Angular bandpass filters based on dielectric resonant waveguide gratings

doi:10.1364/OE.20.022555

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Angular bandpass filters based on dielectric resonant waveguide gratings

Stefan Steiner, Stefanie Kroker, Thomas Käsebier, Ernst-Bernhard Kley, and Andreas Tünnermann »View Author Affiliations

Optics Express, Vol. 20, Issue 20, pp. 22555-22562 (2012)
http://dx.doi.org/10.1364/OE.20.022555

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▸ Article Outline
– Abstract
1. Introduction
2. Design consideration
3. Fabrication
4. Measurement
5. Conclusion
– References and links

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Abstract

We report on a novel concept for transmissive optical elements based on resonant waveguide gratings (RWGs), which enables the realization of direction selective filters. Hereby, the broadband reflectivity of an RWG for nearly normal incidence angles is combined with high diffractive efficiency in transmission for a specific angle of incidence. Silicon is used as material with high refractive index and good compatibility with semiconductor fabrication. By adjusting the grating parameters different transmission angles and angular widths of the transmission range are feasible. First experimental results of the introduced filters provide a high transmission up to 63% at an incidence angle of 45° with a full width at half maximum of 20°.

1. Introduction

Direction selective filter elements are important devices for numerous optical applications in detection and imaging. Hereby, the large variety of filter applications requires manifold optical properties. For example, a spectral or polarization selectivity, as well as a sensitivity with respect to the incidence angle of the investigated light are of interest. The latter feature is necessary for filters used in particle sensors, especially. Resonant waveguide gratings are known for their very selective behavior concerning wavelength, polarization and direction of the incident light [1

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985). [CrossRef]

–5

Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications” Opt. Express 12, 5661–5674 (2004). [CrossRef] [PubMed]

]. Over the past years several optical elements using RWGs based on silicon were demonstrated, such as highly efficient mirrors [6

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Phot. Tech. Lett. 16, 1676–1678 (2004). [CrossRef]

, 7

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104, 163903 (2010). [CrossRef] [PubMed]

] and narrowband reflective filters [8

Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, and R. Magnusson, “High-efficiency guided-mode resonance filter,” Opt. Lett. 23, 1556–1558 (1998). [CrossRef]

, 9

S. Tibuleac and R. Magnusson, “Narrow-linewidth bandpass filters with diffractive thin-film layers,” Opt. Lett. 26, 584–586 (2001). [CrossRef]

]. Likewise it was shown that silicon based elements can act as color filters at lower wavelengths in the visible spectral range [10

Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Phot. Tech. Lett. 18, 2126–2128 (2006). [CrossRef]

]. Despite the material absorption of silicon those filters can be realized as transmissive elements.

In this paper we propose an optical filter design to realize angular bandpass filters working in transmission based on resonant waveguide gratings. Exemplary, we demonstrate the feasibility of an element with a transmission maximum for incidence angles of about 45° with a full width at half maximum (FWHM) of less than 20° for TE-polarized light. The concepts can also be adapted TM-polarized light. Due to silicon is used in most semiconductor technologies, the fabrication of these filters fits perfectly in common fabrication techniques in semiconductor industry. This work is focused on transmission elements due to the fact that these elements can be either attached or directly fabricated on top of the sensors.

2. Design consideration

Generally a RWG consists of a modulated high-index layer on top of a low-index substrate or layer e.g. as shown in Fig. 1(a) and (b). Usually RWGs can provide a high reflectivity at a specific wavelength, incidence angle and polarization of the incident light. In order to realize a high reflectivity it has to be ensured that outside the grating no (higher) diffraction order exists. For normal incidence this requires [7

p < \frac{λ}{n_{l}} .

(1)

Fig. 1 Schematic sketch of the considered angular bandpass filter and its working principle. The light is not transmitted for incident angles shown in (a) but transmitted for the angle in (b).

The optical performance of strongly modulated RWGs, also known as high-contrast gratings [6

], can be very intelligibly described by means of coupled modes propagating from the top to the bottom of the grating and vice versa [11

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981). [CrossRef]

–13

V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, “Theoretical analysis of subwavelength high contrast grating reflectors,” Opt. Express 18, 16973–16988 (2010). [CrossRef] [PubMed]

]. To realize a parameter tolerant design two propagating modes, that are excited by the incident light, in the high-index layer are necessary [6

, 12

P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled bloch-mode insight,” J. Lightwave Technol. 24, 2442–2449 (2006). [CrossRef]

]. This fact sets a lower and an upper limit for the grating period p depending on the wavelength λ, the incidence angle θ, the duty cycle f, and the refractive index of the grating. The lower one is determined by the cutoff of the second mode, the upper by the excitation of a third propagating mode. It is found, that RWGs can efficiently reflect for a specific angle of incidence they are optimized for, e.g. θ = 0. But for angles outside the bandwidth of the reflector a broad angular transmission window is found [14

S. Kroker, F. Brückner, E.B. Kley, and A. Tünnermann, “Enhanced angular tolerance of resonant waveguide grating reflectors,” Opt. Lett. 36, 537–539 (2011). [CrossRef] [PubMed]

]. This is not suitable for filter applications where a narrowband transmission is required. Therefore we combine the high reflectivity of an RWG optimized for normal incidence with a high diffraction efficiency of a transmission grating at the angle, where the transmission window is desired. That means we choose the grating period such that it allows for the additional propagation of the first diffraction orders at the target angle θ_target of 45°. Together with relation (1) this yields:

\frac{λ}{n_{l} + sin θ_{target}} < p < \frac{λ}{n_{l}},

(2)

where p is the period of the grating, n_l the index of the low-index region and θ_target the angle of the desired transmission range. With (1) it is ensured, that at normal incidence only the zeroth diffraction order is allowed. If we consider a silicon grating (n = 3.677, k = 0.0075 at λ = 850 nm) with a moderate duty cycle (f = 0.5) on top of a fused silica substrate (n = 1.453) this condition automatically ensures that for normal incidence two propagating Bloch modes exist in the grating. For θ_target the limits for grating period become

464 nm < p < 586 nm .

(3)

For periods close to the lower boundary, i.e. the cutoff of the first diffraction orders around the target angle it is expected that their efficiencies are very small and the diffraction angles are close to 90°. For larger periods the first orders appear at smaller angles of incidence and therewith smaller diffraction angles. For applications in sensoring this is advantageous to detect the transmitted light. On the other hand periods too close to the upper limit only allow a efficient reflection for angles near to normal incidence. As an intermediate value we choose a period of 550 nm, in order to meet these demands and get possibly high diffraction efficiency at 45°. Once, an appropriate grating period is found, the minimum depth of the grating can be estimated by [15

S. Kroker, T. Kasebier, F. Brückner, F. Fuchs, E. B. Kley, and A. Tünnermann, “Reflective cavity couplers based on resonant waveguide gratings,” Opt. Express 19, 16466–16479 (2011). [CrossRef] [PubMed]

h = \frac{λ}{n_{eff}^{(0)} (θ = 0 °) - n_{eff}^{(1)} (θ = 0 °)},

(4)

where

n_{eff}^{(0)}

and

n_{eff}^{(1)}

are the effective refractive indices of the two propagating modes, that can be calculated according to Botten and McPhredan [11

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981). [CrossRef]

]. For normal incidence this relation leads to a range from h = 165 nm to 240 nm for the thickness of the silicon grating. At 45° the situation becomes more complicated since more than two modes significantly contribute. For the bandpass filter we aim for a maximum total transmission, i.e. the sum of the zeroth and first diffraction orders should be maximized. With Rigorous Coupled Wave Analysis [16

M. G. Moharam and T. K. Gaylord, “Rigorous Coupled-Wave Analysis of Planar-Grating Diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981). [CrossRef]

] we find an optimum depth of the silicon grating of 200 nm. The design wavelength of 850 nm is the central wavelength of a light-emitting-diode source, but the concepts are also applicable down to the VIS or to larger wavelengths, as well. With silicon as high-index material the absorption increases for smaller wavelengths, but an adaption down to 500 nm is feasible. As a result of using a resonant setup the deviations in fabrication have to be small to obtain a vanishing transmission for nearly normal incidence. For example the duty cycle should not vary more than 0.01 (2%) in order to get a transmission below 8% for normal incidence. In contrast such fabrication deviations have a minor impact on the transmissive range because this effect is non-resonant. Figure 2(a) shows the total transmission in dependence of the incidence angle with an overall transmission of over 70% at 51° incidence. Due to the fact that k of silicon is unequal zero, the absorption reaches 29% at 51°, but decreases rapidly to nearly zero for other angles, what limits the transmission in the desired angular spectrum. It is found that structuring of the substrate can reduce the transmission for small angles by maintaining the transmission behavior (see Fig.2(b)). Assuming a sub-grating with a grating depth of 300 nm and a duty cycle identical to the high-index grating the transmission for small incidence angles nearly vanishes. Likewise the center angle of the transmission range is shifted to the desired value of 45°. In the fused silica layer only the zeroth Bloch mode can propagate and an effective index layer is generated [17

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996). [CrossRef]

], whose effective refractive index decreases with reducing the duty cycle of this sub grating. Hence, the cutoff of the first diffraction order is shifted to larger angles (from 5° up to ca. 19°) which suppresses the transmission more efficiently. Furthermore the angle of maximum reflection is tuned from 5° down to 0°, leading to a reflectivity of nearly 100% at angles close to normal incidence and transmissions smaller than 2%. Exemplarily the contribution of the two diffraction orders to the overall transmission is shown in Fig. 3 for both configurations of Fig. 2. By comparison it can be seen that the first orders get slightly more intensity in the setup of Fig. 2 (b) and have a maximum of about 50% around the target angle of 45°. Likewise the zeroth order has a decreased intensity, leading to a narrower range either. As already mentioned, for normal incidence only the zeroth order exists, due to the small grating period and is almost completely reflected. For an angle of about 35° the transmission of the zeroth order rises while the reflection decreases. This is determined by geometric parameters of the grating and adds about 45% in configuration (a) of Fig. 2 and 20% to transmission in (b) in the desired angular range (see Fig.3(a)). Thus, both parts of transmission contributed by zeroth and first orders have to be matched in order to achieve an effective element. For incidence angles towards 90° the transmission is additionally limited by the Fresnel reflection at interfaces. This leads to a rapid decrease of the transmitted diffraction orders for light incident from those directions. The width of the transmission range can be changed by varying the duty cycle of the fused silica grating (see Fig. 4). In this example the FWHM of the transmission increases from about 15° for a duty cycle of f =0.25 to 32° for f =1. By the same variation the center of the transmission is shifted slightly from 44° to 52°. The center of the transmission range can either be shifted slightly by changing the grating period (see Fig. 5). For example the center wavelength can be shifted from 35° for a period of 530 nm to 45° for 550 nm. The maximum of the transmission decreases for larger periods due to higher reflection in this angular range.

Fig. 2 Incidence angle (relating to the perpendicular) dependent total transmission of the designed filter without (a) and with sub grating in the substrate (b) utilizing a duty cycle of 0.5.

Fig. 3 Transmission of the zeroth (black and dashed line) and first orders (−1^st, 1^st) (red line) as a function of the incidence angle for the configurations shown in Fig. 2.

Fig. 4 Changing the width of the total transmission range by varying the duty cycle of the fused silica grating, e.g. about 15° FWHM for f = 0.25 (black and dashed line); 20° for f = 0.5 (red); 26° for f = 0.75 (blue and dotted); 32° for f = 1 (green and dot-and-dashed). The center of the transmission is shifted slightly from 44° to 52°.

Fig. 5 The center angle of the total transmission range can be shifted by varying the period of the resonant waveguide grating, e.g. from 35° for p=530 nm to 45° for p=550 nm.

Fig. 6 SEM image of a fabricated angular bandpass grating. The period is 550 nm, the depths are 200 nm for the silicon grating and 300 nm for the fused silica grating. Platinum was deposited on the sample locally in order to protect the structure during milling.

3. Fabrication

For fabrication of a structure according to Fig. 2 a standard fused silica wafer with a 200 nm silicon layer was used. This wafer was coated with a 50 nm Chromium layer serving as etching mask during silicon and fused silica etching. Afterwards a layer electron sensitive resist was deposited on top by using a spin coater and exposed by means of electron beam lithography for an area of 20×20 mm². As mentioned before, the design grating parameters were a period of 550 nm and a duty cycle of 0.5. The developed binary resist profile was transferred subsequently into the chromium layer by utilizing a reactive induced etching (RIE) process. With this chromium mask the silicon layer was etched with an anisotropic inductively coupled plasma (ICP) dry-etching process. Afterwards the sub grating was structured into the fused silica masked by the chromium and silicon layer using an anisotropic reactive ion beam etch process (RIBE). Here this process was stopped after a depth of 300 nm was reached. Figure 3 depicts a scanning electron microscope (SEM) cross-sectional view of the fabricated angular bandpass grating. The grating was coated with platinum locally, to protect the structure during milling using a focused ion beam (FIB). The grating is almost binary and the desired parameters are reached within the parameter tolerances that predict a proper angular function.

Fig. 7 Measured total transmission of the sample shown in Fig. 3 at 850 nm wavelength and TE- polarization in comparison with the simulation (red line). The maximum transmission is 63% in combination with a range of about 30° FWHM. For small angles of incidence the transmission is smaller than 20%.

4. Measurement

The measurement of the angle dependent total transmission is shown in Fig. 4, using a laser diode at 850 nm wavelength (TE-polarized) as light source. Due to the fact that the zeroth and first diffraction orders propagate in different directions an integrating sphere was used in order to measure both parts of the total transmission simply and simultaneously. Other detectors are also applicable whereby this is no confinement for possible applications. The transmission reaches a maximum of 63% at the desired angle of 45° and a slightly larger angular width of 30° FWHM than the simulations have predicted (FWHM of 20°). The transmission for incidence angles below 35° is lower than 0.2. The difference between the measurement and the calculation is a result from a deviation of the refractive index of the silicon layer. This decreases the efficiency of the resonant reflection at small angles as observed. On the behavior of the transmission range these deviations of the refractive index only have a minor impact. That means that the coating process to deposit the high-index layer is critical for the optimal bandpass function of the element.

5. Conclusion

Concluding, we have proposed a grating configuration to realize transmissive direction selective filter elements whose optical function is based on resonant waveguide gratings. A first experimental realization exhibits a maximum transmission of 63% at the target angle of 45° with a FWHM of 30°.The proposed material combination is perfectly compatible with well-established fabrication processes in semiconductor industry. This allows, for example, an easy integration of the proposed filter elements in particle sensors or detectors.

Acknowledgment

Financial support from the Federal Ministry of Education and Research (BMBF) (project ”KDOptiMi20”, grant number 16SV5472K) is acknowledged.

References and links

1.	G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985). [CrossRef]
2.	S. S. Wang, R. Magnusson, and J. S. Bagby, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470–1474 (1990). [CrossRef]
3.	R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992). [CrossRef]
4.	R. Magnusson and S. S. Wang, “Transmission bandpass guided-mode resonance filters,” Appl. Phys. Lett. 34, 8106–8109 (1995).
5.	Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications” Opt. Express 12, 5661–5674 (2004). [CrossRef] [PubMed]
6.	C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Phot. Tech. Lett. 16, 1676–1678 (2004). [CrossRef]
7.	F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104, 163903 (2010). [CrossRef] [PubMed]
8.	Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, and R. Magnusson, “High-efficiency guided-mode resonance filter,” Opt. Lett. 23, 1556–1558 (1998). [CrossRef]
9.	S. Tibuleac and R. Magnusson, “Narrow-linewidth bandpass filters with diffractive thin-film layers,” Opt. Lett. 26, 584–586 (2001). [CrossRef]
10.	Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Phot. Tech. Lett. 18, 2126–2128 (2006). [CrossRef]
11.	L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981). [CrossRef]
12.	P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled bloch-mode insight,” J. Lightwave Technol. 24, 2442–2449 (2006). [CrossRef]
13.	V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, “Theoretical analysis of subwavelength high contrast grating reflectors,” Opt. Express 18, 16973–16988 (2010). [CrossRef] [PubMed]
14.	S. Kroker, F. Brückner, E.B. Kley, and A. Tünnermann, “Enhanced angular tolerance of resonant waveguide grating reflectors,” Opt. Lett. 36, 537–539 (2011). [CrossRef] [PubMed]
15.	S. Kroker, T. Kasebier, F. Brückner, F. Fuchs, E. B. Kley, and A. Tünnermann, “Reflective cavity couplers based on resonant waveguide gratings,” Opt. Express 19, 16466–16479 (2011). [CrossRef] [PubMed]
16.	M. G. Moharam and T. K. Gaylord, “Rigorous Coupled-Wave Analysis of Planar-Grating Diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981). [CrossRef]
17.	P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996). [CrossRef]

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.2770) Diffraction and gratings : Gratings
(220.4000) Optical design and fabrication : Microstructure fabrication
(230.3990) Optical devices : Micro-optical devices
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Diffraction and Gratings

History
Original Manuscript: June 26, 2012
Revised Manuscript: August 23, 2012
Manuscript Accepted: August 23, 2012
Published: September 17, 2012

Citation
Stefan Steiner, Stefanie Kroker, Thomas Käsebier, Ernst-Bernhard Kley, and Andreas Tünnermann, "Angular bandpass filters based on dielectric resonant waveguide gratings," Opt. Express 20, 22555-22562 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-20-22555

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References

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron.15, 886–887 (1985). [CrossRef]
S. S. Wang, R. Magnusson, and J. S. Bagby, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A7, 1470–1474 (1990). [CrossRef]
R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett.61, 1022–1024 (1992). [CrossRef]
R. Magnusson and S. S. Wang, “Transmission bandpass guided-mode resonance filters,” Appl. Phys. Lett.34, 8106–8109 (1995).
Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications” Opt. Express12, 5661–5674 (2004). [CrossRef] [PubMed]
C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Phot. Tech. Lett.16, 1676–1678 (2004). [CrossRef]
F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett.104, 163903 (2010). [CrossRef] [PubMed]
Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, and R. Magnusson, “High-efficiency guided-mode resonance filter,” Opt. Lett.23, 1556–1558 (1998). [CrossRef]
S. Tibuleac and R. Magnusson, “Narrow-linewidth bandpass filters with diffractive thin-film layers,” Opt. Lett.26, 584–586 (2001). [CrossRef]
Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Phot. Tech. Lett.18, 2126–2128 (2006). [CrossRef]
L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta.28, 413–428 (1981). [CrossRef]
P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled bloch-mode insight,” J. Lightwave Technol.24, 2442–2449 (2006). [CrossRef]
V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, “Theoretical analysis of subwavelength high contrast grating reflectors,” Opt. Express18, 16973–16988 (2010). [CrossRef] [PubMed]
S. Kroker, F. Brückner, E.B. Kley, and A. Tünnermann, “Enhanced angular tolerance of resonant waveguide grating reflectors,” Opt. Lett.36, 537–539 (2011). [CrossRef] [PubMed]
S. Kroker, T. Kasebier, F. Brückner, F. Fuchs, E. B. Kley, and A. Tünnermann, “Reflective cavity couplers based on resonant waveguide gratings,” Opt. Express19, 16466–16479 (2011). [CrossRef] [PubMed]
M. G. Moharam and T. K. Gaylord, “Rigorous Coupled-Wave Analysis of Planar-Grating Diffraction,” J. Opt. Soc. Am.71, 811–818 (1981). [CrossRef]
P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt.43, 2063–2085 (1996). [CrossRef]

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