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SECTION I

Introduction

Subwavelength optical fibers, with core dimensions less than the wavelength of the light, have properties that differ significantly from conventional fibers. When the core dimensions are selected to provide optimal mode confinement (i.e., minimum effective mode area, Formula$A_{\rm eff}$), it is possible to produce fibers with extreme values of nonlinearity Formula$(\gamma)$ [1], [2]. It has recently been discovered that the modes that propagate in such fibers have significant energy polarized along the propagation direction. In other words, the modes stop being transverse, which leads to significantly higher values of nonlinearity than would otherwise occur [2]. For smaller sizes, significant fractions of the mode also become located in air outside the core, which is the basis for using these fibers as gas or liquid sensing platforms [3], [4].

When a hole of subwavelength diameter is introduced within the core region of any optical fiber, it has a notable impact on the characteristics of the propagating mode. The electric field at the interface of the hole is discontinuous; light intensity on the low index side of the interface of the air hole scales with the squared refractive index contrast at the interface [5]. Using this principle, high index silicon-on-insulator (SOI) waveguide structures [6] were proposed by Almeida in 2004. The air “slot” embedded between two high index silicon slabs acts as a waveguide, propagating light with its peak intensity 20 times higher than is possible using conventional silica planar waveguides. Conventional semiconductor processes allow relatively easy fabrication of such structures, and as a result, research in on-chip high index SOI-based slot waveguide devices has flourished. One opportunity such devices enable is the filling of the slot with novel materials; for example, highly nonlinear silicon nanocrystals have been used to demonstrate ultrafast all-optical switching [7] and four-wave mixing [8]. Increased light-sample interaction in a slot waveguide ring resonator [9] has enabled the realization of label-free detection with a volume refractive index detection limit of Formula$5 \times 10^{-6}$ RIUs: the highest detection sensitivity reported for an integrated planar ring resonator [10]. A wide variety of slot waveguide structures are possible; they have been used to produce polarization-independent couplers [11], dispersion compensators [12], and polarization splitters [13]. The combination of high optical confinement and the potential for using small sample volumes in the slot also make such structures attractive as single photon sources for quantum information processing [14]. Besides these applications, understanding ways of controlling light on the nanoscale via structuring of materials is also of fundamental interest.

Although relatively easy to fabricate, SOI waveguides have relatively high attenuation (of order 10 dB/cm) [15], which limits their useful length to centimeters at most. Due to long effective length, low loss, and flexibility in fiber geometries, fibers with subwavelength holes are a tantalizing alternative platform for exploring light-material interactions inside nanoscale structures. The concentration of optical energy within an air hole in a fiber core was first demonstrated for a silica microstructured fiber (MOF) [16], and holes as small as 110 nm were fabricated in the silica fiber core. Moving to higher index soft glasses offer an attractive alternative to silica due to the availability of high index glasses, which significantly increase light enhancement. Combining high index and low melting temperature, soft glasses have been fabricated into MOFs [17], [18] with ultra-high nonlinearity [19] and/or strong evanescent field for sensing applications [20].

Building on existing techniques for fabricating preforms and fibers, the MOFs with a single core hole have been fabricated with no additional increase of the loss due to introduction of the core hole. The minimum hole size of 20 nm was achieved, which is believed to be the smallest hole reported in the core of any fiber to date [21]. Flexibility in extrusion die design, the use of multiple drawing steps to provide large scale-down ratios, and improved process control have enabled the fabrication of this fiber. This work demonstrates the ability to create tens of nanometer sized holes in the optical fibers. In general, the four-ring MOFs exhibit somewhat weaker enhancement than nanowires with the same core size due to the relatively lower index contrast between core and the microstructured cladding. A free-standing nanowire represents the limit in index contrast that can be achieved for MOFs made from the same host material and closely approximates the behavior of MOFs with large air filling fractions.

In this paper, we report for the first time the limits of the subwavelength intensity enhancement that is possible in soft glass free-standing nanowires and explore the dependence of this effect on the geometry and index contrast within the nanowires through theoretical modeling. To explore the impact of the tiny core holes for nonlinear applications, we consider a silicon nanowire with a core hole filled with silicon nanocrystals and find that this approach is a means of significantly increasing the fiber nonlinearity.

SECTION II

Minimum Mode Effective Area Formula$(A_{\rm eff})$ and Its Corresponding Power Fraction

Commercial F2 lead silicate glass (from Schott Glass Co.) and Formula$\hbox{As}_{2}\hbox{S}_{3}$ chalcogenide glass were chosen as soft glass host materials for our modeling of light enhancement. The F2 glass with refractive index Formula${n} = 1.61$ at Formula$\lambda = 632\ \hbox{nm}$ has low softening temperature (592 °C), which has led to the development of a broad range of fiber designs via the flexible extrusion technique to fabricate MOFs in-house for sensing and nonlinear applications [16], [17], [18], [19], as well as with nanoscale hole(s) in the core region, as reported in [21]. The Formula$\hbox{As}_{2}\hbox{S}_{3}$ chalcogenide glass has much higher refractive index (Formula${n} = 2.6$ at Formula$\lambda = 632\ \hbox{nm}$) for increased light enhancement. Its absorption edge at the visible is around 620 nm, which enable the subwavelength fibers based on it to be used in high-resolution imaging. Also, suspended core fibers based on this material have been successfully drawn using mechanical machining techniques [22]. As a comparison, the light enhancement of the nanowires based on silica glass (Formula${n} = 1.46$ at Formula$\lambda = 632\ \hbox{nm}$) is also calculated. A finite element method (FEM) was used to study mode field distributions of the nanowires via the commercial FEM package COMSOL Multiphysics. The light wavelength is fixed to be 632 nm unless otherwise specified. We have calculated the mode propagation constant Formula$\beta$ for a 400-nm-diameter F2 nanowire using FEM, and compared it with that obtained using the well-known exact analytical solution for a step-index fiber. We have found that both values are the same within four-digit significant figures Formula$(\beta = 1.3074 \times 10^{5}\ \hbox{cm}^{-1})$.

Free-standing nanowires have been chosen as substrate structure for modeling to maximize light enhancement inside a hole located within the central of the nanowire's core [see Fig. 1(a)]. The outer diameter of the nanowire is Formula$d$, and a nanoscale air hole of diameter Formula$D$ runs down the length of the nanowire with its refractive index denoted as Formula$n_{g}$. Strong light intensity in the low index Formula$(n_{h})$ hole is expected due to high index contrast at the interface [5] and continuity of the normal component of electric displacement field. By virtue of the boundary conditions, the normal component of the electric field Formula$E_{h}$ on the low index side of the interface is higher than that of the electric field Formula$E_{g}$ in the high index side, with Formula$E_{h}/E_{g}$ equal to the square of the ratio of the indices at both sides of the interface Formula$(n_{g}^{2}/n_{h}^{2})$. Due to nanometer scale of the hole, Formula$E_{h}$ only undergoes slight decay within the hole and, thus, maintains a high intensity across the whole range. This has been confirmed in Fig. 1(b), which displays electric field intensity of one fundamental mode of a nanowire.

Figure 1
Fig. 1. (a) Schematic of a nanowire of index Formula$n_{g}$ and diameter Formula$d$ with single core hole of diameter Formula$D$ of index Formula$n_{h}$. In (b)–(f), results for a 200-nm Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire with a 30-nm centralized hole are shown. Left column: Spatial mode field distribution. Right column: Corresponding cross-section profile along Formula$x$-axis (black curve) and Formula$y$-axis (red curve). (b) Electric field intensity Formula$\vert E_{xyz} \vert^{2}$ of the fundamental mode polarized along the Formula$x$-axis. (c) Transverse electric field intensity Formula$\vert E_{t} \vert^{2}$ for the combined field of the two orthogonal fundamental modes with phase difference of Formula$\pi/2$. (d) Total electric field Formula$\vert E_{xyz} \vert^{2}$ of the combined modes. (e) Formula$z$-component of the Poynting vector (power flow) of the fundamental mode field shown in (b). (f) Power flow of the combined modes. (g) Normalized power flow of the combined modes of a 200-nm Formula$\hbox{As}_{2}\hbox{S}_{3}$ hole-free nanowire. The dashed line is normalized power flow from (f).

Here, we considered a 200-nm Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire with a 30-nm air hole in the wire center as an example to illustrate light enhancement. The fundamental mode in Fig. 1(b) is polarized along the Formula$x$-axis. Its electric field intensity and two cross-sectional profiles at the directions parallel and orthogonal to the Formula$x$-axis are shown. From the profile parallel to the mode polarization direction (black line), it can be seen that the intensity inside the hole is much stronger than within the glass because of high index contrast at the interface. However, along the direction orthogonal to the mode polarization, the intensity is continuous at the interface. The z-component of the time-averaged Poynting vector of the mode field (which describes the power flow), as shown in Fig. 1(e), presents similar spatial characteristics. The asymmetric spatial distribution of the electric field intensity and power flow of the single fundamental mode, as shown in Fig. 1(b) and (e), mandates the need for care in defining a measure of the light enhancement within the hole. Here, we have combined the two fundamental modes with orthogonal polarizations to construct a field with their phase difference of Formula$\pi/2$. This leads to a circularly symmetric power flow because light polarizes at two orthogonal directions and results in circularly symmetric distribution of intensity of transverse field components.

Fig. 1(c)(g) display cross section profiles of the electric field intensity and power flow for the combined fundamental modes. Writing the electric fields along the three axes as Formula$E_{x}$, Formula$E_{y}$, and Formula$E_{z}$, the transverse electric field intensity Formula$\vert E_{t}\vert^{2} = \vert E_{x}\vert^{2} + \vert E_{y}\vert^{2}$ and the total electric intensity Formula$\vert E_{xyz} \vert^{2} = \vert E_{x} \vert^{2} + \vert E_{y} \vert^{2} + \vert E_{z} \vert^{2}$ are separately calculated for the combined modes and are displayed in Fig. 1(c) and (d). It can be seen that the transverse electric field intensity Formula$\vert E_{t} \vert^{2}$ of the combined modes shown in Fig. 1(c) is circularly symmetric but that the total electric field Formula$\vert E_{xyz} \vert^{2}$ in Fig. 1(d) is not due to the contribution of Formula$E_{z}$, which is not negligible when the fiber size is subwavelength in scale [2]. The corresponding power flow Formula$S_{z} = (1/2){\rm Re}[E_{xyz}\times H_{xyz}^{\ast} \bullet \mathhat{z}]$ (Formula$H_{xyz}^{\ast}$ is the conjugate of the total magnetic field Formula$H_{xyz}$) shown in Fig. 1(f) also presents circular symmetry.

To explore the degree to which the light enhancement can be maximized in the centralized hole, it is important to note that the hole-free substrate nanowire allows the strongest confinement of light, with the highest intensity in the core center. When the diameter of a hole-free nanowire is chosen so that the mode effective area Formula$(A_{\rm eff}^{\rm hole - free})$ is minimized, the peak intensity in the center of the nanowire is correspondingly maximized. Here, the mode effective area Formula$A_{\rm eff}$ is defined as Formula$A_{\rm eff} = \vert \int_{A\infty} S_{z}\,dA \vert^{2}/\int_{A\infty}\vert S_{z} \vert^{2}\,dA$, where Formula$A\infty$ is defined to be the infinite transverse cross section [4]. In the presence of a centralized core hole, it is also reasonable to hypothesize that the value of the intensity in the hole is also maximized for geometries in which the mode effective area Formula$A_{\rm eff}^{\rm hole}$ of the nanowire with a centralized hole is minimized. To verify this, the values of Formula$A_{\rm eff}^{\rm hole}$ and fraction of the modal power in the hole are calculated for nanowires with a fixed hole size as a function of the diameter Formula$d$ of the nanowires for both glass types, and the results are shown in Fig. 2. Power fraction Formula$\alpha$ is defined as the power confined in the hole as a fraction of the total mode power and expressed as Formula$\alpha = \int_{H} S_{z}\,dA/ \int_{\infty} S_{z}\,dA$, where Formula$H$ is the hole area. For comparison, the Formula$A_{\rm eff}^{\rm hole - free}$ values of the hole-free nanowire are also displayed (dark yellow). As expected, for all the nanowires considered here, as the core diameter decreases, Formula$A_{\rm eff}$ decreases, reaching a minimum value (the tightest mode confinement) at nanowire diameter of Formula$d_{\min}$ and then increasing for nanowire dimensions below this. The values of Formula$d_{\min}$ that correspond to a minimum Formula$A_{\rm eff}^{\rm hole - free}$ are 360 nm and 200 nm for the F2 and Formula$\hbox{As}_{2} \hbox{S}_{3}$ hole-free nanowire, respectively. Smaller Formula$d_{\min}$ values for the Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire with a centralized hole reflects the fact that the higher index material confines light more tightly. Values of Formula$A_{\rm eff}$ slightly increase when a hole is introduced in the center, since it serves to push light field into outside of the nanowire, and the Formula$d_{\min}$ of the nanowire and its corresponding minimum Formula$A_{\rm eff}$ also increase. In essence, the presence of the sub-wavelength hole decreases the effective refractive index of the core, reducing its capacity to confine light and thus increasing the mode area due to more light pushed out of the nanowire. The nanowires with a lower index have a correspondingly larger value of Formula$d_{\min}$, and for example, for the case of a 100-nm hole introduced in the center of the nanowire, values of Formula$d_{\min}$ are increased to 420 nm and 250 nm, respectively for the F2 and Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowires. It can also be observed that for a range of core dimensions of Formula$d_{\min} \pm 50\ \hbox{nm}$, the Formula$A_{\rm eff}$ values do not vary significantly, which provides a useful guide to the diameter control required during the nanowire fabrication.

Figure 2
Fig. 2. Dependence of Formula$A_{\rm eff}$ and power fraction on nanowire diameter with single centralized hole. (a) F2 nanowire with hole diameters of 0 nm, 50 nm, 100 nm, and 140 nm. (b) Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire with hole diameters of 0 nm, 10 nm, 50 nm, and 100 nm.

It can also be seen from Fig. 2 that for the same hole size, the power fraction within the hole increases to a maximum for a nanowire of diameter Formula$d_{\max}$, reducing for smaller nanowires. These simulations indicate that Formula$d_{\max}$ is usually smaller than Formula$d_{\min}$ (as an example, the Formula$d_{\max}$ and Formula$d_{\min}$ have been shown in Fig. 2(a) for the F2 nanowire with a 140-nm hole). It is noted that the power fraction in the hole is dependent on hole position and field distribution across the cross section of the fiber. The mode effective area, on the other hand, reflects the area size of the power flow passing through a plane perpendicular to the direction of propagation. As a result, it is not expected that Formula$d_{\max}$ is the same as Formula$d_{\min}$. Observe that when the hole size is reduced, the power fraction becomes less sensitive to change of the nanowire size. For a 10-nm hole within the Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire, the power fraction varies negligibly with changed nanowire dimensions.

SECTION III

Light Enhancement and Average Mode Intensity

Section 2 showed that a tightly confined mode leads to maximal light intensity in the centralized hole of the nanowire. To understand the impact of the subwavelength hole on light localization within the nanowire with minimum Formula$A_{\rm eff}$, we consider the light enhancement and average mode intensity inside the hole as ways to describe the capacity of the hole to localize light. Due to circular symmetry, the power flow normalized to its total power of the combined modes is chosen for characterization of light localization. Fig. 1(g) shows the normalized power flow and its cross-sectional profile (black curve) for the 200-nm Formula$\hbox{As}_{2}\hbox{S}_{3}$ solid nanowire. As a comparison, the cross-sectional profile from Fig. 1(f) is also illustrated in the same figure as a red dashed curve. The light enhancement is defined as the ratio of the power confined in the hole of the nanowire to that confined in the same area of the corresponding hole-free nanowire. It can be expressed as Formula$\int_{A} S_{z1}\,dA/\int_{A} S_{z2}\,dA$, where Formula$S_{z1}$ is the power flow for the nanowire with a centralized hole, and Formula$S_{z2}$ is that for the hole-free nanowire. The dependence of light enhancement on the hole diameter Formula$D$ is calculated for the three glass nanowires (silica, F2, and Formula$\hbox{As}_{2}\hbox{S}_{3}$) with their outside diameter Formula$d$ corresponding to minimum Formula$A_{\rm eff}$, and the results are shown in Fig. 3(a). It can be seen that for all the glasses, the light enhancement increases with reduced hole size. Due to their small relative index difference, the silica and F2 nanowire show very similar light enhancement, while a much higher index Formula$\hbox{As}_{2}\hbox{S}_{3}$ produces more difference. The light enhancement is equivalent to 1 when the hole diameter is around 70–80 nm for the silica and F2 nanowire and 50 nm for the Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire. That means the light power confined in the hole starts to become higher than that confined in the same hole area in its corresponding hole-free nanowire when the hole diameter Formula$D$ of the nanowire is smaller than this critical value. The high index Formula$\hbox{As}_{2} \hbox{S}_{3}$ nanowire shows stronger light enhancement than the low index silica and F2 nanowire only at smaller hole sizes (less than 30 nm). Its maximum light enhancement of 1.7 times is achieved when the hole size is less than 10 nm.

Figure 3
Fig. 3. (a) Dependence of three parameters on hole diameter for silica, F2, and Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire. (a) Light enhancement. (b) Average mode intensity and power fraction. Intensity units are Formula$\mu\hbox{W}/\mu \hbox{m}^{2}$, assuming the total mode power is 1 Formula$\mu\hbox{W}$.

The average mode intensities as shown in Fig. 3(b) as black curves are calculated by integrating the normalized power flow over the hole and then dividing by the hole area. As expected, they increase with reduced hole size, and the hole in the Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire presents much higher intensity than the silica and F2 nanowire when the hole size become smaller (< 100 nm). When the hole diameter is less than 10 nm, the average mode intensity inside the hole of the Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire is nearly eight times of that inside the hole of the silica nanowire.

The reason why the light enhancement and average mode intensity is higher within smaller holes can be attributed to field decay coefficient inside the hole. According to optical waveguide theory [23], the normal component of the electric field immediately inside the hole is equal to square of the index contrast Formula$(n_{g}^{2}/n_{h}^{2})$ at the interface and then decays with increasing distance to the interface at an exponential rate. The field decay coefficient scales to Formula$\sqrt{1/2 (1 - n_{g}^{2}/n_{h}^{2})}$ [23]. This means that the light intensity in the hole of the Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire attenuates at a faster rate than in the same hole of the silica and F2 nanowire. This explains why light enhancement only becomes prominent at smaller hole diameters that is less than 70 nm for the silica and F2 nanowire and 50 nm for the Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire. Thus the advantage of the high index Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire only becomes evident for holes smaller than 30 nm. Due to higher index contrast and tighter confinement, this material yields higher absolute intensity than the low index silica and F2 nanowire.

The fraction of the modal power located inside the holes are also calculated and shown in Fig. 3(b) as blue curves. The power fraction increases with increased hole size. With the same hole size, the Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire has a higher power faction in the hole compared with the silica and F2 nanowire due to tighter confinement. Our calculation also shows the confinement loss of the nanowires with the centralized core hole is still negligible compared with that of the hole-free nanowires.

SECTION IV

Highly Localized Electric Field Intensity for Light–Matter Interactions

Although the power flow is used to describe light enhancement due to its circular symmetry distribution, for applications including nonlinearity and sensing, if the hole is filled with highly nonlinear materials or target materials for sensing, the light–matter interactions that occur are more directly related to the electric field. Thus, the localized electric field in the low index region is also investigated. Here, we focus our discussion on the impact of the total electric field Formula$E_{xyz}$ of one fundamental mode on the effective nonlinear coefficient Formula$\gamma$ of the nanowire due to its relation to square of the normalized electric field intensity Formula$\vert {E}_{xyz}\vert^{4}$ [2]. This may predict a stronger impact of the electric field on enhancement of the nonlinear coefficient when the hole is filled with a high nonlinear material compared with sensing applications, where the power absorbed by target materials is, in general, proportional to Formula$\vert E_{xyz} \vert^{2}$ [24].

It was recently demonstrated that the effective nonlinear coefficient of a nanowire can be a factor of two higher than that obtained from scalar definition because the Formula$z$-component of the electric field Formula$E_{z}$ plays a key role for these structures [2]. The effective nonlinear coefficient Formula$\gamma$ is related to the normalized electric field intensity by the relation Formula$\gamma = (2\pi/\lambda) \int_{A} n^{2}n_{2}\vert {E}_{xyz} \vert^{4}\,dA$, where Formula$n$ is material refractive index, Formula$n_{2}$ is the Kerr nonlinear coefficient of the material, and Formula$A$ is the cross-sectional area of the nanowire. Compared with Formula$\vert E_{xyz} \vert^{2}$ shown in Fig. 1(b), an increased contrast in value of Formula$\vert {E}_{xyz} \vert^{4}$ between the hole and its surrounding area can be expected, as confirmed in Fig. 4(a) for 200-nm Formula$\hbox{As}_{2} \hbox{S}_{3}$ nanowire with a 30-nm hole.

Figure 4
Fig. 4. (a) Cross-sections of Formula$\vert E_{xyz}\vert^{4}$ parallel (black curve) and orthogonal (red curve) to the mode polarization based on normalized Formula$\vert E_{xyz} \vert^{2}$ shown in Fig. 1(b) for 200-nm Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire at Formula$\lambda = 632\ \hbox{nm}$. (b) Calculated nonlinear coefficient Formula$\gamma$ of the silicon nanowire with a centralized hole filled with silicon nanocrystals, as a function of the nanowire diameter at Formula$\lambda = 1550\ \hbox{nm}$.

If the core hole is then filled with a material with a higher material nonlinearity than the host nanowire, the value of the fiber's nonlinear coefficient Formula$\gamma$ will increase, and we show here that this effect is magnified by the light enhanced effect that is possible within these sub-wavelength air holes. As an example, we calculated Formula$\gamma$ at the wavelength of 1550 nm for silicon nanowires filled with silicon nanocrystals, which have similar linear refractive index to silica but higher nonlinear coefficient and have been used in planar waveguide platform for nonlinear processing [7], [8]. The fabrication of the structured fibers may be possible by directly drawing bulk porous silicon preform with centralized hole filled with grown silicon nanocrystals [25], [26]. Due to potential to achieve much longer length for light–matter interaction, the required power for nonlinear processing should be largely reduced compared with planar silicon slot waveguide devices.

The nonlinear coefficient Formula$\gamma$ combines contributions from the host silicon in the ring of the nanowire and silicon nanocrystals filled into the centralized hole as shown in Fig. 1(a). The linear refractive index Formula$n$ and Kerr nonlinear coefficient Formula$n_{2}$ for silicon are Formula$n = 3.5$, Formula$n_{2} = 4 \times 10^{-18}\ \hbox{m}^{2}/\hbox{W}$ [2], and silicon nanocrystals are Formula$n = 1.5$, Formula$n_{2} = 4 \times 10^{-17}\ \hbox{m}^{2}/\hbox{W}$ [27]. The calculated Formula$\gamma$ as a function of the hole size is displayed in Fig. 4(b). For every point, the nanowire diameter is chosen to correspond to minimum Formula$A_{\rm eff}$ for maximized light confinement. The first point corresponding to zero hole diameter is a hole-free silicon nanowire with a 350-nm diameter. The last point corresponding to a 160-nm (filled) hole has a nanowire diameter of 420 nm. It can be seen from Fig. 4(b) that the nonlinear coefficient Formula$\gamma$ increases with increased hole diameter up to a maximum at the hole diameter of 80 nm and then decreases. The achieved optimized nonlinear coefficient Formula$\gamma$ is about 30% higher than is possible in the solid silicon wire. For other combinations of the different fiber substrate and filling materials, detailed calculations need to be performed for possible improvement in nonlinearity and the optimized core hole size for filling.

SECTION V

Conclusion

We have performed the first systematic investigations of the light enhancement that is possible in optical nanowires with nanoscale air holes in the core. More specifically, we have considered F2 and Formula$\hbox{As}_{2}\hbox{S}_{3}$ soft glass nanowires, and compared them with conventional silica nanowires. The modeling results reveal that the power fraction is found for the nanowire with diameters close to that required to provide the tightest mode confinement (i.e. minimum Formula$A_{\rm eff}$). The light enhancement inside the hole of the nanowires with minimum Formula$A_{\rm eff}$ becomes significant only when the hole size is less than a critical value: 70 nm for the silica and F2 nanowire and 50 nm for the Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire. The average mode intensity within the hole linearly increases with reduced core hole size. The high index Formula$\hbox{As}_{2}\hbox{S}_{3}$ nanowire provides light intensity in the hole eight times higher than that in the silica nanowire when the core hole diameter is less than 10 nm. For nonlinear applications of the nanowires, combination of the silicon host nanowire and high nonlinear silicon nanocrystals filling provides 30% enhancement in the nonlinear coefficient. These conclusions are based on the results dependent on the hole size for a fixed wavelength. The important parameter here is the ratio of the fiber's structural parameters to the wavelength. To the first-order approximation (ignoring material dispersion), these results are equivalent to changing the wavelength and keeping the hole diameter constant.

Although free-standing nanowires discussed here represent the limit in index contrast for the highest light enhancement with the same core size compared with other structured fibers, such nanowires are fragile and difficult to handle. They are also fully exposed to the environment, which can lead to contamination and degradation [28]. Thus, suspended nanowires are a good practical alternative [18]. An effort to fabricate nanoscale holes in the suspended soft glass nanowires for investigation of the light enhancement will be made in our next step. Such fibers could ultimately be employed for the purpose of including high nonlinearity and high sensitivity detection.

Footnotes

This work was supported by the Australian Research Council (ARC) by an ARC Postdoctoral Fellowship and an ARC Federation Fellowship under DP0880436. Corresponding author: Y. Ruan (e-mail: yinlan.ruan@adelaide.edu.au).

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Y. Ruan

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