beam divergence half-angle of a diffraction-limited Gaussian beam, and θ

_{x(QCL)}and θ

_{y(QCL)}are the divergence half-angles of the QCL beams. The M

^{2}value of the beam exiting from the HCWs can be defined as the ratio between the half-angle beam divergence of the beam and the theoretical half-angle beam divergence:

_{1}(x,y) guided mode exits from the waveguide. For both, the QCLs and the waveguide outputs, half-angle beam divergences of the real beam can be calculated by extracting the beam widths w

_{x}and w

_{y}from the beam profiles acquired at different distances using the experimental approach reported in [22]. Results obtained for the output of all four QCLs together with results for the same beams after exiting the 15-cm-long HCW are listed in Table 2.

^{2}values confirm that the laser beam exiting from the L = 15 cm HCW shows a substantial improvement in spatial quality with respect to the input laser beam. Similar M

^{2}values were obtained for the 30-cm- and 50-cm-long HCWs.

## 5. Total Losses and Coupling Efficiency

_{n}are the attenuation coefficients related to the n-th guided modes. These coefficients depend on the laser wavelength and the optical properties of the dielectric and metallic layers deposited inside the HCW. For their estimation, we used the relation provided by Miyagi and Kawakami [23]:

_{m}and k

_{m}are the real and imaginary parts of the complex index of the silver layer, n

_{d}is the complex index of the silver iodine layer, and u

_{n}is the n-th root of the zero-order Bessel function. The values of n

_{m}, k

_{m}, and n

_{d}were calculated by using relations reported in [24]. Experimental values of the HCW total losses can be calculated from the ratio between the power at the waveguide entrance I

_{0}and that measured at the fiber exit I

_{S}as:

_{n}(x,y), with n ranging from 1 to 5, propagate inside the waveguide.

_{exp}, reported in Table 3, together with the theoretical values calculated by using Equations (1) and (2). A very good data agreement (<7% discrepancy) was obtained.

## 6. Influence of Bore Diameter and HCW Length on the Output Beam Quality

^{3}dependence (Equation (7)) predicts a strong increase in HCW losses as the fiber bore diameter is reduced. A large bore diameter cannot ensure a single-mode profile at the waveguide output. From Equation (6), we can see that for large bore sizes α

_{n}is small and higher-order modes have lower losses with respect to those obtained for small bore sizes, for which α

_{n}is larger. For example, calculations of attenuation coefficients using Equations (7) and (8) at λ = 7.6 μm and L = 1 m show that, for d = 200 μm, losses related to the second-order mode (n = 2) are 11.3 dB, but decreases to 3.3 dB when d is 300 μm. Thus, there is significantly less mode mixing at the HCW output in waveguides with reduced bore size. Mode mixing can be reduced by increasing the fiber length at the expense of larger optical losses. The spatial quality of the input laser beam must also be taken into account, since it influences the input power percentage coupled into the guided modes (see Equation (2)). The larger the amount of input power coupled into the high-order modes, the larger their contributions to total propagation losses will be. As a result, a HCW with a small bore size can exhibit a single-mode output profile, but with optical losses significantly higher than those theoretically predicted. To investigate the influence of the HCW bore size on optical losses and output beam profile, we coupled a 200-µm- and 300-µm-core-sized HCWs, both having a length of 15 cm, with a Daylight Solution external cavity QCL (DLS-QCL) emitting at 7.6 μm. The beam profile at the DLS-QCL exit is shown in Figure 6a, characterized by w

_{x}= 2.56 mm and w

_{y}= 1.79 mm. The DLS-QCL was coupled with a 200-µm-core-sized HCW by using a coupling lens with a focal length of 25 mm (resulting in w

_{0,x}/d = 0.48 and w

_{0,y}/d = 0.67). For the 300-µm-core-sized HCW, a focal length of 50 mm (w

_{0,x}/d = 0.63 and w

_{0,y}/d = 0.88) was used. The output profiles of the 200-μm- and 300-μm-core-sized HCWs (both with L = 15 cm) are shown in Figure 6b,c, respectively.

_{1}mode. To verify whether the contribution to higher-order modes at the 300-μm-core-sized HCW exit can be suppressed by increasing the fiber length, we coupled the DLS-QCL with a 100-cm-long, 300-µm-core-sized HCW. The coupling conditions were the same as used for 300-μm-core-sized HCW. The acquired output beam profile is reported in Figure 6d. Clearly, the profile is still multimodal, with optical losses of 3.45 dB (1.62 dB are the theoretical losses), demonstrating that the only way to achieve single-mode beam delivery in the spectral range of 4.5–7.6 μm is to use HCWs with a bore size as small as 200 μm. For this condition, a length as short as 15 cm is sufficient to provide a single-mode output, even if the spatial quality of the input laser beam is not good. For longer fibers, single-mode output is ensured but optical losses increase. For the spectral range 8–11 μm, both 200-μm and 300-μm diameters can guarantee single-mode beam delivery [16,17,18], but it is preferable to employ a bore size of 300 μm, since it provides lower optical losses.

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Hollow-core waveguide (HCW) relative absorbance measured in the range 1–12 μm using a FTIR spectrometer.

**Figure 2.**Schematic of the experimental setup used to optically couple quantum cascade laser (QCL) sources and the HCWs. A ZnSe lens is used to focus the collimated beam exiting from the QCL onto the waveguide entrance. An infrared pyrocamera detects the profile of the beam exiting from the HCW.

**Figure 3.**(

**a**–

**d**) Beam profiles of the QCL at 7.3 μm (

**a**), at 4.9 μm (

**b**), at 4.5 μm (

**c**), and at 3.7 μm (

**d**), recorded by positioning the infrared pyro-camera 7 cm away from the QCL exit. (

**e**–

**m**) The HCW output beam profiles were measured for the 15-cm- (

**e**–

**h**) and 30-cm-long (

**k**–

**m**) waveguides. The focusing lens was positioned at a distance of 7 cm from the QCL output, and the pyrocamera was located at ~2 cm from the HCW exit.

**Figure 4.**(

**a**–

**d**) Total losses (${\u25cf}$) measured when coupling the 7.3-μm- (

**a**), 4.9-μm- (

**b**), 4.5-μm- (

**c**) and 3.7-μm-QCL (

**d**) beams into the HCWs having lengths of 15, 30, and 50 cm, plotted as a function of the HCW length. Dashed lines are linear fits to the data. Solid lines are the theoretical losses calculated by using Equations (6) and (7).

**Figure 5.**(

**a**–

**d**) Total losses as a function of the QCLs emitting wavelengths for HCWs with L = 15 cm (▀), 30 cm (${\u2580}$), and 50 cm (${\u2580}$).

**Figure 6.**(

**a**) Beam profile at the exit of DLS-QCL emitting at 7.6 μm. (

**b**–

**d**) Beam profiles with a 200-μm-core-sized and 15-cm-long HCW (

**b**); 300-μm-core-sized and 15-cm-long HCW (

**c**); and 300-μm-core-sized and 100-cm-long HCW (

**d**) exits. The focusing lens was positioned at a distance of 5 cm from the QCL output and the pyrocamera was located at ~2 cm from the HCWs exit.

**Table 1.**w

_{x}and w

_{y}values calculated by using the second-order moments method; w

_{0,x}and w

_{o,y}values calculated from Equation (3) when a coupling lens with a focal length f is employed.

7.3-μm QCL | 4.9-μm QCL | 4.5-μm QCL | 3.7-μm QCL | |
---|---|---|---|---|

w_{x} (mm) | 5.26 | 4.24 | 4.19 | 4.27 |

w_{y} (mm) | 4.79 | 3.97 | 3.48 | 3.67 |

f (mm) | 50 | 75 | 75 | 75 |

w_{0,x} (μm) | 132 | 114 | 96 | 100 |

w_{0,y} (μm) | 144 | 122 | 120 | 116 |

**Table 2.**Divergence angles and M

^{2}values for four QCLs and the 15-cm-long HCW, in two directions (x and y) orthogonal to the QCL beam propagating z-direction.

7.3-μm QCL | 4.9-μm QCL | 4.5-μm QCL | 3.7-μm QCL | |
---|---|---|---|---|

θ_{x,QCL} (mrad) | 2.1 | 1.9 | 1.5 | 1.3 |

θ_{y,QCL} (mrad) | 2.0 | 1.7 | 2.2 | 1.1 |

M^{2}_{x, QCL} | 4.75 | 5.16 | 4.39 | 4.71 |

M^{2}_{y, QCL} | 4.12 | 4.32 | 4.85 | 3.42 |

θ_{x,HCW} (mrad) | 30.72 | 22.48 | 21.97 | 20.48 |

θ_{y,HCW} (mrad) | 31.53 | 22.22 | 22.30 | 19.92 |

M^{2}_{x, HCW} | 1.12 | 1.18 | 1.26 | 1.44 |

M^{2}_{y, HCW} | 1.15 | 1.17 | 1.28 | 1.40 |

**Table 3.**Theoretical coupling efficiencies into the lowest-order mode η

_{1}and experimental η

_{ext}values.

7.3-μm QCL | 4.9-μm QCL | 4.5-μm QCL | 3.7-μm QCL | |
---|---|---|---|---|

η_{1} | 0.94 | 0.96 | 0.95 | 0.96 |

η_{exp} | 0.88 | 0.92 | 0.89 | 0.92 |

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**MDPI and ACS Style**

Patimisco, P.; Sampaolo, A.; Mihai, L.; Giglio, M.; Kriesel, J.; Sporea, D.; Scamarcio, G.; Tittel, F.K.; Spagnolo, V.
Low-Loss Coupling of Quantum Cascade Lasers into Hollow-Core Waveguides with Single-Mode Output in the 3.7–7.6 μm Spectral Range. *Sensors* **2016**, *16*, 533.
https://doi.org/10.3390/s16040533

**AMA Style**

Patimisco P, Sampaolo A, Mihai L, Giglio M, Kriesel J, Sporea D, Scamarcio G, Tittel FK, Spagnolo V.
Low-Loss Coupling of Quantum Cascade Lasers into Hollow-Core Waveguides with Single-Mode Output in the 3.7–7.6 μm Spectral Range. *Sensors*. 2016; 16(4):533.
https://doi.org/10.3390/s16040533

**Chicago/Turabian Style**

Patimisco, Pietro, Angelo Sampaolo, Laura Mihai, Marilena Giglio, Jason Kriesel, Dan Sporea, Gaetano Scamarcio, Frank K. Tittel, and Vincenzo Spagnolo.
2016. "Low-Loss Coupling of Quantum Cascade Lasers into Hollow-Core Waveguides with Single-Mode Output in the 3.7–7.6 μm Spectral Range" *Sensors* 16, no. 4: 533.
https://doi.org/10.3390/s16040533