Open Access
Add to BibSonomy
Abstract
We present a generalized method for designing a novel circular multi-pass cell (MPC) with multifold overall optical path length, or alternatively enlarged path-to-volume ratio in the same magnification compared to traditional version, by exploiting the vertical dimension of cavity mirrors. Multiple rows of reflection spots can be generated on arbitrary number of different horizontal planes within the cell that consists of two easy-fabricating circular spherical mirrors. Base on this method, one can arbitrarily determine the interval of reflection spots in both horizontal and vertical directions, so that almost seamless and regular distributed dense spot pattern, and consequently large path-to-volume ratio can be achieved. A series of q-preserving configurations of the multiple-row circular multi-pass cell are calculated and simulated, in which the q-parameters of probe Gaussian beams can be approximately unchanged after the whole transmission within the cells. The maximum optical path length among these simulation cases is 201.8 m within 427.2 mL volume. Furthermore, we demonstrate a practical optical setup with 21.9 m optical path length within 100.1 mL, which is the smallest volume case among the existing actual MPCs with similar overall optical path lengths.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Multi-pass cells (MPCs) are the key device of the trace gas absorption spectroscopy detection systems. MPC can provide long optical path length (OPL) that improve the absorption signal-to-noise ratio of extremely low gas concentrations or weak absorption line strengths within compact volumes. Circular multi-pass cell (CMPC) was first presented by Chernin [1,2], consists of only one circular mirror, and possesses distinct advantage that the overall height is extremely low. Variations that entrance and exit beams share the same hole were presented subsequently [3–5], and enabled the OPL of CMPC to be adjusted by changing incident angle of entrance beam. Furthermore, CMPCs that implemented with toroidal [6–8] and paraboloid [9] circular mirrors were presented to form concentric configurations that probe beams could be more stable throughout the propagation inside the MPC. More recently, we proposed a new version of CMPC that consists of two identical spherical circular mirrors [10]. Two rows of spots pattern are formed on different horizontal planes, so that the OPL of the CMPC are double. Moreover, extreme stable Gaussian-beam-propagation can be achieved by parameter optimization, that the q-parameters can stay unchanged after the whole intracavity transmission [11].
The conception of q-preserving configuration was first presented by Ozharar and Sennaroglu, which means in that kind of MPC configurations, the q-parameters of entrance and exit Gaussian beams could remain the same [13]. Then we presented a quantitative method for seeking q-preserving configurations of various MPCs, by calculating Frobenius norm (F-norm) of the difference between 4×4 transfer matrixes and identity matrix [11]. Based on this quantitative criterion, we found optimal q-preserving structures of FO-MMS and double-row CMPC (DR-CMPC) by parameter optimization, with the matrix deviation of 0.0047 and 0.0051, while the corresponding total OPLs are 33.6 m and 67.8 m, respectively.
In this work, a new version of CMPC is proposed for the first time, which consists of two spherical circular mirrors with identical radii of curvature, and multiple horizontal rows of spots can be generated on the internal surfaces of the mirrors. The two mirrors are piled up vertically and share the same axis of rotational symmetry. N (an arbitrary integer greater than 2) rows of regular star polygon spot patterns (both patterns are the same as the patterns in traditional CMPC) are formed on different horizontal planes within the MPC, respectively. Therefore, we can achieve multifold OPL compared to traditional circular cell, or multifold PVR by reducing radii of curvatures to 1/N, while OPL does not change. The horizontal distance between adjacent spots within the same row and the vertical distance between adjacent rows can be arbitrary predefined by parametric design, therefore almost seamless spots pattern can be achieved. Several design examples are demonstrated, and the maximum OPL among the cases is 201.8 m within 427.2 mL, while the minimum volume is 100.1 mL, in which 21.9 m OPL are achieved. Furthermore, a practical experiment setup and spot pattern of the 21.9 m, 100.1 mL case are demonstrated. The entrance and exit holes are spatially separated to avoid overlap of the pre- and post-transfer optics. The OPL can be readily adjusted by rotating one of the mirrors around the axis of rotational symmetry, similar as in [10]. The long OPL, remarkable PVR, readily adjustment, stable beam transmission and low cost suggest promising prospects of CMPC in versatile applications, such as gas-phase optical delay lines [12,13], gas/liquid absorption spectroscopy [7,9], and nonlinear pulse compression [14–16].
2. Conception and parametric design of MR-CMPC
The optical setup of a multi-row circular multi-pass cell (MR-CMPC) consists of two circular spherical mirrors, M1 and M2, with same radii of curvature, while the heights and the position of sphere centers are different, as shown in Figs. 1(a) and 1(b). The optical configuration of MR-CMPC can be defined by the parameters set of (N, R, p, q, c, φ), where N is an arbitrary integer (>2), and indicate the number of spots-pattern-rows; R, p and q, similar to the cases in traditional CMPC, are radii of curvature of spherical mirrors, number of edges of the regular star polygon patterns, and number of segments that the corresponding arc of one side is divided by other vertexes [6,10]; p and q should be relative prime integers, besides q = q0 and q = p-q0 indicate the same regular star polygon pattern, so that we can predetermine that q < p/2; parameter c determine the intervals between two rows of reflection spots, which is about 4c; in traditional CMPC, incident angle θ0 can be determined by p and q, as [6]:
while in MR-CMPC, when R, p, q and c are predefined, the incident angle θ can be determined by multiplying a correction factor, κ, based on similar second-order approximate analytical trace in [10], as:
Fig. 1. The optical configuration of MR-CMPC when (a) N is an even number; (b) N is an odd number. Two samples of reflection sequences, with parameters of (c) N = 4, p = 14, q = 5; (d) N = 3, p = 14, q = 5. The brown circles represent the positions of reflection spots, while the number on them represent the sequences of appearance. For the clarity, the height of each circular mirror are dramatically exaggerated.
The positions of spherical centers are important for determining the number and interval of reflection-spot-rows. In the right-hand space rectangular coordinate system in Figs. 1(a) and 1(b), the horizontal plane that incident beam lies on is x-O-z plane, and both centers of sphere are all at y-axis, which is the axis of rotational symmetry of both spherical reflection surfaces. The distance between spherical center of M1, PC1, and x-O-z plane equals to parameter c. The position of PC1 is above/below x-O-z plane when the number of rows, N, is even/odd, as shown in Figs. 1(a) and 1(b), so that the coordinate of PC1 is (0, (−1)N·c, 0). The distance between center of sphere of M2, PC2, and x-O-z plane can be expressed as:
3. Q-preserving configurations of MR-CMPC
Q-preserving configurations, as its name implies, means that the q-parameters of entrance and exit Gaussian beams could remain the same within this kind of configurations of MPCs. The quantitative criterion to distinguish the q-preserving configuration is the deviation between the overall 4×4 transfer matrix of the MPC and identity matrix [11]. This deviation can be defined as the F-norm of the difference between the two matrixes, as [11]:
Fig. 2. With the change of parameter c, the deviations between the transfer matrixes of MR-CMPCs and identity matrix (a) while N = 3, (p, q) = (146, 71), (170, 83) and (194, 95); (b) while N = 4, (p, q) = (146, 71), (170, 83) and (194, 95); (c) N = 5, (p, q) = (162, 79), (182, 89) and (202, 99)
The minimum deviations of each parameter set are also obtained, as shown in Table 1. One can see from Table 1 that all of the zO are very close to R, which is in good agreement with theoretical expectation above. For N = 3, the minimum deviation is 0.0510, corresponding to the parameter set of R = 100mm, p = 170, q = 83, c = 1.883 mm, zO=99.868 mm, the overall transfer matrix is:
Table 1. The minimum deviations of each set of parameter after optimization
For N = 4, the minimum deviation is 0.0857, corresponding to the parameter set of R = 100mm, p = 194, q = 95, c = 0.918 mm, zO=99.813 mm, the overall transfer matrix is:
For N = 5, the minimum deviation is 0.0744, corresponding to the parameter set of R = 100mm, p = 202, q = 99, c = 0.859 mm, zO=100.024 mm, the overall transfer matrix is:
From Eqs. (11)∼(13), one can see that all of the transfer matrixes are very close to fourth order identity matrix, which means extremely stable Gaussian-beam-passes are achieved in these MR-CMPC configurations with long overall OPL and small volume.
4. Simulation and experiment
Based on the analysis and discussion above, we make optical path simulations of MR-CMPC samples with parameters in Table 1, by ray tracing software TracePro, as show in Fig. 3. The diameter of light source is set to be 2 mm, which is common for laser source in practical use. The incident focal length is set to be 200 mm, and the initial focus point of the incident beam is set to the position 100 mm (=R) apart from the entrance point on the mirror surface. Furthermore, the parameters φ of each configuration are set to be (Nπ–2Nθ), so that maximum overall OPLs are achieved for each configuration. To make it clear that the spot sizes and beam propagation within the cell, three views and OPL plot of the simulation example in Fig. 3(i) are demonstrated in Figs. 4(a)–4(d). We can see that multi-rows of reflection spots appear uniformly at designated positions on the circular mirrors, and the size of spots do not increase significantly, in Figs. 4(a)–4(c). There is only a sharp peak at about 201.8 m, which is the predesigned OPL, in OPL plot in Fig. 4(d), while the number of rays corresponding to other OPL are all zero, which means none of rays exit the cell prematurely.
Fig. 3. Optical path simulations of MR-CMPC samples with parameters of R = 100 mm, (a) N = 3, p = 146, q = 71, c = 2.201 mm, and φ=350.162°; (b) N = 3, p = 170, q = 83, c = 1.883 mm, and φ=351.545°; (c) N = 3, p = 194, q = 95, c = 1.641 mm, and φ=352.588°; (d) N = 4, p = 146, q = 71, c = 1.262 mm, and φ=165.222°; (e) N = 4, p = 170, q = 83, c = 1.063 mm, and φ=167.300°; (f) N = 4, p = 194, q = 95, c = 0.918 mm, and φ=168.868°; (g) N = 5, p = 162, q = 79, c = 1.109 mm, and φ=342.252°; (h) N = 5, p = 182, q = 89, c = 0.967 mm, and φ=344.208°; (i) N = 5, p = 202, q = 99, c = 0.859 mm, and φ=345.772°.
Fig. 4. Three views and OPL plot of MR-CMPC with parameters of N = 5, R = 100 mm, p = 202, q = 99, c = 0.859 mm, and φ=345.772°. (a) Front view; (b) Side view; (c) Top view; (d) OPL plot at a dummy surface near the exit aperture, generated by TracePro.
With comprehensive consideration of the overall OPL and volume, we make a design with parameter sets of N = 3, R = 50 mm, p = 74, q = 35, c = 1.5 mm, φ=340.632°. The simulation of the design and the practical optical setup are shown in Figs. 5(a) and 5(b), respectively. The fabrication and coating approaches of MR-CMPC are similar with traditional circular multi-pass cell. The spherical circular mirrors are fabricated by diamond turned (wuhan leiya optoelectronics technology co., ltd). Metal dielectric enhanced reflective films are coated on internal surfaces of circular mirrors (wuhan leiya optoelectronics technology co., ltd). The structure of the film layer is metal gold and multilayer medium consists of YF3 and ZnSe materials, which can improve the reflectivity of the corresponding band of multilayer medium around 660 nm (reflectivity > 98.5%), while broad high reflectivity band of metal in IR are generally reserved (reflectivity >95% in 2 µm∼20 µm). The coating can be changed to fulfill various requirements of high reflectivity wavelength band. The actual optical path is visualized by a 660nm-diode laser (MLL-III-660L-180mW, Changchun New Industries Optoelectronics Tech. Co., Ltd, ∼1 mm output spot diameter and the angle of divergence is smaller than 2 mrad) through a MR-CMPC. The order of appearance of spots is in good agreement with the design scenario: the spots appearing at regular intervals in the horizontal direction and switch back and forth in vertical direction.
Fig. 5. (a) Optical simulation of the design with parameter sets of N = 3, R = 50 mm, p = 74, q = 35, c = 1.5 mm, φ=340.632°; (b) The actual optical setup and folded beam path, visualized by aerating smog. A rotating view of the entire circular cell can be seen in Visualization 1.
For suppressing the interference of stray light, we mount an absorption mask inside the MPC, similar as in [8]. In Fig. 5(b), the first several folded beams are clearly visible, and all of the through-holes on the mask (corresponding to designated positions of reflection spots on the circular mirrors) are illuminated, which means the laser beam experience the entire predefined 220-time-folded path. The overall OPL of this design is 21.9 m, while the minimum aerating volume is 100.1 mL.
5. Conclusion
The concept of MR-CMPC is proposed for the first time, which consists of two circular spherical mirrors with the same radii of curvature. The two mirrors are piled up vertically and share the same axis of rotational symmetry. As its name implies, there are multiple-rows of reflection spots appearing on N (>2) horizontal planes on the circular mirrors. Consequently, N times of overall OPL can be achieved compare to traditional circular cell, or alternatively, multifold PVR can be obtained by reducing radii of curvatures to 1/N. Both the horizontal and vertical distances of reflection spots can be arbitrary predefined by changing parameters, such as R, p and c. And when these two distances are approximately equal to the size of spots, which means almost seamless spot patterns, and extreme large PVR can be achieved within the MR-CPMCs. Furthermore, the overall OPL can be readily adjusted by rotating one of the spherical mirror around the axis of rotational symmetry, with a rough angular precision. Several design and simulation examples of q-preserving configurations are also demonstrated, 201.8 m maximum OPL can be achieved within volume of 427.2 mL, which means extremely long OPL and stable Gaussian-beam-pass can be achieved simultaneously within the MPCs that consist of inexpensive and easy-fabricating spherical reflection surfaces. Moreover, an actual experiment setup and spot pattern of the 21.9 m, 100.1 mL case is demonstrated.
Funding
National Key Scientific Instrument and Equipment Development Projects of China (2018YFF0109600).
References
1. S. M. Chernin, “Multipass systems of new generation in high-resolution spectroscopy for fundamental and applied atmosphere investigations,” Proc. SPIE 2366, 408–418 (1995). [CrossRef]
2. S. M. Chernin, “New generation of multipass systems in high resolution spectroscopy,” Spectrochim. Acta, Part A 52(8), 1009–1022 (1996). [CrossRef]
3. J. Riedel, S. Yan, H. Kawamata, and K. Liu, “A simple yet effective multipass reflector for vibrational excitation in molecular beams,” Rev. Sci. Instrum. 79(3), 033105 (2008). [CrossRef]
4. B. E. Bernacki, Multipass Optical device and process for gas and analyte determination. U.S. Patent 7876443 (25 January 2011).
5. A. Manninen, B. Tuzson, H. Looser, Y. Bonetti, and L. Emmenegger, “Versatile multipass cell for laser spectroscopic trace gas analysis,” Appl. Phys. B: Lasers Opt. 109(3), 461–466 (2012). [CrossRef]
6. B. Tuzson, M. Mangold, H. Looser, A. Manninen, and L. Emmenegger, “Compact multipass optical cell for laser spectroscopy,” Opt. Lett. 38(3), 257–259 (2013). [CrossRef]
7. P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014). [CrossRef]
8. M. Graf, H. Looser, L. Emmenegger, and B. Tuzson, “Beam folding analysis and optimization of mask-enhanced toroidal multipass cells,” Opt. Lett. 42(16), 3137–3140 (2017). [CrossRef]
9. M. Markus, B. Tuzson, M. Hundt, J. Jágerská, H. Looser, and L. Emmenegger, “Circular paraboloid reflection cell for laser spectroscopic trace gas analysis,” J. Opt. Soc. Am. A 33(5), 913–919 (2016). [CrossRef]
10. Z. Yang, Y. Guo, X. Ming, and L. Sun, “Generalized optical design of the Double-row circular multi-pass cell,” Sensors 18(8), 2680 (2018). [CrossRef]
11. Z. Yang, M. Zou, and L. Sun, “Generalized method for seeking q-preserving configurations of multi-pass cells,” Opt. Express 27(10), 14054–14063 (2019). [CrossRef]
13. D. Herriott, H. Kogelnik, and R. Kompfner, “Off-axis paths in spherical mirror interferometers,” Appl. Opt. 3(4), 523–526 (1964). [CrossRef]
14. D. R. Herriott and H. J. Schulte, “Folded optical delay lines,” Appl. Opt. 4(8), 883–889 (1965). [CrossRef]
15. J. Schulte, T. Sartorius, J. Weitenberg, A. Vernaleken, and P. Russbueldt, “Nonlinear pulse compression in a multi-pass cell,” Opt. Lett. 41(19), 4511–4514 (2016). [CrossRef]
16. M. Ueffing, S. Reiger, M. Kaumanns, V. Pervak, M. Trubetskov, T. Nubbemeyer, and F. Krausz, “Nonlinear pulse compression in a gas-filled multipass cell,” Opt. Lett. 43(9), 2070–2073 (2018). [CrossRef]
17. L. Lavenu, M. Natile, F. Guichard, Y. Zaouter, X. Delen, M. Hanna, E. Mottay, and P. Georges, “Nonlinear pulse compression based on a gas-filled multipass cell,” Opt. Lett. 43(10), 2252–2255 (2018). [CrossRef]
