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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 9 — Apr. 28, 2008
  • pp: 6340–6351
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Porous polymer fibers for low-loss Terahertz guiding

Alireza Hassani, Alexandre Dupuis, and Maksim Skorobogatiy  »View Author Affiliations


Optics Express, Vol. 16, Issue 9, pp. 6340-6351 (2008)
http://dx.doi.org/10.1364/OE.16.006340


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Abstract

We propose two designs of effectively single mode porous polymer fibers for low-loss guiding of terahertz radiation. First, we present a fiber of several wavelengths in diameter containing an array of sub-wavelength holes separated by sub-wavelength material veins. Second, we detail a large diameter hollow core photonic bandgap Bragg fiber made of solid film layers suspended in air by a network of circular bridges. Numerical simulations of radiation, absorption and bending losses are presented; strategies for the experimental realization of both fibers are suggested. Emphasis is put on the optimization of the fiber geometries to increase the fraction of power guided in the air inside of the fiber, thereby alleviating the effects of material absorption and interaction with the environment. Total fiber loss of less than 10 dB/m, bending radii as tight as 3 cm, and fiber bandwidth of ~1 THz is predicted for the porous fibers with sub-wavelength holes. Performance of this fiber type is also compared to that of the equivalent sub-wavelength rod-in-the-air fiber with a conclusion that suggested porous fibers outperform considerably the rod-in-the-air fiber designs. For the porous Bragg fibers total loss of less than 5 dB/m, bending radii as tight as 12 cm, and fiber bandwidth of ~0.1 THz are predicted. Coupling to the surface states of a multilayer reflector facilitated by the material bridges is determined as primary mechanism responsible for the reduction of the bandwidth of a porous Bragg fiber. In all the simulations, polymer fiber material is assumed to be Teflon with bulk absorption loss of 130 dB/m.

© 2008 Optical Society of America

1. Introduction

Terahertz radiation, with wavelengths from 30 to 3000 microns, has big potential for applications such as biomedical sensing, noninvasive imaging and spectroscopy. On one hand, the rich spectrum of THz spectroscopy has allowed for the study and label-free detection of proteins [1

1. J. Xu, K.W. Plaxco, and S.J. Allen, “Probing the collective vibrational dynamics of a protein in liquid water by terahertz absorption spectroscopy”, Protein Sci. 15, 1175–1181 (2006). [CrossRef] [PubMed]

], explosives [2

2. D.J. Cook, B.K. Decker, and M.G. Allen, “Quantitative THz Spectroscopy of Explosive Materials,” OSA conf.: Optical Terahertz Science and Technology, PSI-SR-1196 (2005).

], pharmaceutical durgs [3

3. C.J. Strachan, P.F. Taday, D.A. Newnham, K.C. Gordon, J.A. Zeitler, M. Pepper, and T. Rades, “Using Terahertz Pulsed Spectroscopy to Quantify Pharmaceutical Polymorphism and Crystallinity,” J. Pharmaceutical Sci. 94, 837–846 (2005). [CrossRef]

], and the hybridization of DNA [4

4. M. Nagel, P.H. Bolivar, M. Brucherseifer, H. Kurz, A. Bosserhoff, and R. Bttner, “Integrated THz technology for label-free genetic diagnostics,” Appl. Phys. Lett. 80, 154–156 (2002). [CrossRef]

]. On the other hand, the substantial subsurface penetration of terahertz wavelengths has driven a large amount of work on THz imaging [5

5. W.L. Chan, J. Deibel, and D.M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70, 1325–1379 (2007). [CrossRef]

]. Applications range from non-destructive quality control of electronic circuits [6

6. T. Kiwa, M. Tonouchi, M. Yamashita, and K. Kawase, “Laser terahertz-emission microscope for inspecting electrical faults in integrated circuits,” Opt. Lett. 28, 2058–2060 (2003). [CrossRef] [PubMed]

] to the spatial mapping of specific organic compounds for security applications [7

7. K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Non-destructive terahertz imaging of illicit drugs using spectral fingerprints,” Opt. Express 11, 2549–2554 (2003). [CrossRef] [PubMed]

]. Although THz radiation is strongly absorbed by water, the combination of spectroscopy and imaging has been used to demonstrate the differentiation of biological tissues [8

8. T. Lffler, T. Bauer, K.J. Siebert, H.G. Roskos, A. Fitzgerald, and S. Czasch, “Terahertz dark-field imaging of biomedical tissue,” Opt. Express 9, 616–621 (2001). [CrossRef]

]. Terahertz sources are generally bulky and designing efficient THz waveguides, in order to remotely deliver the broadband THz radiation, would be a big step towards commercialization of compact and robust THz systems. However, almost all materials are highly absorbent in the THz region making design of low loss waveguides challenging. Even air might exhibit high absorption loss if the water vapor content in it is not controlled. Before discussing porous fiber designs, we begin with a review of the recent advances in THz waveguides.

Whereas the losses of circular metallic tubes [9

9. G. Gallot, S.P. Jamison, R.W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17, 851–863 (2000). [CrossRef]

], like stainless steel hypodermic needles, have a propagation loss on the order of 500 dB/m, recent techniques have considerably reduced the loss. On one hand, the use of thin metal layers on the inner surface of dielectric tubes [10

10. J.A. Harrington, R. George, P. Pedersen, and E. Mueller, “Hollow polycarbonate waveguides with inner Cu coatings for delivery of terahertz radiation,” Opt. Express 12, 5263–5268 (2004). [CrossRef] [PubMed]

, 11

11. C. Themistos, B.M.A. Rahman, M. Rajarajan, K.T.V. Grattan, B. Bowden, and J. A. Harrington, “Characterization of silver/polystyrene (PS)-coated hollow glass waveguides at THz frequency,” J. Lightwave Technol. 25, 2456–2462 (2007). [CrossRef]

, 12

12. C.T. Ito, Y. Matsuura, M. Miyagi, H. Minamide, and H. Ito, “Flexible terahertz fiber optics with low bend-induced losses,” J. Opt. Soc. Am. B 24, 1230–1235 (2007). [CrossRef]

], a technique which was initially developed for guiding CO 2 laser light, has been shown to successfully guide in the THz region. A thin Cu layer in a polystyrene tube10 and a thin Ag layer in a silica tube [12

12. C.T. Ito, Y. Matsuura, M. Miyagi, H. Minamide, and H. Ito, “Flexible terahertz fiber optics with low bend-induced losses,” J. Opt. Soc. Am. B 24, 1230–1235 (2007). [CrossRef]

] have respectively been shown to have losses of 3.9 dB/m and 8.5 dB/m. On the other hand, surface plasmon mediated guidance on metallic wires has recently raised interest [13

13. K. Wang and D.M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432, 376–379 (2004). [CrossRef] [PubMed]

] because of the lowest predicted propagation losses [14

14. Q. Cao and J. Jahns “Azimuthally polarized surface plasmons as effective terahertz waveguides,” Opt. Express 13, 511–518 (2005). [CrossRef] [PubMed]

] of 0.9 dB/m. However, it is very difficult to excite the plasmons because their azimuthal polarization. Typical coupling losses are very high with less than 1% of the incident power transmitted; even with the development of specialized antennas only 50% coupling is achieved. Furthermore, the bending losses are very high and the surface plasmon is a very delocalized mode [14

14. Q. Cao and J. Jahns “Azimuthally polarized surface plasmons as effective terahertz waveguides,” Opt. Express 13, 511–518 (2005). [CrossRef] [PubMed]

]. Since the mode extends many times the diameter of the wire into the ambient air, modes of these waveguides are expected to couple strongly to the cladding environment. For higher coupling efficiency, and highly confined mode, hollow core waveguides are preferable. As an additional advantage, hollow waveguides offer the possibility of putting an analyte directly into the waveguide core, thus dramatically increasing sensitivity in spectroscopic and sensor applications.

Because of the high absorption losses in dielectrics, a variety of guiding mechanisms have been studied in order to reduce the propagation losses. On one hand, the resonance in the dielectric constant of ferroelectric polyvinylidene fluoride (PVDF) has been exploited for demonstrating a hollow core ncore<1 waveguide and a hollow core Bragg fiber [15

15. T. Hidaka, H. Minamide, H. Ito, J. Nishizawa, K. Tamura, and S. Ichikawa, “Ferroelectric PVDF cladding terahertz waveguide,” J. Lightwave Technol. 23, 2469–2473 (2005). [CrossRef]

, 16

16. M. Skorobogatiy and A. Dupuis, “Ferroelectric all-polymer hollow Bragg fibers for terahertz guidance,” Appl. Phys. Lett. 90, 113514 (2007). [CrossRef]

] with losses lower than 10 dB/m. However, PVDF is a semi-crystalline polymer that has many phases and a complicated poling procedure is required for achieving the ferroelectric state. Another hollow core design was discussed by Yu et al. [17

17. R.-J. Yu, Y.-Q. Zhang, B. Zhang, C.-R. Wang, and C.-Q. Wu, “New cobweb-structure hollow Bragg optical fibers,” Optoelectronics Lett. 3, 10–13 (2007). [CrossRef]

] is of a hollow Bragg fiber where solid layers are separated by air and supported by a network of solid supports, similarly to the air/silica Bragg fibers for the near-IR applications described in [18

18. F. Poli, M. Foroni, D. Giovanelli, A. Cucinotta, S. Selleri, J.B. Jensen, J. Laegsgaard, A. Bjarklev, G. Vienne, C. Jakobsen, and J. Broeng, “Silica bridge impact on hollow-core Bragg fiber transmission properties,” Proceedings OFC/NFOEC, 1–3 (2007).

]. Other photonic crystal structures have been tried [19

19. H. Park, M. Cho, J. Kim, and H. Han, “Terahertz pulse transmission in plastic photonic crystal fibres”, Phys. Med. Biol. 43, 3765–3769 (2002). [CrossRef]

, 20

20. M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, “Teflon photonic crystal fiber as terahertz waveguide,” Jap. J. Appl. Phys. 43, 317–319 (2004). [CrossRef]

], but the absorption in a solid core remains considerable.

In yet another approach, many sub-wavelength waveguides have been developed [21

21. S.P. Jamison, R.W. McGowan, and D. Grischkowsky, “Single-mode waveguide propagation and reshaping of sub-ps terahertz pulses in sapphire fibers,” Appl. Phys. Lett. 76, 1987–1989 (2000). [CrossRef]

, 22

22. L.-J. Chen, H.-W. Chen, T.-F. Kao, J.-Y. Lu, and C.-K. Sun, “Low-loss subwavelength plastic fiber for terahertz waveguiding,” Opt. Lett. 31, 306–308 (2006). [CrossRef]

, 23

23. M. Nagel, A. Marchewka, and H. Kurz, “Low-index discontinuity terahertz waveguides,” Opt. Express 14, 9944–9954 (2006). [CrossRef] [PubMed]

]. A solid sub-wavelength rod acts as a high refractive index core with surrounding air acting as a lower refractive index cladding. The field of the guided mode extends far into the surrounding air resulting in low absorption loss. Main disadvantage of rod-in-the-air subwavelength designs is that most of the power is propagated outside of the waveguide core, thus resulting in strong coupling to the environment, which is typically unwanted in power guiding applications. Alternatively, Nagel et al. [23

23. M. Nagel, A. Marchewka, and H. Kurz, “Low-index discontinuity terahertz waveguides,” Opt. Express 14, 9944–9954 (2006). [CrossRef] [PubMed]

] have demonstrated that addition of a sub-wavelength hole within a solid core increases the guided field within the air hole, thus reducing the absorption losses. Main disadvantage of a subwavelength hole design is that most of the power is still conducted in the high loss material of a core.

While losses of all-dielectric fibers are currently higher than those of hollow core metallized fibers, we believe that porous fiber geometry of a relatively large diameter could be designed to compete with the hollow metallized fibers. The driving factor for the development of porous all-dielectric fibers is that such fibers can be fabricated from a single material using standard fiber drawing techniques, which is, potentially, simpler than fabrication of metal coated waveguides due to omission of a coating step.

In this paper we present two designs of highly porous fibers that rely on two different guiding mechanisms – the total internal reflection (TIR) and photonic bandgap (PBG) guidance. The geometries of these structures are optimized to increase the fraction of power guided in the air inside of a fiber, thereby reducing the absorption losses and interaction with the environment. The paper is organized as follows. We first present a TIR guiding sub-wavelength fiber containing multiple sub-wavelength holes (see Fig. 1(a)), and compare its performance with that of a subwavelength rod-in-the-air fiber. We then present a PBG guiding porous Bragg fiber (see Fig. 1(b)) featuring a periodic array of concentric material layers separated by air, and supported with a network of circular bridges. Finally we conclude with a summary of the findings.

Fig. 1. Schematics of two porous fibers studied in this paper. a) Cross-section of a porous fiber with multiple sub-wavelength holes of diameter dλ separated by pitch Λ. b) Cross-section of a porous Bragg fiber featuring periodic sequence of concentric material rings of thickness h suspended in air by a network of circular bridges of diameter drod.

2. Porous fibers with multiple sub-wavelength holes

We start by reminding the reader briefly the optical properties of porous TIR fibers which were recently detailed in [24

24. A. Hassani, A. Dupuis, and M. Skorobogatiy, “Low Loss Porous Terahertz Fibers Containing Multiple Subwavelength Holes,” Appl. Phys. Lett 92, 071101 (2008). [CrossRef]

]. Our goal is to then perform a comprehensive comparative analysis of TIR porous fibers, sub-wavelength rod fibers, and porous TIR and photonic band gap Bragg fibers - all the excellent candidates for low loss guiding in THz regime.

The first structure we consider consists of a polymer rod having a hexagonal array of air holes (see Fig. 1(a)). Note that a periodic array of holes is not necessary as the guiding mechanism remains total internal reflection and not the photonic bandgap effect. The main task is to design a fiber having a relatively large core diameter for efficient light coupling, while at the same time having a significant fraction of light inside of the fiber air holes to reduce losses due to absorption of a fiber material, as well as to reduce interaction with the environment. In all the simulations presented in this section porous fiber is single mode. Experimentally, such porous fibers can be realized by capillary stacking and drawing technique (see an inset of Fig. 1(a)).

For the fiber material we assume a polymer of refractive index nmat=1.5, which is a typical value for most polymers at 1 THz. Refractive index of air is 1. First, we consider the fiber having 4 layers of subwavelength holes of two possible sizes d/λ=[0.1,0.15], where d is the hole diameter and λ is the operating wavelength. Center-to-center distance between the two holes (lattice pitch) is defined as Λ. Finally, fiber diameter is considered to be 9Λ. In the remainder of this section the air hole size is fixed for each design, while the thickness of the material veins is varied (larger d/Λ ratios correspond to thinner veins). Fully vectorial finite element method is used for the calculation of the eigen modes of a fiber. In our simulations, design wavelength is fixed λ=300 µm (frequency of 1 THz), unless specified otherwise.

Fig. 2. a) Effective refractive index of the fundamental core mode versus d/Λ for the two fiber designs having hole diameters of d/λ=[0.1,0.15]. For the fiber with d/λ=0.1, distribution of the power flux in the waveguide crossection Sz is shown for d/Λ=0.8 in the inset (a). b) Fraction of modal power guided in the air as a function of d/Λ. The two upper curves show the total power fraction in the air (air plus cladding) while the two lower curves indicate the power fraction in the air holes only.

η=airSzdAtotalSzdA
SzRe(ẑ·totaldAE×H*),
(1)

f=αmodeαmat=Re(nmat)matE2dARe(ẑ·totaldAE×H*),
(2)

where α mat is the bulk absorption losses of the core material (assuming that air has no loss). Figure 3(a) presents the normalized absorption loss of the fundamental core mode as a function of d/Λ. Not surprisingly, for higher air filling fractions (larger d/Λ) absorption loss is greatly reduced. For example, for a fiber with d/λ=0.1, d/Λ=0.95 the normalized absorption loss is ~0.08. Considering that the fiber is made of a low loss polymer such as Teflon [20

20. M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, “Teflon photonic crystal fiber as terahertz waveguide,” Jap. J. Appl. Phys. 43, 317–319 (2004). [CrossRef]

] with bulk absorption loss of αmat=0.3 cm-1⋍130 dB/m at 1 THz we obtain the fundamental mode loss α mode=10.4 dB/m.

Another important parameter to consider is radiation loss due to macrobending. In general, calculation of bending induced loss for microstructured fibers is not an easy task. In our case, however, due to Gaussian like envelope of the fundamental mode we can approximate our fiber as a low refractive index-contrast step-index fiber for which analytical approximation of bending loss is readily available [26

26. M.D. Nielsen, N.A. Mortensen, M. Albertsen, J.R. Folkenberg, A. Bjarklev, and D. Bonacinni, “Predicting macrobending loss for large-mode area photonic crystal fibers,” Opt. Express 12, 1775–1779 (2004). [CrossRef] [PubMed]

]:

απ81Aeff1β(β2βcl2)14exp(23Rb(β2βcl2)32β2)Rb(β2βcl2)β2+Rc1λRbexp(Rbλ·const),
(3)

Aeff=[I(r)rdr]2[I2(r)rdr],
(4)

Fig. 3. a) Normalized absorption loss versus d/Λ for two porous fiber designs. b) Total of the bending and absorption losses versus d/Λ for the Teflon-based porous fiber with d/λ=0.1 operating at 0.5 THz.

Fig. 4. Comparison of the propagation characteristics of the fundamental mode of a porous fiber (solid curves) with those of the fundamental mode of the equivalent rod-in-the-air subwavelength fiber (dashed curves). a) Normalized fiber and mode diameters. b) Modal effective refractive indices. c) Modal losses due to macro-bending.

Finally, we comment on the overall size of a porous single mode fiber featuring N layers of holes. As follows from the schematic of Fig. 1(a), the diameter of a porous fiber is:

Dp=(2N+1)Λ=λ[(2N+1)(dλ)(dΛ)]λ(2N+1)(dλ).
(5)

Fig. 5. Various implementations of porous fibers. a) Increasing the number of layers in a porous fiber leads to modes with larger effective mode diameters. In the lower plot a typical performance of a 4 layer porous fiber designed for λ=300 µm is shown. b) Schematic of a 25 layer porous Bragg fiber and flux distribution in its fundamental mode.

We conclude this section by presenting performance of a typical porous fiber as a function of the wavelength of operation. The fiber in question is designed for λ=300 µm, has 4 layers of holes, and is characterized by d/λ=0.1, d/Λ 0.88. Fiber diameter is Dλ. The material of the fiber is assumed to be Teflon polymer with bulk material loss αmat=130 dB/m. In Fig. 5(a) we demonstrate absorption and bending losses of such a fiber assuming a very tight Rb=1 cm bending radius. The fiber is effectively insensitive to bending as bending loss stays much smaller than the absorption loss even for very tight bending radii. We also see that performance of this fiber is broadband with total propagation loss less than 20 dB/cm across the whole 200–400 µm wavelength region assuming the presence of bends as tight as Rb=1 cm.

3. Porous photonic bandgap Bragg fibers with a network of bridges

In the remainder of the paper, we analyze guiding of THz radiation using porous photonic bandgap Bragg fiber. Schematic of such a fiber is shown in Fig. 1(b); Bragg fiber consists of a sequence of concentric material layers suspended in air by a network of material bridges in the shape of sub-wavelength rods. For the reference, porous Bragg fiber geometry was recently discussed by Yu et al. [17

17. R.-J. Yu, Y.-Q. Zhang, B. Zhang, C.-R. Wang, and C.-Q. Wu, “New cobweb-structure hollow Bragg optical fibers,” Optoelectronics Lett. 3, 10–13 (2007). [CrossRef]

], where instead of rods, thin material bridges were proposed, however, practical implementation of such a geometry may be challenging. Analysis of transmission properties of the air/silica based Bragg fibers with bridges for near IR applications was also presented recently in [18

18. F. Poli, M. Foroni, D. Giovanelli, A. Cucinotta, S. Selleri, J.B. Jensen, J. Laegsgaard, A. Bjarklev, G. Vienne, C. Jakobsen, and J. Broeng, “Silica bridge impact on hollow-core Bragg fiber transmission properties,” Proceedings OFC/NFOEC, 1–3 (2007).

].

As detailed in Fig. 1(b), proposed fiber consists of a sequence of circular material layers of thickness h suspended in air by circular bridges (rods) of diameter drod. Thickness of the air layers is the same as the diameter of circular bridges. Since the bridges are small, the layers containing the bridges have an effective index close to that of air. Thus, the alternating layers of polymer and air yield a high index-contrast Bragg fiber. Core radius Rc of a hollow Bragg fiber is assumed to be considerably larger than the wavelength of propagating light. Guidance in the hollow core is enabled by the photonic bandgap of a multilayer reflector. In the ideal Bragg fiber without bridges, for a design wavelength λc to coincide with the center of a photonic bangap of a multilayer reflector, thicknesses of the material and air layers have to be chosen to satisfy the following relation [16

16. M. Skorobogatiy and A. Dupuis, “Ferroelectric all-polymer hollow Bragg fibers for terahertz guidance,” Appl. Phys. Lett. 90, 113514 (2007). [CrossRef]

]:

Fig. 6. Radiation losses (solid lines) and absorption losses (dashed lines) of the hollow core Bragg fibers for various bridge sizes drod=[100,200,300] µm. For comparison, radiation loss of the equivalent Bragg fibers without rods are presented as dotted lines. Inset II shows Sz flux distribution in the fundamental core guided mode positioned at the minimum of the local bandgap at λ=378 µm. Insets I and III show field distributions in the fundamental core mode at the wavelengths of coupling with different surface states.
drodnair2neff2+hnmat2neff2=λc2.
(6)

Taking into account that in a large hollow core fiber the lowest loss core mode has effective refractive index neff slightly lower but very close to that of air nair, we conclude that rod size does not affect considerably the resonance condition (6) and, therefore, can be chosen at will, while material layer thickness has to be chosen as h=λc(2nmat2nair2) . Note that this choice of material thickness is only an approximation, and therefore one should not expect exact matching of the wavelength of the center of a reflector bandgap with λc. In what follows we consider several designs of a 3 layer Bragg fiber with the following parameters nmat=1.6, nair=1, drod=[100,200,300] µm. Design wavelength is λc=300 µm, leading to the h=120 µm choice of a material layer thickness. Fiber core radius is assumed to be Rc=1 mm⋍3.3λ 0. Finally, fiber material loss is assumed to be comparable to that of a Teflon polymer αmat=130 dB/m.

In Fig. 6 we present radiation losses (solid curves) and absorption losses (dashed curves) of the fundamental HE 11 core guided mode of a Bragg fiber with bridges for various bridge sizes. For comparison, radiation losses of the fundamental core mode of equivalent Bragg fibers with identical parameters, however, without the dielectric bridges, are shown as dotted curves. Overall, radiation losses of the Bragg fibers with bridges follow radiation losses of the equivalent Bragg fibers without bridges. However, bandgaps of the Bragg fibers with bridges are fractured due to crossing of the core mode dispersion relation with those of the surface states. At the minima of the local bandgaps (see inset II in Fig. 6), field distribution of the fundamental core guided mode is Gaussian-like and it is well confined inside of the hollow core. For example, for drod=200 µm at λ=378 µm the total waveguide loss is ~8.7 dB/m and the bandwidth is ~10 µm. In principal, by adding only few more layers into Bragg reflector (5-7 material layers instead of 3 material layers shown in Fig. 1(b)), radiation loss can be reduced below absorption loss resulting in fibers of ~5 dB/m total loss in the case of drod=200 µm, and fibers of ~1 dB/m total loss in the case of drod=100 µm. At the wavelengths of crossing with surface states (see insets I and III in Fig. 6), radiation and absorption losses increase considerably due to excitation of the highly lossy surface states localized inside of the material layers of a Bragg reflector. As seen from the insets I and II in Fig. 6, fields of the surface states are concentrated in the vicinity, or directly, at the material bridges separating separating concentric layers of a Bragg reflector. By comparing the loss data in Fig. 6 for various fiber designs one concludes that when bridge size increases, the number of surface states also increases. Therefore, to improve fiber bandwidth one has to avoid fracturing of the reflector bandgap with surface states, which is, in principle possible, by reducing the thickness of the bridges. of the bridges. However, even in the best case scenario of ideal Bragg fibers without any bridges, bandwidth of a plastic-based fiber with nmat ~1.6 is relatively small and on the order of ~100 µm~0.3 THz.

Fig. 7. Bending losses of a porous Bragg fiber without bridges designed and operated at λc=300 µm. Bending loss is strongly sensitive to the polarization of an HE 11 mode, with the polarization in the plane of a bend being the lossiest. In the insets we show Sz flux distributions at the output of the 90° bends of various radii.

We conclude this section by mentioning in passing that we have attempted fabrication of porous Bragg fibers experimentally. Inset in Fig. 1(b) presents optical microscope image showing a small part of the cross-section of a porousmultilayer. The fiber wasmade by co-rolling of a solid PMMA film with a second PMMA film that had windows cut into it. Once rolled, the windows formed the air gaps and the remaining bridges of the cut film formed bridges separating the solid film layers. Preliminary bolometer measurements of THz transmission through porous Bragg fibers having 1 cm hollow core diameter resulted in total loss estimate of ~40 dB/m. We are currently pursuing more detailed transmission measurements of these fibers.

4. Conclusions

References and links

1.

J. Xu, K.W. Plaxco, and S.J. Allen, “Probing the collective vibrational dynamics of a protein in liquid water by terahertz absorption spectroscopy”, Protein Sci. 15, 1175–1181 (2006). [CrossRef] [PubMed]

2.

D.J. Cook, B.K. Decker, and M.G. Allen, “Quantitative THz Spectroscopy of Explosive Materials,” OSA conf.: Optical Terahertz Science and Technology, PSI-SR-1196 (2005).

3.

C.J. Strachan, P.F. Taday, D.A. Newnham, K.C. Gordon, J.A. Zeitler, M. Pepper, and T. Rades, “Using Terahertz Pulsed Spectroscopy to Quantify Pharmaceutical Polymorphism and Crystallinity,” J. Pharmaceutical Sci. 94, 837–846 (2005). [CrossRef]

4.

M. Nagel, P.H. Bolivar, M. Brucherseifer, H. Kurz, A. Bosserhoff, and R. Bttner, “Integrated THz technology for label-free genetic diagnostics,” Appl. Phys. Lett. 80, 154–156 (2002). [CrossRef]

5.

W.L. Chan, J. Deibel, and D.M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70, 1325–1379 (2007). [CrossRef]

6.

T. Kiwa, M. Tonouchi, M. Yamashita, and K. Kawase, “Laser terahertz-emission microscope for inspecting electrical faults in integrated circuits,” Opt. Lett. 28, 2058–2060 (2003). [CrossRef] [PubMed]

7.

K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Non-destructive terahertz imaging of illicit drugs using spectral fingerprints,” Opt. Express 11, 2549–2554 (2003). [CrossRef] [PubMed]

8.

T. Lffler, T. Bauer, K.J. Siebert, H.G. Roskos, A. Fitzgerald, and S. Czasch, “Terahertz dark-field imaging of biomedical tissue,” Opt. Express 9, 616–621 (2001). [CrossRef]

9.

G. Gallot, S.P. Jamison, R.W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17, 851–863 (2000). [CrossRef]

10.

J.A. Harrington, R. George, P. Pedersen, and E. Mueller, “Hollow polycarbonate waveguides with inner Cu coatings for delivery of terahertz radiation,” Opt. Express 12, 5263–5268 (2004). [CrossRef] [PubMed]

11.

C. Themistos, B.M.A. Rahman, M. Rajarajan, K.T.V. Grattan, B. Bowden, and J. A. Harrington, “Characterization of silver/polystyrene (PS)-coated hollow glass waveguides at THz frequency,” J. Lightwave Technol. 25, 2456–2462 (2007). [CrossRef]

12.

C.T. Ito, Y. Matsuura, M. Miyagi, H. Minamide, and H. Ito, “Flexible terahertz fiber optics with low bend-induced losses,” J. Opt. Soc. Am. B 24, 1230–1235 (2007). [CrossRef]

13.

K. Wang and D.M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432, 376–379 (2004). [CrossRef] [PubMed]

14.

Q. Cao and J. Jahns “Azimuthally polarized surface plasmons as effective terahertz waveguides,” Opt. Express 13, 511–518 (2005). [CrossRef] [PubMed]

15.

T. Hidaka, H. Minamide, H. Ito, J. Nishizawa, K. Tamura, and S. Ichikawa, “Ferroelectric PVDF cladding terahertz waveguide,” J. Lightwave Technol. 23, 2469–2473 (2005). [CrossRef]

16.

M. Skorobogatiy and A. Dupuis, “Ferroelectric all-polymer hollow Bragg fibers for terahertz guidance,” Appl. Phys. Lett. 90, 113514 (2007). [CrossRef]

17.

R.-J. Yu, Y.-Q. Zhang, B. Zhang, C.-R. Wang, and C.-Q. Wu, “New cobweb-structure hollow Bragg optical fibers,” Optoelectronics Lett. 3, 10–13 (2007). [CrossRef]

18.

F. Poli, M. Foroni, D. Giovanelli, A. Cucinotta, S. Selleri, J.B. Jensen, J. Laegsgaard, A. Bjarklev, G. Vienne, C. Jakobsen, and J. Broeng, “Silica bridge impact on hollow-core Bragg fiber transmission properties,” Proceedings OFC/NFOEC, 1–3 (2007).

19.

H. Park, M. Cho, J. Kim, and H. Han, “Terahertz pulse transmission in plastic photonic crystal fibres”, Phys. Med. Biol. 43, 3765–3769 (2002). [CrossRef]

20.

M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, “Teflon photonic crystal fiber as terahertz waveguide,” Jap. J. Appl. Phys. 43, 317–319 (2004). [CrossRef]

21.

S.P. Jamison, R.W. McGowan, and D. Grischkowsky, “Single-mode waveguide propagation and reshaping of sub-ps terahertz pulses in sapphire fibers,” Appl. Phys. Lett. 76, 1987–1989 (2000). [CrossRef]

22.

L.-J. Chen, H.-W. Chen, T.-F. Kao, J.-Y. Lu, and C.-K. Sun, “Low-loss subwavelength plastic fiber for terahertz waveguiding,” Opt. Lett. 31, 306–308 (2006). [CrossRef]

23.

M. Nagel, A. Marchewka, and H. Kurz, “Low-index discontinuity terahertz waveguides,” Opt. Express 14, 9944–9954 (2006). [CrossRef] [PubMed]

24.

A. Hassani, A. Dupuis, and M. Skorobogatiy, “Low Loss Porous Terahertz Fibers Containing Multiple Subwavelength Holes,” Appl. Phys. Lett 92, 071101 (2008). [CrossRef]

25.

A.W. Snyder and J.D. Love, “Optical Waveguide Theory,” Chapman Hall, New York, (1983).

26.

M.D. Nielsen, N.A. Mortensen, M. Albertsen, J.R. Folkenberg, A. Bjarklev, and D. Bonacinni, “Predicting macrobending loss for large-mode area photonic crystal fibers,” Opt. Express 12, 1775–1779 (2004). [CrossRef] [PubMed]

27.

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

28.

S.G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weiseberg, T.D. Engeness, M. Soljacic, S.A. Jacobs, J.D. Joannopoulos, and Y. Fink, “Low-Loss Asymptotically Single-Mode Propagation in Large Core OmniGuide Fibers,” Opt. Express 9, 748 (2001). [CrossRef] [PubMed]

29.

M. Skorobogatiy, S.A. Jacobs, S.G. Johnson, and Y. Fink, “Geometric variations in high index-contrast waveguides, coupled mode theory in curvilinear coordinates,” Opt. Express 10, 1227–1243 (2002). [PubMed]

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(230.1480) Optical devices : Bragg reflectors
(060.4005) Fiber optics and optical communications : Microstructured fibers
(060.5295) Fiber optics and optical communications : Photonic crystal fibers

ToC Category:
Photonic Crystal Fibers

History
Original Manuscript: January 28, 2008
Revised Manuscript: April 8, 2008
Manuscript Accepted: April 10, 2008
Published: April 21, 2008

Citation
Alireza Hassani, Alexandre Dupuis, and Maksim Skorobogatiy, "Porous polymer fibers for low-loss Terahertz guiding," Opt. Express 16, 6340-6351 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-9-6340


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References

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  16. M. Skorobogatiy and A. Dupuis, "Ferroelectric all-polymer hollow Bragg fibers for terahertz guidance," Appl. Phys. Lett. 90, 113514 (2007). [CrossRef]
  17. R.-J. Yu, Y.-Q. Zhang, B. Zhang, C.-R. Wang, and C.-Q. Wu, "New cobweb-structure hollow Bragg optical fibers," Optoelectronics Lett. 3, 10-13 (2007). [CrossRef]
  18. F. Poli, M. Foroni, D. Giovanelli, A. Cucinotta, S. Selleri, J. B. Jensen, J. Laegsgaard, A. Bjarklev, G. Vienne, C. Jakobsen, and J. Broeng, "Silica bridge impact on hollow-core Bragg fiber transmission properties," Proceedings OFC/NFOEC, 1-3 (2007).
  19. H. Park, M. Cho, J. Kim, and H. Han, "Terahertz pulse transmission in plastic photonic crystal fibres," Phys. Med. Biol. 43, 3765-3769 (2002). [CrossRef]
  20. M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, "Teflon photonic crystal fiber as terahertz waveguide," Jap. J. Appl. Phys. 43, 317-319 (2004). [CrossRef]
  21. S. P. Jamison, R. W. McGowan, and D. Grischkowsky, "Single-mode waveguide propagation and reshaping of sub-ps terahertz pulses in sapphire fibers," Appl. Phys. Lett. 76, 1987-1989 (2000). [CrossRef]
  22. L.-J. Chen, H.-W. Chen, T.-F. Kao, J.-Y. Lu, and C.-K. Sun, "Low-loss subwavelength plastic fiber for terahertz waveguiding," Opt. Lett. 31, 306-308 (2006). [CrossRef]
  23. M. Nagel, A. Marchewka, and H. Kurz, "Low-index discontinuity terahertz waveguides," Opt. Express 14, 9944-9954 (2006). [CrossRef] [PubMed]
  24. A. Hassani, A. Dupuis, and M. Skorobogatiy, "Low Loss Porous Terahertz Fibers Containing Multiple Subwavelength Holes," Appl. Phys. Lett 92, 071101 (2008). [CrossRef]
  25. A. W. Snyder and J. D. Love, Optical Waveguide Theory Chapman Hall, New York, (1983).
  26. M. D. Nielsen, N. A. Mortensen, M. Albertsen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, "Predicting macrobending loss for large-mode area photonic crystal fibers," Opt. Express 12, 1775-1779 (2004). [CrossRef] [PubMed]
  27. N. A. Mortensen, "Effective area of photonic crystal fibers," Opt. Express 10, 341-348 (2002). [PubMed]
  28. S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weiseberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, "Low-Loss Asymptotically Single-Mode Propagation in Large Core OmniGuide Fibers," Opt. Express 9, 748 (2001). [CrossRef] [PubMed]
  29. M. Skorobogatiy, S. A. Jacobs, S. G. Johnson, and Y. Fink, "Geometric variations in high index-contrast waveguides, coupled mode theory in curvilinear coordinates," Opt. Express 10, 1227-1243 (2002). [PubMed]

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