- Email: [email protected]
Design considerations for efficient planar-optical systems
Optics Communications 267 (2006) 74–78 www.elsevier.com/locate/optcom
Design considerations for efficient planar-optical systems Martin Amberg *, Stefen Sinzinger Technical University of Ilmenau, P.O. Box 10 05 65, 98684 Ilmenau, Germany Received 16 February 2005; received in revised form 2 June 2006; accepted 3 June 2006
Abstract Planar integrated free-space optics is well suited for various applications, e.g., in telecommunication, optical interconnects and security application. However the overall efficiency of purely diffractive systems is low, i.e., in the range of a few percent. We show that it is possible to raise the efficiency significantly by integration of refractive optical elements (prisms, wedges) for coupling into the substrate. In this case, the systems design is particularly challenging. We compare the impact of different coupling mechanisms on the optical designs of integrated 4f-imaging systems. 2006 Elsevier B.V. All rights reserved. Keywords: Integrated-free-space optics; Microoptics; Diffractive optics; Off-the-shelf refractive elements
1. State of art: planar integrated free space optics Planar integrated free space optics [1] combines the advantages of free space optics and the precise alignment possibilities of planar fabrication technology. The concept is to fold the optical system into a thick glass substrate. Optical elements, either diffractive or refractive ones, are integrated on the surfaces of the substrate. The light travels between the reflection-coated surfaces of the substrate on a zigzag path. It was shown by different authors that these optical systems, e.g., applied in optical interconnections, relay systems and security applications, can be optimised to have good optical properties [2–7]. Diffractive optical elements are well suited for the implementation of planar-optical systems since they provide large design flexibility. Their most important disadvantage is the trade off between optical functionality and efficiency. To illustrate this efficiency problem we base our considerations on the parameters of a system reported previously [3] especially the 4f-imaging part with two optimised lenses with a numerical apertures NA = 0.148 of the whole integrated system. Assuming a minimum feature size of 1 lm, these *
Corresponding author. Tel.: +49 3677 691806; fax: +49 3677 691281. E-mail address: [email protected] (M. Amberg).
0030-4018/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2006.06.041
lenses could be implemented as four phase level elements. This results in a theoretical scalar efficiency of 81% for each of the lenses. The scalar efficiency of gratings, necessary for coupling into the substrate, is about 41% because only a two-phase level structure can achieve sufficiently large deflection angles [12]. Just coupling in and out of the substrate leads to a loss of nearly 84%. These are maximum for the diffraction efficiencies estimated from scalar theory. Any more rigorous calculation which becomes necessary because of the small feature sizes will yield lower efficiencies. Nevertheless the scalar values may be sufficient for our comparative study. Ultra high resolution e-beam lithography can be applied to implement efficient diffractive profiles. Here however we adopt the concept of the hybrid integration of refractive off-the-shelf coupling prisms as a less expansive alternative to raise the overall efficiency of the system [8]. The future prospective is the integration of such refractive optical elements through ultra precision micromachining. In this contribution we investigate the influence of the coupling mechanism on the optical quality of the system. In Section 2 we introduce various coupling concepts and in Section 3 we show the influence of the different coupling mechanisms on the optical imaging properties of the planar-optical systems. Section 4 concludes the paper.
M. Amberg, S. Sinzinger / Optics Communications 267 (2006) 74–78
2. Coupling mechanisms Within this paper we compare three different coupling mechanisms: grating-, wedge- and a combined wedge–grating coupling. Fig. 1 shows the setups with the different coupling techniques. The diffractive lenses (DL 1, DL 2, DL 3) are optimised for imaging along the folded optical axis according to the calculations in [9]. The phase-profile of the lenses is described by a parabolic ellipsoid with the parameters a1x2 and a2y2 in both coordinate axes, respectively. In order to minimize the astigmatism generated by the oblique incidence of the beam onto the lenses, the parameters a1 and a2 are different in both coordinate axes. The lenses are optimised for ideal performance in a strict 4fgeometry. In combination with coupling gratings in a 4f-setup, using two identical lenses, a strict 1:1 imaging is the consequence. It is therefore well suited for the implementation of integrated planar-optical systems with high resolution. Using wedges for coupling leads to a violation of the pure 4f-geometry since the object and image planes are located above the substrate surfaces and the optical path length for object points varies with the y-coordinate. This leads to a deterioration of the imaging quality. For our calculations the object planes and image planes are assumed parallel to the substrate surface and the distance to the substrate surface is minimized. The coordinate systems origin (x, y) = (0, 0) is located in the middle of the objectplane. In order to determine the systems quality we evaluate
a
75
the spot diagrams of the images of object points located at (x, y) = (1 mm, 1 mm) (1 mm, 0 mm) (1 mm, 1 mm) (0 mm, 1 mm) (0 mm, 0 mm) (0 mm, 1 mm) (1 mm, 1 mm) (1 mm, 0 mm) and (1 mm, 1 mm) which results in an image field size of 2 · 2 mm2. In Section 3.2 we show the design of a grating coupled 4fsystem as known from the literature. In the systems, shown in Sections 3.2 and 3.3, wedges are used for coupling. However in Section 3.3 an additional four phase level grating is integrated to minimize the necessary wedge angle. For a better comparison of the impact of the different coupling techniques we perform all calculations for the same substrate thickness d = 12 mm, coupling angle a = 11.77, numerical aperture NA = 0.05 of the object space, object-field-size (a square field 2 · 2 mm2), the same magnification (b 0 = 1) and design wavelength k = 633 nm. We assume the parameters of all systems to be identical in order to show the influence of the different coupling mechanisms on the optical design. Within this paper the focus is on design considerations. The fabrication of the systems is of minor importance. Up to now most PIFSO systems have been fabricated by RIE etching the diffractive elements into the glass substrate after generating the structures by mask lithography and development of the resist e.g., binary structures for multi level elements or analog profiles generated by grey-scale lithography [15]. Here we look on the application of off-the-shelf elements due to their good optical quality. Alternative fabrication techniques like ultra precision micro machining eventually will help to fabricate fully integrated planar optical systems incorporating refractive elements. 3. Influence of coupling mechanisms on optical system design 3.1. Grating coupling
b
c
Fig. 1. Coupling mechanisms: (a) grating- (b) wedge- and (c) combined wedge–grating coupling.
Compared to the following system setups the grating coupled system is a real 4f-setup. Thus, just two diffractive lenses (DL 1 and DL 2) are needed for good imaging properties of the whole object field. Standard for planar integrated free space optics is to use diffraction gratings for coupling the light onto the zigzag path. Depending on the coupling angle fairly small grating periods need to be implemented. Since we assume the fabrication with a minimum feature size of about 1 lm the necessary grating period (K = 2.13 lm) can only be implemented with two phase levels. As shown in Fig. 2 the spot diagrams of the nine object field points are very good. The average size of the point spread function (PSF) for the nine selected object points is 1.5 lm with nearly the same size across the whole image plane starting at 1.2 lm and going up to 1.9 lm at the edges for the ideal system i.e., without taking fabrication tolerances and the diffraction into account. Thus is smaller than the diffraction limited psf (4 lm) and the system shows diffraction limitated performance over the whole image field. The spot diagrams clearly show that the astigmatism is well corrected due to the different focal
76
M. Amberg, S. Sinzinger / Optics Communications 267 (2006) 74–78
through refractive wedges. If the whole deflection of the beam is performed with such wedges we can immediately improve the efficiency to: g ¼ g2wedge g2DL1;DL2 gDL3 g7mirror ¼ 12 0:812 0:95 0:987 ¼ 0:54
Fig. 2. Spot diagram for a grating coupled system with corresponding locations of the object points (e.g. (1, 1) is the location (1 mm, 1 mm) in the object field).
length in x- and y-direction of the diffractive lenses. But due to non paraxial system setup aperture aberration appear. The price for this good imaging quality however is the poor efficiency of the system. Assuming binary implementation of the coupling gratings, four phase level lenses and a 98% [13] reflectivity of the mirror coatings, we can calculated the theoretical efficiency of the system: g ¼ g2grating g2DL1;DL2 g7mirror ¼ 0:4052 0:812 0:987 ¼ 0:093 ð1Þ 3.2. Wedge coupling In order to improve the overall efficiency we now want to investigate systems with the beam coupling is performed
a
ð2Þ
In this case however the systems geometry has changed significantly since the object- and image-planes need to be shifted to planes above the substrate surface. Compared to the grating coupled system the precise distance from the object plane to the first diffractive lens (DL 1) and from the second lens (DL 2) to the image plane cannot be exactly one half of the distance between DL 1 and DL 2. For our optical design we assume wedges made of BK7glass with a refractive index of n = 1.51 at the design wavelength k = 633 nm. This results in a wedge angle of b = 32.83 for the desired coupling angle a = 11.77. In addition to the shift of the object and image planes the optical path length of the light from object points with different positions along the y-axis is varying. According to Figs. 1b and 3b it is obvious that the optical path length for light from object points with lower y-coordinates e.g., object point 1 is smaller since the light travels relatively longer distances in air. An additional reason for different optical path length stems from the different z-locations of refraction. In contrast to object point 1 (OP1) a signal from object point 2 (OP2) in Fig. 3b is travelling a longer way in the wedge before entering the substrate. For the presented setup the optical path length difference DLopt for signals from OP1 and OP2 is about DLopt = 0.6 mm. The optical path length is defined as DL = n Æ l with l being the geometrical path length and n the refractive index. As the signal starting at OP2 has a longer optical path when coupled in as well as when coupled out the optical path length difference is doubled to about 1.2 mm. Optimised ray tracing calculations of the system show strong aberration along the y-axis. If object points at y = 0 are ideally focused we find a positive or negative defocus for object points located at a negative
b
Fig. 3. Ray trace results for wedge coupling (a) spot diagram and (b) optical path length difference for different object points (OP) when coupling with wedges into the system.
M. Amberg, S. Sinzinger / Optics Communications 267 (2006) 74–78
77
y-field coordinates is about 16 lm (Fig. 5b) and therefore nearly one third compared to the purely wedge-coupled system. This illustrates a very good optical quality, which is paid for by a decrease of the overall efficiency (compared to a purely wedge coupled system) which results as: g ¼ g2wedge g2grating g2DL1;DL2 gDL3 g7mirror ¼ 12 0:812 0:812 0:95 0:987 ¼ 0:35
Fig. 4. Possible setup for implementing a parallel object and image plane as suggested in [14] for planar integrated free space optical systems.
or positive y-coordinate. This is supported by the ray-tracing calculations shown in Fig. 3a. This also has consequences on the signal latency which need to be taken into account for optical interconnect applications [10]. This rather poor design quality is already improved by introducing an additional optical element (DL 3) indicated in Fig. 1b [11]. 3.3. Combined wedge–grating coupling As we have seen in the previous section the imaging quality which can be achieved for planar integrated free space optical systems with wedge coupling is not satisfactory. In order to achieve better imaging quality it is necessary to minimize the optical path length differences. This is e.g., possible by using more than one coupling prism, i.e., micro-prism arrays or by reducing the wedge angle of the coupling prism. Our goal is to use cheap components and thus we focus on the latter case. In order to reach the same coupling angle we suggest to combine the wedge with an efficient multilevel diffraction grating. If we assume a grating period of K = 4 lm (four phase level implementation) a wedge angle of b = 15.52 is necessary for the overall coupling angle a = 11.77. The resulting reduction of the optical path length difference leads to a better performance of the optical system. The spot diameter of the object points at the maximum
a
ð3Þ
It is interesting to mention that in addition to the optimised coupling the combination between grating and prism can also be used to achieve performance with reduced wavelength sensitivity. This additional degree of freedom might be interesting for a variety of applications. Critic might come up on the fact that the object and imaged plane are above the substrate surface. Adding an additional glass wafer or metal plate with the height of the prisms on top of the substrate with the diffractive elements (see Fig. 4) it is possible to use e.g., MT connectors for input and output devices [14] in a stacked system. Therefore it is necessary to cut openings for the prisms into the metal plate. 4. Conclusions We demonstrate the influence of wedge coupling on the optical design of planar integrated free space optical systems. For various applications the combination of wedge and grating coupling represents a good alternative. It enables to achieve moderately high efficiency and decent optical quality which cheap optical components additionally it allows one to adjust the coupling angle flexibly without the need of custom made wedges. Table 1 compares the coupling efficiencies and average spot size diameter for the different coupling techniques discussed in this paper. It is Table 1 Comparison of system efficiency and spot size diameter Coupling technique
Efficiency
Minimum spotszie (lm)
Maximum spot size (lm)
Grating Wedge Wedge + grating
0.093 0.56 0.35
1.2 2.2 1.2
1.9 63 16.1
b
Fig. 5. Ray trace results for combined wedge–grating coupling: (a) layout and (b) spot diagram.
78
M. Amberg, S. Sinzinger / Optics Communications 267 (2006) 74–78
interesting to mention that the wedge-coupled system can be optimised for excellent line imaging along the x-axis. Acknowledgements The authors gratefully acknowledge the financial support provided by Deutsche Forschungsgesellschaft (DFG) through the SONS Programme of the European Science Foundation, which is also funded by the European Commission, Sixth Framework Programme. References [1] J. Jahns, A. Huang, Proc. IEEE 82 (1994) 1623. [2] M. Gruber, Planar-integrierte photonische Mikrosysteme zur parallelen optischen Kommunikation in der Informationstechnik von morgen, Logos Verlag, Berlin, 2003.
[3] [4] [5] [6] [7]
[8] [9] [10] [11] [12] [13] [14] [15]
S. Sinzinger, Opt. Commun. 290 (2002) 69. J. Jahns, B. Acklin, Opt. Lett. 18 (1993) 1594. T. Shiono, H. Ogawa, Opt. Lett. 17 (1992) 565. S. Reinhorn, S. Gorodeisky, A.A. Friesem, Y. Amitai, Opt. Lett. 20 (1995) 495. S. Sinzinger, J. Jahns, V.A. Daria, J. Glueckstad, Planar Microoptical Systems for Correlation and Security Applications, in: B. Javidi (Ed.), Optical and Digital Techniques for Information Security, Springer, New York, 2005. M. Amberg, S. Sinzinger, Proc. MOC04-Jena, Germany (2004). M. Testorf, J. Jahns, J. Opt. Soc. Am. A 28 (1997) 1569. A.W. Lohmann, A.S. Marathay, Appl. Opt. 28 (1989) 3838. Q. Cao, M. Gruber, J. Jahns, Appl. Opt. 43 (16) (2004) 3306. G.J. Swanson, W.B. Veldkamp, Opt. Eng. 28 (1989) 605. M. Gruber, T. Seiler, A.-C. Wei, Appl. Opt. 45 (4) (2006) 662. M. Gruber, J. Jahns, E. Joudi, S. Sinzinger, Appl. Opt. 40 (17) (2001) 2902. R. Heming, M. Gruber, J. Jahns, L.-C. Wittig, E.-B. Kley, DGaO Proc. (2005).
Design considerations for efficient planar-optical systems Martin Amberg *, Stefen Sinzinger Technical University of Ilmenau, P.O. Box 10 05 65, 98684 Ilmenau, Germany Received 16 February 2005; received in revised form 2 June 2006; accepted 3 June 2006
Abstract Planar integrated free-space optics is well suited for various applications, e.g., in telecommunication, optical interconnects and security application. However the overall efficiency of purely diffractive systems is low, i.e., in the range of a few percent. We show that it is possible to raise the efficiency significantly by integration of refractive optical elements (prisms, wedges) for coupling into the substrate. In this case, the systems design is particularly challenging. We compare the impact of different coupling mechanisms on the optical designs of integrated 4f-imaging systems. 2006 Elsevier B.V. All rights reserved. Keywords: Integrated-free-space optics; Microoptics; Diffractive optics; Off-the-shelf refractive elements
1. State of art: planar integrated free space optics Planar integrated free space optics [1] combines the advantages of free space optics and the precise alignment possibilities of planar fabrication technology. The concept is to fold the optical system into a thick glass substrate. Optical elements, either diffractive or refractive ones, are integrated on the surfaces of the substrate. The light travels between the reflection-coated surfaces of the substrate on a zigzag path. It was shown by different authors that these optical systems, e.g., applied in optical interconnections, relay systems and security applications, can be optimised to have good optical properties [2–7]. Diffractive optical elements are well suited for the implementation of planar-optical systems since they provide large design flexibility. Their most important disadvantage is the trade off between optical functionality and efficiency. To illustrate this efficiency problem we base our considerations on the parameters of a system reported previously [3] especially the 4f-imaging part with two optimised lenses with a numerical apertures NA = 0.148 of the whole integrated system. Assuming a minimum feature size of 1 lm, these *
Corresponding author. Tel.: +49 3677 691806; fax: +49 3677 691281. E-mail address: [email protected] (M. Amberg).
0030-4018/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2006.06.041
lenses could be implemented as four phase level elements. This results in a theoretical scalar efficiency of 81% for each of the lenses. The scalar efficiency of gratings, necessary for coupling into the substrate, is about 41% because only a two-phase level structure can achieve sufficiently large deflection angles [12]. Just coupling in and out of the substrate leads to a loss of nearly 84%. These are maximum for the diffraction efficiencies estimated from scalar theory. Any more rigorous calculation which becomes necessary because of the small feature sizes will yield lower efficiencies. Nevertheless the scalar values may be sufficient for our comparative study. Ultra high resolution e-beam lithography can be applied to implement efficient diffractive profiles. Here however we adopt the concept of the hybrid integration of refractive off-the-shelf coupling prisms as a less expansive alternative to raise the overall efficiency of the system [8]. The future prospective is the integration of such refractive optical elements through ultra precision micromachining. In this contribution we investigate the influence of the coupling mechanism on the optical quality of the system. In Section 2 we introduce various coupling concepts and in Section 3 we show the influence of the different coupling mechanisms on the optical imaging properties of the planar-optical systems. Section 4 concludes the paper.
M. Amberg, S. Sinzinger / Optics Communications 267 (2006) 74–78
2. Coupling mechanisms Within this paper we compare three different coupling mechanisms: grating-, wedge- and a combined wedge–grating coupling. Fig. 1 shows the setups with the different coupling techniques. The diffractive lenses (DL 1, DL 2, DL 3) are optimised for imaging along the folded optical axis according to the calculations in [9]. The phase-profile of the lenses is described by a parabolic ellipsoid with the parameters a1x2 and a2y2 in both coordinate axes, respectively. In order to minimize the astigmatism generated by the oblique incidence of the beam onto the lenses, the parameters a1 and a2 are different in both coordinate axes. The lenses are optimised for ideal performance in a strict 4fgeometry. In combination with coupling gratings in a 4f-setup, using two identical lenses, a strict 1:1 imaging is the consequence. It is therefore well suited for the implementation of integrated planar-optical systems with high resolution. Using wedges for coupling leads to a violation of the pure 4f-geometry since the object and image planes are located above the substrate surfaces and the optical path length for object points varies with the y-coordinate. This leads to a deterioration of the imaging quality. For our calculations the object planes and image planes are assumed parallel to the substrate surface and the distance to the substrate surface is minimized. The coordinate systems origin (x, y) = (0, 0) is located in the middle of the objectplane. In order to determine the systems quality we evaluate
a
75
the spot diagrams of the images of object points located at (x, y) = (1 mm, 1 mm) (1 mm, 0 mm) (1 mm, 1 mm) (0 mm, 1 mm) (0 mm, 0 mm) (0 mm, 1 mm) (1 mm, 1 mm) (1 mm, 0 mm) and (1 mm, 1 mm) which results in an image field size of 2 · 2 mm2. In Section 3.2 we show the design of a grating coupled 4fsystem as known from the literature. In the systems, shown in Sections 3.2 and 3.3, wedges are used for coupling. However in Section 3.3 an additional four phase level grating is integrated to minimize the necessary wedge angle. For a better comparison of the impact of the different coupling techniques we perform all calculations for the same substrate thickness d = 12 mm, coupling angle a = 11.77, numerical aperture NA = 0.05 of the object space, object-field-size (a square field 2 · 2 mm2), the same magnification (b 0 = 1) and design wavelength k = 633 nm. We assume the parameters of all systems to be identical in order to show the influence of the different coupling mechanisms on the optical design. Within this paper the focus is on design considerations. The fabrication of the systems is of minor importance. Up to now most PIFSO systems have been fabricated by RIE etching the diffractive elements into the glass substrate after generating the structures by mask lithography and development of the resist e.g., binary structures for multi level elements or analog profiles generated by grey-scale lithography [15]. Here we look on the application of off-the-shelf elements due to their good optical quality. Alternative fabrication techniques like ultra precision micro machining eventually will help to fabricate fully integrated planar optical systems incorporating refractive elements. 3. Influence of coupling mechanisms on optical system design 3.1. Grating coupling
b
c
Fig. 1. Coupling mechanisms: (a) grating- (b) wedge- and (c) combined wedge–grating coupling.
Compared to the following system setups the grating coupled system is a real 4f-setup. Thus, just two diffractive lenses (DL 1 and DL 2) are needed for good imaging properties of the whole object field. Standard for planar integrated free space optics is to use diffraction gratings for coupling the light onto the zigzag path. Depending on the coupling angle fairly small grating periods need to be implemented. Since we assume the fabrication with a minimum feature size of about 1 lm the necessary grating period (K = 2.13 lm) can only be implemented with two phase levels. As shown in Fig. 2 the spot diagrams of the nine object field points are very good. The average size of the point spread function (PSF) for the nine selected object points is 1.5 lm with nearly the same size across the whole image plane starting at 1.2 lm and going up to 1.9 lm at the edges for the ideal system i.e., without taking fabrication tolerances and the diffraction into account. Thus is smaller than the diffraction limited psf (4 lm) and the system shows diffraction limitated performance over the whole image field. The spot diagrams clearly show that the astigmatism is well corrected due to the different focal
76
M. Amberg, S. Sinzinger / Optics Communications 267 (2006) 74–78
through refractive wedges. If the whole deflection of the beam is performed with such wedges we can immediately improve the efficiency to: g ¼ g2wedge g2DL1;DL2 gDL3 g7mirror ¼ 12 0:812 0:95 0:987 ¼ 0:54
Fig. 2. Spot diagram for a grating coupled system with corresponding locations of the object points (e.g. (1, 1) is the location (1 mm, 1 mm) in the object field).
length in x- and y-direction of the diffractive lenses. But due to non paraxial system setup aperture aberration appear. The price for this good imaging quality however is the poor efficiency of the system. Assuming binary implementation of the coupling gratings, four phase level lenses and a 98% [13] reflectivity of the mirror coatings, we can calculated the theoretical efficiency of the system: g ¼ g2grating g2DL1;DL2 g7mirror ¼ 0:4052 0:812 0:987 ¼ 0:093 ð1Þ 3.2. Wedge coupling In order to improve the overall efficiency we now want to investigate systems with the beam coupling is performed
a
ð2Þ
In this case however the systems geometry has changed significantly since the object- and image-planes need to be shifted to planes above the substrate surface. Compared to the grating coupled system the precise distance from the object plane to the first diffractive lens (DL 1) and from the second lens (DL 2) to the image plane cannot be exactly one half of the distance between DL 1 and DL 2. For our optical design we assume wedges made of BK7glass with a refractive index of n = 1.51 at the design wavelength k = 633 nm. This results in a wedge angle of b = 32.83 for the desired coupling angle a = 11.77. In addition to the shift of the object and image planes the optical path length of the light from object points with different positions along the y-axis is varying. According to Figs. 1b and 3b it is obvious that the optical path length for light from object points with lower y-coordinates e.g., object point 1 is smaller since the light travels relatively longer distances in air. An additional reason for different optical path length stems from the different z-locations of refraction. In contrast to object point 1 (OP1) a signal from object point 2 (OP2) in Fig. 3b is travelling a longer way in the wedge before entering the substrate. For the presented setup the optical path length difference DLopt for signals from OP1 and OP2 is about DLopt = 0.6 mm. The optical path length is defined as DL = n Æ l with l being the geometrical path length and n the refractive index. As the signal starting at OP2 has a longer optical path when coupled in as well as when coupled out the optical path length difference is doubled to about 1.2 mm. Optimised ray tracing calculations of the system show strong aberration along the y-axis. If object points at y = 0 are ideally focused we find a positive or negative defocus for object points located at a negative
b
Fig. 3. Ray trace results for wedge coupling (a) spot diagram and (b) optical path length difference for different object points (OP) when coupling with wedges into the system.
M. Amberg, S. Sinzinger / Optics Communications 267 (2006) 74–78
77
y-field coordinates is about 16 lm (Fig. 5b) and therefore nearly one third compared to the purely wedge-coupled system. This illustrates a very good optical quality, which is paid for by a decrease of the overall efficiency (compared to a purely wedge coupled system) which results as: g ¼ g2wedge g2grating g2DL1;DL2 gDL3 g7mirror ¼ 12 0:812 0:812 0:95 0:987 ¼ 0:35
Fig. 4. Possible setup for implementing a parallel object and image plane as suggested in [14] for planar integrated free space optical systems.
or positive y-coordinate. This is supported by the ray-tracing calculations shown in Fig. 3a. This also has consequences on the signal latency which need to be taken into account for optical interconnect applications [10]. This rather poor design quality is already improved by introducing an additional optical element (DL 3) indicated in Fig. 1b [11]. 3.3. Combined wedge–grating coupling As we have seen in the previous section the imaging quality which can be achieved for planar integrated free space optical systems with wedge coupling is not satisfactory. In order to achieve better imaging quality it is necessary to minimize the optical path length differences. This is e.g., possible by using more than one coupling prism, i.e., micro-prism arrays or by reducing the wedge angle of the coupling prism. Our goal is to use cheap components and thus we focus on the latter case. In order to reach the same coupling angle we suggest to combine the wedge with an efficient multilevel diffraction grating. If we assume a grating period of K = 4 lm (four phase level implementation) a wedge angle of b = 15.52 is necessary for the overall coupling angle a = 11.77. The resulting reduction of the optical path length difference leads to a better performance of the optical system. The spot diameter of the object points at the maximum
a
ð3Þ
It is interesting to mention that in addition to the optimised coupling the combination between grating and prism can also be used to achieve performance with reduced wavelength sensitivity. This additional degree of freedom might be interesting for a variety of applications. Critic might come up on the fact that the object and imaged plane are above the substrate surface. Adding an additional glass wafer or metal plate with the height of the prisms on top of the substrate with the diffractive elements (see Fig. 4) it is possible to use e.g., MT connectors for input and output devices [14] in a stacked system. Therefore it is necessary to cut openings for the prisms into the metal plate. 4. Conclusions We demonstrate the influence of wedge coupling on the optical design of planar integrated free space optical systems. For various applications the combination of wedge and grating coupling represents a good alternative. It enables to achieve moderately high efficiency and decent optical quality which cheap optical components additionally it allows one to adjust the coupling angle flexibly without the need of custom made wedges. Table 1 compares the coupling efficiencies and average spot size diameter for the different coupling techniques discussed in this paper. It is Table 1 Comparison of system efficiency and spot size diameter Coupling technique
Efficiency
Minimum spotszie (lm)
Maximum spot size (lm)
Grating Wedge Wedge + grating
0.093 0.56 0.35
1.2 2.2 1.2
1.9 63 16.1
b
Fig. 5. Ray trace results for combined wedge–grating coupling: (a) layout and (b) spot diagram.
78
M. Amberg, S. Sinzinger / Optics Communications 267 (2006) 74–78
interesting to mention that the wedge-coupled system can be optimised for excellent line imaging along the x-axis. Acknowledgements The authors gratefully acknowledge the financial support provided by Deutsche Forschungsgesellschaft (DFG) through the SONS Programme of the European Science Foundation, which is also funded by the European Commission, Sixth Framework Programme. References [1] J. Jahns, A. Huang, Proc. IEEE 82 (1994) 1623. [2] M. Gruber, Planar-integrierte photonische Mikrosysteme zur parallelen optischen Kommunikation in der Informationstechnik von morgen, Logos Verlag, Berlin, 2003.
[3] [4] [5] [6] [7]
[8] [9] [10] [11] [12] [13] [14] [15]
S. Sinzinger, Opt. Commun. 290 (2002) 69. J. Jahns, B. Acklin, Opt. Lett. 18 (1993) 1594. T. Shiono, H. Ogawa, Opt. Lett. 17 (1992) 565. S. Reinhorn, S. Gorodeisky, A.A. Friesem, Y. Amitai, Opt. Lett. 20 (1995) 495. S. Sinzinger, J. Jahns, V.A. Daria, J. Glueckstad, Planar Microoptical Systems for Correlation and Security Applications, in: B. Javidi (Ed.), Optical and Digital Techniques for Information Security, Springer, New York, 2005. M. Amberg, S. Sinzinger, Proc. MOC04-Jena, Germany (2004). M. Testorf, J. Jahns, J. Opt. Soc. Am. A 28 (1997) 1569. A.W. Lohmann, A.S. Marathay, Appl. Opt. 28 (1989) 3838. Q. Cao, M. Gruber, J. Jahns, Appl. Opt. 43 (16) (2004) 3306. G.J. Swanson, W.B. Veldkamp, Opt. Eng. 28 (1989) 605. M. Gruber, T. Seiler, A.-C. Wei, Appl. Opt. 45 (4) (2006) 662. M. Gruber, J. Jahns, E. Joudi, S. Sinzinger, Appl. Opt. 40 (17) (2001) 2902. R. Heming, M. Gruber, J. Jahns, L.-C. Wittig, E.-B. Kley, DGaO Proc. (2005).