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Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 4 — Feb. 24, 2003
  • pp: 347–358
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Multiple source generation using air-structured optical waveguides for optical field shaping and transformation within and beyond the waveguide

J. Canning, E. Buckley, and K. Lyytikainen  »View Author Affiliations


Optics Express, Vol. 11, Issue 4, pp. 347-358 (2003)
http://dx.doi.org/10.1364/OE.11.000347


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Abstract

In this paper we review recent results describing the generation of optical modes within waveguides based on coherent scattering from artificially structured interfaces. The generation of optical waveguide propagation similar to free space propagation enables possible solutions to controlling and shaping optical field generation in free space using coherent scattering of multiple sources. It is shown that the controlled fabrication of such sources can be done simply with air-material structured waveguides such as air-silica structured fibres. Further, the technique of coherent superposition is well known in Fresnel optics, exploiting zone plates to correct the necessary phase adjustments for a desired lens performance. Similarly, in waveguide form this allows fine control of the interference process resulting in the desired mode field and its properties within the waveguide, at the end of the waveguide in the near field regime and well beyond the waveguide into the far field. A factor that can contribute significantly to the coherent scattering within the Fresnel waveguide is resonant-like scattering inside the low index regions since the critical angle of propagation can be very small, increasing Fresnel reflections between interfaces. The results presented here open up a range of hitherto unexplored possibilities in controlling and shaping at first glance disparate phenomena, including free space diffraction.

© 2002 Optical Society of America

1. Introduction

2. The Fresnel fibre

Since the simplest fibre is of cylindrical geometry it may be concluded that the optimal index distribution for obtaining a propagating mode with a peak intensity at the centre based entirely on coherent superposition of scattered light is a radial one about the centre of the cylinder where the main propagating axis might be. From this logic the phase reversal characteristic of zone plates should correspond closely to the positioning of the boundaries of the refractive index variations at the zeroes of, say, the ideal mode of a typical step index waveguide. The natural wave solution for a cylindrical waveguide is a Bessel solution, the simplest being one of the first order, J0 . For the Fresnel cylindrical waveguide the intensity follows an Airy-like distribution: II0[2J0(r)/r] 2 where r represents the radial position of the field within the waveguide. It is informative to note that Bessel solutions, analogous to the ones solved in free space for ideal non-diffracting waves, exist in optical waveguides because of the confinement principle balancing the diffraction of the mode. Consequently, this balancing act between the physical method of confinement over the tendency of an optical mode to diffract in free space, is appropriately referred to as a soliton-like solution [3

3. J. Canning, “Diffraction-Free Mode Generation and Propagation in Optical Waveguides,” Opt. Comm. , 207 (1–6) pp. 35–39 (2002) [CrossRef]

,8

8. J. Canning, E. Buckley, and K. Lyytikainen, “Propagation in Air by Field Superposition of Scattered Light within a Fresnel Fibre,” Accepted to Opt. Lett. (2002)

,9

9. J. Canning, K. Sommer, S. Huntington, and A.L.G. Carter, “Silica based fibre Fresnel lens,” Opt. Commun. 199, 375 (2001) [CrossRef]

] despite the traditionally linear view of this particular problem. Further, the possibility of using coherent superposition from multiple source generation as the principle means of overcoming free space diffraction entertains some extremely interesting ideas and consequences. (Note: One can read the insightful diagnosis of Snyder [13

13. A.W. Snyder, D.J. Mitchell, and Y. Kivshar, “Unification of linear and nonlinear wave optics,” Modern Physics Letters B 91479–1506 (1995) [CrossRef]

] to see that even non-linear processes can be broken down into a series of linear processes. The implicit generalisation one may therefore make is that traditional solitons are no more a simple solution of linear processes overcoming another – this greatly expands the concept of a soliton and its underlying physics, supporting the argument mentioned above of soliton-like solutions when free-space diffraction or beam spreading is overcome in a waveguide).

Therefore it was realised a useful index contrast with air was found to be eminently suitable for such work since the index contrast is much larger. As mentioned earlier, such an index contrast is readily available in fibre form as a result of a recently reinvigorated field focussing on the fabrication of air-silica structured optical fibre. No dopants need to be employed and in this case rather than well defined rings determining the Fresnel zones, we opted to employ air holes spaced along the virtual Fresnel zones of the waveguide. Our treatment is not dissimilar to that found in aperture based Fresnel zone plates where holes were employed in an opaque medium used to make up the Fresnel zones for lens applications in the microwave [15

15. Y.J. Guo and S.K. Barton, “Fresnel zone plate reflector incorporating rings,” IEEE Microwave & Guided Wave Letts. 3, 417 (1993) [CrossRef]

] and x-ray regions [16

16. L. Kipp, M. Skibowski, R. Johnson, R. Bendt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188, 2001 [CrossRef] [PubMed]

]. However, to our knowledge a transmissivebased phase plate incorporating air holes in a transmission medium (such as silica) has not been previously reported. Thus in later sections we show how such fibre “zone plates” can be used as very short lenses (~1mm or less) spliced onto standard fibre. The extension of the lens thickness to “infinite” lengths for operation as a novel waveguide also contributes to the functionality of the Fresnel lens since it demonstrates a “lens” that can be made flexible and long, enabling light to be transported around bends, for example, whilst retaining its far field capability to focus. The issue of loss over long lengths can be readily addressed in these fibres by improving the basic design we have sued to increase the air-fraction appropriately – recent demonstrations of ultra-low loss fibres (<0.5dB/km) indicate this is possible [17

17. L. Farr, J.C. Knight, B.J. Mangand, and T. Roberts, “Low loss photonic crystal fibre,” European Conference on Optical Communication (ECOC 2002), Copenhagen Denamrk, post-deadline paper PD13, (2002)

]. This could have significant future applications where light is collected and transported by the same structure – the use of plastics can allow large diameter versions for use, for example, in free space optical communications, significantly reducing the costs (by eliminating the requirement of bulk optics to direct and collimate light). Hence the potential of enabling such a technology to be “disruptive” – an oft-misused word - in certain communication links, including local area networks (LANs), exists. It should be noted that the long extension of these zone plates means that multiple scattering along the waveguide will also involve an angular or wavelength dependent resonant scattering analogous (though not localised to one volume of space) to Mie scattering in spheres. At the minimum critical angle of propagation, the interface Fresnel reflections between high and low index can be significant and hence resonant-like effects along the waveguide potentially strong. These larger Fresnel reflections are responsible for the low number of rings required in photonic crystal fibres to achieve efficient propagation.

3. Fibre fabrication

Fig. 2. (a) cross-section of fibre preform; (b) cross-section of drawn fibre; (c) near field profile observed at 1550nm; (d) near-field profile observed at 632.8nm.

Fig. 3. Cross-section of Fresnel fibre with centre hole.

4. Near field properties

Fig. 5. Near-field profiles of Fresnel fibre with central hole at three wavelengths.

5. Far field properties

Another feature of propagation achieved by coherent scattering is the extension of the principle of superposition beyond the near field into the far-field. As the various fields go in and out of phase away from the fibre end, complex interference effects are observed. For example, at 1550nm the profile changes from Gaussian-like to a ring distribution and back again, is seen before eventual dissipation occurs. Figure 6 shows the far-field profile at various positions away from the fibre end face revealing at least two effective foci of the fibre. Figure 6 (100µm) shows the first focus where the light is brought to a point with six weaker lobes around it. The intensity exceeds that of the light at the end face, indicating that waveguide field spreading at the output has been overcome. As the fields travel further out, interference leads to complex image reconstruction of the fields within the waveguide. The second “ring” focus (Fig. 6 (200µm)) shows the construction of light within the high index region of the waveguide where the light is inbetween the holes. Note the apparent π/6 rotation of the ring with respect to the six lobes surrounding the first focus point. This is repeated again at the second focus (Fig. 6 (300µm)) at approximately twice the distance of the original. This second focus has a central lobe of greater peak intensity and narrower transverse profile than the first. The π/6 shift in the reconstructed images at each point coincide between the superposed fields actually in the holes and the waveguide fields inbetween the holes. Therefore, image reconstruction at the focus is of the superposed fields that exist not within the high index region but in the low index region air holes, indicative of the role of multiple scattering phenomenon, akin to Mie resonances, in the propagation process of air-silica structured fibres generally.

Fig. 6. Far-field profiles at varying distance away from the Fresnel fibre end face. Image reconstruction is observed at ach plane. The white arrows denote a π/6 rotation between the various images in the far-field.

The multiple image “foci” are consistent with those expected from phase zone plates and their position is approximated by ~r02/nλ where n is an integer multiple [1

1. J. Ojeda-Castenada and C. Gomez-Reino, Selected Papers on Zone Plates; (SPIE Milestone Series1996), Vol. MS 128

,2

2. H.D. Hristov, Fresnel Zones in Wireless Links, Zone Plate Lenses and Antennas, (Artech House2000)

]. Unlike the recently demonstrated Fresnel lens fabricated by controlled chemical deposition and etching [9

9. J. Canning, K. Sommer, S. Huntington, and A.L.G. Carter, “Silica based fibre Fresnel lens,” Opt. Commun. 199, 375 (2001) [CrossRef]

], it does not require any etching procedure or complex graded dopant distributions. Thus there is potential in constructing novel Fresnel lenses and Fresnel beam shapers for numerous applications. The phase sensitivity of this process can be used to generate or enhance numerous sensor configurations with possible applications in surface microscopy. It is anticipated that since the underlying physics of air-silica structured fibres generally relies on coherent scattering, similar complex superposition phenomena in the far-field should be observed within conventional air-guiding photonic crystal fibres. Some evidence is indicated in the observation of a π/6 shift of one previously reported photonic crystal fibre [23

23. N. A. Mortensen and J. R. Folkenber, “Near-field to far-field transition of photonic crystal fibers: symmetries and interference phenomena,” Opt. Express 10, (11), 475–481, (2002) [CrossRef] [PubMed]

].

The potential for tailoring and shaping an arbitrary field profile using this method of waveguide fabrication is significant. By arbitrarily tailoring the phase profile and to some extent the amplitude profile it is in principle possible to generate multiple reconstructions of complex field structures within the waveguides in free space. This has enormous potential for beam shaping and positioning generally. When examined in 3-D space we have clearly generated an optical void or bubble where a volume of space is encapsulated in an optical field. A schematic of this is presented in Fig. 7. Such optical bubbles may have applications for example in micro- or nano- particle manipulation for a range of applications in areas such as nanotechnology and biotechnology (DNA cleaving and manipulation come to mind). The notion of wrapping a field around an object could in principle be scaled up to macrodimensions.

The optical bubble above can be used as a spatial field or phase interferometer by observing appropriate interactions with a desired measurand. Further, multiple image construction from several waveguide structures can be envisaged inbetween a point of combination to further enhance all these effects provided control of coherence is maintained (free space versions of optical devices based on interference effects are potentially realisable). Thus we have demonstrated the first steps to real all-optical manipulation in space, operating “remotely” from the generator source. Controlling the temporal and amplitude properties of the light, as well as phase, traveling along each guide, enhances it. This has the potential of significantly impacting the optical component and holographic industries. These concepts are not limited to device performance – they potentially underpin a range of phenomena hitherto unconsidered, including extending the ideas to other fields that invoke similar superposition principles. In particular there exists the possibility of generating more efficient means of controlling and extending free space diffraction well beyond the Rayleigh range.

Fig. 7. Representation of the optical field “bubble” generated between the two foci of the Fresnel fibre or lens. A micro- or nano- particle is caught within in.
Fig. 8. Schematic illustration of Fresnel lens spliced onto fibre tip. Cross-section

6. Micro-optic zone plates

The use of zone plates to obtain focusing has seen a major resurgence within applications particularly involved with the focusing of wavelengths of light for which there is very little practical conventional optics available, such as extreme UV and X-rays [1

1. J. Ojeda-Castenada and C. Gomez-Reino, Selected Papers on Zone Plates; (SPIE Milestone Series1996), Vol. MS 128

,16

16. L. Kipp, M. Skibowski, R. Johnson, R. Bendt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188, 2001 [CrossRef] [PubMed]

]. These wavelengths are of increasing importance as the drive for higher resolution lithography continues. Conventional Fresnel lenses of this sort are often associated only with amplitude zone plates, which consist of concentric rings of transparent and opaque material, including air and metal. However, there are also other geometric variations including the use of arrays of apertures and non-circular apertures [1

1. J. Ojeda-Castenada and C. Gomez-Reino, Selected Papers on Zone Plates; (SPIE Milestone Series1996), Vol. MS 128

,2

2. H.D. Hristov, Fresnel Zones in Wireless Links, Zone Plate Lenses and Antennas, (Artech House2000)

and refs therein]. The more recent variation at these wavelengths involved random hole distributions in a metal within defined zones [16

16. L. Kipp, M. Skibowski, R. Johnson, R. Bendt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188, 2001 [CrossRef] [PubMed]

]. This is a stochastically varying approach to the same solution found for microwaves [2

2. H.D. Hristov, Fresnel Zones in Wireless Links, Zone Plate Lenses and Antennas, (Artech House2000)

]. Thus there is no doubt that there are defined applications in the microwave and short wavelength regions that benefit from the continued evolution of this technology.

In addition to the traditional Fresnel zone plate arising essentially from interference effects due to diffraction of light from slits of various distribution profiles, there are phase zone plates made up of concentric rings of, for example, air and other transparent media where the phase retardation of the optical field in these domains allows appropriate constructive interference of all the light at the focal point [1

1. J. Ojeda-Castenada and C. Gomez-Reino, Selected Papers on Zone Plates; (SPIE Milestone Series1996), Vol. MS 128

,2

2. H.D. Hristov, Fresnel Zones in Wireless Links, Zone Plate Lenses and Antennas, (Artech House2000)

]. The Fresnel fibre described above is an example of a similar device using cylinders of air as apertures in a transmissive medium. Both types of zone plates, amplitude and phase, are generally characterised by several phenomena, including the existence of multiple foci and wavelength dispersion. These features are also characteristic of the Fresnel fibre. However, it is worthwhile noting that these zone plates can be modified at the boundaries by non-discrete edge topologies, such as a sinusoidal surface variation, to generate only one focus [24

24. H.J. Lezec, A. Degiron, E. Devauk, R.A. Linke, L. Martin-Moreno, F.J. Grcia-Visal, and T.W. Ebbeson, “Beaming light from a subwavelength aperture,” Science 297, (5582), 820–822, (2002) [CrossRef] [PubMed]

].

A 1mm section of our Fresnel fibre is spliced onto the end of standard single mode optical fibre (SMF28). Figure 8 shows a schematic of the device. The ease of splicing combined with straightforward fibre fabrication processes to generate hundreds of metres of Fresnel fibre can lead to mass production of cheap lenses. In this case we used a fixed wavelength from a tuneable laser source to characterise the device. The near field properties are somewhat different to the case when a long length of fibre is used. Both the near and farfield profiles at 1510nm are summarised in Fig. 9. It is observed that the asymmetry of the profiles appears more significant. By scanning the microscope objective such that the imaging plane is well inside the fibre section itself it is possible to crudely image the extent of the field profile at that point inside the waveguide (also taking into account the amount of light confined by the fibre beyond the image plane). With the long length of fibre, when the coupling is appropriate it is observed that there is no change of the mode with peak intensity inside the hole. However, over a short length of 1mm where the light coupling into various leaky states is not filtered out before probing, the field within the fibre was found to vary between ring and focus. Coupling is also not matched perfectly in this case as a result of the splicing an asymmetric Fresnel fibre to a symmetric conventional fibre. Within experimental uncertainty, it appears that the near-field is defined by a ring profile for this particular lens, indicating that the propagating solution is sensitive to coupling.

Fig. 9. Field profiles within, at the end and in the far field of the Fresnel fibre lens at 1510nm.

The contribution from dispersion to the case where an EDFA is used, was determined by examining the performance of the lens at a few wavelengths spanning the EDFA spectrum. Figure 10 summarises these results. Initially the position of the reconstructed images are all identical at all wavelengths. The image position, ƒ n , is approximately described by relationship, ƒ n ~ nƒ. 1 where n is an integer multiple and ƒ 1 the position of the first focus point, which is close in agreement with the classical Fresnel lens formula for concentric rings: ƒ n~r02/nλ. Further away from the end face, however, the distance between foci increases and there is growing difference in this position between wavelengths. At this stage the intensity is dropping rapidly and the light slowly diverging away (Fig. 9). Despite dispersion becoming noticeable at further foci, at practical working ranges available to the first two foci, there is no significant change in focus across the wavelength span shown. The increasing disparity further away may be useful for applications such as dispersion compensation. Alternatively, this form of spatial sensitivity to wavelength at greater distances could be used as a novel and simple spectrum analyser.

7. Discussion and conclusions

Fig. 10. Position from the end face of the Fresnel lens for different wavelengths from a tunable laser source. The field within the lens is taken only at 1510nm.

We have demonstrated a high-index core waveguide such that propagation at longer wavelengths is possible but not at shorter wavelengths. The fibre design chosen is based on optimising the size and position of holes to so-called Fresnel zones of a cylindrical waveguide such that the interstitial hole spacing can be significantly larger than the propagating wavelength. Propagation in this regime will be highly dependent on coherent scattering.

In addition, we demonstrated a similar waveguide with a higher air-fraction and a central hole surrounded by a high index region. This particular fibre has a propagating solution in the central hole at longer wavelengths but not at shorter wavelengths, where propagation in the “ring” is preferred. From the far-field data reconstruction of both the ring fields and the hole peaks are obtained at various distances. There is direct evidence of image reconstruction of light within the low-index holes as well as the central hole, indicating the importance of resonant, or multiple, scattering within the cylinders in determining the properties of the wave guidance in our fibres. This effect is optimised in terms of coherent superposition when there is a Fresnel (or Bragg in some cases) condition satisfied. We note that this resonant phenomenon also underpins the classical ARROW waveguide where there exists propagation in a low index region surrounded by a ring of high index medium [25

25. M.A. Duguay, Y. Kokubun, T.L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49, 1, 13–15, (1986) [CrossRef]

]. A recent analysis of photonic crystal fibres by analogy with ARROW waveguides has also indicated some correlation between the two [26

26. N.M. Litchinitser, A.K. Abeeluck, C. Headley, and B.J. Eggleton, “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27, 1592–1594, (2002) [CrossRef]

], further supporting the classification of photonic bandgap fibres within the Fresnel waveguide umbrella. Combined with the observation of π/6 rotation of the fields in free space, this contribution underpins the constructive interference effects leading to a peak optical field within the central hole. However, over short lengths such as that used by our lens, this contribution adds to that obtained by guidance within the high index region and hence we observed both ring and central point profiles propagating over short lengths at 1550nm when the image is probed within the waveguide. Over long lengths we could only observe a dominant centre profile where interference leads to the peak intensity within the hole and not the ring. We did not observe a ring profile within the fibre.

Clearly, the ability to tailor single and multiple scattering by controlling the size, position and distribution of the cylindrical (though they obviously need not be circular in cross-section nor uniform in size) interfaces enables us to design complex optical waveguides and optical components. Extremely refined control over properties such as dispersion is possible. By way of example, we have demonstrated the Fresnel fibre, which utilises the generic waveguide propagation principle of coherent scattering. Further, a new class of micro-optic phase zone plates operating in the visible to near-IR were demonstrated. The sort of technologies, which can be readily incorporated into a subsystem or system using standard technologies such as fibre splicing, can be fabricated cheaply and in bulk. They offer, for example, a competitive lens alternative to current micro-optical elements such as GRIN and ball lenses. In addition, they also offer a way of reducing losses in interconnects involving Fresnel fibres and compact photonic crystal circuits or devices both in tapered and untapered forms.

From a fundamental viewpoint, the analogy between free space localised optical fields and waveguide fields recognizes the generic commonality between the two field representations. In this instance, it has enabled us to understand wave guidance generally and to invent some novel forms of waveguides. Likewise, the waveguide itself has enabled the control and manipulation of optical fields in free space (i.e. in the far field). We have done this with one waveguide only, though the ideas scale to combinations of waveguides all with correlations in phase space that allow future sophisticated manifestations of the optical field structure. The imposition of time (for example with pulsed light or switching) can allow a dynamic restructuring of optical fields structures for numerous applications including holography and communication. It is now conceivable that many of today’s optical functionality in waveguide circuits could be achieved in free space using such architectures thereby negating some of the complex and costly fabrication processes involved with photonic circuit design. This would be particularly important for 3-D circuit functionality that has not yet been practically demonstrated. Playing around with interference effects can also remove material considerations for local switching and a new era where optical devices with no matter are involved (at least in the immediate vicinity) may come to fruition.

Acknowledgements

B. Reed and J. Zagari are thanked for milling the preform and assisting the drawing of the fibre respectively. This work was funded by an Australian Research Council (ARC) Large Grant. J Canning acknowledges an ARC QEII Fellowship.

References and links

1.

J. Ojeda-Castenada and C. Gomez-Reino, Selected Papers on Zone Plates; (SPIE Milestone Series1996), Vol. MS 128

2.

H.D. Hristov, Fresnel Zones in Wireless Links, Zone Plate Lenses and Antennas, (Artech House2000)

3.

J. Canning, “Diffraction-Free Mode Generation and Propagation in Optical Waveguides,” Opt. Comm. , 207 (1–6) pp. 35–39 (2002) [CrossRef]

4.

M.V. Perez, C. Gomez-Reino, and J.M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Optica Acta33, (9), 1161–1176, (1986). Reprinted in J. Ojeda-Castaneda and C. Gomez-Reino (ed), Selected Papers on Zone Plates, Washington: (SPIE Opt. Eng. Press 1996) [CrossRef]

5.

S.V. Khukhlevsky, “Optical waveguide fields as free space waves,” Europhys. Lett. 54, 461, (2001), [CrossRef]

6.

S.V. Khukhlevsky, G. Nyitray, and V.L. Kantsyrev, “Fields of optical waveguides as waves in free space,” Phys Rev. E. 64(2), 026603, (2001)

7.

J. Canning, E. Buckley, K. Lyytikainen, and T. Ryan, “Wavelength Dependent Leakage in a Fresnel-Based Air-Silica Structured Optical Fibre,” Opt. Commun. , 205, 95 (2002) [CrossRef]

8.

J. Canning, E. Buckley, and K. Lyytikainen, “Propagation in Air by Field Superposition of Scattered Light within a Fresnel Fibre,” Accepted to Opt. Lett. (2002)

9.

J. Canning, K. Sommer, S. Huntington, and A.L.G. Carter, “Silica based fibre Fresnel lens,” Opt. Commun. 199, 375 (2001) [CrossRef]

10.

L. Kaiser and H.W. Astle, “Low-loss single material fibres made from pure fused silica,” Bell System Tech. Journal 53, 1021–1039 (1974)

11.

R.F. Cregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allen, “Single-Mode Photonic Band Gap Guidance of Light in Air,” Science 285, 1537 (1999) [CrossRef] [PubMed]

12.

J.C. Stover, Optical Scattering: Measurement and Analysis, (SPIE Optical Engineering Press1995) [CrossRef]

13.

A.W. Snyder, D.J. Mitchell, and Y. Kivshar, “Unification of linear and nonlinear wave optics,” Modern Physics Letters B 91479–1506 (1995) [CrossRef]

14.

Y. S. Tammela, P. Kiiveri, S. Särkilahti, M. Hotoleanu, H. Valkonen, M. Rajala, J. Kurki, and K. Janka, “Direct Nanoparticle Deposition Process for manufacturing very short high gain Er-doped silica glass fibers,” Proceedings of European Conference Optical Communications (ECOC 2002), Copenhagen Denmark, Volume 4, 9.4.2, (2002)

15.

Y.J. Guo and S.K. Barton, “Fresnel zone plate reflector incorporating rings,” IEEE Microwave & Guided Wave Letts. 3, 417 (1993) [CrossRef]

16.

L. Kipp, M. Skibowski, R. Johnson, R. Bendt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188, 2001 [CrossRef] [PubMed]

17.

L. Farr, J.C. Knight, B.J. Mangand, and T. Roberts, “Low loss photonic crystal fibre,” European Conference on Optical Communication (ECOC 2002), Copenhagen Denamrk, post-deadline paper PD13, (2002)

18.

J. Broeng, T. Sondegaard, S.E. Barkou, P. M. Barbeito, and A. Bjarklev, “Wave guidance by the photonic bandgap effect in optical fibres,” J. Opt. A: Pure Appl. Opt. 1, 477–482 (1999) [CrossRef]

19.

J. West, D. Mueller, K. Koch, J. Fajardo, N. Venkataraman, M. Gallagher, and C. Smith, “Low Loss (13dB/km) Air Core Photonic Band-Gap Fibre,” European Conference on Optical Communications (ECOC 2002), Copenhagen, Denmark, postdeadline paper PD1.1, (2002)

20.

T.A. Birks, J.C. Knight, B.J. Mangan, F. Benaid, P.J. Roberts, and P. St. J. Russel, “Photonic Bandgap Fibres,” European Conference on Optical Communications (ECOC 2002), Copenhagen, Denmark, Symposium paper 1.3, (2002)

21.

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibres,” Science 296, 510–513 (2002). [CrossRef] [PubMed]

22.

W. Lauterborn, T. Kurz, and M. Wiesenfeldt, Coherent Optics, (Springer-Verlag1999)

23.

N. A. Mortensen and J. R. Folkenber, “Near-field to far-field transition of photonic crystal fibers: symmetries and interference phenomena,” Opt. Express 10, (11), 475–481, (2002) [CrossRef] [PubMed]

24.

H.J. Lezec, A. Degiron, E. Devauk, R.A. Linke, L. Martin-Moreno, F.J. Grcia-Visal, and T.W. Ebbeson, “Beaming light from a subwavelength aperture,” Science 297, (5582), 820–822, (2002) [CrossRef] [PubMed]

25.

M.A. Duguay, Y. Kokubun, T.L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49, 1, 13–15, (1986) [CrossRef]

26.

N.M. Litchinitser, A.K. Abeeluck, C. Headley, and B.J. Eggleton, “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27, 1592–1594, (2002) [CrossRef]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(060.2340) Fiber optics and optical communications : Fiber optics components
(160.4670) Materials : Optical materials
(230.1150) Optical devices : All-optical devices

ToC Category:
Research Papers

History
Original Manuscript: December 23, 2002
Revised Manuscript: February 5, 2003
Published: February 24, 2003

Citation
John Canning, E. Buckley, and K. Lyytikainen, "Multiple source generation using air-structured optical waveguides for optical field shaping and transformation within and beyond the waveguide," Opt. Express 11, 347-358 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-4-347


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References

  1. J. Ojeda-Castenada, C. Gomez-Reino, Selected Papers on Zone Plates; (SPIE Milestone Series 1996), Vol. MS 128
  2. H. D. Hristov, Fresnel Zones in Wireless Links, Zone Plate Lenses and Antennas, (Artech House 2000)
  3. J. Canning, �??Diffraction-Free Mode Generation and Propagation in Optical Waveguides,�?? Opt. Commun. 207, 35-39 (2002) [CrossRef]
  4. M.V. Perez, C. Gomez-Reino, J.M. Cuadrado, �??Diffraction patterns and zone plates produced by thin linear axicons,�?? Optica Acta 33, (9), 1161-1176, (1986). Reprinted in J. Ojeda-Castaneda, C. Gomez-Reino (ed), Selected Papers on Zone Plates, Washington: (SPIE Opt. Eng. Press 1996) [CrossRef]
  5. Khukhlevsky, S.V., �??Optical waveguide fields as free space waves,�?? Europhys. Lett. 54, 461, (2001), [CrossRef]
  6. S.V. Khukhlevsky, G. Nyitray, V. L. Kantsyrev, �??Fields of optical waveguides as waves in free space,�?? Phys Rev. E 64, 026603, (2001)
  7. J. Canning, E. Buckley, K. Lyytikainen, T. Ryan, �??Wavelength Dependent Leakage in a Fresnel-Based Air-Silica Structured Optical Fibre,�?? Opt. Commun. 205, 95 (2002) [CrossRef]
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