Fabrication of narrow bandpass filters for wavelength division multiplexing applications A feasibility study

Transcription

1 Indian Journal of Engineering & Materials Sciences Vol. 14, April 2007, pp Fabrication of narrow bandpass filters for wavelength division multiplexing applications A feasibility study A Basu*, K M K Srivatsa, T K Chakraborty & T K Bhattacharya Division of Electronic Materials, National Physical Laboratory, New Delhi , India Received 16 October 2006; accepted 13 March 2007 Thin film multilayer narrow bandpass interference filters are widely used in wavelength division multiplexing (WDM) applications in fibre optic communication systems. These filters must have sharp cut-on and cut-off on either side of the passband and practically zero transmittance outside the passband, over the wavelength range of the application. In an effort to demonstrate the feasibility of fabrication of WDM filters, the simpler designs for these filters (involving deposition of multilayers with layers) have been examined and their fabrication has been demonstrated using a vacuum coating system with limited capabilities, at several wavelengths in the range of interest. This experience has shown that with the use of modern vacuum coating plants equipped with sophisticated coating and monitoring facilities, the fabrication of WDM filters with more complex designs and meeting commercial specifications [at least coarse WDM (CWDM) filters with somewhat less stringent specifications] can be a feasible proposition. IPC Code: G02B 1/10, G02B 5/28 Wavelength division multiplexing (WDM) is an integral component of fibre optic communication systems and enables several channels of information to be encoded on light signals of different wavelengths and transmitted simultaneously over the same optical fibre, to be separated and decoded at the receiving end 1-4. The Fabry Perot multicavity narrow bandpass interference filter is still the most widely used device for the multiplexing and demultiplexing of the different wavelengths transmitted over the optical fibre 5-7. The narrow bandpass filters must have very steep cut-on and cut-off transmittance characteristics as well as very low transmittance at wavelengths other than the transmission wavelength, to avoid crosstalk between the different channels. For Dense WDM (DWDM) applications, the separation between neighbouring wavelength channels is less than 1 nm and so the width of the passband of an individual filter must be less than 0.5 nm, which makes the fabrication of these ultra-narrowband filters an extremely challenging and difficult task. But for Coarse WDM (CWDM) the adjacent wavelength channels are separated by 20 nm or more and so the width of a filter passband can be nm, making the fabrication of these filters a more feasible task. The design techniques for the multilayer stacks used in the fabrication of narrowband filters for *For correspondence ( abasu@mail.nplindia.ernet.in ) WDM applications are described extensively by Thelen 8 and Baumeister 9. These thin film filters are fabricated by plasma and ion-assisted electron beam evaporation 10, by reactive magnetron sputtering (e.g. the 'microplasma' method 11 ) or by plasma impulse chemical vapour deposition 12. There are several manufacturers of thin film bandpass filters for WDM (CWDM as well as DWDM), such as JDS Uniphase, Bookham, Optical Coatings Japan (Techmark), XL Optics, Optarius, Lightwaves2020 and Iridian and Auxora. However, in India there is hardly any R & D activity in the design and fabrication of WDM filters. In fact, C-DOT, which sets the standards for CWDM operations in India, has specified the channel positions for CWDM operations (not for DWDM operations so far) and all optical equipments are imported. Specifications of a typical DWDM filter Filters are designated as 200 GHz ( 1.6 nm bandwidth), 100 GHz ( 0.8 nm bandwidth), 50 GHz ( 0.4 nm bandwidth) or 25 GHz ( 0.2 nm bandwidth) filters, and are chosen according to the wavelength spacing of adjacent channels in the DWDM scheme. For a 100 GHz filter.. Centre wavelengths nm, as per requirements Bandwidth at 90% transmittance (-0.5 db) : 0.8 nm

2 126 INDIAN J. ENG. MATER. SCI., APRIL % transmittance(-3 db): < 0.9 nm [full width at half maximum, FWHM] 0.32% transmittance (-25 db): 1.0 nm 0.1% transmittance (-30 db): 1.1 nm Adjacent channel isolation: > 25 db Temperature coefficient of wavelength shift: < 1 pm/ ºC Operating temperature: - 5 to + 70ºC Specifications of a typical CWDM filter 8 Centre wavelengths: nm, others on request, tolerance ± 0.2 nm Filter design has 5, 7 or 9 cavities. For a 7 cavity filter Bandwidth at 90% transmittance (-0.5 db): > 16 nm 50% transmittance(-3 db): 20 nm [full width at half maximum, FWHM] 0.32% transmittance (-25 db): < 22 nm 0.1% transmittance (-30 db): < 25 nm Ripple in passband: < 0.3 db Temperature coefficient of wavelength shift: < 1 pm/ ºC Operating temperature: - 40 to + 75ºC The bandwidth specifications show how the passband shape is almost perfectly rectangular. The extremely small temperature coefficient of wavelength shift shows that the centre wavelength and bandshape are highly stable with respect to changes in operating temperature. The adjacent passbands are also highly isolated from each other and there is negligible crosstalk. In this paper, the feasibility of fabricating CWDM narrowband filters using an old vacuum coating plant with several limitations has been demonstrated, the simpler designs for these filters have been chosen, comprising multilayer stacks of low index (SiO 2 ) and high index (TiO 2 ) films of quarter-wave optical thicknesses that involve no more than about 35 individual quarterwave films deposited sequentially in the multilayer stack. The deposition of several of these multilayer stacks has been carried out and it has been shown that reasonably good bandpass filter characteristics can be obtained in spite of the limitations of the thin film vacuum coating plant used. Theory The narrow bandpass filters that are used for WDM applications are basically Fabry Perot multicavity interference filters. Their basic structure is a multilayer stack of alternately high index and low index thin films, most of which are one-quarterwave thick at the design wavelength, deposited on an ophthalmic glass or silica substrate 8,9,21. For example, a three cavity multilayer structure could be as follows: where H and L are one-quarterwave thick layers (at a certain design wavelength) of high and low index materials respectively, and the spacer layers have a thickness of 4L (it could be any multiple of 2L). The multilayers at the two ends are the end reflectors while the multilayers between two spacer layers are the coupling reflectors, of the Fabry Perot filter structure. The spectral transmittance characteristics of such a multilayer stack are influenced by the various parameters of the stack as: (i) The higher the ratio n H / n L of the high index to low index materials, the less is the number of films in the end and coupling reflector layers required to achieve a certain reflectance and hence the desired spectral transmittance characteristics of the filter. (ii) If the number of films in each of the end reflector stacks is p, then the number of films in the coupling reflector stacks should be (2p 1) or (2p + 1), with the latter yielding a somewhat narrower transmittance peak. The higher the value of p, the smaller is the bandwidth [more specifically, the full width at half maximum (FWHM)] of the transmittance peak and the sharper the rising and falling edges of the peak. (iii) The greater the thickness of the spacer layers, 2L or 4L or 6L, etc., the smaller is the bandwidth and the sharper the rising and falling edges. (iv) The larger the number of cavities in the multilayer stack, the sharper the rising and falling edges of the transmittance peak. (v) In order to achieve a transmittance peak with sharp rise and fall and a nearly flat top, some layers in the end reflector stacks and the coupling reflector stacks are chosen to be nonquarterwave thick 8,9. However, the basic filter characteristics can be achieved with an allquarterwave multilayer stack, and the present study has been restricted to such stacks because the coating plant can deposit quarterwave stacks only.

3 BASU et al.: FABRICATION OF NARROW BANDPASS FILTERS 127 TiO 2 is chosen as the high index material and SiO 2 as the low index material in most multilayer stacks because of the superior material properties and mutual compatibility of these materials. The calculated transmittance characteristics of a multi-cavity multilayer stack, with different spacer layer thicknesses and different numbers of layers in the end reflector and coupling reflector stacks, are shown in Figs 1-4 for different cases, to illustrate the influences of the various parameters. Fig. 1 shows the transmittance characteristics of the multilayer stack air H L H L H L H 4L H L H L H L H L H L H L H L H 4L H L H L H L H glass with the H (TiO 2 ) and L (SiO 2 ) layers being one quarterwave thick at 900 nm in Fig. 1a and at 1500 nm in Fig. 1b. We see that the transmittance remains close to zero (actually below 0.1%) over a range of nm on either side of the centre wavelength or passband. This serves to indicate how many passbands of a certain bandwidth can be accommodated over this wavelength range for WDM applications. Fig. 2 shows the transmittance characteristics of the same multilayer stack with the thickness of the spacer layer fixed at 4L, but with different numbers of layers in the end and coupling reflector stacks: p = 5, 7 and 9, and (2p + 1) layers in the coupling reflector stacks. The narrowing of the passband and increasing steepness of the rising and falling edges of the passband, with increasing values of p, is evident from these curves. Fig. 3 shows the transmittance characteristics of the same multilayer stack with different thicknesses of the (a) Fig. 2 Transmittance versus wavelength characteristics of a twocavity Fabry Perot multilayer stack having the basic design air HL..LH 4L HL..LH 4L HL..LH glass p q p where p = 5, 7, 9 and q = 2p+1. H and L are one quarterwave thick layers of TiO 2 and SiO 2 respectively, at 900 nm. (b) Fig. 1 Transmittance versus wavelength characteristics of a twocavity Fabry Perot multilayer stack having the basic design air HL..LH 4L HL..LH 4L HL..LH glass p q p where p = 7 and q = 2p+1 = 15. H and L are one quarterwave thick layers of TiO 2 and SiO 2 respectively, at (a) 900 nm and (b) 1500 nm Fig. 3 Transmittance versus wavelength characteristics of a twocavity Fabry Perot multilayer stack having the basic design air HL..LH ml HL..LH ml HL..LH glass p q p where p = 7 and q = 2p+1 = 15. The spacer layers have different thicknesses: m = 2, 4, 6. H and L are one quarterwave thick layers of TiO 2 and SiO 2 respectively, at 900 nm.

4 128 INDIAN J. ENG. MATER. SCI., APRIL 2007 spacer layer: 2L, 4L and 6L. The narrowing of the passband and increasing steepness of the rising and falling edges of the passband, with increasing thickness of the spacer layer, is evident from these curves. Fig. 4 shows the transmittance characteristics of the same type of multilayer stack but with different numbers of cavities: 2, 3, 4 and 5. We see that the steepness of the rising and falling edges of the passband increases with the number of cavities. The increasing ripple in the passband (greater number of variations at the top of the transmittance peak) with increase in the number of cavities can be reduced by using some non-quarterwave layers in the multilayer stack 8,9. It is also possible to obtain similar transmittance characteristics using mh (m = 2, 4, 6, ) spacer layers of high index material instead of ml spacer layers of low index material, with layer sequences of LHL LHL in the reflector multilayer stacks. (a) (b) Fig. 4 Transmittance versus wavelength characteristics of a multi-cavity Fabry Perot multilayer stack having the basic design air HL..LH 4L HL..LH 4L HL..LH HL..LH glass p q q p where p = 7 and q = 2p+1 = 15, for 2 and 3 cavity filters (Fig. 4a) and 4 and 5 cavity filters (Fig. 4b). H and L are one quarterwave thick layers of TiO 2 and SiO 2 respectively, at 900 nm. Further, it has been shown 9 that a thick spacer layer, e.g., 6L, can be replaced by the layer sequence 2H 2L 2H with not much change in the filter characteristics. This fact may be useful in a practical deposition process, for replacing a single thick layer with its problems of inhomogeneities and surface roughness with a few thinner layers, although at the cost of increasing the total number of layers in the multilayer stack. Deposition of multilayers The deposition of the multilayer coatings has been carried out in a Leybold L 560 vacuum coating plant [M/s Leybold, Germany], operating in our laboratory since1987. This is a 50 cm box coater, pumped with a rotary pump and a diffusion pump to a base pressure of about mbar. During reactive evaporation, oxygen can be bled into the chamber through a needle valve. A rotating hemispherical calotte has pockets to hold a large number of substrates and can be heated to a pre-set temperature by flat resistance heaters and a temperature controller. The plant is equipped with two 6 kw electron beam guns. One gun has a multipocket hearth holding pellets of the evaporant, which can be rotated to bring the pellets below the electron beam for evaporation, one by one. The other gun has an annular hearth containing granules of the evaporant, which can be rotated slowly and the electron beam spot can be made to oscillate, in order to scan the surface of the packed granules and enable slow and reasonably uniform evaporation. A quartz crystal thickness monitor is installed in the plant and is interfaced with an Inficon IC6000 deposition rate controller and thickness monitor to maintain an uniform film deposition rate and monitor the physical thickness (in kå) of the deposited film. A L-101 optical thickness monitor [Eddy Co., USA] is installed in the plant and equipped with a grating monochromator to enable monitoring of the optical thickness of the film being deposited, at the wavelength set on the monochromator. Due to its age, lack of regular professional maintenance as well as insufficient spare parts, the coating plant has to be operated under certain restrictions and limitations: (i) The rotary feedthroughs for the electron beam gun hearths start leaking under continuous rotation (no satisfactory indigenous feedthroughs are available) and so the hearths have to be rotated periodically by hand to bring different fresh pellets or regions of the

5 BASU et al.: FABRICATION OF NARROW BANDPASS FILTERS 129 evaporant under the electron beam for evaporation. (ii) The position of the electron beam spot on the evaporant tends to drift periodically (the deflection and scanning control circuits do not always operate in a stable manner) and so manual control is required to keep the spot in the same position during evaporation. (iii) For this reason, the Inficon IC6000 deposition rate controller and thickness monitor is usually not operated in the automatic mode but is controlled manually to try and maintain stable evaporation conditions. (iv) The flow of oxygen being bled into the deposition chamber during reactive evaporation has to be controlled manually by a needle valve and adjusted frequently during evaporation. (v) The optical monitoring of the deposited layers is restricted to manual quarterwave monitoring, and so non-quarterwave layers cannot be deposited. Thus, one is constrained to deposit quarterwave layer sequences only. (vi) Perhaps the most severe limitation is that there is no provision for a test glass exchanger to be installed in the coating plant. Therefore one is constrained to deposit a sequence of at most 15 quarterwave layers (at 1 µm wavelength) in a single coating run, since the sensitivity of the single monitor plate to detect film deposition deteriorates sharply thereafter. Despite all these limitations, the coating plant has been operated, with mostly manual control and monitoring, to deposit the best multilayer optical coatings possible. The multilayer coatings for the narrow bandpass filters have been deposited on ophthalmic glass substrates, 10 mm in diameter and 1 mm thick, polished to a flatness of about λ/2. Some 25 mm diameter plates have also been coated simultaneously in the same coating run, for measurement of the transmittance characteristics of the deposited multilayer coating on a spectrophotometer. A 45 mm diameter glass plate has been used as the optical monitoring plate, mounted centrally in the plant. The substrates to be coated have been placed in cups mounted on the rotating calotte and heated to about 250 C. For the TiO 2 films, pellets of Ti 2 O 3 (99.9% pure, Balzers) have been placed in the multi-pocket hearth, and oxygen bled into the chamber through a needle valve to maintain the chamber pressure at about mbar. The evaporant loses oxygen during evaporation and the residual oxygen overcomes the deficiency and provides additional oxygen to result in TiO 2 films being deposited on the substrate. The rate of deposition has been maintained manually at about 3-5 Å/s. For the SiO 2 films, granules of SiO 2 (99.99% purity, Balzers) have been packed in the annular hearth and the electron beam made to oscillate over the surface of the evaporant to ensure slow and reasonably uniform evaporation, resulting in a deposition rate of 5-15 Å/s. Manual quarterwave monitoring of the deposited layer thickness has been carried out, with the shutter being closed and the electron beam power switched off when a maximum or minimum in the optical thickness monitor reading has been reached. After the desired sequence of layers has been deposited, the deposited coating has been annealed in oxygen at about mbar pressure, to complete the oxidation of the TiO 2 films. After the substrates have cooled down to room temperature, the deposition chamber is opened up to air. Due to the limitation of not having a test glass exchanger with multiple optical monitoring plates, the deposition had to be stopped after about 15 quarterwave layers at most, the chamber opened up to air, a fresh monitor plate inserted and a fresh coating run started for the subsequent layers in the multilayer stack. For narrowband filters with centre wavelengths in the nm region, the layer sequence for the multilayer stack has been chosen to be air L H L H L H L H 4L H L H L H L H L H L H L H 4L H L H L H L H glass This stack has 30 layers {36 quarterwaves) in all. This stack has been judged to yield the best spectral characteristics with this total number of layers and total multilayer thickness. The deposition of this multilayer has been carried out in a sequence of two coating runs, as follows : (I) (II) H L H L H L H 4L H L H L H L H L H L H L H 4L H L H L H L This sequence has been chosen because no more than quarterwave layers can be deposited at these wavelengths before the transmittance of the optical monitoring plate becomes insensitive to further depositions. The centre wavelength of the deposited filter coating has been found to depend on the position of

6 130 INDIAN J. ENG. MATER. SCI., APRIL 2007 the substrate on the calotte, for a particular setting of the wavelength on the monochromator of the optical thickness monitor. Several trial runs have been carried out to determine the substrate position and the setting of the monochromator that would yield the desired centre wavelength of the filter coating. For narrowband filters with centre wavelengths in the nm region, the layer sequence for the multilayer stack has been chosen to be air H L H L H L H L 2H L H L H L H L H L H L H L H L H L 2H L H L H L H L H glass This stack has 35 layers {37 quarterwaves) in all. The spacer layers have been chosen to be 2H rather than 4L as in the earlier case since the physical thickness of a quarterwave layer would be almost twice that of the same layer in the previous case on account of the larger centre wavelength required. The greater the physical thickness of a particular layer, the greater the chances of inhomogeneity and surface roughness of that layer, which would affect the overall filter characteristics adversely. With 2H spacer layers, this stack has been judged to yield the best spectral characteristics with this total number of layers and total multilayer thickness. The deposition of the multilayer has been carried out in a sequence of five coating runs, as: (I) H L H L (II) H L H L 2H L H L (III) H L H L H L H L H L (IV) H L H L 2H L H L (V) H L H L H The reason for breaking-up this multilayer deposition into this sequence of coating runs, rather than the sequence of two approximately equal multilayers, followed earlier for the filters in the nm range, has been based on the following considerations: (I) No more than quarterwave layers can be deposited at these wavelengths before the transmittance of the optical monitoring plate becomes insensitive to further depositions. (II) The error in the thickness (deposited thickness as compared to the design value) of a particular layer in the multilayer stack depends on the position of the layer in the stack. The further away the layer from a spacer layer, the less is the effect of an error in that layer s thickness on the overall spectral characteristics of the multilayer stack. (III) In a multi-cavity structure, the thicknesses of the spacer layers should be very close to each other (differing by less than 1%) in order to obtain a bandpass filter spectral characteristic. (IV) Except for the first deposition run, the thickness of the very first layer in a deposition run may be slightly in error because the layer has to nucleate on a bare monitor plate whereas the filter substrate already has a multilayer deposited on it. So this layer should be chosen to be as far away from a spacer layer as possible, in order to minimize the effect of errors in this layer s actual thickness on the spectral characteristics of the complete multilayer stack. As in the earlier case, the monochromator setting of the optical monitor and the position of the substrate on the calotte determine the centre wavelength of the deposited multilayer filter coating. After the complete multilayer stack has been deposited on the substrate, a clean glass plate has been fixed on top of the deposited multilayer with UV curing epoxy, to protect the multilayer from peeling off or degrading due to exposure to moisture in the atmosphere. Calculations have shown that the spectral characteristics of the multilayer are not significantly affected by the attachment of the glass plate, i.e., replacing the upper medium of air (n = 1.0) by glass (n = 1.52). Results and Discussion The spectral characteristics of typical filter coatings with centre wavelengths in the nm range are shown in Figs 5a and 5b. The calculated spectral characteristics are also shown for comparison. The agreement between the calculated and the achieved results is reasonable, keeping in mind the limitations under which the depositions had to be carried out. Fig. 6 shows the spectral characteristics of seven such filters with different centre wavelengths. It is seen that the bandwidths (FWHM) of these filters are nm, as compared to the calculated FWHM of 12 nm for the calculated curves, while the peak transmittances are 68-83% as compared to the calculated peak transmittance of more than 90%. Moreover, repeatability of the filter centre wavelength and peak transmittance from run to run has been found difficult to achieve, because of the limitations of the deposition process mentioned earlier, due to which the deposition conditions change slightly from run to run and even during a single run.

7 BASU et al.: FABRICATION OF NARROW BANDPASS FILTERS 131 (a) The spectral characteristics of typical filter coatings with centre wavelengths in the nm range are shown in Figs 7a and 7b. The calculated spectral characteristics are also shown for comparison. The agreement between the calculated and the achieved results is poorer than in Figs 5a and 5b, but is still reasonable, keeping in mind the limitations under which the depositions had to be carried out, especially the fact that five coating runs have been executed to complete the deposition of the total multilayer as compared to two in the earlier case. Fig. 8 shows the spectral characteristics of four such filters with different centre wavelengths. It is seen that the bandwidths (FWHM) of these filters are nm, as compared to the calculated FWHM of 13 nm for the calculated curves, while the peak transmittances are 50-70% as compared to the calculated peak transmittance of more than 90%. For (b) Fig. 5 Transmittance versus wavelength characteristics for a 30 layer multilayer coating air L H L H L H L H 4L H L H L H L H L H L H L H 4L H L H L H L H glass The bold curve is the measured characteristic of the deposited multilayer, while the dotted curve is the calculated characteristic. Fig. 5a is for a filter with centre wavelength of 825 nm, while Fig. 5b is for a filter with centre wavelength of 900 nm. (a) Fig. 6 Transmittance versus wavelength characteristics for 30 layer multilayer coatings (sequence as in Fig. 5) for seven different filters with different centre wavelengths in the nm range. (b) Fig. 7 Transmittance versus wavelength characteristics for a 35 layer multilayer coating air H L H L H L H L 2H L H L H L H L H L H L H L H L H L 2H L H L H L H L H glass The bold curve is the measured characteristic of the deposited multilayer, while the dotted curve is the calculated characteristic. Fig. 7a is for a filter with centre wavelength of 1540 nm, while Fig. 7b is for a filter with centre wavelength of 1625 nm

8 132 INDIAN J. ENG. MATER. SCI., APRIL 2007 sharp cut-on and cut-off characteristics. With a modern coating plant having the facilities describedabove (a few such plants exist in India at present), it should be possible to deposit these multilayers with large numbers of layers (approaching 100) and thus fabricate bandpass filters with spectral characteristics close to those of commercially available filters. Fig. 8 Transmittance versus wavelength characteristics for 35 layer multilayer coatings (sequence as in Fig. 7) for four different filters with different centre wavelengths in the nm range the same reasons mentioned above, repeatability of coating runs, to achieve the same centre wavelengths and peak transmittances, has been difficult to achieve. Conclusions The fabrication of two cavity bandpass interference filters in the wavelength ranges nm and nm has been demonstrated. Due to the limitations in the vacuum coating plant used, the spectral transmittance characteristics of the deposited multilayer coatings do not match the calculated characteristics very closely, more so for the filters in the nm range. However, if the multilayer coatings are deposited in a modern vacuum coating plant, equipped with a test glass exchanger, a multicrystal thickness monitor and rate controller, and big electron beam gun hearths that can hold sufficient amounts of evaporants to deposit large numbers of layers, and if very stable deposition conditions can be maintained during the entire coating run, then multilayer coatings can be deposited whose spectral characteristics closely match the calculated characteristics and which have good repeatability from run to run. Moreover, commercially available CWDM bandpass filters have four or five cavities in the multilayer, in order to achieve steep rising and falling edges of the transmittance characteristic, i.e., Acknowledgements This work was executed under a project (no. DST/TSG/ME/2003/48) funded by Technology Systems Group, Department of Science & Technology, Govt. of India, for which the authors gratefully acknowledge the support. They are grateful to Dr. M Kar for providing the spectrophotometric traces for the fabricated bandpass filters, and to the Director, National Physical Laboratory, for encouragement during this study. References 1 Hecht J, Laser Focus World, (Mar/Apr 1999) LaHa M, WDM Solutions, (Oct 2001) en.wikipedia.org [Wikipedia] 4 Fundamentals of DWDM Technology at 5 Baumeister P W, Laser Focus World, (July 2001) Morton D, Soc Vacuum Coaters, 46 th Annual Technical Conf Proc, 2003, Baumeister P W, Optical Coating Technology, 1 st Ed (SPIE Press, Washington), 2004, Ch 1 and 7 8 Thelen A, Design of Optical Interference Coatings, 1 st Ed, (MacGraw Hill Book Company, New York), 1989, Ch Baumeister P W, Appl Opt, 42 (2003) Zoller A, Gotzelmann R, Matl K & Cushing D, Appl Opt, 35 (1996) Scobey M A, Spock D E, Grasis M E & Beattie J A, Proc Opt Fibre Comm Conf (USA), 1996, Bauer S, Klippe L, Rothaar U & Kuhr M, Thin Solid Films, 442 (2003) [JDS Uniphase] [Bookham] [Optical Coatings Japan] [XL Optics] [Optarius], 18 [Lightwaves2020] [Iridian] [Auxora.] 21 MacLeod H A, Thin-film optical filters, 2 nd Ed (Adam Hilger Ltd, Bristol), 1986, Ch 7.