Abstract

The European Space Agency’s space-based DARWIN mission aims to directly detect extrasolar Earth-like planets using nulling interferometry. However, in order to accomplish this using current optical technology, the interferometer input beams must be filtered to remove local wavefront errors. Although short lengths of single-mode fiber are ideal wavefront filters, DARWIN’s operating wavelength range of 4–20 µm presents real challenges for optical fiber technology. In addition to the fact that step-index fibers only offer acceptable coupling efficiency over about one octave of optical bandwidth, very few suitable materials are transparent within this wavelength range. Microstructured optical fibers offer two unique properties that hold great promise for this application; they can be made from a single-material and offer endlessly single-mode guidance. Here we explore the advantages of using a microstructured fiber as a broadband wavefront filter for 4–20 µm.

©2006 Optical Society of America

1. Introduction

1.1 Detecting extrasolar planets

The discovery of an Earth-like body around a neighboring star would have wide ranging significance to astronomy and, in particular, to the search for extra terrestrial life. Since the discovery of the first extrasolar planet in 1995 [1], almost 200 worlds have been detected in orbits around other main sequence stars. However, nearly all of these planets have been found via measurements of their parent star’s radial velocity, a technique that intrinsically favors the detection of massive planets like Jupiter and Saturn. Other techniques, such as those utilizing photometric transits and gravitational microlensing, may be capable of detecting small terrestrial worlds, but are severely limited in application (transit data alone gives no information about a companion’s mass, while microlensing events are, by their very nature, unpredictable and short lived [2]).

An alternative approach considered in the search for small terrestrial planets is direct detection via nulling interferometry, whereby the glare of the parent star is suppressed through the coherent combination of light collected by multiple telescopes [3, 4]. Spectroscopic characterization of light from a planet could also be used to provide clues as to the planets habitability. This is the goal of the European Space Agency’s DARWIN mission and NASA’s Terrestrial Planet Finder (TPF), which aim to use space-based interferometers observing at wavelengths of 4–20 µm to directly detect extrasolar Earth-like planets and characterize them as possible abodes of life [5, 6]. The 4–20 µm observational window is defined by the scientific goal of detecting the spectral signatures of key biomarkers such as O3, H2O and CO2, which are indicative of life. Observation at these wavelengths also aids detection as the brightness contrast between stars and planets falls by several orders of magnitude in the midinfrared [3]. Even so, the requirements on the interferometer are stringent and to adequately detect an Earth-like world using current optical technology, the interferometer input beams must be ‘filtered’ to remove local wavefront errors [7–9].

Single-mode fibers form ideal wavefront filters as the output field profile is solely determined by the modal properties of the fiber. Such wavefront filters are typically referred to as modal filters. However, the observational wavelength range required by DARWIN and the TPF presents significant challenges for optical fiber technology [10]. Since light can only be coupled into a step-index fiber (SIF) with acceptable efficiency over an optical bandwidth of about one octave, more than one fiber must be used. Currently, the accepted solution is to split the wavelength range into 2–4 spectral windows that can each be addressed by individual fibers [9]. In addition, very few suitable materials are transparent within this wavelength range and finding thermally and chemically compatible core and cladding materials with a sufficiently low index contrast to ensure single-mode guidance is problematic. At present, the ability to fabricate fibers for transmission at wavelengths above 4 µm is a significant challenge in its own right.

One promising alternative for this type of application is microstructured optical fiber (MOF) technology, which allows endlessly single-mode structures to be created from materials with highly contrasting refractive indices, such as glass and air [11, 12]. This not only relaxes material requirements, permitting single-material waveguides, but can also offer significant advantages for broadband single-mode applications [13–15]. In this paper we investigate, via numerical calculations, the potential advantages that MOFs could offer relative to step-index designs for modal filtering over the wavelengths of 4–20 µm.

1.2 Outline

In the following sections, the principles of nulling interferometry and single-mode fibers as modal wavefront filters are briefly outlined. The basic properties of MOFs are then reviewed and the relative merits of step-index and microstructured fibers for use as a modal filter in DARWIN / TPF-like applications over the wavelengths of 4–20 µm are explored.

2. Nulling interferometry and wavefront filters: basic principles

2.1 Nulling interferometry

The challenges of directly detecting an Earth-like planetary system lie with the huge brightness contrast and tiny angular separation between a star and any orbiting planet. For example, if viewed from a distance of 4 parsecs, the brightness contrast between Earth and our Sun would be about 106 at best (as shown in Fig. 1(a)), with an angular separation of ~ 0.5 µrad [3]. Nulling interferometry is one method that can be used to separate light arriving from slightly different directions and is particularly well suited to systems with high intensity contrast. The simplest version of a nulling interferometer, known as a Bracewell interferometer [3], involves the coherent combination of light from two identical telescopes and is used here to illustrate the basic principles of this technique. In this configuration, shown in Fig. 1(b), light from the star arrives at both telescopes simultaneously. Light from the planet, however, travels at a slight angle relative to the star-light and is thus collected by each telescope at slightly different times. By introducing a phase delay of λ/2 on the light from one of the telescopes, the star-light can be made to experience destructive interference within the interference pattern and by adjusting the baseline of the interferometer appropriately (i.e. for a telescope spacing of λ/2θ), the light signal originating from the planet can be enhanced via constructive interference.

 figure: Fig. 1.

Fig. 1. (a) Fluxes of the Sun and Earth as seen from a distance of 4 pc (Nλ is the photon flux), adapted from [3]. The DARWIN spectral band is indicated by the shaded region. (b) Schematic of a Bracewell nulling interferometer.

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2.2 Modal wavefront filters for nulling interferometry

The ratio between the interferometer output power at the regions of destructive and constructive interference determines the rejection ratio of the star-light relative to the light from the planet. In order to adequately detect the light of an Earth-sized world orbiting close enough to the star to be within the so-called ‘life zone’ [3], a rejection ratio of 105–106 is required [9]. The rejection ratio of a nulling interferometer is strongly degraded by wavefront errors and the above requirements correspond to instrumental tolerances that cannot be met with current optical technology. However, these tolerances can be relaxed if a wavefront filter is used to eliminate the effect of local disturbances within the amplitude profile and the phase front of the input beams [7–9]. Single-mode waveguides are an attractive solution for this since their output field shape is essentially independent of the launch conditions, enabling correction of both the phase and amplitude profile [8]. Furthermore, single-mode fibers can efficiently correct wavefront defects with both high and low-order spatial frequencies, unlike simple pinholes [8].

The basic principles of a modal wavefront filter formed by a single-mode fiber are illustrated in Fig. 2. Here we assume a simple coupling arrangement where a freely propagating plane wave incident on a circular aperture of radius a is focused by a single thin, diffraction limited lens of focal length ƒ located in the aperture plane α at z=0. The fiber is placed at the focal point z=f in the coupling plane β. In general, an infinite number of modes are excited at the coupling plane. However, all modes other than the fundamental mode (FM) are strongly attenuated and after a certain distance the majority of power is carried in the FM. We note that this coupling arrangement is the simplest one could consider and that more complex systems may offer better broadband performance. However, using this scheme it is possible to present a clear comparison between the performance of MOFs, as calculated here, and the performance of SIF designs, as reported elsewhere in the literature [10, 16]. Within this paper, results extracted from Fig. 3 in [10], which show the coupling efficiency as a function of the normalized frequency, are used for comparison.

The performance of a modal filter of a given length, l, is defined by the output power ratio between the FM and any other leaky higher-order, radiation or cladding modes excited at launch. This can be approximated by considering the output power ratio between the FM and the lowest-order leaky mode (corresponding to the LP11 mode below cut-off [10]), by assuming that all power not coupled into the FM is coupled into the lowest-order leaky mode (LM). The output power ratio in this ‘worst case scenario’ is thus defined as;

A=η10σl(1η)whereσ=lαLM10,

αLM is the leakage loss of the leaky mode (in dB/m) and η is the fraction of power coupled into the FM at launch. By approximating the FM modal field of the fiber by a Gaussian of width ωβ (where ωβ is the width at which the intensity drops to 1/e2 of its peak value), and evaluating the coupling efficiency at the aperture plane, η can be written simply as [17]:

η(λ)=2χ2(1eχ2)2,whereχ=απωβ(λ)fλ

In this approximation, the maximum value of η is 0.81 and corresponds to χ=1.121. From this it can be seen that the coupling system, with a/f as the sole free parameter, can only be optimized at a single wavelength (λopt), for which a/f=1.121λopt/(πωβ). For any given lens system, the broadband coupling efficiency is thus dependent on how ωβ evolves as a function of wavelength.

 figure: Fig. 2.

Fig. 2. Simple coupling arrangement and principles of a modal wavefront filter adapted from Fig. 2. in [10].

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It should be appreciated that in all calculations of η for the MOFs presented here, we take advantage of the simplification offered by approximating the modal field with a Gaussian function. We find this to be an acceptable assumption over the whole of the wavelength range considered (for further details we refer the reader to Section 4.3). However, in single-mode SIFs, the FM expands rapidly towards long wavelengths and this assumption becomes increasingly less valid in the long wavelength limit. For the actual FM of a SIF, the maximum value of η at cut-off (i.e. for V=2.405) is ~ 0.79 and falls to ~ 0.65 at two octaves below cut-off [10, 17]. Consequently, the calculated values of η for SIFs shown here for comparison (extracted from Fig. 3 in [10]), do not include this assumption, and instead use the exact field of the FM.

3. DARWIN modal filter requirements

The work presented here was supported by the European Space Agency and focuses on the specific requirements of the DARWIN mission, which include: (1) A>106 (to ensure sufficient star-light rejection in the interferometer), and (2) a transmission loss (comprising both insertion and waveguide loss) of <1.5 dB over the whole of the 4–20 µm observational window [9]. Since mid-infrared transmitting materials are relatively high loss and fragile in fiber form (compared to silica glass), it is desirable to use as short a fiber length as possible to minimize material losses and limit the amount of bending required. As such, an upper limit of approximately 50 cm for the modal filter length is defined in [9]. Note that for SIF designs, predictions (based on a SIF with an infinite cladding) indicate that it should be possible to achieve A>106 in just a few cm of single-mode fiber [16]. However, in experimental studies on prototype chalcogenide and silver halide based SIFs designed for this application, longer fiber lengths (20–50 cm) were required in practice to obtain single-mode output [9]. Whilst improvements in fabrication technology are expected to help close the gap between theory and experiment in this matter, back-reflections from the high index contrast interface at the outer boundary of the fiber cladding are also found to be a significant contributing factor [9]. This effect can be mitigated to some extent via the application of a strongly absorbing coating material, but almost certainly means that the required length for single-mode output will be longer than predictions for an infinite cladding indicate [9, 16].

4. Microstructured fibers

4.1 Introduction

One promising alternative for this type of application is microstructured optical fiber (MOF) technology, which has been shown to offer significant advantages in applications where broadband operation is required [13–15]. Indeed, recent work has specifically highlighted the improved coupling efficiency of MOF technology for broadband interferometer applications [14, 15]. MOF technology also significantly relaxes the requirements on suitable fiber materials; permitting wave-guiding structures to be created from a single material and enabling scale-invariant single-mode guidance in fibers made from two materials with highly contrasting refractive indices [11, 12]. MOFs have also been fabricated from a wide range of non-silica infrared transmitting materials including polycrystalline silver halide materials, which offer transmission across the entire 4–20 µm wavelength range [18–20]. As such, MOFs offer real promise for broadband single-mode transmission at mid-infrared wavelengths.

However, the optical properties of MOFs are significantly different from SIFs and any comparison must be made carefully. In the following, the key differences between these two fiber types are discussed and the approach taken here to compare the two technologies for use as a modal filter in DARWIN / TPF-like applications is outlined.

4.2 Index-guiding microstructured vs. conventional fibers: basic properties

In a MOF, light is confined to the core by a cladding region with wavelength-scale structure. Most typically, the cladding consists of an array of small, longitudinal air holes in silica glass, and these fibers are known by many names, including (but not limited to) photonic crystal, holey, microstructured and photonic bandgap fibers. In this paper we consider only index-guiding solid core MOFs, defined by a triangular lattice of air holes (with refractive index nair=1) in a high index material (with refractive index nmat), as illustrated in Fig. 3. The key parameters of this type of MOF are the hole-to-hole spacing (Λ), the relative hole size (d/Λ) and the number of rings of holes (N). The guidance mechanism of this type of MOF can be thought of as a modified form of total internal reflection, whereby the air holes lower the average cladding index (nav) by an amount dependent on the fraction of light located within the air holes. As the wavelength (λ) increases, the light penetrates further into each air hole and the values of nav falls, as illustrated in Fig. 4(a). It should be appreciated that while typical fabrication methods lead to highly regular geometric profiles, periodicity is not a fundamental requirement for guidance in this type of MOF [21].

 figure: Fig. 3.

Fig. 3. Defining parameters of index-guiding microstructured fibers.

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The wavelength dependence of the cladding index in a MOF leads directly to a host of unique optical properties, including endlessly single-mode guidance. This phenomenon can be understood by considering the wavelength dependence of the V-parameter, where V∝(nmat2-nav2)1/2/λ. A fiber is single-mode if V is below a certain critical value, which defines the single-mode (SM) cut-off. In a SIF, the cladding index is essentially constant (ignoring the effects of material dispersion) and the V-parameter of the fiber increases steadily towards short wavelengths, resulting in multi-mode guidance above a certain wavelength (λc), as illustrated in Figs 4(b) and (c).

 figure: Fig. 4.

Fig. 4. Schematic illustrations of the optical properties of MOFs (blue dashed line) and SIFs (red solid line) as a function of wavelength; (a) and (b) effective index, (c) V-parameter and (d) effective mode area. ncore and nclad are the core and cladding refractive indices of a SIF.

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In a MOF, the wavelength dependence of the cladding index counteracts the 1/λ dependence of the V-parameter, leading to an almost constant value of V in the short wavelength limit, as shown in Fig. 4(c). If the air holes are located on a regular triangular lattice with d/Λ≤0.4 the absolute value of V can be low enough to ensure single-mode guidance at all wavelengths [22]. The wavelength dependence of the cladding index in a MOF also leads to radically different behavior in terms of the effective mode area (Aeff). In a SIF, the mode size expands dramatically towards long wavelengths, as the fiber becomes increasingly weakly guiding. However, due to the wavelength dependent cladding index, the Aeff of a MOF can be almost constant across a wide wavelength range, as illustrated in Fig. 4(d) [23].

4.3 Microstructured fiber as a modal filter

At first sight, the properties of MOFs, offering endlessly single-mode guidance and relatively constant mode area, seem ideal for broadband modal filtering applications. However, the inherently leaky nature of the MOF geometry must also be taken into consideration. In a MOF with a finite cladding, no true bound modes exist and every mode guided by the fiber (including the FM) has an associated leakage or confinement loss that increases towards long wavelengths [24]. As a result, the confinement loss of the FM (CFM) must be taken into account when considering the overall loss of the modal filter and also when determining its minimum length. Using the same assumptions as for Eq. (1), the minimum length of a MOF modal filter is defined as;

lmin=10log10(A[1η]η)ΔC,whereΔC=CLMCFM

and CLM is the confinement loss of the next lowest loss mode after the FM. The second lowest loss mode of a MOF (once again denoted LM for “leaky-mode”) is an LP11-like mode, as illustrated in Figs 5(b) and (c) [22]. Since ΔC increases towards long wavelengths, lmin is thus defined at the shortest operating wavelength, which corresponds to 4 µm for the case considered here. Note that losses due to end face reflections are not included in any of the results presented here and that intrinsic material losses are not considered in any detail.

 figure: Fig. 5.

Fig. 5. Calculated modal intensity profiles for Λ=20 µm, d/Λ=0.4, N=3 and nmat=2.167. (a) Fundamental mode, CFM=0.002 dB/m (b) and (c) First two higher-order modes, CLM=150 dB/m. Open circles indicate hole positions. (Large open hexagon defines a region of higher density mesh used in the calculations).

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The modal fields and associated confinement losses of each MOF considered here are calculated using commercially available software based on the finite element method, using anisotropic perfectly matched absorbing boundary layers [25]. The confinement losses are extracted directly from the imaginary part of the propagation constant. In all calculations presented here we have assumed a single material fiber with a material index of 2.167, which corresponds to the polycrystalline material silver bromide at 10 µm [26]. The effects of material dispersion have not been included in this study. However, test calculations indicate that ignoring the material dispersion has little effect on the overall performance of the parameters considered here. In addition, it should be appreciated that many infrared transmitting materials have similar values of refractive index [26] and the results presented here are thus generally applicable to a wider range of suitable materials. Example intensity profiles of the first three modes of a MOF with Λ=20 µm, d/Λ=0.4 and three rings of air holes are shown in Fig. 5 for a wavelength of 4 µm.

In all calculations of η presented here, the FM of each MOF considered is approximated by a Gaussian with Aeffωβ2, where Aeff is evaluated from the modal field calculated using the finite element technique mentioned above, using the definition in [27]. For the MOF designs considered here, the overlap between the FM and a Gaussian of optimal width is typically ~ 97 % over the whole 4–20 µm spectral range.

5. Results

5.1 Step (1): Optimal parameter space for broadband coupling efficiency

In the MOF geometry considered here (illustrated in Fig. 3), there are three free parameters; the hole spacing (Λ), the hole size (d) and the number of rings of holes (N). Assuming the FM is reasonably well confined to the core region, the optimal coupling efficiency at a given wavelength depends solely on Λ and d. However, the broadband coupling efficiency is also dependent on the wavelength at which the coupling system is optimized (λopt), which itself has a different optimal value for each fiber geometry considered. In addition, the confinement loss of the FM and the minimum filter length are interlinked quantities that depend on all three fiber parameters (Λ, d and N). As such, the evaluation of a MOF structure for optimal filter performance over the whole operating wavelength range is not a trivial task.

To simplify matters, we look first at defining a single parameter that can be used as a rough gauge of the average coupling efficiency over the 4–20 µm wavelength range for a single MOF structure, independent of λopt. As mentioned above, for the assumption used here, the broadband coupling efficiency for the assumed coupling system is determined solely by ωβ(λ). From Eq. (2) it can be seen that χ (and hence η) will be constant with respect to wavelength if ωβ∝λ; i.e. if Aeff ∝λ2. Fiber parameters that lead to high average values of η can thus be gauged by assessing the relative change in Aeff2 over the relevant wavelength range. This is evaluated here as;

Q=1Pλ1λ2Aeffλ2dλ,=whereP=(Aeffλ2)λ=λ2,

where λ1=4 µm, λ2=20 µm and P acts to normalize Aeff2 against its maximum value. In this definition, low values of Q correspond to high average values of η. Values of Q are plotted in Fig. 6 for MOF structures in the range 9 µm <Λ <21 µm and 0.18 <d/Λ <0.45. This plot demonstrates that low values of Q can be achieved with small values of Λ and d/Λ.

 figure: Fig. 6.

Fig. 6. The parameter Q plotted as a function of Λ and d/Λ for N=7 and nmat=2.167.

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Although the parameter Q is a very simple way of quantifying the broadband coupling efficiency, we find that it works well for the range of fiber structures considered here. To illustrate this, the coupling loss ξ=-10log10[η], for nine different MOFs are plotted in Figs 7(a)–(i), respectively. Values of Λ, d/Λ and Q are indicated on each plot. Results correspond to three different lens systems, optimized at λ=6.0, 8.0 and 10.0 µm, which are representative of the best-case for each fiber considered. The typical coupling loss for a SIF with λc=4.0 µm is shown for comparison in Fig. 7(j) for three different lens systems, optimized at V=2.4, 1.2 and 1.0 (where Vopt∝1/λopt) [10]. These examples not only demonstrate that the parameter Q is a good measure of the average coupling performance, but also show that the MOF geometry can be tailored to offer significantly improved broadband coupling efficiency relative to a SIF that is single-mode over the entire 4–20 µm window.

 figure: Fig. 7.

Fig. 7. (a)–(i) Coupling loss as a function of wavelength for different MOFs. Values of Λ, d/Λ, Q and λopt are indicated on each plot. (j) Coupling loss as a function of wavelength for a SIF with λc=4 µm, extracted from results in Fig. 3 in [10]. Vopt∝1/λopt. nmat=2.167.

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5.2 Step(2): Including the effect of the finite cladding and the minimum fiber length

However, the practicalities of fabrication restrict any MOF design to a relatively modest number of holes and we must therefore consider the confinement losses of the FM(CFM) for structures that are practical to fabricate. Whilst the fabrication techniques for silica-based MOFs are fairly mature (a selection of designs have been commercially available for several years), the technology for fabricating fibers from infrared transmitting non-silica glasses is far less established for both SIFs and MOFs. Currently, the vast majority of single-material MOFs made from non-silica glasses are simple structures comprising just three large air holes [28], although solid MOFs fabricated from two non-silica materials with up to 5 rings of lowindex inclusions have been reported [29]. Here we choose to consider N=7 as the upper limit that is practically feasible to fabricate in materials suitable for the 4–20 µm wavelength range. The maximum tolerable value of CFM is defined here as a 1 dB loss over the minimum length, which is comparable with the lowest possible loss for the coupling system assumed here (see Fig. 2 and associated text). Since confinement losses increase towards long wavelengths, we need only consider CFM at the longest operating wavelength.

In addition, the process of determining an appropriate MOF structure is not merely a case of sufficiently increasing N in order to reduce CFM to practical levels. Increasing N also lowers CLM (such that ΔC decreases), and the minimum fiber length required to achieve a certain value of A thus increases with the addition of each ring of air holes. As such, there is a trade-off between lowering CFM and minimizing the losses that result from material attenuation. This argument also applies equally to the fiber parameters Λ and d/Λ; minimizing the required filter length requires a leaky structure (achieved via small values of Λ, d/Λ), whilst maintaining practically low values of CFM requires the exact opposite (i.e. large values of Λ, d/Λ). To determine the optimal MOF structure for a modal filter it is thus necessary to look at the trade-off between material attenuation (defined by l min, which is determined at λ=4 µm) and CFM (which is largest at λ=20 µm), as a function of Λ, d/Λ and N. At the same time, we must also consider the contribution from coupling loss.

The graphs in Fig. 8 illustrate the relationships between the three fiber parameters (Λ, d/Λ and N) and the three key filter properties (CFM, l min and Q) as a function of N for Λ=10, 15 and 20 µm and d/Λ=0.2, 0.3 and 0.4. Figs 8(a)–(c) show CFM × l min at λ=20 µm and the corresponding values of l min are shown in Figs 8(d)–(f). The grey horizontal lines indicate the upper limits defined previously for CFM and l min. Values of Q are indicated by each curve. All results correspond to a lens system optimized at λ=8 µm, which is representative of the bestcase for each fiber considered. These results illustrate the direct trade-offs between achieving low values of Q and CFM with a minimum number of air holes in as short a length as possible and highlight those MOF designs that are practically useful. Note that values of d/Λ > 0.4 were not considered in any detail as the minimum length required dramatically increases due to the onset of well confined higher-order modes. For example, we find that for Λ=10 µm and d/Λ=0.5, the minimum fiber length is in excess of 10 m.

 figure: Fig. 8.

Fig. 8. (a)–(c) CFM×l min at λ=20 µm as a function of N for Λ=10, 15 and 20 µm. l min (for which A=106 at λ=4 µm) is shown in (d)–(f). In (a) and (d) d/Λ=0.2, in (b) and (e) d/Λ=0.3, and in (c) and (f) d/Λ=0.4. λopt=8 µm and nmat=2.167.

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By looking at Fig. 8, it is possible to determine values of Λ and d/Λ that result in acceptable filter performance for a feasibly low value of N. For example, although a MOF with Λ=10 µm and d/Λ=0.2 has excellent broadband coupling efficiency, it is not possible to adequately confine the FM with a reasonable number of air holes in this case. More detailed results for this fiber, plotted in Fig. 9, clearly illustrate this fact. The sum of the coupling and confinement losses for l=l min (shown separately in Figs 9(a) and (b)), is shown in Fig. 9(c). This plot demonstrates that confinement loss completely overwhelms the fiber transmission for λ>11 µm. Furthermore, the minimum length of fiber required in this example is ~ 20 cm, which is an order of magnitude greater than that required (in principle) for a SIF modal filter [16]. Consequently, despite the excellent coupling efficiency, the overall performance of this MOF is worse than that predicted for a SIF. However, if the hole size is increased to d/Λ=0.4, the FM can be well confined with as few as 7 rings of air holes with l min ~ 50 cm for Λ=10 µm (shown in Figs 8(c) and (f)). Detailed results for this fiber are plotted in Fig. 10.

 figure: Fig.9.

Fig.9. Λ=10 µm, d/Λ=0.2, N=7 and nmat=2.167. (a) Coupling loss as a function of wavelength (b) Confinement loss as a function of wavelength for l=l min (c) sum of coupling and confinement losses for l=l min as a function of wavelength. Values of λopt and l min are indicated on the Fig.

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 figure: Fig.10.

Fig.10. Λ=10 µm, d/Λ=0.4, N=7 and nmat=2.167. (a) Coupling loss as a function of wavelength (b) Confinement loss as a function of wavelength for l=l min (c) sum of coupling and confinement losses for l=l min as a function of wavelength. Values of λopt and l min are indicated on the Fig.

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By comparing the results presented in Figs 9 and 10 it can be seen that although larger air holes result in increased coupling losses, the CFM decreases significantly, resulting in much better overall performance. Indeed, the value of ξ+l minCFM for this MOF represents a significant improvement compared with the coupling losses of a SIF that is single-mode at all wavelengths within the 4–20 µm range, as illustrated in Figs 11(a) and (b). However, this does not necessarily represent a fair comparison since it is possible to lower ξ over a broader wavelength range in a SIF by increasing λc. As examples, Figs 11(c) and (d) show the coupling losses of SIFs with λc=6.6 and 8.4 µm for three representative values of Vopt. Comparing the results in this way, we see that the MOF geometry does indeed offer lower loss transmission over a broader wavelength range than a SIF. For example, for ξ+l minCFM <2 dB, a MOF based modal filter can offer transmission over λ ~ 6.3 - 20 µm, whilst a SIF version only offers ξ <2 dB over λ ~ 8.4–20 µm (for Vopt=1.2 in Fig. 11(d)). Furthermore, while a MOF design enables transmission over the whole 4–20 µm range for ξ+l minCFM <3.7 dB, a similar value can only be achieved for λ ~ 6.6 - 20 µm in a SIF (for Vopt=1.0 in Fig. 11(c)).

 figure: Fig.11.

Fig.11. (a) Coupling loss + confinement loss for l=l min as a function of wavelength for a MOF with Λ=10 µm, d/Λ=0.4, N=7 and nmat=2.167. (b), (c) and (d) Coupling loss as a function of wavelength for SIFs with λc=4.0, 6.6 and 8.4 µm respectively (adapted from Fig. 3 in [10]). Vopt∝1/λopt. Shaded areas indicate regions of multimode guidance.

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5.3 Discussion

Whilst the minimum length required by the MOF studied in Fig. 11 (~ 50 cm) is substantially longer than that predicted for a SIF based modal filter (a few cm) [16], characterization of SIFs made from silver halide materials have demonstrated that the intrinsic material losses can be <1 dB/m over the 4–20 µm wavelength range in a fiber geometry [20]. Based on this value, a length of 50 cm could incur an additional loss of ~0.5 dB, at most. Even with this taken into consideration, a MOF based modal filter still offers an improvement over the capabilities of SIF technology for transmission over the full 4–20 µm window. However, it should be appreciated that such losses are significantly lower than the few dB/cm typical of current state-of-the-art MOFs designed for transmission at these wavelengths [19].

Furthermore, as noted in Section 3, experimental studies indicate that the length of SIF required in practice are longer than predictions based on the performance of a fiber with an infinite cladding [9]. However, while the finite nature of the solid cladding region (i.e. the outer boundary of the fiber) has not been taken into account in the study of MOFs presented here either, it is worth noting that silica MOFs are typically observed to be single-mode in shorter lengths than predictions (for a finite solid outer cladding) specify [30, 31].

The modal filter in DARWIN is also required to be polarization maintaining. While this has not been considered in the study presented here, we note that single-mode MOFs with stress applying parts have been shown to exhibit constant values of birefringence over a broad wavelength range and that form birefringence can also be used to create very high values of birefringence at the structure scales (Λ/λ < 2.5) considered here [32, 33]. It should also be pointed out that recent work has shown that index-guiding MOFs of the type considered here can possess additional core localized modes due to bandgap effects arising from the periodic nature of the cladding region at structure scale similar to those considered here [34]. However, the losses of these modes are typically quite high (in excess of 500 dB/m for silica fibers with Λ/λ ~1.5, d/Λ=0.5 and N=8.) Furthermore, preliminary results indicate that it is possible to minimize the presence of these additional modes by making simple changes to the fiber structure, without adversely affecting the guidance of the FM.

6. Conclusion

Within this paper, we have explored the advantages of using a single-mode microstructured optical fiber (MOF) as a broadband modal filter in the DARWIN nulling interferometer, operating between the wavelengths of 4–20 µm. This spectral range presents significant challenges for optical fiber technology, not least because very few suitable materials are transparent at these wavelengths, but also because the coupling efficiency falls dramatically at wavelengths more than an octave above the single-mode cut-off in step-index fiber (SIF) designs [9]. MOFs offer two unique properties that hold great promise for this application; they can be made from a single-material (or from two materials with highly contrasting refractive indices) and offer endlessly single-mode guidance [11, 12]. However, since the properties of MOFs are significantly different from SIFs, any comparison must be made carefully. By considering structures that are practical to fabricate, and accounting for the overall performance (with the exception of end face reflections), we have shown that a MOF modal filter can potentially offer lower loss transmission over a broader wavelength range than can be achieved with a SIF based design.

Nevertheless, it should be appreciated that the work presented here is only a first step towards developing an optimized modal filter based on MOF technology, a process that should obviously include the design of the coupling optics in parallel. Whilst the results shown here demonstrate that the optical properties of MOFs can be tailored via the fiber geometry to improve performance, we have only considered variations to the most basic parameters: i.e. the number of air holes and their size and spacing within a regular triangular lattice arrangement. The MOF geometry offers many more degrees of design freedom in addition to these basic parameters; for example, a graded index fiber profile can be created simply by grading the size of the air holes. The ability to further optimize the optical performance in this way thus offers a potentially powerful route towards a tailor-made solution for the DARWIN modal filter.

Acknowledgments

This work was supported by the European Space Agency under ESTEC Contract 18609/04/NL/PM, ‘Photonic Crystal (Holey) Fibers for Space Applications’. The authors wish to thank Nicholas Bantin, (Lidar Technologies Ltd, UK), Iain McKenzie (ESTEC, ESA, The Netherlands), Xian Feng and Ravi Vinnakota (ORC, UK) and Oswald Wallner (EADS Astrium GmbH, Germany) for valuable advice and discussions.

References and links

1. M. Mayor and D. Queloz, “A Jupiter-mass companion to a solar-type star,” Nature 378, 355–359 (1995). [CrossRef]  

2. N. Woolf and J. R. Angel, “Astronomical searches for earth-like planets and signs of life,” Astron. Astrophys. 36, 507–537 (1998). [CrossRef]  

3. R. N. Bracewell, “Detecting nonsolar planets by spinning infrared interferometer,” Nature 274, 780–781 (1978). [CrossRef]  

4. J. R. P. Angel, A. Y. S. Cheng, and N. J. Woolf, “A space telescope for infrared spectroscopy of Earth-like planets,” Nature 322, 341–434 (1978). [CrossRef]  

5. C. V. M. Fridlund, “DARWIN - The Infrared Space Interferometry Mission,” ESA bulletin 103, 20–25 (2000). http://www.esa.int/esapub/bulletin/bullet103/fridlund103.pdf

6. http://planetquest.jpl.nasa.gov/Navigator/library/tpfI414.pdf

7. M. Ollivier and J.-M. Mariotti, “Improvement in the rejection rate of a nulling interferometer by spatial filtering,” Appl. Opt. 36, 5340–5346 (1997). [CrossRef]   [PubMed]  

8. B. Mennesson, M. Ollivier, and C. Ruilier, “Use of single-mode waveguides to correct the optical defects of a nulling interferometer,” J. Opt. Soc. Am. A 19, 596–602 (2002). [CrossRef]  

9. DARWIN Payload Definition Document SCI-A/2005/301/Darwin/DMS/LdA

10. O. Wallner, W. R. Leeb, and R. Flatscher, “Design of spatial and modal filters for nulling interferometry,” Proc. SPIE 838, 668–679 (2003). [CrossRef]  

11. P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003). [CrossRef]   [PubMed]  

12. J. C. Knight, “Photonic crystal fibers,” Nature 424, 847–851 (2003). [CrossRef]   [PubMed]  

13. J. C. Baggett, T. M. Monro, and D. J. Richardson, “Mode area limits in practical single-mode fibers,” Conference of Lasers and Electro-Optics 2005 (CLEO’05), Baltimore, USA, 22–27th May 2005, paper CMD6.

14. J. Corbett and J. Allington-Smith, “Coupling starlight into single-mode photonic crystal fiber using a field lens,” Opt. Express 13, 6527–6540 (2005). [CrossRef]   [PubMed]  

15. J. C. Flanagan, D. J. Richardson, M. Foster, and I. Bakalski, “A microstructured wavefront filter for the DARWIN nulling interferometer,” Proc. ‘6th International Conf. on Space Optics,’ ESTEC, Noordwijk, The Netherlands, 27–30 June 2006 (ESA SP-621, June 2006).

16. O. Wallner, W. R. Leeb, and P. J. Winzer, “Minimum length of a single-mode spatial filter,” J. Opt. Soc. Am. A. 192445–2448 (2002). [CrossRef]  

17. O. Wallner, P. J. Winzer, and W. R. Leeb, “Alignment tolerances for plane wave to single-mode fiber coupling and their mitigation by use of pigtailed collimators,” Appl. Opt. 41637–643 (2001). [CrossRef]  

18. E. Eran Rave, P. Ephrat, M. Goldberg, E. Kedmi, and A. Katzir, “Silver Halide Photonic Crystal Fibers for the Middle Infrared,” Appl. Opt. 43, 2236–2241 (2004). [CrossRef]   [PubMed]  

19. E. Rave, S. Sade, A. Millo, and A. Katzir, “Few modes in infrared photonic crystal fibers,” J. Appl. Phys. 97, 033103 (2005). [CrossRef]  

20. L. N. Butvina, E. M. Dianov, N. V. Lichkova, V. N. Zavgorodnev, and L. Kuepper, “Crystalline silver halide fibers with optical losses lower than 50 dB/km in broad IR region and their applications,” in Advances in Fiber Optics, E. M. Dianov, eds., Proc. SPIE4083, 238–253 (2000). [CrossRef]  

21. T. M. Monro, P. J. Bennett, N. G. R. Broderick, and D. J. Richardson, “Holey fibers with random cladding distributions,” Opt. Lett. 25206–208 (2000). [CrossRef]  

22. G. Renversez, F. Bordas, and B. T. Kuhlmey, “Second mode transition in microstructured optical fibers: determination of the critical geometrical parameter and study of the matrix refractive index and effects of cladding size,” Opt. Lett. 30, 1264–1266 (2005). [CrossRef]   [PubMed]  

23. N. A. Mortensen, “Effective area of photonic crystal fibers,” Opt. Express 10, 341–348 (2002). [PubMed]  

24. T. P. White, R. C. McPhedran, C. M. de de Sterke, L. C. Botten, and M. J. Steel, “Confinement losses in microstructured optical fibers,” Opt. Lett. 261660–1662 (2001). [CrossRef]  

25. http://www.comsol.com/products/electro/

26. http://www.crystran.co.uk/products.asp

27. G. P. Agrawal, Nonlinear Fiber Optics, 3rd Ed (Academic Press2001) pp. 44.

28. T. M. Monro, H. Ebendorff-Heidepriem, and X. Feng, “Non-silica microstructured optical fibers,” Ceramic Transactions 163, 29–48 (2005).

29. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. S. J. Russell, “All-solid photonic bandgap fiber,” Opt. Lett. 29, 2369–2371 (2004). [CrossRef]   [PubMed]  

30. H. P. Uranus, H. J. W. M. Hoekstra, and E. van Groesen, “Modes of an endlessly single-mode photonic crystal fiber: a finite element investigation,” Proc. IEEE/LEOS Benelux Chapter, 2004, Ghent.

31. A. Argyros and I. Bassett, “Counting Modes in Optical Fibres with Leaky Modes,” in Symposium on Optical Fiber Measurements SOFM 2002, National Institute of Standards and Technology, Colorado, USA September 24–26 pp. 135–138 (2002).

32. J. Folkenberg, M. Nielsen, N. Mortensen, C. Jakobsen, and H. Simonsen, “Polarization maintaining large mode area photonic crystal fiber,” Opt. Express 12, 956–960 (2004). [CrossRef]   [PubMed]  

33. K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka, and M. Fujita, “Optical properties of a low-loss polarization-maintaining photonic crystal fiber,” Opt. Express 9, 676–680 (2001). [CrossRef]   [PubMed]  

34. M. Yan and P. Shum, “Guidance varieties in photonic crystal fibers,” J. Opt. Soc. Am. B 23, pp. 1684–1691 (2006). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. M. Mayor and D. Queloz, “A Jupiter-mass companion to a solar-type star,” Nature 378, 355–359 (1995).
    [Crossref]
  2. N. Woolf and J. R. Angel, “Astronomical searches for earth-like planets and signs of life,” Astron. Astrophys. 36, 507–537 (1998).
    [Crossref]
  3. R. N. Bracewell, “Detecting nonsolar planets by spinning infrared interferometer,” Nature 274, 780–781 (1978).
    [Crossref]
  4. J. R. P. Angel, A. Y. S. Cheng, and N. J. Woolf, “A space telescope for infrared spectroscopy of Earth-like planets,” Nature 322, 341–434 (1978).
    [Crossref]
  5. C. V. M. Fridlund, “DARWIN - The Infrared Space Interferometry Mission,” ESA bulletin 103, 20–25 (2000). http://www.esa.int/esapub/bulletin/bullet103/fridlund103.pdf
  6. http://planetquest.jpl.nasa.gov/Navigator/library/tpfI414.pdf
  7. M. Ollivier and J.-M. Mariotti, “Improvement in the rejection rate of a nulling interferometer by spatial filtering,” Appl. Opt. 36, 5340–5346 (1997).
    [Crossref] [PubMed]
  8. B. Mennesson, M. Ollivier, and C. Ruilier, “Use of single-mode waveguides to correct the optical defects of a nulling interferometer,” J. Opt. Soc. Am. A 19, 596–602 (2002).
    [Crossref]
  9. DARWIN Payload Definition Document SCI-A/2005/301/Darwin/DMS/LdA
  10. O. Wallner, W. R. Leeb, and R. Flatscher, “Design of spatial and modal filters for nulling interferometry,” Proc. SPIE 838, 668–679 (2003).
    [Crossref]
  11. P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
    [Crossref] [PubMed]
  12. J. C. Knight, “Photonic crystal fibers,” Nature 424, 847–851 (2003).
    [Crossref] [PubMed]
  13. J. C. Baggett, T. M. Monro, and D. J. Richardson, “Mode area limits in practical single-mode fibers,” Conference of Lasers and Electro-Optics 2005 (CLEO’05), Baltimore, USA, 22–27th May 2005, paper CMD6.
  14. J. Corbett and J. Allington-Smith, “Coupling starlight into single-mode photonic crystal fiber using a field lens,” Opt. Express 13, 6527–6540 (2005).
    [Crossref] [PubMed]
  15. J. C. Flanagan, D. J. Richardson, M. Foster, and I. Bakalski, “A microstructured wavefront filter for the DARWIN nulling interferometer,” Proc. ‘6th International Conf. on Space Optics,’ ESTEC, Noordwijk, The Netherlands, 27–30 June 2006 (ESA SP-621, June 2006).
  16. O. Wallner, W. R. Leeb, and P. J. Winzer, “Minimum length of a single-mode spatial filter,” J. Opt. Soc. Am. A. 192445–2448 (2002).
    [Crossref]
  17. O. Wallner, P. J. Winzer, and W. R. Leeb, “Alignment tolerances for plane wave to single-mode fiber coupling and their mitigation by use of pigtailed collimators,” Appl. Opt. 41637–643 (2001).
    [Crossref]
  18. E. Eran Rave, P. Ephrat, M. Goldberg, E. Kedmi, and A. Katzir, “Silver Halide Photonic Crystal Fibers for the Middle Infrared,” Appl. Opt. 43, 2236–2241 (2004).
    [Crossref] [PubMed]
  19. E. Rave, S. Sade, A. Millo, and A. Katzir, “Few modes in infrared photonic crystal fibers,” J. Appl. Phys. 97, 033103 (2005).
    [Crossref]
  20. L. N. Butvina, E. M. Dianov, N. V. Lichkova, V. N. Zavgorodnev, and L. Kuepper, “Crystalline silver halide fibers with optical losses lower than 50 dB/km in broad IR region and their applications,” in Advances in Fiber Optics, E. M. Dianov, eds., Proc. SPIE4083, 238–253 (2000).
    [Crossref]
  21. T. M. Monro, P. J. Bennett, N. G. R. Broderick, and D. J. Richardson, “Holey fibers with random cladding distributions,” Opt. Lett. 25206–208 (2000).
    [Crossref]
  22. G. Renversez, F. Bordas, and B. T. Kuhlmey, “Second mode transition in microstructured optical fibers: determination of the critical geometrical parameter and study of the matrix refractive index and effects of cladding size,” Opt. Lett. 30, 1264–1266 (2005).
    [Crossref] [PubMed]
  23. N. A. Mortensen, “Effective area of photonic crystal fibers,” Opt. Express 10, 341–348 (2002).
    [PubMed]
  24. T. P. White, R. C. McPhedran, C. M. de de Sterke, L. C. Botten, and M. J. Steel, “Confinement losses in microstructured optical fibers,” Opt. Lett. 261660–1662 (2001).
    [Crossref]
  25. http://www.comsol.com/products/electro/
  26. http://www.crystran.co.uk/products.asp
  27. G. P. Agrawal, Nonlinear Fiber Optics, 3rd Ed (Academic Press2001) pp. 44.
  28. T. M. Monro, H. Ebendorff-Heidepriem, and X. Feng, “Non-silica microstructured optical fibers,” Ceramic Transactions 163, 29–48 (2005).
  29. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. S. J. Russell, “All-solid photonic bandgap fiber,” Opt. Lett. 29, 2369–2371 (2004).
    [Crossref] [PubMed]
  30. H. P. Uranus, H. J. W. M. Hoekstra, and E. van Groesen, “Modes of an endlessly single-mode photonic crystal fiber: a finite element investigation,” Proc. IEEE/LEOS Benelux Chapter, 2004, Ghent.
  31. A. Argyros and I. Bassett, “Counting Modes in Optical Fibres with Leaky Modes,” in Symposium on Optical Fiber Measurements SOFM 2002, National Institute of Standards and Technology, Colorado, USA September 24–26 pp. 135–138 (2002).
  32. J. Folkenberg, M. Nielsen, N. Mortensen, C. Jakobsen, and H. Simonsen, “Polarization maintaining large mode area photonic crystal fiber,” Opt. Express 12, 956–960 (2004).
    [Crossref] [PubMed]
  33. K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka, and M. Fujita, “Optical properties of a low-loss polarization-maintaining photonic crystal fiber,” Opt. Express 9, 676–680 (2001).
    [Crossref] [PubMed]
  34. M. Yan and P. Shum, “Guidance varieties in photonic crystal fibers,” J. Opt. Soc. Am. B 23, pp. 1684–1691 (2006).
    [Crossref]

2006 (1)

2005 (4)

2004 (3)

2003 (3)

O. Wallner, W. R. Leeb, and R. Flatscher, “Design of spatial and modal filters for nulling interferometry,” Proc. SPIE 838, 668–679 (2003).
[Crossref]

P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

J. C. Knight, “Photonic crystal fibers,” Nature 424, 847–851 (2003).
[Crossref] [PubMed]

2002 (3)

2001 (3)

2000 (2)

T. M. Monro, P. J. Bennett, N. G. R. Broderick, and D. J. Richardson, “Holey fibers with random cladding distributions,” Opt. Lett. 25206–208 (2000).
[Crossref]

C. V. M. Fridlund, “DARWIN - The Infrared Space Interferometry Mission,” ESA bulletin 103, 20–25 (2000). http://www.esa.int/esapub/bulletin/bullet103/fridlund103.pdf

1998 (1)

N. Woolf and J. R. Angel, “Astronomical searches for earth-like planets and signs of life,” Astron. Astrophys. 36, 507–537 (1998).
[Crossref]

1997 (1)

1995 (1)

M. Mayor and D. Queloz, “A Jupiter-mass companion to a solar-type star,” Nature 378, 355–359 (1995).
[Crossref]

1978 (2)

R. N. Bracewell, “Detecting nonsolar planets by spinning infrared interferometer,” Nature 274, 780–781 (1978).
[Crossref]

J. R. P. Angel, A. Y. S. Cheng, and N. J. Woolf, “A space telescope for infrared spectroscopy of Earth-like planets,” Nature 322, 341–434 (1978).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd Ed (Academic Press2001) pp. 44.

Allington-Smith, J.

Angel, J. R.

N. Woolf and J. R. Angel, “Astronomical searches for earth-like planets and signs of life,” Astron. Astrophys. 36, 507–537 (1998).
[Crossref]

Angel, J. R. P.

J. R. P. Angel, A. Y. S. Cheng, and N. J. Woolf, “A space telescope for infrared spectroscopy of Earth-like planets,” Nature 322, 341–434 (1978).
[Crossref]

Argyros, A.

A. Argyros and I. Bassett, “Counting Modes in Optical Fibres with Leaky Modes,” in Symposium on Optical Fiber Measurements SOFM 2002, National Institute of Standards and Technology, Colorado, USA September 24–26 pp. 135–138 (2002).

Baggett, J. C.

J. C. Baggett, T. M. Monro, and D. J. Richardson, “Mode area limits in practical single-mode fibers,” Conference of Lasers and Electro-Optics 2005 (CLEO’05), Baltimore, USA, 22–27th May 2005, paper CMD6.

Bakalski, I.

J. C. Flanagan, D. J. Richardson, M. Foster, and I. Bakalski, “A microstructured wavefront filter for the DARWIN nulling interferometer,” Proc. ‘6th International Conf. on Space Optics,’ ESTEC, Noordwijk, The Netherlands, 27–30 June 2006 (ESA SP-621, June 2006).

Bassett, I.

A. Argyros and I. Bassett, “Counting Modes in Optical Fibres with Leaky Modes,” in Symposium on Optical Fiber Measurements SOFM 2002, National Institute of Standards and Technology, Colorado, USA September 24–26 pp. 135–138 (2002).

Bennett, P. J.

Bird, D. M.

Bordas, F.

Botten, L. C.

Bracewell, R. N.

R. N. Bracewell, “Detecting nonsolar planets by spinning infrared interferometer,” Nature 274, 780–781 (1978).
[Crossref]

Broderick, N. G. R.

Butvina, L. N.

L. N. Butvina, E. M. Dianov, N. V. Lichkova, V. N. Zavgorodnev, and L. Kuepper, “Crystalline silver halide fibers with optical losses lower than 50 dB/km in broad IR region and their applications,” in Advances in Fiber Optics, E. M. Dianov, eds., Proc. SPIE4083, 238–253 (2000).
[Crossref]

Cheng, A. Y. S.

J. R. P. Angel, A. Y. S. Cheng, and N. J. Woolf, “A space telescope for infrared spectroscopy of Earth-like planets,” Nature 322, 341–434 (1978).
[Crossref]

Corbett, J.

de Sterke, C. M. de

Dianov, E. M.

L. N. Butvina, E. M. Dianov, N. V. Lichkova, V. N. Zavgorodnev, and L. Kuepper, “Crystalline silver halide fibers with optical losses lower than 50 dB/km in broad IR region and their applications,” in Advances in Fiber Optics, E. M. Dianov, eds., Proc. SPIE4083, 238–253 (2000).
[Crossref]

Ebendorff-Heidepriem, H.

T. M. Monro, H. Ebendorff-Heidepriem, and X. Feng, “Non-silica microstructured optical fibers,” Ceramic Transactions 163, 29–48 (2005).

Ephrat, P.

Feng, X.

T. M. Monro, H. Ebendorff-Heidepriem, and X. Feng, “Non-silica microstructured optical fibers,” Ceramic Transactions 163, 29–48 (2005).

Flanagan, J. C.

J. C. Flanagan, D. J. Richardson, M. Foster, and I. Bakalski, “A microstructured wavefront filter for the DARWIN nulling interferometer,” Proc. ‘6th International Conf. on Space Optics,’ ESTEC, Noordwijk, The Netherlands, 27–30 June 2006 (ESA SP-621, June 2006).

Flatscher, R.

O. Wallner, W. R. Leeb, and R. Flatscher, “Design of spatial and modal filters for nulling interferometry,” Proc. SPIE 838, 668–679 (2003).
[Crossref]

Folkenberg, J.

Foster, M.

J. C. Flanagan, D. J. Richardson, M. Foster, and I. Bakalski, “A microstructured wavefront filter for the DARWIN nulling interferometer,” Proc. ‘6th International Conf. on Space Optics,’ ESTEC, Noordwijk, The Netherlands, 27–30 June 2006 (ESA SP-621, June 2006).

Fridlund, C. V. M.

C. V. M. Fridlund, “DARWIN - The Infrared Space Interferometry Mission,” ESA bulletin 103, 20–25 (2000). http://www.esa.int/esapub/bulletin/bullet103/fridlund103.pdf

Fujita, M.

George, A. K.

Goldberg, M.

Hedley, T. D.

Hoekstra, H. J. W. M.

H. P. Uranus, H. J. W. M. Hoekstra, and E. van Groesen, “Modes of an endlessly single-mode photonic crystal fiber: a finite element investigation,” Proc. IEEE/LEOS Benelux Chapter, 2004, Ghent.

Jakobsen, C.

Katzir, A.

E. Rave, S. Sade, A. Millo, and A. Katzir, “Few modes in infrared photonic crystal fibers,” J. Appl. Phys. 97, 033103 (2005).
[Crossref]

E. Eran Rave, P. Ephrat, M. Goldberg, E. Kedmi, and A. Katzir, “Silver Halide Photonic Crystal Fibers for the Middle Infrared,” Appl. Opt. 43, 2236–2241 (2004).
[Crossref] [PubMed]

Kawanishi, S.

Kedmi, E.

Knight, J. C.

Kubota, H.

Kuepper, L.

L. N. Butvina, E. M. Dianov, N. V. Lichkova, V. N. Zavgorodnev, and L. Kuepper, “Crystalline silver halide fibers with optical losses lower than 50 dB/km in broad IR region and their applications,” in Advances in Fiber Optics, E. M. Dianov, eds., Proc. SPIE4083, 238–253 (2000).
[Crossref]

Kuhlmey, B. T.

Leeb, W. R.

O. Wallner, W. R. Leeb, and R. Flatscher, “Design of spatial and modal filters for nulling interferometry,” Proc. SPIE 838, 668–679 (2003).
[Crossref]

O. Wallner, W. R. Leeb, and P. J. Winzer, “Minimum length of a single-mode spatial filter,” J. Opt. Soc. Am. A. 192445–2448 (2002).
[Crossref]

O. Wallner, P. J. Winzer, and W. R. Leeb, “Alignment tolerances for plane wave to single-mode fiber coupling and their mitigation by use of pigtailed collimators,” Appl. Opt. 41637–643 (2001).
[Crossref]

Lichkova, N. V.

L. N. Butvina, E. M. Dianov, N. V. Lichkova, V. N. Zavgorodnev, and L. Kuepper, “Crystalline silver halide fibers with optical losses lower than 50 dB/km in broad IR region and their applications,” in Advances in Fiber Optics, E. M. Dianov, eds., Proc. SPIE4083, 238–253 (2000).
[Crossref]

Luan, F.

Mariotti, J.-M.

Mayor, M.

M. Mayor and D. Queloz, “A Jupiter-mass companion to a solar-type star,” Nature 378, 355–359 (1995).
[Crossref]

McPhedran, R. C.

Mennesson, B.

Millo, A.

E. Rave, S. Sade, A. Millo, and A. Katzir, “Few modes in infrared photonic crystal fibers,” J. Appl. Phys. 97, 033103 (2005).
[Crossref]

Monro, T. M.

T. M. Monro, H. Ebendorff-Heidepriem, and X. Feng, “Non-silica microstructured optical fibers,” Ceramic Transactions 163, 29–48 (2005).

T. M. Monro, P. J. Bennett, N. G. R. Broderick, and D. J. Richardson, “Holey fibers with random cladding distributions,” Opt. Lett. 25206–208 (2000).
[Crossref]

J. C. Baggett, T. M. Monro, and D. J. Richardson, “Mode area limits in practical single-mode fibers,” Conference of Lasers and Electro-Optics 2005 (CLEO’05), Baltimore, USA, 22–27th May 2005, paper CMD6.

Mortensen, N.

Mortensen, N. A.

Nielsen, M.

Ollivier, M.

Pearce, G. J.

Queloz, D.

M. Mayor and D. Queloz, “A Jupiter-mass companion to a solar-type star,” Nature 378, 355–359 (1995).
[Crossref]

Rave, E.

E. Rave, S. Sade, A. Millo, and A. Katzir, “Few modes in infrared photonic crystal fibers,” J. Appl. Phys. 97, 033103 (2005).
[Crossref]

Rave, E. Eran

Renversez, G.

Richardson, D. J.

T. M. Monro, P. J. Bennett, N. G. R. Broderick, and D. J. Richardson, “Holey fibers with random cladding distributions,” Opt. Lett. 25206–208 (2000).
[Crossref]

J. C. Baggett, T. M. Monro, and D. J. Richardson, “Mode area limits in practical single-mode fibers,” Conference of Lasers and Electro-Optics 2005 (CLEO’05), Baltimore, USA, 22–27th May 2005, paper CMD6.

J. C. Flanagan, D. J. Richardson, M. Foster, and I. Bakalski, “A microstructured wavefront filter for the DARWIN nulling interferometer,” Proc. ‘6th International Conf. on Space Optics,’ ESTEC, Noordwijk, The Netherlands, 27–30 June 2006 (ESA SP-621, June 2006).

Ruilier, C.

Russell, P. S. J.

Russell, P. St. J.

P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

Sade, S.

E. Rave, S. Sade, A. Millo, and A. Katzir, “Few modes in infrared photonic crystal fibers,” J. Appl. Phys. 97, 033103 (2005).
[Crossref]

Shum, P.

Simonsen, H.

Steel, M. J.

Suzuki, K.

Tanaka, M.

Uranus, H. P.

H. P. Uranus, H. J. W. M. Hoekstra, and E. van Groesen, “Modes of an endlessly single-mode photonic crystal fiber: a finite element investigation,” Proc. IEEE/LEOS Benelux Chapter, 2004, Ghent.

van Groesen, E.

H. P. Uranus, H. J. W. M. Hoekstra, and E. van Groesen, “Modes of an endlessly single-mode photonic crystal fiber: a finite element investigation,” Proc. IEEE/LEOS Benelux Chapter, 2004, Ghent.

Wallner, O.

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O. Wallner, P. J. Winzer, and W. R. Leeb, “Alignment tolerances for plane wave to single-mode fiber coupling and their mitigation by use of pigtailed collimators,” Appl. Opt. 41637–643 (2001).
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White, T. P.

Winzer, P. J.

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N. Woolf and J. R. Angel, “Astronomical searches for earth-like planets and signs of life,” Astron. Astrophys. 36, 507–537 (1998).
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Yan, M.

Zavgorodnev, V. N.

L. N. Butvina, E. M. Dianov, N. V. Lichkova, V. N. Zavgorodnev, and L. Kuepper, “Crystalline silver halide fibers with optical losses lower than 50 dB/km in broad IR region and their applications,” in Advances in Fiber Optics, E. M. Dianov, eds., Proc. SPIE4083, 238–253 (2000).
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Appl. Opt. (3)

Astron. Astrophys. (1)

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T. M. Monro, H. Ebendorff-Heidepriem, and X. Feng, “Non-silica microstructured optical fibers,” Ceramic Transactions 163, 29–48 (2005).

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J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. A. (1)

O. Wallner, W. R. Leeb, and P. J. Winzer, “Minimum length of a single-mode spatial filter,” J. Opt. Soc. Am. A. 192445–2448 (2002).
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Opt. Lett. (4)

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O. Wallner, W. R. Leeb, and R. Flatscher, “Design of spatial and modal filters for nulling interferometry,” Proc. SPIE 838, 668–679 (2003).
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Science (1)

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http://planetquest.jpl.nasa.gov/Navigator/library/tpfI414.pdf

J. C. Flanagan, D. J. Richardson, M. Foster, and I. Bakalski, “A microstructured wavefront filter for the DARWIN nulling interferometer,” Proc. ‘6th International Conf. on Space Optics,’ ESTEC, Noordwijk, The Netherlands, 27–30 June 2006 (ESA SP-621, June 2006).

J. C. Baggett, T. M. Monro, and D. J. Richardson, “Mode area limits in practical single-mode fibers,” Conference of Lasers and Electro-Optics 2005 (CLEO’05), Baltimore, USA, 22–27th May 2005, paper CMD6.

L. N. Butvina, E. M. Dianov, N. V. Lichkova, V. N. Zavgorodnev, and L. Kuepper, “Crystalline silver halide fibers with optical losses lower than 50 dB/km in broad IR region and their applications,” in Advances in Fiber Optics, E. M. Dianov, eds., Proc. SPIE4083, 238–253 (2000).
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Figures (11)

Fig. 1.
Fig. 1. (a) Fluxes of the Sun and Earth as seen from a distance of 4 pc (Nλ is the photon flux), adapted from [3]. The DARWIN spectral band is indicated by the shaded region. (b) Schematic of a Bracewell nulling interferometer.
Fig. 2.
Fig. 2. Simple coupling arrangement and principles of a modal wavefront filter adapted from Fig. 2. in [10].
Fig. 3.
Fig. 3. Defining parameters of index-guiding microstructured fibers.
Fig. 4.
Fig. 4. Schematic illustrations of the optical properties of MOFs (blue dashed line) and SIFs (red solid line) as a function of wavelength; (a) and (b) effective index, (c) V-parameter and (d) effective mode area. ncore and nclad are the core and cladding refractive indices of a SIF.
Fig. 5.
Fig. 5. Calculated modal intensity profiles for Λ=20 µm, d/Λ=0.4, N=3 and nmat=2.167. (a) Fundamental mode, CFM=0.002 dB/m (b) and (c) First two higher-order modes, CLM=150 dB/m. Open circles indicate hole positions. (Large open hexagon defines a region of higher density mesh used in the calculations).
Fig. 6.
Fig. 6. The parameter Q plotted as a function of Λ and d/Λ for N=7 and nmat=2.167.
Fig. 7.
Fig. 7. (a)–(i) Coupling loss as a function of wavelength for different MOFs. Values of Λ, d/Λ, Q and λopt are indicated on each plot. (j) Coupling loss as a function of wavelength for a SIF with λc=4 µm, extracted from results in Fig. 3 in [10]. Vopt∝1/λopt. nmat=2.167.
Fig. 8.
Fig. 8. (a)–(c) CFM×l min at λ=20 µm as a function of N for Λ=10, 15 and 20 µm. l min (for which A=106 at λ=4 µm) is shown in (d)–(f). In (a) and (d) d/Λ=0.2, in (b) and (e) d/Λ=0.3, and in (c) and (f) d/Λ=0.4. λopt=8 µm and nmat=2.167.
Fig.9.
Fig.9. Λ=10 µm, d/Λ=0.2, N=7 and nmat=2.167. (a) Coupling loss as a function of wavelength (b) Confinement loss as a function of wavelength for l=l min (c) sum of coupling and confinement losses for l=l min as a function of wavelength. Values of λopt and l min are indicated on the Fig.
Fig.10.
Fig.10. Λ=10 µm, d/Λ=0.4, N=7 and nmat=2.167. (a) Coupling loss as a function of wavelength (b) Confinement loss as a function of wavelength for l=l min (c) sum of coupling and confinement losses for l=l min as a function of wavelength. Values of λopt and l min are indicated on the Fig.
Fig.11.
Fig.11. (a) Coupling loss + confinement loss for l=l min as a function of wavelength for a MOF with Λ=10 µm, d/Λ=0.4, N=7 and nmat=2.167. (b), (c) and (d) Coupling loss as a function of wavelength for SIFs with λc=4.0, 6.6 and 8.4 µm respectively (adapted from Fig. 3 in [10]). Vopt∝1/λopt. Shaded areas indicate regions of multimode guidance.

Equations (4)

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A = η 10 σ l ( 1 η ) where σ = l α LM 10 ,
η ( λ ) = 2 χ 2 ( 1 e χ 2 ) 2 , where χ = α π ω β ( λ ) f λ
l min = 10 log 10 ( A [ 1 η ] η ) Δ C , where Δ C = C LM C FM
Q = 1 P λ 1 λ 2 A eff λ 2 d λ , = where P = ( A eff λ 2 ) λ = λ 2 ,

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