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IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 22, NO. 2, MARCH/APRIL 2016 8500215

Specialty Fibers for Terahertz Generation and Transmission: A Review

Ajanta Barh, Bishnu Pada Pal, Senior Member, IEEE, Govind P. Agrawal, Fellow, IEEE, Ravi K. Varshney, and B. M. Azizur Rahman, Senior Member, IEEE

(Invited Paper)

Abstract—Terahertz (THz) frequency range, lying between the optical and microwave frequency ranges covers a significant por- tion of the electro-magnetic spectrum. Though its initial usage started in the 1960s, active research in the THz field started only in the 1990s by researchers from both optics and microwaves dis- ciplines. The use of optical fibers for THz application has attracted considerable attention in recent years. In this paper, we review the progress and current status of optical fiber-based techniques for THz generation and transmission. The first part of this re- view focuses on THz sources. After a review on various types of THz sources, we discuss how specialty optical fibers can be used for THz generation. The second part of this review focuses on the guided wave propagation of THz waves for their transmission. Af- ter discussing various wave guiding schemes, we consider new fiber designs for THz transmission.

Index Terms—Optical waveguides, plastic optical fibers, THz generation, THz transmission.

I. INTRODUCTION

THE terahertz (THz) frequency/wavelength window of theelectro-magnetic spectrum lies between the infrared band and the microwave band (see Fig. 1), and ranges in frequency from 0.1 to 10 THz (equivalently wavelength ranges from 3 mm– 30 μm) [1], [2]. Radiation from any object with temperature > 10 K contains THz wavelengths and almost 98% of cosmic background radiations since Big-Bang event corresponds to THz and far-infrared frequencies [3], [4]. Initially THz radiation was mainly used for passive applications, where THz waves were de- tected to study the chemistry of cold planetary atmosphere and interstellar medium [4]–[6]. It even had different names—sub- millimeter or extreme far-infrared [6], [7]. Over the last 20 years, THz technology has experienced a significant growth, almost in an exponential manner [8] owing to its potential applications.

Manuscript received June 1, 2015; revised September 9, 2015 and October 13, 2015; accepted October 18, 2015. Date of publication October 26, 2015; date of current version January 19, 2016. This work was supported in part by Trilateral UKIERI project entitled “Design and analysis of optical microstructured fiber- based THz waves for transmission and applications.”

A. Barh and R. K. Varshney are with the Department of Physics, In- dian Institute of Technology Delhi, New Delhi 110016, India (e-mail: ajanta. [email protected]; [email protected]).

B. P. Pal is with the School of Natural Sciences, Mahindra Ecole Centrale, Hyderabad 500043, India (e-mail: [email protected]).

G. P. Agrawal is with the Institute of Optics, University of Rochester, Rochester, NY 14627 USA (e-mail: [email protected]).

B. M. A. Rahman is with Department of Electrical and Electronic Engi- neering, City University London, London EC1V 0HB, U.K. (e-mail: b.m.a. [email protected]).

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSTQE.2015.2494537

Fig. 1. Schematic diagram of electro-magnetic spectrum, indicating THz gap between far-infrared and mm wave region. After, Ref. [31].

This frequency range can transfer huge data files via wireless route [9], [10] and can significantly increase the communication data rate over existing microwave technology [9]–[12]. The THz radiation scatters less than optical waves, is non-ionizing, and can yield high resolution images [1], [3], [13]–[15]. THz waves can deeply penetrate through cloths, ceramics, walls, woods, paper, dry air, polymers, but they are absorbed or reflected by metal, water vapor, dust, cloud, and sufficiently dense objects [3], [16]–[18]. Moreover, vibrational or rotational transitions of a wide range of molecular clusters, and electronic transitions of many nano-composites (chemical and biological substances) exhibit strong resonances at THz frequencies, and those absorp- tion bands can serve as their chemical fingerprints [19]–[24]. Additionally, THz waves are also not harmful to human health [25]–[27]. All these excellent qualities of THz radiation make it suitable for imaging of hidden objects, like explosives, metallic weapons, etc., [28]–[30]. It is also useful to monitor the buried defects in IC packages, layer of paints, tiles, or space crafts [31]–[34]. Most importantly, this technology has already begun to make deep inroads in non-invasive medical diagnostics, such as detection of skin cancer, tooth decay, and identification of human tissues based on different refractive indices and linear absorption coefficients at THz frequencies [1], [35]–[38].

THz waves suffer high metallic losses in conventional elec- tronic circuitry, which operates below 100 GHz. It is well estab- lished that for typical radio frequency devices, like electronic circuits, the efficiency as well as the average output power tends to fall inversely with second to fourth power of the operating frequency [2], [35], [39]. Moreover, this high loss and low- efficiency along with the smaller size of electronic devices lead to another problem, the extreme heating effect [39], [40]. An expensive cryogenic/cooling system is eventually required for dealing with this heating issue [40]. Though use of THz waves has significant benefits, THz generation is limited by lack of suit- able narrow band-gap semiconductors [41], [42]. The band-gaps corresponding to lower THz frequencies (< 10 THz) become comparable to the lattice vibration energy, and hence they are

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8500215 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 22, NO. 2, MARCH/APRIL 2016

associated with huge thermal noise [41]. The conventional di- electric waveguides (WGs) such as silica glass fibers are also not useful for guiding THz wave owing to their high transmission losses [43]. Moreover, suitable electro-optic devices are also not available till date. However, the researchers are trying hard on various technology options to fill this THz-gap!

Recent advances in THz technology are motivated by a rapid growth of THz-based active applications mentioned above earlier. The primary challenges are to design and develop appro- priate THz sources, low-loss transmission medium, efficient de- tectors, and other control components [41], [43]. Among these, the most critical one is an efficient, high power, portable and sta- ble THz source [39], [41], [44]. A low-loss transmission medium is also desirable to reduce the overall loss for many applications [43]. The detection of THz wave was performed first in 1890s by using the bolometer [45], [46]. Since then, several proposals have been made [41], [47]–[52], though they were quite expen- sive and required special cooling system. However, the recent development in THz time-domain spectroscopy has boosted the bolometer detection technique significantly [22], [53], [54].

The researchers from both optical and electrical disciplines are striving hard to achieve more and more efficient THz tech- nology by continuously improving the existing devices as well as developing new ones [39], [55]. In this review article, we fo- cus on the optical side of THz technology. Since, it itself forms a vast domain, we concentrate mostly on optical waveguide (OWG) based THz sources and low-loss transmission systems. Research on OWG-based applications began around 2000 [56]– [58]. Among various OWG platforms, optical fibers are most attractive for day-to-day applications, which include high power lasers, long distance transmission, medical endoscopy, sensing, etc., [59]–[61]. Moreover, they can be packaged in a reasonably compact form [62]. Several fiber-based innovative proposals have already been made, especially for loss-less THz guidance.

This review article is organized as follows. In section II, we first survey the schemes for generating THz wave via optical means, and then focus on optical fiber-based proposals. In sec- tion III, we investigate dielectric fiber based designs for THz transmission. Last section provides future prospects.

II. THZ SOURCES

As mentioned above, plenty of THz radiation is available in nature, including cosmic or interstellar background radiation, black-body radiation of any object with temperature > 10 K, ordinary mercury lamp or heated rod of carborundum [3], [8], [63], [64]. However, these are hardly suitable for active appli- cations mentioned earlier. The appropriate source design for the THz band is certainly the most challenging task. To date, several techniques have been proposed, and depending on their working principle they can be divided in three broad categories: (1) parti- cle accelerator based sources, (2) microwave/electronics based techniques, and (3) optics based techniques. Till now, highest av- erage power has been obtained from the first category, which can also provide sources with a continuously tunable wavelength. Unfortunately, these are not cost effective owing to their very large size and complex set up. Few examples are backward wave

oscillators, travelling wave tubes, extended interaction klystron, gyrotrons, free electron lasers, and synchrotron [65]–[68]. In the second category, electronics based THz sources are undoubtedly the more compact ones and can generate CW power with a nar- row line width at room temperature. Though they work fine in the lower frequency end, their efficiency as well as output power drops rapidly as THz frequency increases. In that regime, their metallic structures suffer high losses too [2]. Few examples of electronics-based THz sources are Gunn diodes, high frequency transistors, etc. [69]–[71]. In the third category, optics based sources yield the highest average power at the high end of the THz frequency range. As the operating frequency decreases, thermal noise becomes an unavoidable issue, and consequently, cryogenic cooling systems become necessary. Though a wide range of optical based THz sources are now available, they still lack in efficiency. Another challenge is to find suitable dielectric material as a host for THz operation. Recently, superconductor based THz sources are proposed by exploiting Josephson junc- tions [72]. In the following we will focus mainly on fiber-based THz sources.

A. Review of Reported Optical THz Sources

Depending on the state of operating medium, optical THz sources can be divided in two categories: gaseous and solid-state THz sources. Among these, gas lasers are the oldest ones [73], [74], whereas quantum cascade lasers (QCL) are the newest one [75].

Gas lasers emit THz waves within a wide spectral range as no phonon resonances occur in a gaseous medium. They also prevent any reflection of both the optical pump and generated THz waves. Several organic (e.g., methyl chloride, methanol, vinyl chloride) and inorganic gases (e.g., air, nitrogen, helium, argon, krypton) at low pressure have been used with an intense optical pump (usually CO2 laser) to generate broad-band THz waves [73], [76], [77]. The resulting THz sources are coherent and can yield sufficiently high average power. One noticeable drawback is in their bulky set up; however, their efficiency is still low though steadily improving [77]–[79].

Solid state optical THz sources can be categorized in two classes, one is a laser source and the other is a laser pumped source. The THz-laser sources, such as semiconductor lasers and QCLs, are frequency-tunable and quite compact in size. Such sources include germanium (Ge) or silicon (Si) based laser [80], strained p-Ge laser [81], and electrically pumped photonic- crystal laser [82]. The QCLs are primarily composed of hetero- structured materials (Si/SiGe, GaAs/AlGaAs, InGaAs/InAlAs, GaSb/AlGaSb) with multi-quantum well structures [83]–[89]. They have become quite popular for high THz frequency op- eration, and their output power varies from 1 μW to tens of mW level depending on its operating frequency. Unfortunately, they too require a costly cryogenic cooling system. Till date, lowest THz frequency realized with a QCL is 1.2 THz with CW output power of 0.12 mW at an operating temperature of 10 K [90] and the highest operating temperature is 199.5 K, with las- ing frequency of 3.22 THz, pulse duration of 300 ns, repetition rate of 300 Hz and peak power of > 6 mW [91]. It is worth mentioning that the demonstrated efficiency of QCL is about

BARH et al.: SPECIALTY FIBERS FOR TERAHERTZ GENERATION AND TRANSMISSION: A REVIEW 8500215

Fig. 2. Schematic energy level diagram of the degenerate and non-degenerate FWM processes.

50% under cryogenic operational conditions [92]. However, the drawbacks of QCL are (1) room temperature operation has not been realized yet; (2) design of QCL with lasing frequency < 1 THz is extremely challenging, (3) operation in the short-pulse regime is not easily realizable. These limitations would possibly be overcome in the future through further research innovations. For example, QCLs operable at relatively higher temperatures would possibly be realized through new material systems, and their operating frequency could be reduced to below 1 THz through precise quantum/band-gap engineering [93], [94]. In the second category, a wide variety of laser pumped THz sources had been proposed, such as a photoconductive or dipole an- tenna [95]–[99], a photomixer [100]–[103], a nonlinear crystal or polymer based difference-frequency generator [44], [104]– [107], an optical rectification based source [108]–[111], a THz parametric oscillator [112]–[115], photo-Dember effect in an InAs film [116] or an enhanced surface emitter in a magnetic field [117], [118]. Though research is still continuing in these fields, the maximum efficiency is still below 0.05%. However, in terms of compactness, tunability and CW operation, such THz sources are quite promising [119]. Other approaches include magnetic component of light induced charge separation in di- electric [120], and optical fiber based application. In the next section, we will study this optical fiber based THz generation in detail.

B. Optical Fiber Based THz Generation

THz generation using optical fibers is attractive owing to their versatile characteristics. Most of the proposals are based on conventional fused silica optical fibers [121]–[123], but recently polymer fiber based THz generation has been also proposed [124]. In all cases, nonlinear effects are exploited to generate the THz waves with an optical source acting as the input pump.

The nonlinearity in optical fibers arises from the third or- der susceptibility [χ(3) ] [125], which is commonly exploited to generate new waves [125]–[127]. Among the several nonlinear physical processes, four wave mixing (FWM) is the most rel- evant one for new frequency generation, provided appropriate phase matching condition can be satisfied [125], [128]. In the FWM process, two pump photons (ωp) of the same (degener- ate FWM) or different frequencies (non-degenerate FWM) are converted to a signal photon of lower frequency (ωs < ωp) and an idler photon of higher frequency (ωi > ωp), as shown in Fig. 2: the subscripts p, s and i stand for pump, signal and idler,

Fig. 3. Schematic of (a) collinear and (b) non-collinear phase matching conditions.

respectively. Along with energy conservation (ωp1 + ωp2 = ωs + ωi), momentum conservation must also be simultaneously satisfied for fulfilling the required phase matching condition. By launching a weak idler as a seed at the input along with the pump(s), the FWM efficiency can be improved considerably, as it stimulates the FWM process.

Depending on the momentum conservation, the THz wave can be generated either parallel to the input optical waves [collinear, cf., Fig. 3(a)] or perpendicular (or any other an- gle) to them [non-collinear, cf., Fig. 3(b)]. In Fig. 3, βj is the propagation constant of the jth mode (j = p, s, i). It should be noted that, along with the generation of a THz wave, input seed (idler) will also get amplified [127]. Under the collinear phase matching condition, the THz wave can be collected at the end facet of the optical fiber [121], [124], whereas for non-collinear phase matching, THz is emitted sideways from the cladding of the fiber [121], [122]. The latter geometry is especially attrac- tive for bio-medical applications as it enhances the light-matter interaction significantly.

The frequency shift (ωs = ωp − ωs) strongly depends on both the group velocity dispersion (GVD) and nonlinear parameters of the fiber at the pump wavelength (λp ), which should ideally lie close to the designed fiber’s zero dispersion wavelength [128]. Dispersion parameters are obtained by expanding β(ω) of the fiber in a Taylor series around the pump frequency and are given by βn = dnβ/dωn . By considering dispersion terms up to fifth order, ωs can be approximated as [125], [127]:

Ωs =

√ √ √ √6 |β2 |

β4

(

1 ± √

1 − 2β4γP0 3β22

)

(1)

where, γ = (2πn2)/(λAeff ) is the nonlinear parameter and P0 is the input pump power (CW, degenerate case). The parameter n2 is known as nonlinear index coefficient and is related to χ(3) . The FWM efficiency strongly depends on the following parameters:

1) Residual phase mismatch. 2) Modal overlap among participating waves. 3) Effective nonlinearity of the fiber. 4) Fiber’s losses. 5) Similarity in polarization states. 6) Single mode operation at pump and signal frequency.

8500215 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 22, NO. 2, MARCH/APRIL 2016

1) THz Generation in Conventional Silica Fibers: Conven- tional optical fibers (fused silica) exhibit relatively low losses up to ∼2 μm [129], but become highly lossy at THz wavelengths, which make them unsuitable for THz propagation. One sure way to improve the output power of THz radiation generated inside a fiber is to let it radiate out from the fiber core. Such fiber can be designed by employing the non-collinear phase- matching condition. This was first proposed by Suizu et al. in 2007 [121], when they theoretically investigated surface emit- ted THz waves from a silica optical fiber. As seen in Fig. 3, this approach requires the pump and idler to propagate in opposite directions. The phase matching is achieved by considering the uncertainty in momentum of THz wave because of a small size of the fiber core (radius is few μm), which is a small fraction of the THz wavelength (> 100 μm). The phase matching wave- lengths and the output THz power were calculated by solving nonlinear equations analytically by assuming negligible pump depletion and fiber losses. Under such conditions, the output THz power (PTHz) can be expressed as [121]:

PTHz = 16n5THzn

2 2

9n3oλ3THzw (μ0/ε0) LP1P2Pi (2)

where, nTHz , no , λTHz , and w are the modal index of THz wave, modal index of optical wave (assumed same for all optical waves), wavelength of the THz wave, and the mode field radius (1/e2) of optical wave, respectively. The parameters μ0 and ε0 are the free-space permeability and permittivity, respectively. L is the total fiber length, and, P1 , P2 , and Pi are the input powers of the two pumps and the idler, respectively. The reported results in [121] reveal that by using two optical sources, one at a wavelength of ∼800 nm (ωi) and other at 1.55 μm (ωp1 = ωp2), a THz wave can be generated at the frequency of ∼2.6 THz. By tuning the pump wavelength from 1.48 to 1.62 μm, the THz frequency can also be correspondingly tuned from 2.52 to 2.64 THz. In another paper [122], similar approach has been exploited to generate surface-emitted THz waves, where a more detail derivation of output THz power has been presented. This radiated THz power can be collected by wrapping the fiber around a bobbin (plate/cylindrical) and then by focusing them collectively through suitable lenses. Thus, the total power can be enhanced by using long fiber length. However, the efficiency of this design is still quite low (∼10−6).

Collinear phase matching can be achieved through several routes, such as periodic poling [130], a Bragg-grating geometry [123], or a suitable nonlinear phase shift [129]. THz generation using those techniques has already been studied in silica fibers [121], [123], where, the main drawbacks of collinear phase matching are high material loss and a small core size (compare to the THz wavelength). A small core increases the confine- ment loss or may not support any THz-frequency mode at all! Interestingly, the THz wavelength is comparable to the size of a fiber’s cladding. One solution would be to guide the THz wave through fiber’s cladding. Theoretical results have been reported for such a configuration [121]. It was found that a tunable THz source in the frequency ranges of 6.93–7.33 THz and 1.07–1.12 THz is realizable by tuning the wavelength of the input pump in the range of 1.48–1.62 μm. Fiber Bragg grating (FBG) based

collinear phase matching configuration has also recently been reported in [123], where a FBG is used to compensate the phase mismatch among the interacting waves. In this configuration, the efficiency of nonlinear process can be improved by applying an external static electric field such that the direction of applied field is parallel to the direction of polarization of input beams. This external electric field induces a second order nonlinear ef- fect in the fiber (through Pockel’s effect). The strength of this nonlinearity can be enhanced by increasing the external volt- age. By launching two optical sources (1.555 and 1.588 μm), a THz wave (∼4 THz) could be generated through difference frequency generation (DFG) [44], [123], [125], [131]. Here, the phase matching condition is satisfied only for DFG, and other nonlinear effects such as, second harmonic, third harmonic, and sum frequency generation can be neglected. Tuning range of the generated THz wave depends on the phase matching band width, which in turn depends on the dispersion properties of the FBG as well as on the input waves. Effects of fiber losses have been reduced by considering a small fiber length (∼3 cm). As the input optical waves interact under DFG, they generate THz wave, which radiates out from the end facet of the fiber and collected by a lens. However, the efficiency is still quite low (∼10−4) for this configuration [123].

2) THz Generation in Specialty Polymer Fibers: Recently, a design of a high power THz source has been proposed based on a specialty plastic fiber, where degenerate FWM with collinear phase matching has been exploited to generate THz waves the- oretically [124]. The primary aim was to improve the efficiency by launching pump light from a commercially available mid- infrared source into a dispersion engineered plastic fiber. Mi- crostructured optical fibers (MOFs), with micron scale (order of operating wavelength) features across their cross-section, are often used for engineering dispersion and nonlinearity [60], [125]–[128], [132]–[135]. On the other hand, plastic materi- als, such as Teflon, HDPE, and COC are highly transparent and possess flat material dispersion in the THz range [17], [136]. Moreover, they can be drawn in a fiber form, and re- searchers have already reported their successful fabrication as MOF structures [43], [137]–[139]. From the literature survey it is also evident that several polymer materials exhibit high opti- cal Kerr nonlinearity when prepared with proper processing and doping (n2 ∼10−18–10−17 m2/W) [140], [141]. Combining all these excellent properties, a Teflon based MOF is considered for generating the THz wave, where Teflon with three different re- fractive indices are considered, as different commercial supplier can provide Teflon of different RI [17]. Commercially available CO2 laser emitted at ∼10.6 μm is considered as pump. Since wavelengths of three waves involved in the FWM process are very different, it is a challenge to realize single-mode operation with high modal overlap. A double clad fiber geometry shown in Fig. 4(a) is proposed to balance all the criteria. In this Teflon based microstructured core double clad plastic fiber (MC- DCPF), the central core is formed by using four rings of hexag- onally arranged higher index rods [nr (1.44), see Teflon-type-1 shown as white dots in Fig. 4(a)] embedded in a lower index background [nb(∼ 1.425), Teflon-type-2, dark blue in color], which also forms the uniform cladding (first cladding, radius

BARH et al.: SPECIALTY FIBERS FOR TERAHERTZ GENERATION AND TRANSMISSION: A REVIEW 8500215

Fig. 4. (a) The schematic cross-section of the proposed MC-DCPF. The cen- tral white rods are composed of Teflon-1 (refractive index nr ), the dark blue background is made of Teflon-2 (nb ) and the light blue outer region (cladding for THz wave) is made of Teflon-3 (ncl ). (b) Mode intensity profiles for the pump and THz waves along x-direction (y = 0). After, Ref. [124].

R1) for optical waves. These two regions (composed of nr and nb ) together form the microstructured-core based large mode area fiber geometry for the optical modes (similar to that used in [142]), which essentially increases their mode field diameter. Interestingly, this whole region [up to R1 in Fig. 4(a)] acts as the WG core for the THz wave (λ ∼ 100μm) and its cladding is formed by adding an extra layer of Teflon [Teflon-type-3, refrac- tive index ncl (1.4), light blue in color] around it. Using this con- figuration, it has been shown that a high-power pump (at 10.6 μm with 1 kW power) generates a THz wave at a wavelength near 100 μm (i.e., frequency ∼3 THz) with an idler wavelength at ∼5.6 μm. This idler corresponds to that of a CO laser (available commercially), which can be used as a seed for the FWM pro- cess. The achieved modal overlap among these three participat- ing waves (pump, seed and THz) are very high, which essentially increases the efficiency of THz generation. The 1-D intensity profiles of the fundamental pump and THz modes are shown is Fig. 4(b). They were obtained by calculating the Poynting vector of the corresponding modes. Through rigorous calculation it has been shown that with a pump of 1 kW power along with the seed power of ∼20 W power, a THz wave with 30 W power is gener- ated at the end facet of a 65 m long MC-DCPF with a power con- version efficiency of 3%, which is more than 100 times higher than any other proposal to date on THz sources [124]. Though kW level of power may appear high for a Teflon fiber, the mode effective area of the fiber being relatively large actual pump intensity would be reasonably low to be of any real concern. Alternatively, ns pulses at low repetition rates can also be em- ployed in place of CW pump to reduce the average power level. The output phase matching band-width of the generated THz wave is plotted in Fig. 5. Such long fiber (65 m) can be easily spooled around a cylindrical bobbin to make a compact device, and for a bobbin radius � 10 cm, the bend-loss is negligible.

Table I provides a summary of fiber-based schemes discussed in this section for generating THz waves. It is clear from this table that the efficiency, band-width, and the output THz power are growing gradually. This trend may continue by exploring newer ideas and different fiber structures, made of suitable ma- terials. However, we may stress that these proposals are still at a theoretical stage. The real challenge is to fabricate and use them for real applications.

Fig. 5. The spectrum of generated THz wave at the end of fiber output facet. 3-dB phase matching band-width is ∼70 nm. After, Ref. [124].

TABLE I THZ GENERATION IN FIBER STRUCTURE

Input pump (Optical source)

THz output

Generation scheme

Power λ (μm) Type f (THz) efficiency Reference year

FWM in silica fiber

1 kW (each) 1.48–1.62, 0.8

Pulse/CW 2.52–2.64, 6.93–7.33, 1.07–1.12

∼10−5 [121] 2007

-do- -do- -do- Quasi CW 3.15–3.25 ∼10−6 [122] 2011

DFG in silica fiber

5–35 W 1.555 [&] 1.588

CW 2–30 (peak ∼4)

∼10−4 [123] 2012

FWM in Teflon MOF

1 kW, 20 W 10.58, 5.59

CW Centered ∼3 ∼10−2 [124] 2015

III. GUIDED TRANSMISSION OF THZ

Transferring information via electromagnetic fields requires low-loss and distortion-free wave guiding schemes. Metal wires have been used for centuries for electronic transmission [143], whereas, dielectric WGs have been employed for decades for optical communication [144]. In the case of THz waves, re- searchers are still searching for suitable wave guiding scheme(s).

A. A Brief History of THz WGs

Dry air is perhaps considered to be the best medium for THz transmission in terms of both low-loss and low-dispersion. However, the presence of water vapor, dust, and cloud limits its transmission and exhibits several strong absorption lines over the THz band [18]. Hence, although most of the present THz technology relies on free space transmission and manipulation, the propagation distance is limited by atmospheric losses, which may vary with weather, climate change, geographical location or altitude. For this reason, appropriate THz WGs are impor- tant for a number of applications, such as remote sensing, long range communication, collimated and diffraction limited beam guiding. Moreover, a THz WG can be used as an imaging probe (e.g., in medical endoscopy) [145], or its strong confinement property could be explored to enhance the light-matter interac- tion. The primary barrier for this technology is the lack of a suitable material for the WG structure. Several proposals have already been made in this direction, based on, metallic WGs, dielectric WGs and in some cases metal-dielectric hybrid WGs as discussed below.

8500215 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 22, NO. 2, MARCH/APRIL 2016

Fig. 6. Schematic diagram of non-planar metallic waveguides. (a) Circular (d1 ∼ 250 μm [148]), (b) parallel plate (a ∼25 mm, b ∼ 100 μm [148]), (c) bare metal wire (d2 = 0.9 mm [150]), (d) two-wire (D ∼3 mm, r ∼ 300 μm [151]), and (e) slit waveguide (c = 20 mm, h = 300 μm, g = 270 μm [152]).

Early THz WGs were composed of planar structures where coplanar transmission lines are quite common for microwaves [146], [147]. Unfortunately, they suffer high propagation losses (∼20 cm−1) due to the combined effects of Ohmic loss, absorp- tion loss inside a dielectric substrate, and radiation loss. For this reason, non-planar WG structures became an attracting option. Both metallic (cf., Fig. 6) as well as dielectric based non-planar structures have been proposed in literature. In their early forms non-planar metallic WGs consisted of a circular structure [cf., Fig. 6(a)]. In these, THz modes (both TE and TM) could be con- fined tightly inside their metallic walls. Such WGs are nearly free from radiation and dielectric losses but still suffer from high metallic losses (∼0.7 cm−1 at 1 THz) and high dispersion near the cut-off frequency. A detailed description of such circu- lar WGs and rectangular WGs is given in [148]. Parallel plate WGs [cf., Fig. 6(b)] support a TEM mode, which has no cut-off and hence doesn’t suffer from dispersion. These WGs exhibit lower loss than circular and rectangular WGs [149]. In 2004, the lowest loss (0.03 cm−1) THz transmission through a bare metal wire [cf., Fig. 6(c)] was demonstrated [150] and applied for endoscope application. In a properly designed wire, the THz mode attaches loosely to it (acts as a rail) and spreads in the surrounding medium. This configuration reduces the metallic loss greatly, but the mode becomes less confined. Coupling of a free-space THz mode to this metal wire is also difficult. A two-wire based THz wave guiding scheme [cf., Fig. 6(d)] was proposed in 2010 [151], which supports TEM as well as TE and TM modes; dispersion becomes negligible for the TEM mode. Moreover, the coupling loss reduces significantly, as the TEM mode resembles well with the THz mode generated from a dipole antenna. This geometry confines the THz wave between two wires; however this confinement decreases for a larger ra- dius of metallic wires and for larger separation between them. Another type of geometry, called slit WG [cf., Fig. 6(e)], pro- vides higher mode confinement (0.1–1 THz) with nearly no dispersion [152]. Incidentally, such high confinement also leads to high metallic losses. In conclusion, though several advances have been made towards designing THz-metallic WGs, there exist a strong trade-off between mode confinement and metallic loss. Moreover, most of the proposals are only suitable for short distance transmission (mm length scale).

Fig. 7. Schematic cross-sectional diagram of different TIR-guided fiber struc- ture. (a) Step-index fiber, (b) solid core microstructured fiber, and (c) porous-core fiber. The white circles in (b) and (c) are air holes, which can also be filled by other lower index (compare to core index) material(s). Core diameter varies from few 100–1000’s μm in such THz waveguides.

For integrated circuit applications hybrid plasmonic WG structures have become quite popular. A plasmonic WG can con- fine electromagnetic wave very tightly (sub wavelength scale) in the form of a surface plasmon mode at the interface of a metal and a dielectric medium [153]. This kind of WG has also been investigated for THz waves [154]–[156]. Both the in-plane as well as out-of-plane confinement of THz mode is possible, and its dispersive properties can be tuned arbitrarily by engineering the interface design.

A dielectric WG mainly suffers from frequency dependent material absorption loss, and thus other material systems need to be investigated. High-resistivity (HR) silicon possess extremely low loss and negligible dispersion up to ∼3 THz [157], how- ever, it is only useful for chip scale applications. As an example, researchers have theoretically designed HR-silicon based split WG structure (similar to Fig. 6(e), except that the WG is made of dielectric) for tight confinement of THz waves [158]. Alterna- tively, as discussed earlier, a number of plastic materials, such as Teflon, HDPE, COC and COP, are highly transparent and possess flat material dispersion over the THz range [17], [136], [159], [160]. Moreover, they can be drawn into a fiber form. Several proposals have already been made towards designing plastic based THz WGs. However, in the following we would focus on specialty optical fiber based THz guidance.

B. Optical Fibers for THz Transmission

Electromagnetic waves can be confined to dielectric WGs via index guiding (IG), photonic band-gap (PBG), anti-resonance guiding mechanism, or inhibited coupling guidance. All of them have already been explored for making fiber structures for THz transmission.

1) Index Guided Fiber Structures: The core of an IG-fiber has higher refractive index than the surrounding cladding region, and light is guided in the core via total internal reflectionat the core cladding interface. Three kinds of cross-sectional geome- tries have been proposed for IG-fibers in literature. One is a con- ventional step-index fiber, where the core as well as the cladding regions is composed of uniform materials [cf., Fig. 7(a)]. The second type is a solid core microstructured fiber [cf., Fig. 7(b)], where a uniform core is surrounded by a cladding, consisting of micron scale (order of operating wavelength) periodic or non- periodic refractive index features that run along the fiber length.

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The third type is a porous/microstructured-core fiber, where the core is composed of micron-scale refractive index features, sur- rounded by a uniform cladding [cf., Fig. 7(c)]. Note that we have already discussed a THz source exploiting the third kind of fiber geometry [cf., Fig. 4(a)].

The first dielectric WG for THz guiding was proposed in the year 2000, where a plastic (HDPE) ribbon of rectangular cross- section was used as the core and the surrounding air acted as the cladding [56]. Though the achieved loss was low (∼1 cm−1 over 0.1–3.5 THz) for 10’s of mm length of ribbon, dispersion was too high (1-ps pulse broadens to 20–40 ps even in a relatively short WG because of its single-cycle nature). The first circular core dielectric step index fiber for THz guidance was proposed in 2006 [161]. It was just a simple plastic (PE) wire of sub- wavelength diameter (200 μm) that acted as the fiber core with the surrounding air acting as the cladding. This structure sup- ports a single mode (HE11) at frequencies of up to 0.3 THz. Due to the small value of the core diameter, the mode spreads con- siderably into the surrounding air, which essentially reduces its dielectric loss (∼0.01 cm−1). However, the mode confinement is poor which limits its propagation length, and the bending loss is also quite high. On the other hand, microstructured fibers [cf., Fig. 7(b)] are quite promising, since light guiding is not only controlled by index contrast but can be easily manipulated through multi-parameters of the wave guiding geometry, and the total dispersion becomes a strong function of WG disper- sion [133]–[135]. In 2002, Han et al. experimentally demon- strated a HDPE based solid-core microstructured fiber [138], whose cladding was formed by arranging air holes on HDPE matrix in a periodic triangular fashion. By tuning the structural parameters, both dispersion as well as mode confinement could be tuned appropriately. As a result, the structure offers single mode guidance over 0.1–3 THz with low loss and relatively low dispersion (0.5 cm−1 and 0.3 ps/THz·cm above 0.6 THz). A Teflon based solid-core microstructured fiber was fabricated and first demonstrated for THz guidance (over 0.1–1.3 THz) in 2004 [162]. As the Teflon is a very cost effective and flexible material, it can be drawn into a longer fiber length as compared to other polymers. Moreover, the refractive index of Teflon is also low (∼1.4 in the THz regime [136], [159]), which pro- vides lower index contrast for air-Teflon structures and hence, the scattering loss is reduced too (see the Ref. [163], scattering loss scales as square of the index contrast). The proposed fiber in [162] shows attenuation < 0.12 cm−1 for the targeted THz range. Recently (in 2009), COC (trade name is Topas) material based large mode area (∼1.86 mm2) and small mode area (∼ 0.11 mm2) solid-core microstructured fibers have been fabri- cated for THz guidance [164]. Both of the proposed fibers pos- sess low loss (∼0.09 cm−1) over 0.35–0.65 THz, and quite low dispersion (< 1 ps/THz·cm) over 0.5–1.5 THz. Moreover, the high confinement of fiber modes makes them less bend sensitive. In search of further loss reduction, researchers proposed that the insertion of a loss-less low-index air gap (size must be less than the decay length of the operating wavelength) inside the solid core can reduce the material absorption loss significantly [158]. In such a configuration, the discontinuity of the normal com- ponent of the electric field at the dielectric interface enhances

Fig. 8. The variation of (a) mode-size areas and mode effective index and (b) confinement factor in core air-holes of fundamental mode with outer pitch (Λo ) for do /Λo = 0.8 and λ = 0.3 mm. After, Ref. [167].

Fig. 9. Cross-sectional image of fabricated porous-core fibers. (a) PE-based circular air hole structure. Reprinted from Optics Exp., 2009, Ref. [168]. PMMA-based (b) rectangular air hole structure and (c) spider-web air hole structure. Reprinted from Optics Exp., 2009, Ref. [169].

the field significantly (proportional to the square of the ratio of high and low refractive index) inside the low-index region (here air gap), which results in a lower material loss. The achieved loss in air-gap silica fiber is quite small (∼ 0.12 cm−1 below 0.6 THz), however it increases rapidly at higher frequencies. The study also revealed that, with the best possible design, only 26% power can be coupled into the air hole region. In 2008, two research groups, Hassani et al. [139], [165] and Atakaramians et al. [166] theoretically proposed a porous-core fiber (PoCF) structure [cf., Fig. 7(c)] for efficient THz guiding, where instead of one air-hole, a 2-D periodic array of air holes is included in the core region. In both cases, the PoCF structures are optimized to get maximum power fraction in the air holes. One group investigated the Teflon-based PoCF, where loss (absorption + bending) was less than 0.02 cm−1 at 1 THz with bend-radii as tight as 3 cm [139]. The second group proposed PMMA based PoCF with maximum achievable porosity of∼ 74%. Both power fraction and losses are studied in detail in [166]. Recently, a plas- tic (Teflon)-based porous-core with a porous-cladding fiber has been proposed [167], where air holes are arranged in hexagonal periodic fashion in both the core and the cladding regions. To support the IG-mechanism, the air-filling fraction of the core was chosen lower than that of cladding. The variation of mode- size areas (spot size, Aeff , ASMI) and effective index (ne) of the fundamental mode (Hx11) with the outer pitch (Λo) is shown in Fig. 8(a). The air hole diameters and their separation are denoted as di and Λi for core region, and do and Λo for cladding region, respectively. Fig. 8(b) shows the variation of power confine- ment in the core air-holes with Λo . It takes maximum value for Λo ∼ 0.35 mm. The maximum confinement > 20% is achiev- able in the core air-holes for di/Λi = 0.6 and do/Λo = 0.8, however, the total power in combined air-holes (core + clad) reaches up to 60% with di/Λi = 0.85 and do/Λo = 0.95, which

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TABLE II THZ TRANSMISSION THROUGH INDEX-GUIDED FIBERS

Structure Material Core diameter Loss (cm−1) Dispersion Ref. (year)

Bare plastic ribbon HDPE 2 cm × 150 μm ∼1 (0.1–3.5 THz) 1 ps → 20–40 ps [56] (2000) Plastic wire PE 200 μm ∼0.01 at 0.3 THz —– [161] (2006) Solid-core microstructured clad HDPE + air holes 500 μm ∼0.5 (0.1–3 THz) -0.3 ps/THz·cm (> 0.6 THz) [138] (2002) -do- Teflon + air holes 1 mm < 0.12 (0.1–1.3 THz) —– [162] (2004) -do- COC + air holes 870 μm, 420 μm ∼0.09 (0.35–0.65 THz) < 1 ps/THz·cm (0.5–1.5 THz) [164] (2009) Solid-core with an air gap silica ∼182 μm ∼0.12 (< 0.6 THz) —– [158] (2006) Porous core fiber Teflon + circular air holes ∼340 μm < 0.02 at 1 THz —– [139] (2008) -do- PMMA + -do- 400 μm ∼0.01 at 0.2 THz —– [166] (2008) -do- PE +-do- 350 μm ∼0.01 at 0.3 THz —– [168] (2009) -do- PE +-do- 445 μm, 695 μm < 0.02 (0.1–0.5 THz) < 1 ps/THz·cm (0.1–0.5 THz) [170] (2010) -do- PMMA+ rectangular holes 350 μm —– ne f f < 1 (0.35–0.8 THz) [169] (2009) -do- COC + spider web 600 μm < 0.08 (0.2–0.35 THz) -1.3 to -0.5 ps/m/μm (0.2–0.35 THz) [171] (2011) -do- COC + elliptical air holes 280 μm < 0.05 (0.8–1.2 THz) —– [174] (2013) Randomly porous core Zeonor + circular air holes 390 μm ∼0.06 with 50% porosity -1 to 0.1 ps/m/μm (0.8–1.4 THz) [172] (2010) Porous core and clad Teflon + -do- ∼350 μm ∼0.12 (1 THz) (bend) —– [167] (2012) Rotated porous core COC (Topas) ∼300 μm ∼ 0.066 at 1 THz 1.06 ± 0.12 ps/THz·cm (0.5 – 1.08 THz) [175] (2015) Graded porous core PE 1.35 mm 0.025 – 0.15 (.3–1.5 THz) ∼ 1 ps/THz·cm (0.2–1.5 THz) [176] (2015) Suspended solid and porous core PE + air holes 150 μm and 900 μm ∼ 0.02 (0.28–0.48 THz) —– [173] (2011)

will reduce the modal loss of this WG by 60% of the material loss. The numerical analysis of such a PoCF is relatively easy, however their fabrication is not. In 2009, PE-based PoCF was fabricated by Dupuis et al. [168] and PMMA-based PoCF was fabricated and characterized by Atakaramians et al. [169]. In the former work, the authors fabricated a PE rod with one layer of circular air holes [cf., Fig. 9(a)]. The achieved porosity was ∼40% and the measured loss was ∼0.01 cm−1 in the vicinity of 0.3 THz. In the latter work, the authors fabricated and char- acterized two PMMA-based porous-core structures, one had a rectangular geometry [cf., Fig. 9(b)] and the other had a spider- web structure [cf., Fig. 9(c)]. With these geometries, not only the porosity increased (for rectangular: 65% and for spider- web: 57%), but a strong birefringence (∼ 0.012 at 0.65 THz) also got introduced. Several other proposals have been made in the literature on solid-and porous-core IG-fibers, such as PoCF with ultra-high porosity (∼86%) [170], spider-web PoCF with ultra-low loss and low-dispersion [171], randomly porous fiber with improved properties [172], suspended-solid and porous core fiber [173], PoCF with elliptical holes with high bire- fringence (∼0.0445) [174], rotated porous-core microstructured fiber [175], and graded index PoCF [176]. We have summarized the reported IG-fibers for THz transmission in Table II.

2) Non-Index Guided Fiber Structures: Apart from IG-fiber structures, several other dielectric-based fiber geometries have been proposed and demonstrated. Unlike IG-fibers, light can be guided in the lower refractive index region of such fibers. Since the core is composed of a lower refractive index than the surrounding cladding, it allows the use of air (the best mate- rial for THz guidance) as the core material to further reduce the loss as well as dispersion of the transmitted THz wave. The fundamental guiding mechanisms in such fibers are, PBG- guidance, anti-resonance reflective (ARR)-guidance, inhibited coupling guidance and sometimes simply reflective guidance.

In the case of a PBG-guided fiber, the dielectric cladding consists of periodic refractive index variations. As a result of that, a certain range of frequencies does not propagate across it

Fig. 10. Schematic cross-sectional diagram of a (a) Bragg-fiber with 1-D periodicity in RI, (b) Hollow core PBG-holey fiber with 2-D periodicity in RI in the cladding. Central core is made of air or any other lower index material.

owing to the formation of a PBG [177]. Introduction of a suitable defect region in that otherwise periodic structure would allow the band-gap mode to transmit through it. The PBG-fibers can be classified in two broad categories depending on the type of periodicity in the cladding structure. One is Bragg-fiber [178], [179] where the cladding is formed by a series of concentric al- ternate high and low refractive index layers [cf., Fig. 10(a)]. The other type is holey fiber [134], [180] [cf., Fig. 10(b)], where the cladding is formed by high and low refractive index inclusions in the form of various lattice patterns, such as, triangular, hexag- onal, honeycomb, etc. The transmission loss in such structures is decided primarily by leakage and material absorption loss. Though the dispersion is negligible around the centre of band- gap, it increases rapidly at the band-edges. This technology is well established in the optical domain [180], however, it is still an emerging one for THz applications.

The first proposal of air-core PBG-guided fiber for THz trans- mission was reported by Skorobogatiy et al. in 2007 in the form of an all-polymer Bragg-fiber [181]. The periodic cladding is formed by repeating alternate concentric layers (total 31 layers) of ferroelectric polyvinylidenefluoride (PVDF) and polycarbon- ate (PC) polymer. Over the frequency range of 0.6–2 THz, the PVDF acts as reflecting metal surface and over the range 2– 2.6 THz, the refractive index contrast of PVDF/PC increases sufficiently to provide strong band-gap. As a combined effect,

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Fig. 11. Schematic cross-sectional diagram of hollow core Bragg-fibers with (a) cob-web structure and (b) circular bridges. White regions are air and shaded regions are plastics. (c) Microscopic image of fabricated Bragg-fiber with cir- cular ring of air holes, reprinted from Opt. Lett., 2008, Ref. [183].

Fig. 12. Plot of normalized frequency (Λ/λ) versus in-plane wave-vector (k) for (a) kz = 0 and (b) kz �= 0.The Г, M and K are the coordinates of k.

the structure shows low-loss transmission for THz waves over a wide window (< 0.02 cm−1 over 1–3 THz). Another theoretical result on a cobweb-structured Bragg-fiber [cf., Fig. 11(a)] was reported in 2007 [182], where the cladding consists of alternate layers of air and a polymer material (HDPE) with support- ing polymer bridges. The structure supports lowest loss mode, TE01 , which is non-Gaussian, along with few lossy higher order modes. The achievable loss for fundamental mode is quite low, < 1.9 × 10−5 cm−1 over 0.3–4.3 THz. An air-Teflon multilayer Bragg-fiber with supporting circular bridges [cf., Fig. 11(b)] was proposed in 2008 [139], where very low loss (< 0.02 cm−1

around 1 THz) can be achieved with just three layers of material. In all these studies no dispersion value was reported. First ex- perimental demonstration of a Bragg-fiber for THz wavelength was presented by Ponseca et al. in 2008 [183]. They designed and fabricated hollow core Bragg-fibers with a circular ring of air hole [cf., Fig. 11(c)]. These rings effectively act as high and lower index layers for the Bragg reflections from each interface to occur in phase [179]. They fabricated two similar fibers, where one fiber was 10% smaller in cross-section than the other. By us- ing THz-TDS setup, the propagation of THz wave was studied, and the achieved losses were ∼1.3 cm−1 (over 0.8–1.4 THz) for one fiber and ∼1.1 cm−1 (over 1–1.6 THz) for the other. Recently, two types of air-core Bragg-fiber were designed and fabricated [184], one is air-Teflon based [similar to Fig. 11(b)] and the other is a PE and TiO2-doped PE based multi-layer structure. The authors have made experimental and numerical studies on both fiber structures and shown that both of them possesses quite low loss (< 0.3 cm−1) over 0.1–2 THz and low dispersion (< 1 ps/THz·cm) around center of band-gaps.

In parallel to the Bragg-fiber, several proposals on PBG-holey fibers have been reported in the literature. A numerical analysis of power transmission and dispersion was carried out by Geng

Fig. 13. Air-teflon PBG-holey fiber. (a) Transmission loss and (b) total dis- persion versus frequency.

Fig. 14. Micrograph of the fabricated PBG-fiber. (a) Porous-core honeycomb structure. Reprinted from Optics Exp., 2012, Ref. [188]. (b) Hollow-core hyper- uniform disordered structure. Reprinted from Proc. IEEE IRMMW-THz, 2014, Ref. [191].

et al. in 2008 [185], where they studied a HDPE based struc- ture whose cladding was formed by five rings of circular air holes in a hexagonal pattern and the core was formed with a larger air hole [similar to Fig. 10(b)]. The proposed structure, with a core diameter of ∼600 μm and an air-filling fraction of 0.9, achieved over the 1.55–1.85 THz frequency range, total loss < 0.025 cm−1 and dispersion < ± 1 ps/THz·cm. A similar theoretical analysis has been carried out for Teflon as well as HDPE based hollow-core fiber composed of 3 cladding rings [186]. However, the chosen core diameter (∼2.7 mm) was quite large as compared to the previous one. Due to this larger core, the structure supported unwanted higher order modes also. The Teflon-based fiber yields wider band-gap (∼250 GHz centered at 1 THz) than the HDPE-based fiber (∼190 GHz centered at 0.9 THz), and over this band-gap transmission loss and dispersion were < 0.01 cm−1 and < 2 ps/km·nm, respectively. Recently, a theoretical design of a Teflon-based air core PBG-holey fiber [similar to the Fig. 10(b)] has been proposed for broad-band (> 200 GHz) low-loss THz transmission beyond 1 THz [187]. As the air-Teflon structure provides relatively low refractive in- dex contrast (1:1.44), the band-gap appears only for suitable non-zero values of longitudinal wave vector (kz , along fiber length) (cf., Fig. 12) in such simple hexagonal cladding geome- try [177], [187]. For a core diameter of∼840 μm with only three cladding rings, the achieved transmission loss was < 0.04 cm−1

[cf., Fig. 13(a)] and total dispersion was <10 ps/km·nm over 1.65–1.95 THz (300 GHz) [cf., Fig. 13(b)].

Though detailed theoretical analyses have been made on hollow-core PBG-holey fibers, their experimental realization was quite difficult. Recently, Bao et al. designed and fabricated a porous-core PBG-holey fiber [188]. They employed a hon- eycomb cladding lattice and introduced a porous-core with a similar hole size as in cladding [cf., Fig. 14(a)]. With a high

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TABLE III THZ TRANSMISSION THROUGH NON-IG FIBERS

Structure Material Core dia. Loss (cm−1) Dispersion Reference (year)

All polymer Bragg fiber PVDF + PC 1 mm < 0.02 (1 -3 THz) —— [181] (2007) Spider-web Bragg fiber HDPE + air 16, 20, 30 mm < 1.9e−5 (0.3–4.3 THz) —— [182] (2007) Bragg with circular bridges Teflon + air 2 mm < 0.02 at ∼1 THz —— [139] (2008) Bragg with circular ring of holes PMMA + air 670 μm ∼1.1 (1–1.6 THz) —— [183] (2008) Bragg fiber Teflon + air [&] 6.73 [&] 6.63 < 0.3 (0.1–2 < 1 ps/THz·cm [184] multilayer PE + TiO2 doped PE mm THz) inside PBG (2011) PBG- holey fiber HDPE + air 584 μm < 0.025 (1.55–1.84 THz) < ± 1 ps/THz·cm (1.63–1.8 THz) [185] (2008) -do- Teflon + air [&] HDPE + air ∼2.7 mm < 0.01 (0.8 ∼1.1 THz) < 2 ps/km.nm (0.9–1.1 THz) [186] (2009) -do- Teflon + air 840 μm < 0.04 (1.65–1.95 THz) < ± 2 ps/km.nm (1.7–1.9 THz) [187] (2014) PBG-porous-core honeycomb COC (Topas) + air 800 μm < 0.35 (0.75–1.05 THz) Pulse broadened by 20 times [188] (2012) Porous-core hexagonal PBG -do- ∼850 μm < 0.023 (1.025–1.2 THz) < ± 2.5 ps/THz·cm (0.98- 1.15

THz) [190] (2013)

PBG-hyperuniform clad —— 6 mm —— —— [191] (2014) ARR- microstructured fiber Teflon + air ∼5.5 mm 0.01 at ∼0.8 THz —— [192] (2008) ARR-Kagome lattice PMMA + air 1.6 [&] 2.2 mm 1 (0.75–1 THz) [&] 0.6 (0.65–1

THz) < ± 10 ps/THz·cm (0.8/0.65–1.05 THz)

[193] (2011)

Inhibited coupling-tube lattice Teflon + air (glass support) 0.84 mm <0.012 (2.3–2.85 THz) ne f f (0.98–1) for 1.5–3.4 THz [194] (2010) -do- Material with RI 1.45 + air 7 mm overall ∼0.002 at 2.5 THz —— [195] (2011) -do- PMMA + air 3.24 mm < 0.23 (0.29–0.47 THz [&]

0.61–0.95 THz) ne f f (0.98–1) for 0.35–1 THz [197] (2013)

-do- Zeonex + air 4 mm < 0.014 (0.22–0.31 THz) < 0.002 (0.44–0.64 THz)

14 ps/THz·cm at 0.3 THz [145](2014)

-do- -do- 3.84 mm < 0.003 (0.36–1.09 THz) ne f f (0.99–1) for 0.4–1.2 THz [198] (2015) Single clad pipe PVDF + air 8 mm ∼0.015 (1–2 THz) —— [199] (2005) Fiber with inner metal coating Polycarbonate + Cu ∼3 mm 0.009 at 1.9 THz —— [200] (2004) -do- Polymer + Ag 1 mm 0.017–0.018 (1.2–1.6 THz) —— [201] (2007) Fiber with hybrid inner coating Ag/PS + Silica 2 mm ∼0.002 at 2.5 THz —— [202] (2007) -do- Ag/PE + PC tube 3 mm < 0.007 (1.2–2 THz) —— [203] (2008) Dielectric coated metallic Ag + AgI 1 mm < 0.03 (0.2 ∼3 THz) —— [204] (2013) Plastic with embedded metal wire Zeonex + Indium ∼2 mm ∼0.3 [&] 0.6 (0.55–1 THz) ∼5 ps/THz·cm (0.65–1 THz) [205] (2013) -do- PE + Cu ∼200 μm < 0. 1 (0.1–0.6 THz) 1–3 ps/THz·cm (0.25–1.25 THz) [206] (2013)

air-filling fraction, the porous core acts similar to a hollow core, while simultaneously, it offers easy fabrication, higher preci- sion and better reproducibility of the structure. THz-TDS was used to investigate this fiber’s properties. It was found that, with average diameter of 800 μm, the fiber possess quite low loss (< 0.35 cm−1) over the 0.75–1.05 THz band. Very recently a comprehensive study was carried out by Fan et al. [189] on a similar honeycomb cladding based porous-core PBG fiber. They modeled such complex structure in a simple equivalent step in- dex fiber form and developed a semi-analytical method to solve the modal properties quite accurately. Another theoretical study was carried out by Liang et al. [190] on a similar porous-core PBG structure, except that the cladding geometry was hexago- nal and the hole size and pitch were different for the core and cladding regions. They observed for the fiber with the core di- ameter of ∼850 μm and three cladding rings, the transmission loss was< 0.023 cm−1 over 1.025–1.2 THz and dispersion was < ± 2.5 ps/THz·cm over 0.98–1.15 THz.

Apart from PBG-guidance, researchers have explored few other guiding mechanisms to confine the THz mode within the hollow-core. These include reflection by disordered cladding, ARR-guidance, inhibited coupling guidance and metallic type reflection in single/hybrid clad structure. Recently, a hollow- core fiber with disordered cladding geometry [cf., Fig. 14(b)] was proposed by Laurin et al. [191]. The structural uniformity of this fibers’ cladding can be varied from 0 (disordered) to 1 (crystalline). The authors have numerically investigated such

a fiber structure by assuming a core diameter of 6 mm for operation around 0.3 THz. However, its fabrication is yet to be made [191].

Under the ARR effect, both the core and the microstructured cladding support propagating modes, but they do not couple to each other owing to the anti-resonance effect. Some examples are, hollow-core with a triangular microstructured cladding lat- tice [192] and a hollow-core kagome type microstructure [193]. Under the effect of inhibited coupling, the guided core modes are prevented from efficient coupling to lossy cladding modes owing to low modal overlaps and low density of states in the cladding [194]. Detailed theoretical and numerical analyses were car- ried out in this direction, which includes, tube-lattice fiber with octagonal symmetry [194], tube-lattice with kagome geometry [195], hollow and solid core with circular and polygonal tubes [196]. Recently, the experimental realization of such fiber struc- tures is reported in [145], [197], [198].

Similar to a metallic WG, single clad plastic fiber for THz guidance is also proposed by Hidaka et al. [58], [199], where they have used a PVDF tube to guide the THz mode inside the air core. Several proposals on hybrid (metal-dielectric-polymer) clad hollow-core fibers have also been proposed in literature, such as, cupper (Cu)-coated PC fiber [200], Silver (Ag)-coated polymer fiber [201], Ag/polystyrene (PS) coated hollow glass fiber [202], Ag/PE coated polymer fiber [203], and dielectric coated hollow metallic WG [204]. Recently, a hollow-core plas- tic fiber with two and four embedded metal (Indium, Cu) wires

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has been fabricated for low-loss THz guidance [205], [206]. In one case the guiding relied on dielectric WG mode [205], whereas, in the other case it was achieved via plasmonic mode [206].

Table III summarizes the reported PBG and ARR-guided di- electric fibers for THz wave. Though spider-web structure seems most promising for THz guidance in terms of both low loss and wide band-width, it must be noted that, its larger core size makes it less flexible and multi-moded. This trade-off is true for all other structures also. Thus, the aim would be to develop WGs with lower cross-sectional dimension along with low loss and low dispersion.

IV. CONCLUSION

The use of optical fibers for THz applications has attracted considerable attention in recent years. In this article, we have reviewed the progress and current status of optical fiber based techniques for THz generation and transmission. The first part of this review focused on THz sources. After a brief discussion on various types of THz sources, we discussed how specialty optical fibers can be designed for THz generation. Most of the fiber-based THz generation schemes are based on frequency conversion via nonlinear effect of FWM. The conversion effi- ciency is still quite low but is likely to improve with further research. The second part of this review focused on the guid- ing of THz waves for their transmission over relatively long distance (compared to the THz wavelength). After discussing various wave guiding schemes, we discuss many fiber designs suitable for THz transmission. Solid-core fibers are relatively easy to fabricate and provide widest band-width for single mode operation. However, they are limited by absorption losses of the material used to make them. To minimize that loss, porous-core fibers have been proposed. As we discussed in detail, porous- core fibers show excellent properties in the THz range both in terms of their dispersion and losses. However, as a large portion of field lies in air, they are very sensitive to WG perturba- tions. Hollow-core fibers provide the lowest loss and dispersion over a specific spectral range. The main drawbacks are their limited band-width, difficulty of fabrication and a larger size. Recently researchers are exploiting interesting routes, such as using metal-dielectric hybrid structures [200]–[206] and meta- material [207] to further improve the THz transmission. The field of THz radiation is likely to see considerable progress in the coming years.

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Ajanta Barh received the B.Sc. degree from Calcutta University, Calcutta, In- dia, in 2008, and the M.Sc. and Ph.D. degrees from Indian Institute of Technol- ogy Delhi, New Delhi, India, in 2010 and 2015, respectively, all in physics. Her research interests include specialty fibers for mid-IR and THz wavelengths, si- photonics, nonlinear optics, guided wave components. She is Student Member of the OSA and OSI. She has authored/coauthored of more than 30 articles. She re- ceived the Best Student Paper award in IEEE-CODEC 2012, OSA-PHOTONICS 2014, SPIE-ICOP 2015 conferences and third place in poster session at the Sieg- man International School on Lasers-2015 at Amberg, Germany.

Bishnu P. Pal (SM’10) received the Ph.D. degree from Indian Institute of Tech- nology Delhi, New Delhi, India, in 1975. He is currently a Professor of Physics at Mahindra École Centrale, Hyderabad, India, since July 1, 2014, after retiring as a Professor of Physics from Indian Institute of Technology Delhi. He is a Fel- low of the OSA and SPIE, a Senior Member of the IEEE, an Honorary Foreign Member of the Royal Norwegian Society for Science and Arts, a Member of the OSA Board of Directors (2009–2011), and a Distinguished Lecturer of the IEEE Photonics Society (2005–2007).

Govind P. Agrawal (F’96) received the Ph.D. degree from the Indian Institute of Technology, New Delhi, India, in 1974. He has been a Wyant Professor of optics at the Institute of Optics, University of Rochester, Rochester, NY, USA, since 1989. He has authored/coauthored over 400 research papers, and eight books, recipient of the IPS Quantum Electronics Award’12, Fellow of the OSA, the IEEE, and a Member of the OSA Board (2009–2010).

R. K. Varshney received Ph.D. degree from the Indian Institute of Technology Delhi, New Delhi, India, in 1987, where he is currently Professor of Physics. He was awarded Marie Curie Fellowship and Full Bright Fellowship. He is an author/coauthor of more than 125 research papers, and two books. His research interests include fiber and integrated optics, specialty fibers, fiber optic sensors, nonlinear optics.

B. M. Azizur Rahman (SM’94) received the B.S. and M.S. degrees from the Bangladesh University of Engineering and Technology, Dhaka, Bangladesh, in 1976 and 1979, respectively, and the Ph.D. degree from the University College London, London, U.K. He is currently a Professor with the City University, London. He is a Fellow of the OSA, SPIE and a Senior Member of the IEEE. He has published nearly 500 journal and conference papers and specializes in the use of rigorous and full-vectorial numerical modelling of a wide range of photonic devices.