WO2007048195A1

WO2007048195A1 - Rugate filters

Info

Publication number: WO2007048195A1
Application number: PCT/AU2006/001600
Authority: WO
Inventors: Anne Gerd Imenes; David Robert Mckenzie
Original assignee: The University Of Sydney
Priority date: 2005-10-28
Filing date: 2006-10-27
Publication date: 2007-05-03

Abstract

A method of designing a rugate filter structure and a rugate filter structure are disclosed. The method comprises the step of deriving a refractive index variation as a function of rugate filter thickness such that substantially an equal number of rugate periods, or parts thereof, reflect an incident optical signal at each targeted wavelength or wavelength interval within a stopband of the rugate filter.

Description

RUGATE FILTERS

FIELD OF THE INVENTION

[ 0001 ] The present invention relates broadly to a method of designing a rugate filter structure, and to a rugate filter structure.

BACKGROUND

[ 0002 ] Two main types of dielectric interference filters are the multilayer stack, consisting of discrete layers, and the graded-index filter, which has a continuous transition in refractive index between successive 'layers'. Graded-index coatings are typically used for antireflection purposes where they can match the substrate index to the surrounding media with a smooth, continuous index profile. Rugate filters are graded- index optical coatings characterised by a continuous sinusoidal or sine-like periodic index variation along the direction of the substrate normal. Bragg-like reflections occur from such periodical structures, producing a narrow-band reflection filter, and are also sometimes referred to as notch filters.

[ 0003 ] The rugate structures exhibit similar properties to a quarterwave stack but without the higher-order reflectance peaks, which have their origins in the interference between beams reflected at all the different interfaces in the quarterwave stack. By inserting an antireflection (AR) coating at each interface in a discrete layer coating, the resulting structure resembles a sinusoidal variation of the refractive index throughout. The rugate filter offers extremely high optical performance by the reduction of optical losses due to light scattering at interfaces and by the suppression of higher-order harmonic reflectance bands. [ 0004 ] Compared with discrete multilayer filters of comparable physical dimensions and properties, rugate filters have been reported to offer advantages such as higher mechanical strength and a better toughness, as well as a smaller sensitivity to angle of incidence variations. Although traditionally used as a notch filter, the favorable properties of the rugate coating makes it attractive also for applications where a filter with a broadened spectral region of high reflectivity is desired, such as in an edge, bandstop, or bandpass filter. When the rugate coating is designed for high reflection over an extended spectral region, a large number of rugate cycles is required, especially when the periodic variation in refractive index has to be kept small to avoid the occurrence of sidelobes outside the primary reflectance band.

[ 0005 ] Three methods of increasing the reflectance band of rugate filters have been attempted. The first method places the filters in parallel by using the superposition principle for waves, adding refractive index profiles of different periodicity together into a single index profile of increased complexity. This 'parallel' method is typically applied in the design of narrowband filters such as multiple-line laser mirrors

[ 0006 ] The second method places the filters in series, stacking different rugate filters on top of each other. In this 'serial' method, rugate filters of different periodicity are deposited one after the other, and the individual filters are centered at respective wavelengths chosen so that the correspondingly shifted rejection zones create a broadened rejection band. The bandwidth of the high-reflectance band of each of the rugate filters used in the series is dependent on the peak variation n_p of the rugate index- function. Increasing the value of n_p will increase the bandwidth, which would mean that the overall thickness for a broadband rugate coating could be kept to a minimum. For example, a rugate centered at a wavelength X₀ = 800 nm would have a maximum bandwidth of 167 nm if the low and high refractive indices of the peak variation were m, = 1.43 and nπ = 2.30, respectively.

[ 0007 ] In stacked rugate filters for broadband reflectance, increasing the incidence angle has an effect on the stopband characteristics. The central wavelength is shifted toward shorter wavelengths and the bandwidth is reduced relative to that at normal incidence. If the rugate refractive index profile is adjusted to compensate for the change in angle of incidence, the new coating thickness will be thicker and the reflectance band will again be centered at the original wavelength, but the filter performance at off-normal incidence is poorer than at 0 degrees, due to the difference in bandwidth for the s- and p- polarisation components at off-normal incidence. [ 0008 ] The third method of achieving a broadened spectral region of high reflectance is "frequency chirping", i.e., modulation of the periodicity of the refractive index profile as a function of coating depth z. The rugate period can be varied in either in discrete steps or continuously throughout the coating. The chirped periods will reflect different regions of the spectrum and, depending on their spectral distribution, can create a continuous high-reflectance band over a broadened spectral region. As the region of high reflectance is extended by adding more rugate cycles of different periodicity, the total physical thickness of the structure is increased.

[ 0009 ] Frequency chirping will create a broader reflectance region compared to that of a constant rugate period, however, if the total number of rugate cycles is to be kept the same, the maximum reflectance will decrease as the chirping is increased. This is due to the fact that, for a given total number of rugate cycles, there are fewer cycles that will cause reflection at any given wavelength within the bandstop region.

[ 0010 ] Compared with the stacked rugate approach, the continuous nature of the chirped filter is less sensitive to changes in angle of incidence and when the chirping is performed in an optimum manner, the resulting coating thickness may be kept at a minimum for a given broadband reflectance.

[ 0011 ] A broadband bandpass filter may be composed of two chirped rugate filters in series. In general, the wider the region or regions of high reflectance, the larger the overall thickness of the resulting filter. This is critical for the practical implementation of a broadband rugate filter since, as the coating gets thicker, the requirements to materials and manufacturing techniques become extremely strict.

[ 0012 ] At least preferred embodiments of the present invention seek to provide a method of designing a rugate filter structure and a rugate filter structure, that address one or more of the above mentioned design issues for broadband rugate filters.

SUMMARY

[ 0013 ] In accordance with a first aspect of a rugate filter there is provided a method of designing a rugate filter structure, the method comprising the step of deriving a refractive index variation as a function of rugate filter thickness such that substantially an equal number of rugate periods; or parts thereof, reflect an incident optical signal at each targeted wavelength in a selected wavelength interval of interest. The wavelength interval of interest is generally a stopband in the reflectance and/or transmission profile of the rugate filter structure.

[ 0014 ] The refractive index variation may be formed by at least two rugate filter sections, each having a respective characteristic centre wavelength and spectral bandwidth, and may be derived in accordance with one or more of the following steps: selecting minimum and maximum values for the wavelength interval of interest; selecting the wavelength spacing between the characteristic centre wavelength of individual rugate filter sections; determining the number of and position of the individual rugate filter sections required to reflect an incident optical signal at each targeted wavelength or wavelength interval within a stopband region of the rugate filter structure, determining the number of and position of the rugate filter sections required to achieve a certain value of optical density over the wavelength region of interest; and determining the total number of rugate cycles in the refractive index variation. The at least two rugate filter sections may be contiguous stacks.

[ 0015 ] In accordance with the second aspect, there is provided a method of designing a rugate filter structure, the method comprising the step of deriving a refractive index variation as a function of rugate filter thickness such that a plurality of individual reflectance peaks overlap contiguously so as to form a stop band of the rugate filter.

[ 0016 ] In accordance with a third aspect, there is provided a method of designing one or more rugate filter structures according to the first or second aspects, and where one or more of these rugate structures are either combined or stacked to form a rugate filter exhibiting a broadened spectral response within one or more stopbands.

[ 0017 ] In accordance with a fourth aspect, there is provided a rugate filter structure fabricated based on a design obtained from a method as defined in the first, second or third aspects. The structure may be fabricated by a deposition process that provides a continuously varying index, or an approximation thereof, with very low stress and may be fabricated by a plasma impulse chemical vapour deposition process.

[ 0018 ] In accordance with a fifth aspect, there is provided an optical device comprising: a plurality of rugate filter sections, each filter section comprising a plurality of periods of refractive index variation to form a respective feature in the reflectance and/or transmittance profile of the optical device, each feature having a characteristic centre wavelength and spectral width wherein the features overlap contiguously to form a single feature in the reflectance and/or transmittance profile of the optical device. [ 0019 ] The single feature may have substantially uniform optical response characteristics over a broadened spectral region larger than the spectral width of each of the respective features. The single feature may be a uniform flat-topped feature in the reflectance and/or transmittance profile of the optical device. The single feature may be either a bandpass feature or a bandstop feature in the reflectance and/or transmittance profile of the optical device.

[ 0020 ] Each of the plurality of rugate filter sections may have a different K value, and each of the plurality of rugate filter sections has an equal number of periods or fractions of periods of refractive index variations to produce a broadened region of high reflectance. [ 0021 ] In other arrangements, the plurality of rugate filter sections comprises a large number of refractive index variation periods, each period having a small refractive index variation. The spacing between the characteristic centre wavelength of rugate filter sections having adjacent characteristic centre wavelengths may increase with increasing wavelength and may increase linearly with wavelength. [ 0022 ] The variation in the refractive index of the periods in each of the plurality of rugate filter sections may be uniform throughout the thickness of each respective section, or in parts thereof. In other arrangements, the variation in the refractive index of the periods in at least one of the plurality of rugate filter sections may be non-uniform throughout the thickness of the at least one section. In further arrangements, the refractive index of the periods in at least one of the plurality of rugate filter sections is apodised throughout the thickness of the at least one section. In further arrangements still, the refractive index of the periods in each of the plurality of rugate filter sections is apodised throughout the thickness of each section.

BRIEF DESCRIPTION OF THE DRAWINGS

[ 0023 ] Arrangements of the rugate filters described herein will be better understood and more readily apparent to one of ordinary skill in the art from the following written description, by way of example only, and in conjunction with the drawings, in which:

[ 0024 ] Figures Ia) to c) are plots of reflective index n(z) versus physical thickness z, reflectance R(λ) versus wavelength λ, and reflectance R(X) versus wavelength λ respectively, illustrating a method of designing a rugate filter structure according to an example arrangement. [ 0025 ] Figures 2a) to f) are comparison plots of the product K(z)*z versus physical thickness z, and transmittance T versus wavelength λ for different rugate filter structures according to different arrangements.

[ 0026 ] Figure 3 shows plots of reflectance versus wavelength for a rugate filter structure according to an example arrangement. [ 0027 ] Figure 4 shows plots of reflectance versus wavelength for a rugate filter structure according to an example arrangement.

[ 0028 ] Figure 5 shows plots of reflectance versus wavelength for a rugate filter structure according to an example arrangement.

[ 0029 ] Figure 6 shows plots of reflectance versus wavelength for a rugate filter structure according to an example arrangement.

[ 0030 ] Figures 7A) to C) are plots of the product K(z)*z versus physical thickness z, transmittance T versus wavelength λ, and reflectance R versus wavelength λ respectively of rugate filter structures according to different arrangements. [ 0031 ] Figures 8A) to C) are plots of the product K(z)*z versus physical thickness z, transmittance T versus wavelength λ, and reflectance R versus wavelength λ of a rugate filter structure according to another arrangement.

DETAILED DESCRIPTION

[ 0032 ] The theory and method used for the design of flat-topped, broadband rugate filters according to example arrangements are disclosed. The term 'flat-topped' refers to a highly uniform reflectance across the desired spectral reflective region of the rugate filter. The description is based upon the results from Southwell's coupled wave theory (W. Southwell, "Spectral response calculations of rugate filters using coupled-wave theory," J. Opt. Soc. Am. A 5, 1558-1564 (1988)), which are valid in the limit of small index oscillations (n_p « n_a , where n_p is the peak variation and n_a is the average value of the rugate refractive index profile).

[ 0033 ] The degree of uniformity across the high-reflectance band depends on the distribution of individual rugate periods with a given K-value within the spectral region of interest. The K-value may be defined as the ratio 4τm_a/λ for a rugate cycle of period thickness λ/2n_a, but when varied as a function of thickness z it determines the spatial frequency modulation of the periodic refractive index profile. It has been recognised that it is desirable to have an equal number of rugate periods reflecting at every targeted wavelength λ within the stopband. For a single rugate section of constant K-value, the bandwidth BW₀ of the stopband is given by:

where Δλ is the width of the region of high reflectance, centered at XQ. Figure 1 illustrates a rugate filter constructed from a series of individual simple rugate sections e.g., 102, each producing narrowband reflectance peaks e.g. 100, centered at different wavelengths λj and with corresponding spectral widths of high reflectance Δλ;. The individual rugate sections, e.g., 102, have different Kj values, illustrated in Figure l(a), and the physical thickness Δz; of each section increases with increasing rugate period. [ 0034 ] Let N be defined as the number of sections of different Kj values, where each section consists of S cycles, so that i is an integer i=[l...N ] and the total number of rugate cycles is G = S * N. If the individual stopbands e.g. 100 (Figure Ib) are moved closer together, they will at some point start to overlap (Figure l(c)). As the distance between each λ; gets smaller, the uniformity of the reflectance between the peaks e.g. 104 will continue to improve up to the point where the broadband response is lost and the individual peaks 104 overlap around a single central wavelength, eventually resembling a regular narrow-band rugate filter. When the individual reflectance peaks overlap in a contiguous manner, however, a broad spectral region 106 will arise with improved uniformity and flatness. The absolute value of the reflectance and the degree of uniformity across this broadband region according to example arrangements 106 is thus a matter of choosing suitable parameters for the number of periods S and the spacing parameter W, the latter referring to the relative distance between each of the central wavelengths λj. [ 0035 ] The bandwidth Δλ; of each rugate section only depends on the refractive indices n_p and n_a, and can therefore be treated as a constant, provided these indices remain the same throughout the coating. When the central wavelength λj is increased, the bandwidth of the reflectance band Δλj preferably also increases in a proportional way to keep BWc (equation (I)) constant. Hence, the spacing between individual reflectance bands within the spectral region of interest therefore preferably increases linearly with wavelength, in order to achieve a constant reflectance level across that region in an example arrangement. This can be expressed as follows:

AX_X = BW_C *X_{X (2)}

[ 0036 ] Assuming two adjacent stopbands are to be placed a distance apart so that their bandwidths are contiguous at the BW_C reflectance points, the position of the next stopband is

A₂ = λi + (0.5Δλi + 0.5Δλ₂) ∞ A₁ + Δλ^ ₍₃₎ with the approximation that the difference in bandwidth between two consecutive stopbands is negligible. Combining Eq. (2) and (3), and introducing a constant C = (1 + BWc), one can write λ₂ = λ_ι + BW_c *λ_ι = Cλ_{ι (4)}

[ 0037 ] This procedure may be extended to any number of adjacent stopbands, placed in series to form a contiguous broad region of high reflectance in example arrangements. The resulting expression for the position of the i^th stopband is

and the corresponding Ki- value is _ 4τrn_α _ 4τrπ_α -^ ^λi ^Λl . (6)

[ 0038 ] Consider next the total physical thickness of the rugate coating. The thickness ΔZ_J of each individual section, consisting of S cycles with a given Kj-value, can be calculated from

2n_α . ₍₇₎

[ 0039 ] For N contiguous sections, positioned in series in accordance with Eq. (5), the total thickness is

[ 0040 ] Substituting Eq. (5) into Eq. (8),

Z_N = A (A₁ + Cλi + C²X₁ + • • • + C^-¹A₁)

2n_α V / (9)

= ^- (i + c + c² + - - - + c^N-¹) ²ⁿa ^{V J} . (10)

[ 0041 ] Eq. (10) represents a geometric series which sum may be expressed as SX₁ (I - C] SX₁ , _N N ^ZN = ²^ {^~^⁰ ) ⁼ ^ ^{[C ~ 1}} _{. (11)}

[ 0042 ] Hence, the total thickness of the flat-topped rugate filter in example arrangements can be determined from X₁ and the number of cycles per section, S. For the calculation of the rugate index profile n(z) as a function of the physical coating depth z, Eq. (11) may be used with the subscript i substituted for N, allowing the coating thickness to be determined at the position of any given section. By repeating this calculation for i =

[1...N], the coating depth will be defined in steps throughout the filter. Dividing each step into S x p equal intervals, where p is the number of points defining each rugate cycle, the rugate sinusoidal profile can be determined at each position z throughout the coating.

[ 0043 ] In the design process for the broadband flat-topped rugate filter in an example arrangement, the designer enters the lower and upper wavelength limits of the bandstop region, Xi and X_N. The reference wavelength of the bandstop may be set as the average of these limits. The total width of the stopband, (X_N - X₁), is equal to the sum of all Δλ;, for i = [1...N]:

[ 0044 ] Solving for N gives

₍₁₃₎

[ 0045 ] Eq. (13) determines the number of consecutive narrowband sections that must be positioned in series, to cover the full bandstop region with a given relative spacing distance between each section. The spacing between each section was in the methodology above assumed to be fixed by the constant bandwidth BW₀. It is useful to introduce a spacing parameter W so that the designer is free to position the individual rugate cycles either closer together or further apart in different arrangements. A modified bandwidth BWw is defined, BW _m = W *BW_C

(14) and, by redefining the expression for the constant C as

C = I + BW_{101 (15)} equations (4)-(13) remain the same. [ 0046 ] For instance, the designer enters a weight 0 < W < 1 to decrease the spacing between the individual rugate sections and, hence, improve the optical performance of the rugate broadband reflectance. If the spectral region of high reflectance is to be kept at the same width, this action may require that the total number of rugate cycles is increased. In summary, when the designer selects the upper and lower wavelength boundaries of the stopband and a value for the spacing parameter W in an example arrangement, the required number of and the optimum position of the N contiguous sections will be determined. The designer then has the choice of selecting a value for either S or G, which determines the total number of rugate cycles in the coating and, hence, the resulting optical density (OD) of the resulting broadband reflectance region. [ 0047 ] It is also possible to use the desired OD as a design parameter, instead of the number of rugate cycles in different arrangements.

[ 0048 ] Results for the design of flat-topped, broadband rugate filters according to the described arrangements, and two examples of applications are disclosed below.

[ 0049 ] Figure 2 shows the effect of varying the spacing parameter W on the broadband performance of the flat-topped rugate filter. The filter consists of approximately 400 rugate cycles in total, and has a targeted reflectance band from 500 to 1000 nm. No apodisation or matching functions have in this case been applied to the rugate refractive index profile. The results show the K(z)*z product (curves 200a, 202a, 204a) and the corresponding transmittance profile (curves 200b, 202b, 204b), the latter plotted on a semi-logarithmic scale, for three options of W. In these figures, a low value of transmittance corresponds to a high value of reflectance. In Figure 2 a-b, a spacing parameter of W = 1 allows for only four sections (in this example being stacks), positioned at different central wavelengths, and each section consists of a large number of cycles S of constant periodicity. In Figure 2b, the characteristics of the N=4 individual sections are clearly visible and do not satisfactorily overlap to produce a uniform, broadband reflectance. Furthermore, the reflectance region is shifted toward shorter wavelengths because of the wide stopband achieved with the large number of cycles in each section, and by positioning the first section at X₁ = 500 nm, which extends the high- reflectance region beyond the lower boundary of the bandstop.

[ 0050 ] Reducing W to 0.5 in Figure 2 c)-d), the number of sections (N) doubles and the resulting reflectance characteristics (curve 202b) can be seen to improve, but the discrete steps in the K(z)-function (curve 202a) are still visible and the broadband performance is not yet satisfactory. Reducing W down to 0.1 in Figure 2 e)-f) results in a large number of sections (N) and a relatively smooth K(z)*z function (curve 204a) . The corresponding reflectance characteristics (curve 204c) show a uniform, flat-topped reflectance across the stopband 206, which is also correctly positioned between the selected wavelength boundaries. [ 0051 ] These results show that it can be of benefit to select a small value for W, i.e., let the incremental spacing approach a continuous variation of the rugate period as a function of coating depth. In the following two examples of a filter for laser eyewear protection and for solar beam splitting, W-values between 0.005 and 0.01 have been chosen, and S is set equal to one. The rugate peak variation is also reduced, to stay within the small-index limitation of the coupled wave theory and to prevent the build-up of undesired secondary reflectance peaks outside the primary bandstop.

[ 0052 ] Example arrangements produce a highly uniform and flat-topped broadband reflectance across the desired spectral regions. The quality of the resulting stopband is dependent on the choice of the spacing parameter W and the number of rugate cycles. Best results may be achieved for small values of W, i.e. a tight packing of the N individual rugate sections, and with only a few cycles within each section.

[ 0053 ] The theoretical description above assumes n_p « n_a, and a relative increase in the ratio n_p/n_a results in higher reflectance for a given number of rugate cycles but at the same time secondary reflectance peaks may start to appear. Furthermore, for large n_p values, the input parameters X₁ and X₂ of the bandstop region may no longer be an accurate measure for the bandstop boundaries. Having the choice of increasing the contrast of the index oscillation may still be useful in cases where it is important to keep the total number of rugate cycles and the coating thickness at a minimum.

[ 0054 ] In the description of arranging the reflectance peaks with a constant relative spacing distance, it was assumed that the ratio n_p/n_a is kept constant throughout the coating. This may not be the case when apodising and matching functions are applied to the refractive index profile. The apodisation results in a smaller n_p/n_a ratio and, hence, a smaller spacing between each rugate section. This may be seen as an increase in reflectance in the apodised region at each end of the filter. [ 0055 ] The steepness behaviour of the transition regions of the rugate stopband in example arrangements may be explained as follows. Starting from z = 0, as an increasing number of rugate cycles causes the reflectance peaks of individual rugate sections to overlap at a given reference wavelength λ, there will be a steady build-up of constructive interference, and the absolute value of the reflectance in the corresponding spectral region will increase until an equilibrium has been met for the i'th section. This equilibrium is characterised by an equal number of reflectance peaks overlapping on either side of the i'th stopband (Figure Ic). The number of overlapping reflectance peaks required before this equilibrium is reached depends on the bandwidth and the number of cycles S within each section, as well as the spacing parameter W. [ 0056 ] One implication of the above is that there may be a minimum requirement for the width Δλ of the spectral region to be reflected, since within a narrow spectral region all of the individual rugate reflectance peaks may overlap and hence create a peaking, rather than a flat-topped, reflectance profile. Another implication may be that at the edges of the stopband, an increased variation in reflectance can be seen to appear (compare e.g. region 208 in Figure 2). A solution to this end-effect problem may be found, for instance by adding more rugate cycles with K-values that correspond to the wavelengths where there are fewer cycles overlapping, to maintain constant reflectance. Another solution might involve a gradually decreasing W- value at either end of the rugate coating, which would position the end-cycles closer together and therefore compensate for the decreasing amount of cycles overlapping. [ 0057 ] Introducing real materials with dispersion, the flat-topped rugate profile may suffer slightly, depending on the variation in the ratio n_p/n_a with wavelength. Generally, the refractive index of dielectric materials vary only slowly in the visible and near- infrared region, typically with increasing dispersion toward the ultraviolet wavelengths. By the implementation of numerical optimisation procedures, materials with both dispersion and absorption can be allowed for. For high power applications it may be vital that the materials have very low absorption coefficients, and this property is emphasized when thick coatings are involved. The manufacture of thick rugate coatings may require a deposition process that provides a continuously varying index with very low stress within the coating. For the coating to meet its design criteria, stringent requirements may be imposed on the deposition technique and the materials used. Recent advances in manufacturing capabilities have made the fabrication of such thick coatings a feasible option. When only small compositional variations are used, rugates or multilayer stacks without internal stresses may be attained using techniques such as the plasma impulse chemical vapor deposition. Stacks of thousands of discrete quarter- wave layers or graded-index rugate periods, resulting in a total thickness of several 100 μm or even up to the mm-range, may then be feasible.

[ 0058 ] Example arrangements have applications in a multitude of industrial and research areas, including optics, communications, astronomy, meteorology, and military applications.

[ 0059 ] In the following, characteristics of rugate filters designed in accordance with example arrangements will be described. Solutions for both bandpass and bandstop configurations are suggested.

[ 0060 ] The rugate filters in the example arrangements were designed by specifying the upper and lower wavelengths of the stopband region(s) and the total number of rugate periods, which determines the magnitude of the reflectance within the stopband region(s).

The wavelength boundaries of the stopband regions are carefully chosen, so that an excessively thick coating can be avoided while at the same time accommodating for most of the energy in the incident spectrum. The lower and upper boundaries chosen for the evaluation of the example rugate filter arrangements in Figures 3-6 were set to 300 nm and 2500 nm, respectively. Non-dispersive materials were assumed, and the reflectance caused by the glass-air interface at the back of the substrate was not taken into account. Hence, in practice an antireflective coating may have to be added to the back of the substrate, to ensure high transmittance within the transmissive region(s) of the filter. [ 0061 ] The rugate profiles in the example arrangements have been evaluated with the standard matrix method, by approximating each rugate cycle as a stack of thin discrete layers and assuming small incremental differences in refractive index. The resulting reflectance characteristics were further smoothed over 13-nm intervals (for a rugate filter designed for a mean weighted angle of incidence of the light beam at 54 degrees) and 23- nm intervals (for a rugate filter designed for a mean weighted angle of incidence of the light beam at 14 degrees), to simulate the effects of a cone of incident light. The distribution of the mean weighted angle was assumed to be Gaussian, and was determined as the annual average angular distribution using raytrace simulations for a hybrid PV/thermal central receiver system. [ 0062 ] Figure 3 shows the resulting reflectance profiles for s-polarisation, p- polarisation, average polarisation, and a target profile 400, 402, 404, and 406 respectively for a rugate bandstop filter according to an example arrangement designed for, and at 54 degrees incidence. Figure 4 shows a comparison of the same bandstop filter of Figure 3 when used at an incidence angle of 14 degrees (curve 502) and a different rugate bandstop filter in accordance with another example arrangement (curve 500), designed for the angle of incidence of 14 degrees. For the other example arrangement (curve 500), the refractive index n(z) is varied more rapidly with thickness z (more rapid frequency chirping) so as to accommodate for the effect of reducing the angle from 54 to 14 degrees (and thereby also reducing the thickness of the filter at 14 degrees, compared with the thickness at 54 degrees).

[ 0063 ] Similarly, the reflectance profiles for s-polarisation, p-polarisation, average polarisation, and a target profile 600, 602, 604, and 606 respectively of the rugate bandpass filter designed for, and at 54 degrees incidence is shown in Figure 5. The response at 14 degrees incidence can be seen in Figure 6, curve 702 for the bandpass filter designed for 54 degrees, and curve 700 for the bandpass filter designed for 14 degrees.

[ 0064 ] For the rugate filters plotted at the 54-degrees design angle in Figures 3 and 5, the main cause of deviation from the target function is believed to be the step in refractive index between air and the lowest allowed refractive index at the front of the coating, which has been set to Π_L = 1.45 due to the availability of practical materials. This step results in a broadband transmittance loss in the passband region(s). The transmittance loss increases as a function of incidence angle, as seen by comparing Figure 3 with Figure 4, and Figure 5 with Figure 6. [ 0065 ] The polarisation splitting is apparent within the transmissive regions, but is almost negligible across the high-reflection regions. The uniformity of the reflectance profile causes the rugate filter to be relatively insensitive to changes in the angle of incidence, compared with e.g. discrete filters. Discrete filters typically show a larger variation in the polarisation splitting and the filter performance as the incidence angle changes. The rugate filters in example arrangements were found to have a slightly better solar-to-electric energy conversion efficiency for the hybrid PV/thermal receiver system, compared with discrete bandpass and bandstop filters.

[ 0066 ] A high optical performance for the rugate filters in example arrangements is achieved by using a small refractive index variation (n_p) and a large number of cycles. With the chirping method applied in this study, the result is coating thicknesses up to the millimetre-range when the filters are designed to reflect the major part of the broadband solar spectrum. By assuming a larger value for n_p in the rugate sinusoidal variation, the coating thickness can be significantly reduced. This may have to be balanced against an increase in the undesired sidelobes. For the manufacture of such extremely thick coatings, a deposition process that provides a continuously varying index with very low stress within the coating is preferable. For the coating to meet design criteria of high performance and durability, stringent requirements are preferably imposed on the deposition technique and the materials used, i.e. good adhesion to the substrate, suitable thermal expansion coefficients, and, in particular, negligible absorption coefficients of the deposited materials. Low-scatter, defect-free optical thin film coatings may e.g. be produced by high temperature plasma enhanced chemical vapour deposition (PCVD) methods, which have shown high surface and bulk damage thresholds. The latter can be important in high-flux applications, such as in solar central receiver systems where the concentration ratio on the filter surface may reach several hundred suns, and where 'hot spots' may arise from an inhomogeneous distribution of the incident solar flux.

[ 0067 ] The methodology disclosed in example arrangement may be used in a large range of systems, such as large dishes or troughs used for light collection, that will have a broad distribution of angles incident on an optical filter or a spectral receiver positioned in the focal region of the system. The rugate filter in example arrangements can be designed for an incident angle that on average gives high performance over a range of angles.

[ 0068 ] The rugate filter of example arrangements can be a desirable design approach due to the simplicity of the design process, where the required level of reflectance and the position of the band-edges can be specified, and due to the smaller sensitivity to changes in incidence angle. The latter implies that, the rugate filter of example arrangements can perform reasonably well if designed for an angle of incidence that takes into account the spectral shift of the band-edges, as well as the angle at which most of the light is incident. The disclosed methodology in example arrangements represents a framework which is easy to adapt to a given situation. Other solutions to the design problem are possible, and the final design may be chosen based on an evaluation of the practical considerations, such as manufacture limitations, cost, and coating durability, versus the useful optical throughput or energy output that can be expected from the system.

[ 0069 ] In the following, two applications of example arrangements are described: (1) a reflective coating for laser protection eyewear, and (2) a spectral beam splitter for improved solar power conversion in a hybrid receiver solar concentrating system.

(1) A reflective coating for laser protection eyewear

[ 0070 ] Laser protection eyewear is an important industry with applications within a range of research disciplines, as well as for military purposes. One example of a high- power laser is the copper vapor laser, with two laser lines at 511 nm and 578 nm (green/yellow region) . Commercial laser safety goggles are available with a peak OD in the range of 5-6, but typically characterised by a highly non-uniform reflectance for the different laser line regions. Depending on the application and the output power of the laser, a lower or higher OD-level may be desired. The laser protection would also be more effective and predictable if the reflectance was kept uniform across the desired spectral range. As an example, a broadband, flat-topped rugate filter has been designed in example arrangements for two different OD-levels of laser protection. It was also taken into account that the laser beams may be incident from an off-normal angle of incidence and still cause damage of the eye. Assuming n_a = 1.9 and allowing for an angular range from normal incidence up to 45°, the two laser lines will experience a wavelength shift from 511 to 474 nm, and from 578 to 536 nm. The resulting broadband protective laser coatings, shown in Figure 7 for normal incidence, have been designed for a band-stop region of 470-580 nm, blocking both of the laser lines at all angles up to 45°. A partial linear apodisation over 20 cycles and quintic matching over 3 cycles were applied to all the rugate designs shown in Figure 7. The first design (curves 800a, 802a, 804a) assumes refractive indices indices «χ = 1.8 and n_# = 2.0, and has a total number of rugate cycles C = 1051 (W = 0.005, S = 1). This results in a total thickness of 145 μm, and the broadband OD-level is approximately 9. The second design (curves 800b, 802b, 804b) also assumes indices «/, = 1.8 and TI_H — 2.0, and has a total number of rugate cycles C = 584 (W = 0.009, S = 1). This results in a total thickness of 80.5 μm, and the broadband OD-level is approximately 4. To allow for end effects, the lower and upper wavelength limits during the design of these flat-topped rugate filters were set to 455 and 600 nm, respectively. If a larger value of n_p is assumed, the coating thickness can be reduced but at the expense of the steepness of the stopband edges. The third design (curves 800c, 802c, 804c) assumes refractive indices m = 1.7 and «_# = 2.1, and has a total number of rugate cycles C = 214 (W = 0.017, S = 1). This results in a coating thickness of 29.5 μm, and the broadband OD-level is between 4 and 5. To achieve uniform reflectance across the desired stopband region, the lower and upper wavelength limits in this case were shifted to 430 and 630 nra, respectively.

[ 0071 ] A high degree of uniformity is achieved across the desired spectral region, providing a reliable and predictable level of protection from the two laser lines, for a range of incidence angles. There is still red and blue light on either side of this stopband that is transmitted through with very little loss, providing some visibility for the user of the protective eyewear in the example arrangements. It should be noted that, although the reflectance stays flat as the angle of incidence is increased, the OD-level for average polarised light may decrease due to polarisation splitting. The coating performance may therefore depend on the polarisation direction of the incident laser radiation.

(2) A spectral beam splitter for improved solar power conversion

[ 0072 ] The electric conversion efficiency of a solar concentrating system can be improved by employing a spectrally selective filter (beam splitter) that divides the solar radiation into optimised components for two or more receivers. A broadband spectral beam splitter was designed in another example arrangement for an application for the flat-topped rugate filter. The filter was optimised for maximum annual energy output in a hybrid photovoltaic/thermal central receiver system. In this example arrangement, two flat-topped stopbands, designed for two different spectral regions, are placed in series. The first stopband covers the wavelength region 300-590 nm, and the second stopband covers the wavelength region 1090-2500 nm. The results can be seen in Figure 8. The performance is highly satisfactory in both the reflective and the transmissive regions of the bandpass filter (curves 900, 902 respectively). The total thickness of such a filter is very large, and for the design shown, assuming n_L=1.9, nπ = 2.0, and W = 0.01, the final coating consists of 5836 cycles and has a total thickness of 1.7 mm (see curve 904). [ 0073 ] It will be appreciated by a person skilled in the art that numerous variations and/or modifications may be made to the present invention as shown in the specific embodiments without departing from the spirit or scope of the invention as broadly described. The present embodiments are, therefore, to be considered in all respects to be illustrative and not restrictive.

Claims

CLAIMS:

1. A method of designing a rugate filter structure, the method comprising the step of: deriving a refractive index variation as a function of rugate filter thickness such that substantially an equal number of rugate periods, or parts thereof, reflect an incident optical signal at each targeted wavelength in a selected wavelength interval of interest.

2. A method as claimed in claim 1 wherein the refractive index variation, being formed by at least two rugate filter sections each having a respective characteristic centre wavelength and spectral width, is derived by the steps of: selecting the wavelength spacing between the characteristic centre wavelength of the individual rugate filter sections; and determining the number of and wavelength position of the individual rugate filter sections required to reflect an incident optical signal at each targeted wavelength or wavelength interval within a stopband region of the rugate filter structure;

3. A method as claimed in claim 1, wherein the refractive index variation, being formed by at least two rugate filter sections each having a respective characteristic centre wavelength and spectral width, is derived by the steps of: selecting the wavelength spacing between the characteristic centre wavelength of the individual rugate filter sections; and determining the number of and position of the individual rugate filter sections required to achieve a desired value of optical density over the wavelength region of interest.

4. A method as claimed in claim 3, further comprising the step of determining the total number of rugate cycles in the refractive index variation.

5. A method as claimed in any one of claims 2 to 4, further comprising the step of initially selecting minimum and maximum values for the wavelength interval of interest.

6. A method as claimed in any one of claims 2 to 5 wherein the at least two rugate filter sections are contiguous stacks.

7. A method as claimed in any one of the preceeding claims wherein the wavelength interval of interest is either a passband or a stopband in the reflectance and/or transmission profile of the rugate filter structure.

8. A method of designing a rugate filter structure, the method comprising the step of: deriving a refractive index variation as a function of rugate filter thickness such that a plurality of individual reflectance peaks overlap contiguously so as to form a stop band respectively of the rugate filter.

9. A method of designing a rugate filter structure, the method comprising the step of: deriving a refractive index variation as a function of rugate filter thickness so that the stopband has a uniform reflectance within it.

10. A method of designing a rugate filter structure, the method comprising the step of: deriving a refractive index variation as a function of rugate filter thickness so that the spacing between the centre wavelengths of the contiguous rugate sections, each having the same number of periods or fraction of a period, is increased in proportion to the centre wavelength of the contiguous rugate sections.

11. A method of designing a rugate filter structure as claimed in any one of the preceding claims, where one or more of the rugate structures are either combined or stacked to form a rugate filter exhibiting a broadened spectral response within one or more stopbands.

12. An optical device where the desired reflectance and/or transmittance profile is achieved by means of the method as claimed in any one of claims 1 to 11.

13. An optical device as claimed in claim 12, wherein the device comprises one or more of a group of edge filter designs, bandpass designs, bandstop designs, beam splitter designs, or any other design where a uniform optical response characteristics over a broadened spectral region is desired.

14. A rugate filter structure fabricated based on a design obtained from a method as claimed in claims any one of claims 1 to 11.

15. A rugate filter structure as claimed in claim 14 fabricated by a deposition process that provides a continuously varying index, or approximations thereof made from individual layers, with very low stress.

16. A rugate filter structure as claimed in claim 14 fabricated by a plasma impulse chemical vapour deposition process.

17. An optical device comprising: a plurality of rugate filter sections, each filter section comprising a plurality of periods of refractive index variation to form a respective feature in the reflectance and/or transmittance profile of the optical device, each feature having a characteristic centre wavelength and spectral width wherein the features overlap contiguously to form a single feature in the reflectance and/or transmittance profile of the optical device.

18. An optical device as claimed in claim 17 wherein the single feature has substantially uniform optical response characteristics over a broadened spectral region larger than the spectral width of each of the respective features.

19. An optical device as claimed in claim 18 wherein the single feature is a uniform flat-topped feature in the reflectance and/or transmittance profile of the optical device.

20. An optical device as claimed in claim any one of claims 17 to 19 wherein the single feature is either a bandpass feature or a bandstop feature in the reflectance and/or transmittance profile of the optical device.

21. An optical device as claimed in any one of claims 17 to 20 wherein each of the plurality of rugate filter sections has a different K value, where K is given by 47m_a/λ, n_a is the average of the refractive index of the rugate structure, and the K- value of the individual section with ordinal number i is:

_ 4πn_α _ K _1.;

Ai Al where C is l+n_p/2n_a where n_p is the difference between the maximum and minimum refractive index of the rugate index variation.

22. A rugate as claimed in claim 21 wherein the factor C is given by l+W*n_p/2n_a, where W is a constant with numerical value between 0 and 1.

23. An optical device as claimed in any one of claims 17 to 22 wherein each of the plurality of rugate filter sections has an equal number of periods or fractions of periods of refractive index variations.

24. An optical device as claimed in any one of claims 17 to 23 wherein each of the plurality of rugate filter sections comprises a large number of refractive index variation periods, each period having a small refractive index variation.

25. An optical device as claimed in any one of claims 17 to 24 wherein the spacing between the characteristic centre wavelength of individual rugate filter sections having adjacent characteristic centre wavelengths increases with increasing wavelength.

26. An optical device as claimed in claim 25 wherein the spacing between characteristic centre wavelengths increases linearly with wavelength.

27. An optical device as claimed in any one of claims 17 to 26 wherein the variation in the refractive index of the periods in each of the plurality of rugate filter sections is uniform throughout the thickness of each respective section, or in parts thereof.

28. An optical device as claimed in any one of claims 17 to 26 wherein the variation in the refractive index of the periods in at least one of the plurality of rugate filter sections is non-uniform throughout the thickness of the at least one section.

29. An optical device as claimed in any one of claims 17 to 26 wherein the variation in the refractive index of the periods in at least one of the plurality of rugate filter sections is apodised throughout the thickness of the at least one section.

30. An optical device as claimed in any one of claims 17 to 26 wherein the variation in the refractive index of the periods in each of the plurality of rugate filter sections is apodised throughout the thickness of each section.