ICOP 2009-International Conference on Optics and Photonics Oct.-1 Nov.2009
Chandigarh,India,30
MICROSTRUCTURED FIBERS AND WAVEGUIDES WITH A CHIRPED CLADDING: A NEW VERSATILE DESIGN PLATFORM TO ENHANCE THEIR FUNCTIONALITY (Invited talk) Bishnu P. Pal, Somnath Ghosh, and R. K. Varshney Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016, INDIA Tel: +91-11-26591331, Fax: +91-11-26581114, e-mail:
[email protected] Abstract: Finite chirped cladding is proposed as a novel design tool to simultaneously attain wider bandgap and reduced temporal dispersion in microstructured optical fibers and waveguides as compared to its perfectly periodic cladding counterpart. This feature design route also affords an additional degree of freedom for tuning the center of the band gap as well as attainment of reduced transmission loss. Thus chirped cladding could be gainfully exploited to engineer bandgaps for specific applications like delivery of high intensity ultrashort pulses useful in biomedical optics and defense, or realizing integrated optical circuits, etc.
1. INTRODUCTION The phenomena of light guidance through deliberately introduced defect layer(s) in otherwise periodic index geometry were first studied almost three decades ago [1], which led to the emergence of the concept of photonic bandgap guidance (PBG). Recent developments in the technology for deposition of individual thin layers with great precision and control have resulted in a resurgence of interest in light guidance through PBG microstructured optical fibers (MOF) and waveguides (MOW). These light confining structures have indeed become a research field of intense contemporary interest [2-4]. Unlike conventional waveguides/fibers, if light of wavelengths that fall within the photonic bandgap is made to be incident on such structures, it could be effectively confined in the central region of the structure thereby mimicking the core of an optical waveguiding structure. The extent of the bandgap is decided by the periodicity defining parameters of the structure. In view of the multitude of parameters to play around, design freedom afforded by these structures could be exploited to tailor their loss and dispersion characteristics as well as achieve guidance of light even in an air core or guidance of light even through sharp bends. These attractive features of PBG structures have indeed led to a large number of proposals for their potential applications in areas like integrated optical devices for conveying information, biomedical optics (like high power laser beam delivery), and mid-IR photonics [5-7]. Due to their tailorable nonlinearity and dispersion, these structures are also attractive for pulse reshaping, supercontinuum generation, pulse compression, parabolic pulse generation [8-10] and many other nonlinear applications, which are difficult to attain with conventional optical waveguides/fibers.
Distortion-less low-loss propagation of short pulses of tens-of femto seconds duration through the MOFs/MOWs is fundamental to these applications (even for delivery of high intense optical pulses required in surgical applications). To fulfill this goal, it is important to choose the operating wavelength as the center of the photonic bandgap. Thus affordability to tune the center of the bandgap is a desirable feature in photonic bandgap guided devices for their wavelength-specific applications. If we deliberately design the cladding geometry with linearly varying non-identical unit cells through increment or decrement in spatial or index periods across the cladding, the resultant periodic-like structure is referred to as a chirped MOF/MOW. In this paper, we report our recent studies [11-12] which have shown how such chirped features result in significant modification of the propagation characteristics of Bragg reflection Waveguides (BRW) and Bragg fibers. We also discuss a recently reported chirped holey-type photonic crystal fiber (PCF) designed and fabricated by Skibina et al [13], in which amorphization-like effect due to the spatial chirp was seen to favour reduction in the geometric dispersion. Studies in that direction has shown that introduction of certain aperiodicity in the cladding region could be gainfully exploited as a platform for bandgap engineering. This feature could be exploited in applications like delivery of high intensity ultrashort pulses useful in biomedical optics and defense, or realizing integrated optical circuits, etc,. 2. THEORY AND MODELING The control of light flow through a PBG microstructured geometry is dictated by the spatial and refractive index periodicity of the cladding layers and bandwidth of such structures are limited by the unit cells of their multilayer claddings. On the other hand in case of chirped microstructured geometries
ICOP 2009-International Conference on Optics and Photonics Chandigarh,India,30 Oct.-1 Nov.2009 (schematically shown in Fig.1), their bandgap could profiles in different geometries ,we would follow two be engineered through appropriate choice of the unit different approaches like Matrix method [26] to study cells of the cladding. For example, the very first 1D transverse or radial chirp, and finite element neighbouring index layer adjacent to the central core method for chirped PCF. yields its own characteristic bandwidth, which gets modulated by the subsequent aperiodic cell units. As 3. RESULTS a result, the overall structure exhibits Bragg The unique dispersion relation of a particular resonances in a distributed manner (unlike that over a periodic structure defines the bandgap of the relatively narrow wavelength band exhibited by its geometry. Introduction of chirp in spatial or perfectly periodic counterpart) across a wider refractive index periodicity of an ordered periodic frequency band and hence lesser selectivity to the structure essentially modifies the allowed and operating wavelength. In the following we will forbidden frequency range of a perfectly periodic highlight the modifications in propagation structure. Independent of the geometry of the characteristics and special features of these (three periodicity (transverse, radial or annular), the different chirped microstructured geometries of interacting bandgaps of successive layers enhances different dimensions of refractive index periodicities) the effective bandwidth of the chirped design (w.r.t chirped clad geometries. the original geometry). If we consider a linear x variation in spatial or index periodicity, we could achieve ultra-large transmission window for any of the waveguide geometries shown in Fig.1. We now designate the spatial dimensions of the first cladding a) y bi-layer adjacent to the core as (d1)initial and (d2)initial, respectively, and the final cladding unit cell as (d1)final n1 and (d2)final. A measure of the chirp could be defined n2 through a chirp factor (fj) Core (d j ) final (for j = 1, 2) fj =
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Results are shown in Fig.2, where from it could be seen that an enhancement of the PBG by as much as ~ 66% of a chirped Bragg-like fiber (CBLF) could be achieved as compared to the estimated bandgap afforded by its Bragg fiber counterpart with perfectly periodic claddings consisting of 6 bilayers. From this figure it is evident that the transmission window widens in the longer wavelength side of the bandedge. It is worth mentioning that one could achieve enhancement of the bandgap on both the short and long wavelength band edges by continually varying the chirp factor starting with f1 1. Similar characteristic could be achieved by a chirped BRW, even in case of a chirped PCF. A B
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Fig. 1. Chirped geometries under study: a) Schematic of a chirped BRW. The aperiodicity (1D) could be in terms of spatial or index variation. b) A chirped (1D radial) all solid (soft glass based) Bragg like fiber (CBLF) geometry. c) A spatially chirped hollow core To analyze properties of aperiodic photonic crystalthe fibermodal (After [13]).
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Fig. 2. Numerically simulated loss spectra, A: original Bragg fiber, B: its CBLF counterpart
We separately considered both up and down linear chirp; the former corresponding to a linear increase
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ICOP 2009-International Conference on Optics and Photonics Chandigarh,India,30 Oct.-1 Nov.2009 while the later implied linear decrease in thicknesses reduced. Thus this novel design route could be of the cladding layers. Our study revealed that a judiciously exploited to minimize the traditional particular up-chirp (f > 1) for a particular chirped sharp dispersive resonances (which is a strong BRW geometry could significantly reduce radiation coupled resonance of light across the all-identical loss of the original BRW. In particular, for a chosen periods). Thus we expect a low and flat dispersion sample BRW, we have plotted in Fig.3 the estimated over a wide wavelength range behavior of these new loss as a function of the chirp factor. This figure chirped structures. In Fig.5 we have shown the indicates that loss is minimum for an up-chirp factor variation of group velocity dispersion (GVD) with ‘f’ = 1.6812, thereby implying maximum mode wavelength for a Bragg fiber and its CBLF counter confinement. part in which f1 varies from 0.8 to 1.5 from the inner most bi-layers to the outer most bi-layers. It is 2.35 apparent from the figure that there is a substantial 2.30 decrease in net dispersion in the case of CBLF as compared to its Bragg fiber counterpart geometry. 2.25 Dispersion in the CBLF is lower in magnitude 2.20 throughout the band and it significantly reduces at the band-edges. This should be attractive from the 2.15 point of view of propagation of short pulses with tens 2.10 of femto-seconds (fs) duration through such a medium since shorter temporal pulse implies broader 2.05 spectral width, and hence these pulses could be 1.60 1.62 1.64 1.66 1.68 1.70 1.72 significantly influenced by the higher order Chirp factor ( f ) dispersion at the band edges. Thus from the point of Fig. 3. Leakage loss versus chirp factor for the sample view of fiber design, wide photonic band gap along chirped BRW; loss is minimum for ‘f’ = 1.6812. with low dispersion at the band edges should be attractive for such applications. This is indeed Very similar results could be obtained even if we demonstrated in Fig.6, wherein we depict temporal design a linearly index chirped waveguide geometry. outputs after propagation through a meter long CBLF In Fig.4 we show one such result. and its counterpart Bragg fiber, for an input pulse of 4 width 50 fs. Through further optimization with regard 3.5 to appropriate choice of the chirp factor for a CBLF, one could achieve much less distortion in pulse 3 propagation. This feature should be very useful in 2.5 medical endoscopy involving high energy pulse 2 delivery through an optical fiber. Moreover, 1.5 elimination of dispersive nature in a bandgap guided 1 structure is of immense practical importance from 0.5 communication and signal processing points of view. Similar feature of a chirped PCF has been shown in 0 -0.5 -5
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Fig. 4. An index chirped BRW profile and the supported modal field profile. GVD (fs2/m)
These enhancements of the stop-band and reduction in magnitude of radiation loss could be seen also in their higher order bandgaps. It may be worthwhile to point out that in order to exploit these features for tailoring light propagation within the modified bandgap effectively, one needs to choose the chirp rate in a suitable manner for a particular higher order band gap (different from that corresponding to the fundamental gap). In a chirped microstructured cladding geometry, due to the distributed Bragg mirrors of different wavelength ranges and the presence of comparatively weak resonances, the wavelength selectivity of the over all design for the guided light is remarkably
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Fig. 5. GVD versus operating wavelength; Solid curve-A: for a CBLF, dotted curve-B: for its counterpart Bragg fiber.
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ICOP 2009-International Conference on Optics and Photonics Chandigarh,India,30 Oct.-1 Nov.2009 [13]. In that fabricated chirped holey PCF, due to the Moreover, the propose technique of chirped cladding amorphization-like effect induced by geometry chirp, could be exploited as a design tool for propagation of short but high intensity optical pulses required for 1 applications in e.g. biomedical optics. 0.8
ACKNOWLEDGEMENT The work is partially supported by the ongoing IndoUK Collaboration project on “Application specific Microstructured Optical Fibers” under the UK-India Education and Research Initiative (UKIERI) program. REFERENCES
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Fig. 6. Output pulses relative to an input pulse of width 50 fs (shown as a dotted curve) after propagation through meter long fibers; solid curve: output pulse from the CBLF, dashed curve: output pulse from its counterpart Bragg fiber
helped to achieve reduced GVD. Moreover, for dispersion tailoring, 1D chirped structure is very efficient. We have also designed optimally chirped CBLF for dispersion compensation over C and Lband of EDFA. Since Bragg resonances are not sufficiently strong for a particular frequency range due to the bi-layers being non-identical, the confinement losses are relatively lower in a chirped structure. It can be seen that at the transition frequencies from one stop band to the next (for the next cladding period), small kinks or ripples appear within the enhanced PBG of the chirped geometry. By increasing the number of bi-layers for a given chirp factor, these kinks or ripples in loss or dispersion spectra could be smoothened. Increase in the number of bi-layers was seen to also reduce overall confinement loss of a chirped design as expected. Similar features should be attainable in chirped BRWs/ CBLFs/ chirped PCFs with air or solid cores and distributed photonic band gap guidance is provided by high and low refractive index bi-layers with a certain amount of aperiodicity. 5. CONCLUSIONS In conclusion, our designed chirped clad waveguide/ fiber geometry is a novel design tool to engineer bandgaps of microstructured optical fibers and waveguides with lower dispersion and moderately low loss. We have shown the potentiality and suitability of our design tool for broadband low loss transmission while simultaneously maintaining low dispersion. We believe this technique could be gainfully exploited in tailoring dispersion properties for applications like super continuum generation and ultra-short pulse propagation. Thus our proposal to exploit quasi-periodic claddings in an otherwise photonic band gap guided optical structure should prove to be a versatile tool with respect to designing of application-specific microstructured light guides.
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