Photonic Crystals For Integrated Optics Thomas F
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Photonic Crystals For Integrated Optics Thomas F

Krauss School of Physics and Astronomy University of St Andrews St Andrews Fife KY16 9SS Abstract Planar photonic crystals provide a promising platform for future miniaturised integrated optical circuits Important concepts and design rules for waveg

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Photonic Crystals For Integrated Optics Thomas F




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Photonic Crystals For Integrated Optics Thomas F. Krauss School of Physics and Astronomy, University of St. Andrews, St. Andrews, Fife, KY16 9SS Abstract. Planar photonic crystals provide a promising platform for future miniaturised integrated optical circuits. Important concepts and design rules for waveguides, dispersive and cavity-based building blocks are discussed in order to provide a critical assessment of whether this promise is justified. 1. INTRODUCTION Photonic crystals exhibit several properties that are desirable for photonic integrated circuits, mainly strong

confinement and dispersion. The confinement can be exploited for compact channel waveguides, sharp bends and high isolation between adjacent channels "i.e. low crosstalk), whereas the dispersive properties lend themselves for wavelength separation "e.g. “superprism” effect) and pulse shape modification, e.g. pulse compression. In order to exploit these properties and make maximum use of the planar processing technologies developed by the silicon microelectronics industry, light needs to be confined in the third "i.e. the vertical) dimension. The use of a classical waveguide is therefore the

key to success of planar photonic crystals and has already enabled rapid progress in mapping out their more fundamental properties, i.e. their transmission, reflection and diffraction behaviour [',(]. The waveguide geometry has also lead to some of the first device applications [3-6] and is enabling the tremendous current interest in photonic crystals for integrated optics [,,-]. .ome of the design rules and key operational aspects of planar photonic crystal devices are discussed in this paper. 1.1 Design considerations The confinement of planar photonic crystals in the third, i.e. the

vertical direction, is provided by a “classical” waveguide based on total internal reflection. This configuration has obvious advantages, such as growth of layered structures by established epitaxial methods and compatibility with other planar optoelectronic elements. There are, however, major problems that need to be addressed when designing the structure. The naive point of view is as follows "fig. ')/ 0 high refractive index contrast is typically achieved by etching, so the structure is separated into areas of high-index material, typically semiconductor "with the in-built waveguide

structure) and air. 1ight is then only guided in the semiconductor and not while travelling through the air, so diffraction loss and scattering into the third dimension "i.e., out of the plane of the waveguide) is inevitable. This loss can be minimised by increasing
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the fill-fraction of semiconductor, for example by designing a lattice of pillars with narrow air-gaps or a semiconductor honeycomb structure with small air-holes. 2n 2n a) b) c) (n FIGUR 1. a) 0 deeply etched waveguide, designed according to 3conventional wisdom3 for maximum reflectivity with the high and low

index layers 42n thick. This configuration suffers from diffraction losses, because light is not guided in the low index region and diffracts out of the waveguide plane. b) 0nother source of loss is an insufficient etch depth. If the microstructure is not etched deeply enough, the tail of their guided mode does not interact with the microstructure and radiates away. c) If the air-gaps, i.e. the etched holes or slots, are small and etched deeply enough, there is very little loss, as long as the fundamental criterion for obtaining photonic bandgap effects, i.e. the 5ragg condition, is fulfilled

by designing the optical length of the structure as an integer multiple of half-wavelengths. The principle of this approach is that light can 3hop3 across the narrow gaps without suffering excessive loss, whilst still experiencing the full refractive index contrast between semiconductor and air. This solution compromises the highest achievable bandgap and is in direct contrast to the 3 423 "“6ie”) condition used in multilayer mirrors that requires the optical path in both the low and the high index regions to be a quarter wavelength long for maximum interaction. It also compromises the

possibility of achieving full bandgaps, i.e. for both T8 and T6 polarisation. 9ur approach, however, has been used to show many convincing P5: effects in semiconductor waveguide structures as proof-of-principle, allowing the observation of high transmission, reflection and very sharp filtering characteristics [3,';]. Next, what vertical structure to use? The two main alternatives are low or high vertical index, e.g. semiconductor "“laser-like”) heterostructure vs. high index membrane, including :a0s on 0l9x [''], and silicon on insulator ".9I) ['(]. The membrane approach predicts well-confined

modes, void of losses, in principle [2,'3], and a variety of impressive results have been achieved with this approach, e.g. lasing from a single defect ['2]. The low index contrast approach, on the other hand, has proven remarkably successful, allowing, for example, the demonstration of high Q microcavities ['?] and high reflectivity laser mirrors [?]. @omparative analyses have shown that low losses ['6] and high Q cavities ['A] can also be achieved in low-index structures. 0lso, keeping the substrate, e.g. in a semiconductor heterostructure, has the great advantage of allowing current

injection and providing heat dissipation, issues of great practical importance.
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9verall, low propagation losses and high Q cavities can be obtained with both low and high contrast waveguides, each requiring different specific designs. The choice is ultimately determined by the particular problem and material system at hand. 2. APPLICATIONS IN INT GRAT D OPTICS The size and simplicity of current photonic integrated circuits, with components of several mm to cm in length that allow only a few different functions to be combined on the same chip, are more reminiscent of the

state-of-the-art in electronics achieved in the late 6;’s than than the modern day highly integrated microelectronic circuits. Photonics has a lot of catching up to do, and planar photonic crystals offer the required enabling platform. In order to illustrate this point, figure ( shows a schematic circuit combining a variety of different functions that can be realised on a lengthscale of several ';’s of m. Fibre coupler (in) Monolithic wavelength converter Highly dispersive element (“superprism”) Channel waveguide Coupled cavity waveguide Fibre coupler (out) FIGUR 2 . .chematic of a

variety of photonic functions that could be realised in a photonic crystal based integrated circuit. The circles represent holes etched into a semiconducctor heterostructure. The circuit combines different types of waveguides, i.e. channel waveguides "fig.3) and coupled cavity waveguides [',,'-], to connect the different functions of the circuit, here a dispersive element "“superprism”) and a wavelength converter. 0 fibre coupler has been proposed recently [(;] to address the access problem, which is one of the biggest engineering challenges that need to be overcome before photonic crystal

circuits can be implemented in practise. The access problem arises from the fact that fibres have a circular cross-section of ?-Am diameter, whereas photonic crystal waveguides feature cross-sections of only several ';;’s of nm, leading to a severe mode mismatch that is responsible for insertion losses of the order of (;-3;d5.
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2.1 Channel waveguides 1ike the dopants in semiconductors, it is the intentional breakage of symmetry that gives photonic crystals their added functionality. 9ne of the most obvious breakages of symmetry is the omission of a row of holes to

create a channel waveguide. The surrounding photonic crystal can then be regarded as a perfect, omnidirectional mirror at bandgap frequencies that strongly confines the light. 0n additional aspect of the mirror property is the fact that high levels of isolation can be achieved between adjacent waveguides, a critical property in multi-channel circuits. @ross-talk is a major problem in such circuits, and isolation levels in excess of 3;d5 are often required. Planar photonic lattices achieve 2-'; d54unit cell, so 3; d5 can be achieved with just a few unit cells. Figure 3 0 photonic crystal

channel waveguide, made by omitting a single set of rows. Note how the 6; bend follows the lattice symmetry. 6icrograph courtesy of @. .mith, Fniversity of :lasgow. 1osses are the key issue in these waveguidesG we can distinguish three major loss mechanisms, a) scattering losses at imperfections, b) out-of plane losses, and c) losses caused by T84T6 coupling. a) .cattering at imperfections. Intrinsically, photonic crystal channel waveguides should not suffer from any in-plane losses, simply because the photonic crystal is designed to forbid all propagating modes at the operating

wavelength. .cattering from imperfections should therefore have a much lower impact than in ridge waveguides of comparable size. In a multimode waveguide, however, this type of scattering may excite higher order modes. b) 9ut-of plane losses. He believe that out-of plane diffraction and scattering provide the dominant loss mechanisms in photonic crystal waveguides. These losses are caused by the issues discussed in section '.', i.e. the lack of guiding in the holes and their insufficient etch depth, causing part of the waveguide mode to be scattered away "fig. '). These losses can be minimised

by increasing the aspect ratio of the etched holes. c) T84T6 mode coupling. The photonic crystal surrounding the channel waveguide in fig. 3 exhibits a bandgap for T8 polarisation only. This is of little consequence in most cases, except when significant polarisation mixing occurs, which depends on the asymmetry of the vertical waveguide structure. The more asymmetric the structure "a :a0s waveguide on an oxidised 0l:a0s cladding, for example ['']), the stronger the effect. 9nce the "confined) T8 mode has been converted to T6, it no
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longer experiences the bandgap and is

therefore free to leak out of the channel waveguide and propagate through the crystal. Preliminary results from channel waveguides consisting of a line of three omitted holes indicate losses in the range of ?; cm -' [(']. This apparently very high value, however, must be viewed in the context of circuit size/ a ';; m long channel waveguide suffers around (d5 loss. @onsidered in this context, the losses are much more acceptable than it may appear at first sight, particularly since it is the first quantitative measurement of such waveguide losses, we are only at the beginning of the

learning curve and can therefore expect much improved numbers in the future. 2.2 Coupled cavity waveguides 0 different type of confinement effect is at the heart of the recently proposed @@Hs "“coupled cavity waveguides”) [',] or @I9Hs "“@oupled resonator optical waveguide”) [((] where a waveguide is formed via an array of coupled defects in a photonic lattice. Jarying the type of defect and their spacing gives an element of control over the propagation of light from defect to defect, and it allows tailoring of the wavelength response of the structure and of its group velocity. Figure 4

8volution of the transmission through a coupled defect waveguide as a function of the spacing between defects. For a ' in ( structure, i.e. a set of cavities consisting of a single missing hole separated by a single hole, the response is relatively broad. It sharpens up considerably for a ' in 3, and resembles the response of an uncoupled cavity by the time the separation has reached ' in ?. @ourtesy of 0ndrew Ieynolds, Fniversity of :lasgow. Impressive experimental results that have demonstrated light travelling with very little propagation loss and around sharp bends have already been

obtained in the microwave-regime ['-], which turns @@Hs into real competitors to the more “conventional” channel waveguides. 2.3 Wavelength dispersion via “superprism 5eam steering and dispersion effects in periodic structures have been known for a while [(3,(2] and have been rediscovered recently with the intense interest in both
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photonic crystals and their application in wavelength division multiplexing systems. The superprism effect described by Kawakami and co-workers [-] uses an asymmetry of the bandstructure near the :amma-point, where the wavevector changes much more

dramatically in -K than in -6 with a change of frequency. 0n angular dispersion of ?; for a change of input wavelength from --; nm to ';;; nm has been observed, which translates, when scaled to the '.?? m regime, into ≈( degrees for a ?;:Lz channel spacing "?;:hz≈;.2nm M '.??m) in a typical wavelength division multiplexing "HN6) system. 0ssuming that the output waveguides are laterally spaced by ? m, the length of crystal required to separate the different channels would be around '?; m, which is impressively small compared to the phased

array waveguides commonly used. .everal aspects need to be considered when engineering such a structure/ a) The crystal strongly disperses the beam not only as a function of input wavelength, but also as a function of input angle. If a guided mode "that can be understood as a superposition of a set of plane waves propagating at different angles) impinges on the structure, the different angular components will lead to a broadening of the beam and thereby to cross-talk between the different wavelength channels. 0 careful choice of the operating point within the bandstructure is required to

minimise this effect. b) The angular dispersion curve "input wavelength vs. output angle) is non-linear, i.e. different wavelengths are dispersed at different angles. The positioning of the output waveguides must therefore be adjusted in order to achieve equal wavelength separation between the different channels. c) 9perating near the -point means that the guided modes have a high k , i.e. a high out-of-plane component, are therefore difficult to confine and likely to be lossy. This is acceptable in the “autocloned” structure of [-], because it is three- dimensionally periodic and therefore

strongly confines light in the vertical direction as well. 0 conventional waveguide configuration would struggle, however. 2.4 Add/Drop multiplexer 0 very desirable function to be realised in a photonic crystal microcircuit is that of an add4drop multiplexer, a key component in a wavelength division multiplexing "HN6) system. It allows the selective removal or addition of a particular wavelength channel and thereby allows all the channels to be fully utilised. 0 photonic crystal 0dd4 Nrop was first proposed in '--A [(?], and it is based on the resonance created by two defects in the lattice

that enable coupling between two channel waveguides at resonance frequency. Hhile the concept has been “demonstrated” convincingly via numerical simulation, its experimental realisation is not so straightforward, and requires serious compromises to be made. The core of the problem is the strong dependence of the resonance on the size of the defect, which is illustrated, in simplified form, in fig.?.
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0.2 0.4 0.6 0.8 154515501555 /4 central defect (114nm @ n=3.4) /4 + 2 central defect (114.2nm @ n=3.4) Wavelength (nm) Transmission Model system Figure /. Illustration of

the dependence of the wavelength response on the defect size in a photonic lattice. 5y changing the defect size from 42 "''2 nm) by ( O to ''2.( nm, the wavelength response shifts by approximately ' nm or '(? :Lz at '.?? m. @onsidering that fabrication accuracy is of the order of '; nm, such tolerances can not be met. Two consequences arise out of this exampleG a) a different approach is required whereby the wavelength dependence is determined by a larger ensemble of defects or by the lattice itself, as in the case of the superprism, so that size fluctuations average out and the

wavelength response depends less critically on the size of an individual feature, and b) the strong dependence offers opportunities for tuning, since only minute changes of the optical properties of the defect are required in order to adjust its wavelength response. 2./ Semiconductor lasers with microstructured mirrors Periodic microstructures that consist of alternating layers of semiconductor material and air can be regarded as the extreme limit of the type of 5ragg grating commonly used in distributed feedback "NF5) and distributed 5ragg reflector "N5I) lasers. The difference is the

refractive index contrast, which is typically less than 'P in a NF54N5I laser, but as large as 3.?/' in the case discussed here. This leads to a very much shorter interaction length of around ' m instead of the ';;Qs of microns in a NF54N5I laser and thereby opens the opportunity of creating edge-emitting laser elements with very small optical volume. This degree of compactness and the associated ability of very low threshold and high frequency operation has hitherto been reserved for vertical cavity surface emitting lasers "J@.81s), which is why the ultrashort 5ragg mirror lasers are

sometimes being referred to as “horizontal J@.81s”. The best measured mirror reflectivities are around -? P [?] and the shortest lasers of this type yet realised are (;m long, amongst the shortest edge-emitters demonstrated to date. The key to the high reflectivity are the design rules established
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in section '.', i.e. the use of “narrow gaps” etched as deeply as the vertical extent of the mode. The fact that a semiconductor laser requires active material adds another constraint, i.e. the requirement for an upper cladding in order to avoid absorption at the metallic

contacts. The thickness of the upper cladding can be minimised from the typical '.?m to less than ;.? m, however, without compromising the operation of the device [?]. Projected threshold currents are below ';;0 [(6] and therefore as low as that of the best J@.81s, although demonstrated threshold currents are still, somewhat disappointingly, in the m0 – range "fig.3) [?, (A]. 0.0 5.0 10.0 15.0 Current (mA) Power (a.u.) 5.010.0 Figure 0 1-I curve and micrograph of (; m long semiconductor laser with microstructured mirrors, cross-section of the mirror shown in the

inset. @ourtesy of 1.Iaffaele, Fniversity of :lasgow. 3. CONCLUSION Photonic crystal waveguides are currently the subject of intense research in many laboratories. He believe that the key to their success is a properly designed waveguide and microstructure, where the guided mode is disturbed as little as possible while experiencing the high index contrast that gives rise to the rich bandstructure and the photonic bandgap phenomena. The waveguide should be symmetric, to avoid polarisation coupling, the etched features should be narrow, to maintain guiding, and the depth of these features should

be as deep as possible to ensure that the entire mode experiences the periodicity – any part of the mode that does not, inevitably radiates away. Following these considerations, the photonic crystal consisting of a matrix of etched holes "as opposed to the structure consisting of “pillars” of high-index material) is still the most promising, which is also evidenced by the increasing number of groups using this geometry. The debate as to whether to use low or high index contrast waveguides continues, but it becomes increasingly evident that both schemes can be used to their advantage if

designed properly. The fabrication of these structures is now well established, particularly in the :a0s40l:a0s and the .i9 4.i systems. The figure of merit for etching a matrix of holes is their aspect ratio, i.e. the smaller the holes and the deeper they are etched, the lower the predicted losses. Laving optimised the process on a standard II8 machine, we believe that further improvement requires the use of more sophisticated techniques,
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such as 8@I4I@P techniques that can produce denser plasmas, or the use of ion beam etching due to its higher physical etching component and

lower operating pressure. 0s far as device realisations are concerned, we are experiencing a wealth of results, particularly in integrated optics applications. @hannel waveguides and sharp bends are being attempted in many laboratories, but real results are still few and far between. 9ne of the few quantitative measurements available to date [('] has established a higher limit of ?; cm -' for the loss, which no doubt can be further improved. He believe that it is only a matter of time until genuinely low loss weaveguides "low loss on the scale of the circuit size, i.e. ';;’s of m) are

available. @oupled cavity waveguides "@@Hs) have emerged [',, ((] and recently been demonstrated convincingly ['-]. They may offer many advantages, such as spectral control, low insertion and propagation loss ['-] that channel waveguides struggle to compete with, although they only have, by their very nature, a narrow transmission bandwidth. The focus has also shifted from devices relying on the bandgap property to devices exploring the richness of the bandstructure, such as the “superprism” [-] and the use of periodic structures for dispersion compensation and pulse compression [(,]. 9ne of

the by-products of this shift of interest is the fact that a photonic bandgap is no longer necessary for the operation of these devices – they can be realised equally well, or better, in weakly corrugated waveguides or in low-index systems, such as polymers and glasses. Lere, we can expect a wealth of further device proposals, although problems such as the channel separation in HN6 systems, linearity of dispersion, and the reproducibility of obtaining a particular target wavelength are serious issues that need to be addressed. 0n area where photonic crystals have yet to convincingly stake

their claim is the field of light emitting devices. 0lthough high extraction 18Ns [6, (-] and ultracompact lasers with high reflectivity P5: mirrors [?] have now been demonstrated, the ultimate dream of thresholdless lasers that motivated research in the early years of photonic crystals is still a distance away. 4. AC1NOWL DG2 NTS I would like to acknowledge the Nanoelectronics Iesearch @entre at :lasgow Fniversity for technical support and the 8ngineering and Physical .ciences Iesearch @ouncil "8P.I@) as well as the Ioyal .ociety for financial support. Niscussions with I. Ne 1a Iue, @. .mith

and L. 5enisty have proven invaluable and results obtained by 0. Ieynolds and 1. Iaffaele are acknowledged. /. R F R NC S '. T. F. Krauss, I. 6. Ne 1a Iue and .. 5rand, Nature 3,3, 6---A;(, "'--6). (. L. 5enisty, @. Heisbuch, N. 1abilloy, 6. Iattier, @.S.6. .mith, T.F. Krauss, I. 6. Ne 1a Iue, I. Loudre, F. 9esterle, @. Souanin and N. @assagne, Journ. Lightwave Tech. 13 , (;63-(;AA "'---). 3. T. F. Krauss, 5. Jogele, @. I. .tanley, and I. 6. NelaIue, IEEE Phot. Techn. Lett. 45 'A6-'A, "'--A).
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