We study the higher order guided modes in an air-silica microstructure fiber comprising a ring of six large air-holes surrounding a Germanium doped core. We characterize the modes experimentally using an intra-core Bragg grating. The experimentally observed modes are then accurately modeled by beam propagation simulations using an index profile similar to the observed fiber cross section. Theory and experiment confirm the presence of “inner cladding” modes with approximate cylindrical symmetry near the core, similar to conventional cladding modes, but which strongly exhibit the symmetry of the microstructure at large radius. Such modes are useful in fabricating robust tunable grating filters and we show that the Bragg grating is a useful diagnostic to measure their effective indices and intensity profiles.
© Optical Society of America
Air-silica micro-structure fibers (ASMF)  have attracted wide interest over the past few years due to their unique guidance properties and ability to control light propagation. These fibers are typically all-silica and incorporate air-holes that run along the length of the fiber. A wide range of different air-silica microstructure fibers have been explored. These include: photonic band gap fiber, which guides light because of a bandgap in the cladding ; crystal fiber , which comprises a core surrounded by an array of air-holes in the cladding region and guides light by total internal reflection; air-clad fiber  in which a ring of air-holes is introduced into the cladding that forms an inner cladding region; and high delta microstructure fiber , which consists of silica core surrounded by closely spaced air-holes. Each fiber has different geometric air-hole shapes with unique optical properties and different potential applications.
The interest in such fibers lies in their robust and controllable cladding modes, which can potentially be exploited in the design of novel photonic components. One way to study the modal properties of such complex fibers is to exploit grating facilitated phase matching. In particular, a Bragg grating holographically written into a photosensitive region of such a fiber can excite higher order (cladding) modes that propagate in the cladding region. By simple inspection of the transmission spectrum of the grating we can learn about the propagating modes and obtain complete characterization. An example of this was recently reported by Eggleton et al. who studied the optical propagation characteristics of cladding modes in a crystal fiber . Although much attention has been given to the core guidance properties of these fibers [2,3,5], and some simple models have been presented to describe the higher order modes [3,6,7], a more complete experimental as well as computational description of the higher order modes has only recently been reported [8,9]. As previously discussed , beam propagation method is a useful computational tool to fully characterize modes in such complicated fibers.
In this paper, we use a Bragg grating to measure the effective indices and mode intensity patterns of a fiber with large air-holes in the cladding (Fig. 1) and then compute these same quantities using a scalar beam propagation algorithm applied to a realistic index profile. This fiber, shown in Fig.1, has a variety of interesting potential applications. Specifically, this fiber allows for the infusion of different novel materials, such as polymers, into the large air holes . Moreover, the air-holes create an effective “inner cladding” for the lower order cladding modes, a feature that has been exploited in design of tunable filters . For example, Westbrook et al. manipulated the propagation of light thermally in hybrid polymer-silica microstructure fiber gratings by changing the refractive index of the polymer introduced inside the air-hole regions [4,7,8,10]. Further potential applications of such fibers include grating based devices such as dispersion control long period gratings devices .
2. Bragg grating characterization
The interaction of light with a Bragg grating written into the core of a fiber is well-understood [12,13]. Light propagating in the core of a fiber incident upon a Bragg grating couples to a backward propagating core mode in addition to other counter-propagating cladding modes. Fig. 2 (a) shows a schematic of a Bragg grating in a conventional fiber and illustrates grating facilitated coupling to cladding modes that are confined by the silica-air interface. Coupling to these cladding modes manifests as sharp peaks in the transmission spectrum as shown in Fig.2 (b). Each peak corresponds to a particular mode.
A resonance occurs when the core is phase matched to a given cladding mode. The phase matching conditions, expressed in term of wave vectors are: βcore+βclad,i=K, where βcore, βclad,i are respectively, the propagation constants of the incident (forward) core mode and the backward coupled ith cladding modes, K=2π/L is the wave vector of the grating, and Λ is the period of the grating. When expressed in terms of resonance wavelengths, the conditions are :
where λcore, λcore, λclad,i and nclad,i are the resonance wavelengths and the effective indices of the core and the ith cladding modes respectively.
3. Fiber description and modal characterization
The ASMF is shown in Fig. 1(a) with six approximately cylindrical air-holes surrounding an inner cladding region of ~30µm in diameter. The fiber has a Germanium (Ge) doped core, with diameter ~8µm and Δ=(n1-n2)/n1~0.35%, where n1 and n2 are the refractive indices of the Ge core and the silica respectively. The outer diameter is 125µm and the outer cladding ring thickness, the region of silica between the outer surface of the fiber and the air-holes, is about 14mm. The interstitial region between the holes is about 5.8µm.
The fiber was deuterium loaded to enhance the photosensitivity of the Germanium core for writing the Bragg grating. Periodic modulation in the refractive index of the core was achieved by exposing a length of 4 cm of the fiber to ultraviolet light (242nm) through a phase mask  of period 1.075mm (Λ=1.075µm/2) at a fluence of 240mJ/cm2 from a frequency-doubled excimer-pumped dye laser. The amplitude of the index-modulation (Δn) is of the order of ~8×10-4.
Fig. 3 shows the transmission spectrum of the Bragg grating written into the core of the ASMF with the polymer jacket stripped off. The ASMF reveals a dramatically different mode spectrum when compared to the conventional fiber grating spectrum, shown in Fig. 2 (b).
The first peak on the right side of the transmission spectrum, labeled A in Fig. 3, corresponds to excitation of the backward propagating core mode. The other resonances on the shorter wavelength side of the main peak correspond to coupling to higher order modes (cladding modes) with smaller coupling strength, and are analogous to, but qualitatively different from the conventional cladding modes discussed in section II. Only the four lowest order cladding modes (labeled B, C, D and E) in the transmission spectrum of the ASMF in Fig. 3(b) have large coupling with the core mode. As we show below, these modes correspond to those confined primarily in the inner cladding region.
A general feature of the cladding mode spectrum of the ASMF is that the wavelength spacing Δλ(=λp+1-λp) between adjacent modes of the air-silica microstructure fiber is larger than that of the conventional fiber cladding resonance of Fig. 2(b). This is because Δλ, the wavelength spacing between two adjacent cladding mode resonances, scales as the inverse square of cladding diameter [7,8]. Because the ASMF cladding modes are confined primarily in the “inner cladding” region, they have a correspondingly larger wavelength separation than conventional cladding modes, which are confined in the entire silica diameter . The spacing between the core (main resonance) mode and the first cladding mode depends on the core-cladding index difference (Δ) as well as on the location and size of the air-holes.
Because the lower order cladding modes are well confined in the inner cladding region, we expect that they are insensitive  to the external refractive index surrounding the fiber. The transmission spectrum of the ASMF immersed in an index matching fluid is shown in dashed line in Fig. 6. The solid line represents the transmission spectrum of the ASMF grating in air. Note that the modes confined in the inner cladding region are mostly insensitive to the outer environment. On the other hand, the higher mode, as shown in the inset, is slightly affected by the external refractive index for reasons discussed later.
We also recorded images of the ASMF cladding mode power distributions using the setup shown in Fig. 7. Light incident from a tunable laser is coupled into the core of the fiber by means of a 40× objective after being collimated by means of a 10× objective When the wavelength of the incident light satisfies the Bragg conditions, Eqs. (1) & (2), it is coupled to backward propagating core and cladding modes. These modes are observed by means of a camera on a screen.
Fig. 8(a) below shows the experimental transmission spectrum and the corresponding mode images (bottom). The lower order modes (A, B, C, D and E) are mainly confined inside the inner-cladding region. They are surrounded by the holes and their propagation is governed by the total internal reflection at the interface of the cladding-holes. However, the higher order mode (F) spreads throughout the fiber through the interstitial in the cladding between the holes.
4. Beam propagation simulation
An accurate beam-propagation simulation (BPM) was then used, on BeamPROP software (Rsoft, Inc.), to determine the modal spectrum and mode intensity profiles of the fiber. Briefly, this method calculates the eigenvalues and eigenfunctions of the wave equation assuming weak guidance by propagating a given input E-field down the waveguide and performing a Fourier transform over the propagated distance z [8,9,14]. The structure simulated by BPM is shown in Fig. 1(b). The shapes defining the air regions were chosen to closely match the real image of the fiber cross section. The core index difference was 0.005, and it was assumed that the core was circular and had a diameter of 8 mm. The cladding was modeled as either air or silica: the black regions were assumed to be n=1 while the white regions were taken to be n=1.444, the refractive index of silica at 1550nm. A beam of symmetric rectangular profile centered on axis of the core was launched into the structure in order to generate Fourier coefficients corresponding to several higher order modes.
Fig. 8 (b) shows the simulated mode spectrum plotted (in blue) and the simulated mode profiles. BPM simulates the effective indices (neff) of the excited modes . The resonant wavelengths corresponding to these modes are calculated using Eqs. (1–2). The simulated plot reveals the values of the relative power, which is related to the overlap ratio between the core and each of the excited modes, versus wavelength. The experimental and simulated core-ith cladding effective index differences, (Δnexp) and (Δnsim) respectively, where Δnexp=ncore-nclad, i, agree to 10% (see Table 1).
The simulated modes, shown in Fig. 10, are very similar to those observed experimentally. The profile and the distribution of the energy of the modes are clearly affected by the presence of the holes. The circular shapes of the modes of a conventional fiber are lost in this ASMF. Instead the images exhibit symmetry of the air-hole geometry. However, at small radius near the core, the inner cladding modes have approximate cylindrical symmetry and hence have large overlap with the core mode.
Fig. 11 shows a simulation of the profile of a higher order mode. The energy of this mode tunnels to the outer silica region. As we discussed above, this higher order mode (F), in Fig. 11(b), is slightly affected by the outer refractive index. So the mode is confined by the inner (silica—air-hole) interface and the outer (silica-air) interface.
We note that our simulations do not show all of the observed modes. Some of these, such as the resonance falling between B and C, in Fig. 8 (b), are found to be odd order modes, which we have neglected due to the symmetric launch in our beam propagation simulations. The presence of odd mode resonances in the Bragg grating is consistent with ultraviolet induced asymmetry across the core . In launching an off-axis rectangular profile, the odd modes are observed on the simulated spectrum, in Fig. 12(a), which correspond to those measured in the transmission spectrum, Fig.12 (b).
5. Comparison with conventional fiber
In order to compare our results with the conventional fiber, a simulated mode spectrum was computed for a conventional fiber with cladding diameter equal to that of the inner cladding of the air-silica microstructure fiber, which is approximately 40µm.
The three main cladding modes that are confined in the inner cladding region, as was discussed above, are observed again, Fig. 13. So we can conclude that the air-silica microstructure fiber can be compared to a conventional fiber with a cladding diameter the same size as the inner cladding diameter of the ASMF. This is important, for example, in applications that exploit a small cladding diameter to enhance the tunability of filters , but which also require the cladding modes to be isolated from the environment and hence insensitive to the condition of the outer surface of the fiber .
The modes of an air-silica microstructure fiber comprising six large air-holes in the cladding have been observed and compared to beam propagation simulations using a realistic index profile of the fiber cross section (Fig. 1(b)). A Bragg grating was written into the core of the fiber to characterize the cladding modes. The measured mode spectrum is in very good agreement with the simulated results. The propagating modes in the inner cladding region of the air-silica microstructure fiber can be compared to those of a conventional fiber with the same cladding diameter and the same optical waveguide properties, a feature that can be exploited in the design of tunable filters and grating devices.
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