Beam shaping system based on a prism array for improving the throughput of a dispersive spectrometer Zhendong Shi,1,2 Liang Fang,1 Bin Fan,1 and Chongxi Zhou1,* 1
State Key Laboratory of Optical Technologies for Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Science, Chengdu 610209, China 2
University of the Chinese Academy of Sciences, Beijing 100049, China *Corresponding author: [email protected]
Received 9 December 2014; revised 14 February 2015; accepted 17 February 2015; posted 19 February 2015 (Doc. ID 229475); published 25 March 2015
A beam shaping system (BSS) for improving the throughput of a dispersive spectrometer is presented by employing two anamorphic lenses and a prism array to segment the beam. The BSS was designed based on the inverse method of beam shaping for laser diode bars and the means of an optical slicer. In an experiment, a BSS was set up so that the incident light of a neon lamp with a circular spot from an input fiber was transformed into an elliptical spot coupled into a slit of a spectrometer without a change of divergence. Spectral measurement results demonstrate that the throughput of the dispersive spectrometer was doubled without loss of spectral resolution. The BSS can be combined with the existing dispersive spectrometer to improve the luminous flux and signal-to-noise ratio. © 2015 Optical Society of America OCIS codes: (230.5480) Prisms; (140.3300) Laser beam shaping; (120.4820) Optical systems; (120.6200) Spectrometers and spectroscopic instrumentation. http://dx.doi.org/10.1364/AO.54.002715
1. Introduction
In designs of dispersive spectrometers [1,2], a narrow slit that can improve the spectral resolution results in loss of light, so the spectral resolution of the conventional spectrometer in the detection of weak signals is limited to some extent. A slicer technique is effective to achieve high spectral resolution with maximal throughput [1,3–9]. The image slicer that divides up and rearranges the image is utilized to reduce the loss of light at the slit of the stellar spectrograph for astronomical observation by Bowen [4]. The Bowen–Walraven imaging slicer [7] operates on an identical principle, but the mirror array is replaced by the integration of a parallel plate and a 1559-128X/15/102715-05$15.00/0 © 2015 Optical Society of America
wedge-cut prism, and the strips are tilted along the cross-dispersion direction. Since the image slicing above is performed close to the telescope focal plane, the slicing components need to be tiny, and it is harder to implement due to the high precision and alignment required. An alternate method is to perform the beam slicing in the collimated space of the spectrometer, in order to produce the effect of a virtual slit [1,6]. Although the slicers can be manufactured in large size, the beam transformation also depends on many pieces of separated mirrors, resulting in difficulty in adjustment and assembly. In addition, the slicer technique is also employed in beam shaping for high-power laser diode (LD) bars [10–16]. A serious asymmetry output beam from the LD in the orthogonal directions is transformed into a symmetrical beam, to be coupled into a multimode fiber [11,15,16]. 1 April 2015 / Vol. 54, No. 10 / APPLIED OPTICS
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Based on the inverse method of beam shaping from the LD and the means of an optical slicer, a beam shaping system (BSS) consisting of two anamorphic lenses and a prism array is introduced to improve the throughput of the dispersive spectrometer. The prism array performs segmentation of the beam. The reflections between the separated mirrors [4,8,9] is replaced by total internal reflections on two orthogonal 45 deg hypotenuses in the subprism, and the prism array structure located in the collimated space of the BSS. The BSS transforms the circular beam from the input fiber into an elliptic beam without a change in divergence. Although the conventional method by just employing an anamorphic lens can also change the shape of the beam, the divergence will be larger in the minor axis of the resulting elliptical beam, which may cause additional stray light inside the spectrometer and fail to improve the energy utilization. The conventional method can reduce the beam divergence and help improve the beam quality in the major axis. In general, this conventional method cannot maintain uniform beam divergence in the minor and major axes of the elliptical beam. Since conventional optics is circular, the beam should be optimized for uniform beam divergence. By using the BSS, an elliptical beam with uniform divergence can be created to match standard optics within the spectrometer. In this paper, the principle of the BSS is presented, and it is verified experimentally that the BSS is an effective way to improve the throughput at the slit by calculating the ratio of the light energy in the slit and the total light energy. Further, the BSS was connected with a dispersive spectrometer to verify that the energy utilization ratio was increased by two times on average with the same spectral resolution. The BSS as a miniature and modular unit independent of the dispersive spectrometer was compatible with the dispersive spectrometer with slit and fiber access, and combined with them to improve the luminous flux and signal-to-noise ratio.
2. Designs A. Device Concept
The layout of the BSS is shown in Fig. 1(a). An incident light from the optical fiber end face is collimated by cylindrical Lens1 and Lens2 in the vertical and horizontal directions separately. After passing through the prism array, segmentation of the beam and rotation of the subbeam are achieved. Then the rearranged beam is focused by cylindrical Lens3 and Lens4 in the horizontal and vertical directions to realize an elliptic spot with the same divergence as that of the incident spot. The inset of Fig. 1(a) describes the structure and function of the prism array. The height (H) and width (N × W) of the prism array are roughly equal to the lengths of the minor and major axes of the collimated elliptical beam, respectively, where the N, H, and W are the number, height, and width of the subprism, respectively. Each subprism has two 45 deg inclinations perpendicular to each other. By total internal reflection of two inclined surfaces, the optical axis of the collimated elliptical beam is rotated 90 deg, and each subbeam is rotated 90 deg around its propagation direction. The input and output of the prism array remain the same size approximately, but the half-divergences in the horizontal and vertical directions are exchanged. The BSS could be combined with the dispersive spectrometer with slit and fiber access as shown in Fig. 1(b). Without the BSS, after the beam from the fiber passes through the slit, most of the energy is lost. However, by adding the BSS before the slit, the circular spot at the optical fiber end face is transformed into the elliptic spot without a change of divergence. The elliptic spot aligns to the slit of the spectrometer, and the energy can pass easily through the slit. It is noted that the consistency of the divergence of the incident and exit spot is very important for strict limits of the numerical aperture (N.A) of the input fiber connected with the spectrometer. If the divergence of the incident beam is greater than
Fig. 1. (a) Schematic diagram of the beam transformation of the BSS. The prism array achieves the segmentation of the beam and the rotation of the subbeam as shown in the inset. N, H, and W are the number, height, and width of the subprism, respectively. (b) Schematic diagram of the spot passing through the slit with and without the use of the BSS, respectively. (c) Critical incident angles of the total internal reflection in BK7 glass for different wavelengths. 2716
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the divergence of the input fiber (corresponding to its N.A), the size of the beam is larger than the size of the optical element and the energy exceeding the aperture of the optical element cannot be utilized and becomes the stray light of the spectrometer. It prevents the improvement of energy utilization. As a result, it is an inappropriate way to reduce merely the size of the spot by a single cylindrical lens, because the divergence increases in spite of the decrease of the size of the spot. Figure 1(c) shows the critical incident angles with different wavelengths when total internal reflection occurs in BK7 glass [17]. The 45 deg incident angle is greater than the arbitrary critical incident angle within the wavelength range from 0.4 to 1.4 μm, as indicated by the red dotted line, which indicates that a wide spectral band satisfying total internal reflection can be obtained. B.
Design Principle
To improve the throughput of the dispersive spectrometer, the BSS is required to change the circular spot to the elliptic spot and maintain uniform beam divergence of the incident and exit spot. Based on geometrical optics, the beam parameter products (BPPs) [12,14,15] in the vertical (BPPC-V ) and horizontal (BPPC-H ) directions are constant in the collimating (C) section, respectively:
BPPC-V D0 θ0 ∕2 D1 θ1 ∕2 ; BPPC-H D0 θ0 ∕2 D2 θ2 ∕2
D1 2f 1 θ0 : D2 2f 2 θ0
θ1 D0 ∕2f 1 : θ2 D0 ∕2f 2
BPPP-V 1∕N × D2 ∕2 × θ2 1∕N × BPPC-V : BPPP-H N × D1 ∕2 × θ1 N × BPPC-H 4
As seen from Eqs. (1) and (4), the prism array modifies the BPPs in the vertical and horizontal directions. BPPP-V is changed to 1∕N of the BPPC-V of incident spot from the fiber, and BPPP-H is N times BPPC-H . In the focusing (F) section, the BPPs in the orthogonal directions are also constant, respectively:
BPPF-V D2 θ2 ∕2N DW θW ∕2 ; BPPF-H ND1 θ1 ∕2 DL θL ∕2
2
3
According to Eq. (3), the collimating effect of the incident beam depends on the focal length of the cylindrical lens (f 1 < f 2 , θ1 > θ2 ). In the prism (P) array section shown in the inset of Fig. 1, the prism array performs segmentation of the beam and rotation of the subbeam, which exchanges the half-divergence between the vertical (θ1 → θ2 ) and horizontal (θ2 → θ1 ) directions for the input and output of the prism array. The size of its output in the
5
where DW , DL and θW , θL represent the width and length and the corresponding half-divergence of the elliptical spot in the focusing plane. DL and DW are deduced approximately:
1
where the f 1 and f 2 represent the focal lengths of cylindrical Lens1 and Lens2. From Eqs. (1) and (2), θ1 and θ2 can be expressed as
where the D0 and θ0 represent the diameter and the half-divergence of the optical fiber, and D1 , D2 and θ1 , θ2 represent the beam diameters and the corresponding half-divergences in the direction of the minor and major axes of the collimated elliptical beam. All the parameters of the BSS are shown in Fig. 1(a). The beam sizes of D1 and D2 are determined approximately by the focal length of the cylindrical lens f and the half-divergence θ:
vertical direction is 1∕N of the beam size of its input in the horizontal direction, and the size of its output in the horizontal direction is N times larger than that of its input in the vertical direction, where N is the number of the subprism. Therefore, the BPPs of its output in the vertical (BPPP-V ) and horizontal (BPPP-H ) directions are
DL 2f 3 θ1 ; DW 2f 4 θ2
6
where f 3 and f 4 are the focal lengths of cylindrical Lens3 and Lens4. From Eqs. (1), (5), and (6), we have
θL f 1 Nθ0 ∕f 3 : θW f 2 θ0 ∕Nf 4
7
To make the half-divergences of the incident and exit spots uniform (θW θ0 , θL θ0 ), the ratio of the focal lengths f and the subprism number N must meet
N f 3 ∕f 1 : N f 2 ∕f 4
8
In other words, the ratio of the focal lengths of the corresponding cylindrical lens matches the subprism number to maintain the same divergence. Finally, by Eqs. (3), (6), (7), and (8), the parameters of the elliptic spot at the focal plane are as follows:
θL θ0 ; DL ND0 : θW θ0 ; DW D0 ∕N
9
Based on the constant BPP in the corresponding direction of the focusing section, and the condition of the same exit divergence as the incident one (θW θL θ0 ), the size in the vertical direction of the exit spot is changed to 1∕N of the size of the 1 April 2015 / Vol. 54, No. 10 / APPLIED OPTICS
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incident spot. Conversely, the size in the horizontal direction of the exit spot is N times larger than that of the incident spot. In short, the prism array changes the shape of the focal spot by modifying the BPPs in the vertical and horizontal directions. 3. Experiments
To demonstrate the beam transformation by the BSS and verify the improvement of the energy utilization of the incident light for the dispersive spectrometer, a BSS was set up as shown in Fig. 2(a). The light source was a spectral calibration neon lamp (AvalightCAL) produced by Avantes, Inc. The neon lamp
Fig. 2. (a) Experiment setup of the BSS. The details of the prism array are shown in the inset. Plane A, optical fiber end face; plane B, input plane of the prism array; plane C, output plane of the prism array; plane D, focal plane. (b) Intensity profile at plane B. (c) Intensity profile at plane C.
was attached to an optical fiber with a diameter of 200 μm and a N.A of 0.22. The beam from the optical fiber end face was collimated by cylindrical Lens1 and Lens2 with focal lengths of 10 and 40 mm in the vertical and horizontal directions. The prism array consists of four subprisms with the height (H) of 4.4 mm and width (W) of 4.4 mm, as shown in the inset of Fig. 2(a). Finally, the beam passing through the prism array was focused by focusing cylindrical Lens3 and Lens4 with focal lengths of 40 and 10 mm in the horizontal and vertical directions, which have the same parameters as cylindrical Lens2 and Lens1, respectively, in order to decrease the production cost of the cylindrical lens. The beam transformation process of the prism array was observed by a Mintron CCD camera. The energy distribution of the collimated beam at plane B is shown in Fig. 2(b). The lengths of the major and minor axes were approximately 17.2 mm × 4.4 mm. At plane C, the collimated beam passing through the prism array was divided into four subbeams, and each subbeam was rotated 90 deg, as shown in Fig. 2(c). In Fig. 3(a), the circular energy distribution at the optical fiber end face [plane A in Fig. 2(a)] is shown, and through the BSS, the elliptic energy distribution is obtained in the focal plane [plane D in Fig. 2(a)], as shown in Fig. 3(b). Intensity profiles were observed and measured by a Beam Diagnostics Digital CMOS Camera (Lasercam) from Coherent, Inc. The increase of energy transmittance by the BSS was verified by calculating the ratio of the light energy in the slit and the total light energy. The ratio of the light energy (Eslit ) between the two dotted lines with the distance of 50 μm and the total energy (Etotal ) as shown in Fig. 3 was regarded as the energy transmittance (η) of the 50 μm slit: η
Fig. 3. Two-dimensional intensity profiles at (a) plane A and (b) plane D shown in Fig. 2(a). Two dotted lines with the distance of 50 μm represent the slit.
Eslit × 100%: Etotal
(10)
The calculated results of the energy transmittance were 71% and 34% with and without adding the BSS, respectively. The ratio between the two
Fig. 4. (a) Schematic diagram of the combination of the spectrometer and the BSS. OAP, 60 deg off-axis parabolic reflector. (b) Spectral intensity with and without the use of the BSS. 2718
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calculated energy transmittances above was 2.09; thereby the change of the intensity profile of the light spot by the beam transformation made energy concentrated in the slit and enhanced the energy utilization. Due to the degradation of the focusing image on account of the aberrations of the cylindrical lenses, the sizes of the spot were a little more than those of 800 μm × 50 μm calculated by Eq. (9). Moreover, it can be expected that if the aberration were eliminated further, the energy transmittance would be improved further. In addition, we further demonstrated the improvement of the energy utilization of a grating spectrometer combined with the BSS by measuring the intensity of the spectrum. The spectrometer includes an entrance slit with a width of 50 μm, a 60 deg offaxis parabolic reflector (OAP) with an effective focal length of 33.85 mm, a grating period of 1200 lines/ mm, a focusing achromatic lens with an effective focal length of 50 mm, and a charge-coupled device (CCD) (Toshiba TCD1304AP). The shaped elliptic spot can be regarded as the incident light source of the grating spectrometer. In Fig. 4(b), the spectral intensity of the neon lamp without the use of the BSS is shown by the black solid curve, and the spectral intensity through the BSS with the same spectral resolution [full width at half-maximum (FWHM)] is shown by the red dashed curve. By detecting the peak intensities of six wavelengths of 841.8 nm, 849.5 nm, etc., in the near-infrared region, the average ratio of spectral intensity with and without the use of the BSS was 2.06. The experimental energy utilization ratio agreed approximately with the calculated one in Fig. 3, which indirectly demonstrated that there was no obvious change of the divergence angle after passing through the BSS. 4. Conclusions
A novel method using a prism array to perform beam transformation in the BSS is proposed to improve the energy utilization of the incident light for the dispersive spectrometer. The experiment demonstrates that the energy utilization by the BSS was double that of directly using a fiber and the same spectral resolution was retained in conditions of adding the BSS or not. The BSS as a modular unit independent of the spectrometer was compatible with the various existing dispersive spectrometers, and combined with them to improve the luminous flux and the signal-to-noise ratio. For this method, with the increase of the number of prisms, the beam size in the minor axis of an elliptic beam will proportionately decrease. Moreover, the smaller the slit width, the more the room for improvement in throughput by the BSS. However, as the beam size in the minor axis becomes smaller, it puts forward a higher requirement for the beam collimation and focusing and
the alignment of the prism array. In addition, beam shaping based on the prism array could also be an effective way to optimize divergence for the LD to improve the beam quality. The authors are grateful to the National Program for Significant Scientific Instruments Development of China (2011YQ03012407), the National Natural Science Foundation of China (No. 61308064), and the National Basic Research Program of China (973 Program) (No. 2014CB744204). Thanks to Libo Zhong for valuable discussions. References 1. J. T. Meade, B. B. Behr, and A. R. Hajian, “A new highresolution, high-throughput spectrometer: first experience as applied to Raman spectroscopy,” Proc. SPIE 8374, 83740V (2012). 2. Z. Shi, L. Fang, and C. Zhou, “Dispersive element based on grating and tunable Fabry–Perot filter in miniature spectrometer,” Appl. Opt. 53, 76–81 (2014). 3. N. Hagen and M. W. Kudenov, “Review of snapshot spectral imaging technologies,” Opt. Eng. 52, 090901 (2013). 4. I. Bowen, “The image-slicer, a device for reducing loss of light at slit of stellar spectrograph,” Astrophys. J. 88, 113–124 (1938). 5. F. Diego, “Confocal image slicer,” Appl. Opt. 32, 6284–6287 (1993). 6. J. T. Meade, A. R. Hajian, and A. T. Cenko, “Optical slicer for improving the spectral resolution of a dispersive spectrograph,” U.S. patent 8,384,896 (26 Feb. 2013). 7. T. Walraven and J. Walraven, “Some features of the Leiden radial velocity instrument,” in Proc. ESO/CERN Conference on Auxiliary Instrumentation for Large Telescopes (1972), pp. 175–183. 8. R. Content, “A new design for integral field spectroscopy with 8-m telescopes,” Proc. SPIE 2871, 1295–1305 (1997). 9. R. Content, “Image slicer for integral field spectroscopy with NGST,” Proc. SPIE 3356, 122–133 (1998). 10. Z. Huang, L. Xiong, H. Liu, Z. Wang, P. Zhang, Z. Nie, D. Wu, and X. Liu, “Double-cutting beam shaping technique for highpower diode laser area light source,” Opt. Eng. 52, 106108 (2013). 11. S. H. Ghasemi, M.-R. Hantehzadeh, J. Sabbaghzadeh, D. Dorranian, M. Lafooti, V. Vatani, R. Rezaei-Nasirabad, A. Hemmati, A. A. Amidian, and S. A. Alavian, “Beam shaping design for coupling high power diode laser stack to fiber,” Appl. Opt. 50, 2927–2930 (2011). 12. Y. Lutz and J. Poyet, “Laser diode stack beam shaping for efficient and compact long-range laser illuminator design,” Opt. Laser Technol. 57, 90–95 (2014). 13. S. Yamaguchi, T. Kobayashi, Y. Saito, and K. Chiba, “Collimation of emissions from a high-power multistripe laser-diode bar with multiprism array coupling and focusing to a small spot,” Opt. Lett. 20, 898–900 (1995). 14. G. Zheng, C. Du, C. Zhou, and C. Zheng, “Laser diode stack beam shaping by reflective two-wedge-angle prism arrays,” Opt. Eng. 44, 044203 (2005). 15. Y. Liao, K. Du, S. Falter, J. Zhang, M. Quade, P. Loosen, and R. Poprawe, “Highly efficient diode-stack, end-pumped Nd:YAG slab laser with symmetrized beam quality,” Appl. Opt. 36, 5872–5875 (1997). 16. W. Clarkson and D. Hanna, “Two-mirror beam-shaping technique for high-power diode bars,” Opt. Lett. 21, 375–377 (1996). 17. M. Wakaki, T. Shibuya, and K. Kudo, Physical Properties and Data of Optical Materials (CRC Press, 2010).
1 April 2015 / Vol. 54, No. 10 / APPLIED OPTICS
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State Key Laboratory of Optical Technologies for Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Science, Chengdu 610209, China 2
University of the Chinese Academy of Sciences, Beijing 100049, China *Corresponding author: [email protected]
Received 9 December 2014; revised 14 February 2015; accepted 17 February 2015; posted 19 February 2015 (Doc. ID 229475); published 25 March 2015
A beam shaping system (BSS) for improving the throughput of a dispersive spectrometer is presented by employing two anamorphic lenses and a prism array to segment the beam. The BSS was designed based on the inverse method of beam shaping for laser diode bars and the means of an optical slicer. In an experiment, a BSS was set up so that the incident light of a neon lamp with a circular spot from an input fiber was transformed into an elliptical spot coupled into a slit of a spectrometer without a change of divergence. Spectral measurement results demonstrate that the throughput of the dispersive spectrometer was doubled without loss of spectral resolution. The BSS can be combined with the existing dispersive spectrometer to improve the luminous flux and signal-to-noise ratio. © 2015 Optical Society of America OCIS codes: (230.5480) Prisms; (140.3300) Laser beam shaping; (120.4820) Optical systems; (120.6200) Spectrometers and spectroscopic instrumentation. http://dx.doi.org/10.1364/AO.54.002715
1. Introduction
In designs of dispersive spectrometers [1,2], a narrow slit that can improve the spectral resolution results in loss of light, so the spectral resolution of the conventional spectrometer in the detection of weak signals is limited to some extent. A slicer technique is effective to achieve high spectral resolution with maximal throughput [1,3–9]. The image slicer that divides up and rearranges the image is utilized to reduce the loss of light at the slit of the stellar spectrograph for astronomical observation by Bowen [4]. The Bowen–Walraven imaging slicer [7] operates on an identical principle, but the mirror array is replaced by the integration of a parallel plate and a 1559-128X/15/102715-05$15.00/0 © 2015 Optical Society of America
wedge-cut prism, and the strips are tilted along the cross-dispersion direction. Since the image slicing above is performed close to the telescope focal plane, the slicing components need to be tiny, and it is harder to implement due to the high precision and alignment required. An alternate method is to perform the beam slicing in the collimated space of the spectrometer, in order to produce the effect of a virtual slit [1,6]. Although the slicers can be manufactured in large size, the beam transformation also depends on many pieces of separated mirrors, resulting in difficulty in adjustment and assembly. In addition, the slicer technique is also employed in beam shaping for high-power laser diode (LD) bars [10–16]. A serious asymmetry output beam from the LD in the orthogonal directions is transformed into a symmetrical beam, to be coupled into a multimode fiber [11,15,16]. 1 April 2015 / Vol. 54, No. 10 / APPLIED OPTICS
2715
Based on the inverse method of beam shaping from the LD and the means of an optical slicer, a beam shaping system (BSS) consisting of two anamorphic lenses and a prism array is introduced to improve the throughput of the dispersive spectrometer. The prism array performs segmentation of the beam. The reflections between the separated mirrors [4,8,9] is replaced by total internal reflections on two orthogonal 45 deg hypotenuses in the subprism, and the prism array structure located in the collimated space of the BSS. The BSS transforms the circular beam from the input fiber into an elliptic beam without a change in divergence. Although the conventional method by just employing an anamorphic lens can also change the shape of the beam, the divergence will be larger in the minor axis of the resulting elliptical beam, which may cause additional stray light inside the spectrometer and fail to improve the energy utilization. The conventional method can reduce the beam divergence and help improve the beam quality in the major axis. In general, this conventional method cannot maintain uniform beam divergence in the minor and major axes of the elliptical beam. Since conventional optics is circular, the beam should be optimized for uniform beam divergence. By using the BSS, an elliptical beam with uniform divergence can be created to match standard optics within the spectrometer. In this paper, the principle of the BSS is presented, and it is verified experimentally that the BSS is an effective way to improve the throughput at the slit by calculating the ratio of the light energy in the slit and the total light energy. Further, the BSS was connected with a dispersive spectrometer to verify that the energy utilization ratio was increased by two times on average with the same spectral resolution. The BSS as a miniature and modular unit independent of the dispersive spectrometer was compatible with the dispersive spectrometer with slit and fiber access, and combined with them to improve the luminous flux and signal-to-noise ratio.
2. Designs A. Device Concept
The layout of the BSS is shown in Fig. 1(a). An incident light from the optical fiber end face is collimated by cylindrical Lens1 and Lens2 in the vertical and horizontal directions separately. After passing through the prism array, segmentation of the beam and rotation of the subbeam are achieved. Then the rearranged beam is focused by cylindrical Lens3 and Lens4 in the horizontal and vertical directions to realize an elliptic spot with the same divergence as that of the incident spot. The inset of Fig. 1(a) describes the structure and function of the prism array. The height (H) and width (N × W) of the prism array are roughly equal to the lengths of the minor and major axes of the collimated elliptical beam, respectively, where the N, H, and W are the number, height, and width of the subprism, respectively. Each subprism has two 45 deg inclinations perpendicular to each other. By total internal reflection of two inclined surfaces, the optical axis of the collimated elliptical beam is rotated 90 deg, and each subbeam is rotated 90 deg around its propagation direction. The input and output of the prism array remain the same size approximately, but the half-divergences in the horizontal and vertical directions are exchanged. The BSS could be combined with the dispersive spectrometer with slit and fiber access as shown in Fig. 1(b). Without the BSS, after the beam from the fiber passes through the slit, most of the energy is lost. However, by adding the BSS before the slit, the circular spot at the optical fiber end face is transformed into the elliptic spot without a change of divergence. The elliptic spot aligns to the slit of the spectrometer, and the energy can pass easily through the slit. It is noted that the consistency of the divergence of the incident and exit spot is very important for strict limits of the numerical aperture (N.A) of the input fiber connected with the spectrometer. If the divergence of the incident beam is greater than
Fig. 1. (a) Schematic diagram of the beam transformation of the BSS. The prism array achieves the segmentation of the beam and the rotation of the subbeam as shown in the inset. N, H, and W are the number, height, and width of the subprism, respectively. (b) Schematic diagram of the spot passing through the slit with and without the use of the BSS, respectively. (c) Critical incident angles of the total internal reflection in BK7 glass for different wavelengths. 2716
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the divergence of the input fiber (corresponding to its N.A), the size of the beam is larger than the size of the optical element and the energy exceeding the aperture of the optical element cannot be utilized and becomes the stray light of the spectrometer. It prevents the improvement of energy utilization. As a result, it is an inappropriate way to reduce merely the size of the spot by a single cylindrical lens, because the divergence increases in spite of the decrease of the size of the spot. Figure 1(c) shows the critical incident angles with different wavelengths when total internal reflection occurs in BK7 glass [17]. The 45 deg incident angle is greater than the arbitrary critical incident angle within the wavelength range from 0.4 to 1.4 μm, as indicated by the red dotted line, which indicates that a wide spectral band satisfying total internal reflection can be obtained. B.
Design Principle
To improve the throughput of the dispersive spectrometer, the BSS is required to change the circular spot to the elliptic spot and maintain uniform beam divergence of the incident and exit spot. Based on geometrical optics, the beam parameter products (BPPs) [12,14,15] in the vertical (BPPC-V ) and horizontal (BPPC-H ) directions are constant in the collimating (C) section, respectively:
BPPC-V D0 θ0 ∕2 D1 θ1 ∕2 ; BPPC-H D0 θ0 ∕2 D2 θ2 ∕2
D1 2f 1 θ0 : D2 2f 2 θ0
θ1 D0 ∕2f 1 : θ2 D0 ∕2f 2
BPPP-V 1∕N × D2 ∕2 × θ2 1∕N × BPPC-V : BPPP-H N × D1 ∕2 × θ1 N × BPPC-H 4
As seen from Eqs. (1) and (4), the prism array modifies the BPPs in the vertical and horizontal directions. BPPP-V is changed to 1∕N of the BPPC-V of incident spot from the fiber, and BPPP-H is N times BPPC-H . In the focusing (F) section, the BPPs in the orthogonal directions are also constant, respectively:
BPPF-V D2 θ2 ∕2N DW θW ∕2 ; BPPF-H ND1 θ1 ∕2 DL θL ∕2
2
3
According to Eq. (3), the collimating effect of the incident beam depends on the focal length of the cylindrical lens (f 1 < f 2 , θ1 > θ2 ). In the prism (P) array section shown in the inset of Fig. 1, the prism array performs segmentation of the beam and rotation of the subbeam, which exchanges the half-divergence between the vertical (θ1 → θ2 ) and horizontal (θ2 → θ1 ) directions for the input and output of the prism array. The size of its output in the
5
where DW , DL and θW , θL represent the width and length and the corresponding half-divergence of the elliptical spot in the focusing plane. DL and DW are deduced approximately:
1
where the f 1 and f 2 represent the focal lengths of cylindrical Lens1 and Lens2. From Eqs. (1) and (2), θ1 and θ2 can be expressed as
where the D0 and θ0 represent the diameter and the half-divergence of the optical fiber, and D1 , D2 and θ1 , θ2 represent the beam diameters and the corresponding half-divergences in the direction of the minor and major axes of the collimated elliptical beam. All the parameters of the BSS are shown in Fig. 1(a). The beam sizes of D1 and D2 are determined approximately by the focal length of the cylindrical lens f and the half-divergence θ:
vertical direction is 1∕N of the beam size of its input in the horizontal direction, and the size of its output in the horizontal direction is N times larger than that of its input in the vertical direction, where N is the number of the subprism. Therefore, the BPPs of its output in the vertical (BPPP-V ) and horizontal (BPPP-H ) directions are
DL 2f 3 θ1 ; DW 2f 4 θ2
6
where f 3 and f 4 are the focal lengths of cylindrical Lens3 and Lens4. From Eqs. (1), (5), and (6), we have
θL f 1 Nθ0 ∕f 3 : θW f 2 θ0 ∕Nf 4
7
To make the half-divergences of the incident and exit spots uniform (θW θ0 , θL θ0 ), the ratio of the focal lengths f and the subprism number N must meet
N f 3 ∕f 1 : N f 2 ∕f 4
8
In other words, the ratio of the focal lengths of the corresponding cylindrical lens matches the subprism number to maintain the same divergence. Finally, by Eqs. (3), (6), (7), and (8), the parameters of the elliptic spot at the focal plane are as follows:
θL θ0 ; DL ND0 : θW θ0 ; DW D0 ∕N
9
Based on the constant BPP in the corresponding direction of the focusing section, and the condition of the same exit divergence as the incident one (θW θL θ0 ), the size in the vertical direction of the exit spot is changed to 1∕N of the size of the 1 April 2015 / Vol. 54, No. 10 / APPLIED OPTICS
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incident spot. Conversely, the size in the horizontal direction of the exit spot is N times larger than that of the incident spot. In short, the prism array changes the shape of the focal spot by modifying the BPPs in the vertical and horizontal directions. 3. Experiments
To demonstrate the beam transformation by the BSS and verify the improvement of the energy utilization of the incident light for the dispersive spectrometer, a BSS was set up as shown in Fig. 2(a). The light source was a spectral calibration neon lamp (AvalightCAL) produced by Avantes, Inc. The neon lamp
Fig. 2. (a) Experiment setup of the BSS. The details of the prism array are shown in the inset. Plane A, optical fiber end face; plane B, input plane of the prism array; plane C, output plane of the prism array; plane D, focal plane. (b) Intensity profile at plane B. (c) Intensity profile at plane C.
was attached to an optical fiber with a diameter of 200 μm and a N.A of 0.22. The beam from the optical fiber end face was collimated by cylindrical Lens1 and Lens2 with focal lengths of 10 and 40 mm in the vertical and horizontal directions. The prism array consists of four subprisms with the height (H) of 4.4 mm and width (W) of 4.4 mm, as shown in the inset of Fig. 2(a). Finally, the beam passing through the prism array was focused by focusing cylindrical Lens3 and Lens4 with focal lengths of 40 and 10 mm in the horizontal and vertical directions, which have the same parameters as cylindrical Lens2 and Lens1, respectively, in order to decrease the production cost of the cylindrical lens. The beam transformation process of the prism array was observed by a Mintron CCD camera. The energy distribution of the collimated beam at plane B is shown in Fig. 2(b). The lengths of the major and minor axes were approximately 17.2 mm × 4.4 mm. At plane C, the collimated beam passing through the prism array was divided into four subbeams, and each subbeam was rotated 90 deg, as shown in Fig. 2(c). In Fig. 3(a), the circular energy distribution at the optical fiber end face [plane A in Fig. 2(a)] is shown, and through the BSS, the elliptic energy distribution is obtained in the focal plane [plane D in Fig. 2(a)], as shown in Fig. 3(b). Intensity profiles were observed and measured by a Beam Diagnostics Digital CMOS Camera (Lasercam) from Coherent, Inc. The increase of energy transmittance by the BSS was verified by calculating the ratio of the light energy in the slit and the total light energy. The ratio of the light energy (Eslit ) between the two dotted lines with the distance of 50 μm and the total energy (Etotal ) as shown in Fig. 3 was regarded as the energy transmittance (η) of the 50 μm slit: η
Fig. 3. Two-dimensional intensity profiles at (a) plane A and (b) plane D shown in Fig. 2(a). Two dotted lines with the distance of 50 μm represent the slit.
Eslit × 100%: Etotal
(10)
The calculated results of the energy transmittance were 71% and 34% with and without adding the BSS, respectively. The ratio between the two
Fig. 4. (a) Schematic diagram of the combination of the spectrometer and the BSS. OAP, 60 deg off-axis parabolic reflector. (b) Spectral intensity with and without the use of the BSS. 2718
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calculated energy transmittances above was 2.09; thereby the change of the intensity profile of the light spot by the beam transformation made energy concentrated in the slit and enhanced the energy utilization. Due to the degradation of the focusing image on account of the aberrations of the cylindrical lenses, the sizes of the spot were a little more than those of 800 μm × 50 μm calculated by Eq. (9). Moreover, it can be expected that if the aberration were eliminated further, the energy transmittance would be improved further. In addition, we further demonstrated the improvement of the energy utilization of a grating spectrometer combined with the BSS by measuring the intensity of the spectrum. The spectrometer includes an entrance slit with a width of 50 μm, a 60 deg offaxis parabolic reflector (OAP) with an effective focal length of 33.85 mm, a grating period of 1200 lines/ mm, a focusing achromatic lens with an effective focal length of 50 mm, and a charge-coupled device (CCD) (Toshiba TCD1304AP). The shaped elliptic spot can be regarded as the incident light source of the grating spectrometer. In Fig. 4(b), the spectral intensity of the neon lamp without the use of the BSS is shown by the black solid curve, and the spectral intensity through the BSS with the same spectral resolution [full width at half-maximum (FWHM)] is shown by the red dashed curve. By detecting the peak intensities of six wavelengths of 841.8 nm, 849.5 nm, etc., in the near-infrared region, the average ratio of spectral intensity with and without the use of the BSS was 2.06. The experimental energy utilization ratio agreed approximately with the calculated one in Fig. 3, which indirectly demonstrated that there was no obvious change of the divergence angle after passing through the BSS. 4. Conclusions
A novel method using a prism array to perform beam transformation in the BSS is proposed to improve the energy utilization of the incident light for the dispersive spectrometer. The experiment demonstrates that the energy utilization by the BSS was double that of directly using a fiber and the same spectral resolution was retained in conditions of adding the BSS or not. The BSS as a modular unit independent of the spectrometer was compatible with the various existing dispersive spectrometers, and combined with them to improve the luminous flux and the signal-to-noise ratio. For this method, with the increase of the number of prisms, the beam size in the minor axis of an elliptic beam will proportionately decrease. Moreover, the smaller the slit width, the more the room for improvement in throughput by the BSS. However, as the beam size in the minor axis becomes smaller, it puts forward a higher requirement for the beam collimation and focusing and
the alignment of the prism array. In addition, beam shaping based on the prism array could also be an effective way to optimize divergence for the LD to improve the beam quality. The authors are grateful to the National Program for Significant Scientific Instruments Development of China (2011YQ03012407), the National Natural Science Foundation of China (No. 61308064), and the National Basic Research Program of China (973 Program) (No. 2014CB744204). Thanks to Libo Zhong for valuable discussions. References 1. J. T. Meade, B. B. Behr, and A. R. Hajian, “A new highresolution, high-throughput spectrometer: first experience as applied to Raman spectroscopy,” Proc. SPIE 8374, 83740V (2012). 2. Z. Shi, L. Fang, and C. Zhou, “Dispersive element based on grating and tunable Fabry–Perot filter in miniature spectrometer,” Appl. Opt. 53, 76–81 (2014). 3. N. Hagen and M. W. Kudenov, “Review of snapshot spectral imaging technologies,” Opt. Eng. 52, 090901 (2013). 4. I. Bowen, “The image-slicer, a device for reducing loss of light at slit of stellar spectrograph,” Astrophys. J. 88, 113–124 (1938). 5. F. Diego, “Confocal image slicer,” Appl. Opt. 32, 6284–6287 (1993). 6. J. T. Meade, A. R. Hajian, and A. T. Cenko, “Optical slicer for improving the spectral resolution of a dispersive spectrograph,” U.S. patent 8,384,896 (26 Feb. 2013). 7. T. Walraven and J. Walraven, “Some features of the Leiden radial velocity instrument,” in Proc. ESO/CERN Conference on Auxiliary Instrumentation for Large Telescopes (1972), pp. 175–183. 8. R. Content, “A new design for integral field spectroscopy with 8-m telescopes,” Proc. SPIE 2871, 1295–1305 (1997). 9. R. Content, “Image slicer for integral field spectroscopy with NGST,” Proc. SPIE 3356, 122–133 (1998). 10. Z. Huang, L. Xiong, H. Liu, Z. Wang, P. Zhang, Z. Nie, D. Wu, and X. Liu, “Double-cutting beam shaping technique for highpower diode laser area light source,” Opt. Eng. 52, 106108 (2013). 11. S. H. Ghasemi, M.-R. Hantehzadeh, J. Sabbaghzadeh, D. Dorranian, M. Lafooti, V. Vatani, R. Rezaei-Nasirabad, A. Hemmati, A. A. Amidian, and S. A. Alavian, “Beam shaping design for coupling high power diode laser stack to fiber,” Appl. Opt. 50, 2927–2930 (2011). 12. Y. Lutz and J. Poyet, “Laser diode stack beam shaping for efficient and compact long-range laser illuminator design,” Opt. Laser Technol. 57, 90–95 (2014). 13. S. Yamaguchi, T. Kobayashi, Y. Saito, and K. Chiba, “Collimation of emissions from a high-power multistripe laser-diode bar with multiprism array coupling and focusing to a small spot,” Opt. Lett. 20, 898–900 (1995). 14. G. Zheng, C. Du, C. Zhou, and C. Zheng, “Laser diode stack beam shaping by reflective two-wedge-angle prism arrays,” Opt. Eng. 44, 044203 (2005). 15. Y. Liao, K. Du, S. Falter, J. Zhang, M. Quade, P. Loosen, and R. Poprawe, “Highly efficient diode-stack, end-pumped Nd:YAG slab laser with symmetrized beam quality,” Appl. Opt. 36, 5872–5875 (1997). 16. W. Clarkson and D. Hanna, “Two-mirror beam-shaping technique for high-power diode bars,” Opt. Lett. 21, 375–377 (1996). 17. M. Wakaki, T. Shibuya, and K. Kudo, Physical Properties and Data of Optical Materials (CRC Press, 2010).
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