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This paper presents the analysis of a 2 cm long in-fiber polymer waveguide formed on the platform of a D-shaped optical fiber. Numerical simulations provide an understanding of the major loss mechanisms for feasible in-fiber polymer waveguide geometries. The primary loss mechanism is determined to be excitation of slab modes on the flat surface of the fiber with transition geometry being the next major contribution to loss.
©2004 Optical Society of America
1. Introduction
In-fiber devices have received attention because they allow optical signals to be generated and manipulated entirely in the optical fiber domain. Existing in-fiber devices such as erbium-doped fiber amplifiers and Bragg gratings have demonstrated these advantages [1, 2]. Side-polished fibers are another variety of in-fiber device used in some applications [3], although they limit device length and only permit interaction with the evanescent field of the fiber. In-fiber devices have also been constructed using fiber made completely out of polymer [4].
Prior work in our laboratory [5, 6] demonstrated how to etch an arbitrary length of D-fiber to remove the core of the fiber and then replace that section of the core with another optical material. Possible applications for such in-fiber waveguides include amplitude and phase modulation, fiber sensors, tunable filters, frequency converters, etc.
Previous papers [5, 6] focused on the experimental techniques used to produce such devices. However, there is a need to examine the major loss mechanisms associated with this new in-fiber polymer waveguide section. This paper provides a detailed investigation into the major loss mechanisms and exploits the graphical capabilities of this journal. Section 2 provides an overview of the fabrication of in-fiber polymer waveguides and Section 3 presents the analysis of primary loss mechanisms in these waveguides.
2. Background
2.1. D-fiber platform
Figure 1 is an illustration of a D-shaped optical fiber composed of a germania-doped core, a fluorine-doped cladding, and an undoped supercladding. The protective jacket is not shown in the figure. The core of the fiber is approximately 2×4 µm in size and is located roughly 10 µm from the flat side of the D-fiber. The fiber manufacturing process results in a small undoped section in the center of the core.
Fig. 1. The elliptical germania doped D-fiber core is surrounded by a lower index fluorine doped cladding region.
The differential doping of the fiber allows for selective chemical etching with hydrofluoric (HF) acid [7]. In a previous paper [5] we show how to use this selective chemical etching to controllably remove a portion of the core of the D-fiber while leaving the fluorine doped cladding intact, preserving the structural integrity of the fiber. Figure 2 shows a movie of the core etch, demonstrating the differential etch rates of the core and cladding. The etch depth is chosen to allow for the formation of a single mode polymer waveguide near the center of the fiber. Figure 3 is a cross-sectional scanning electron microscope (SEM) image of an etched D-fiber with a groove along the flat side of the fiber into which polymer is deposited.
2.2. Polymer waveguide
The polymer is deposited by spin casting and forms a waveguide that is contiguous with the core of the unetched portion of the fiber. In this research we use polymethyl methacrylate (PMMA) as the host polymer with DR1-azo dye as the guest chromophore. After the polymer is deposited on the fiber, the fiber is spun in a standard commercial spinner, forming a polymer waveguide in the groove left by the wet etch.
Fig. 3. SEM images of a D-fiber and a typical etch profile. The cladding has been etched only slightly while about half of the core has been removed.
As demonstrated in an earlier paper [6], polymer waveguide thickness can be changed by varying the polymer viscosity. Figure 4 shows cross-sectional SEM images of polymer waveguide sections with increasing viscosities. These images show that a layer of polymer in the groove is accompanied by a layer of polymer on the flat surface. Figure 4(a) shows that the polymer in the groove is substantially thicker than the polymer layer on the flat surface when a low viscosity polymer is applied. Figures 4(b) and 4(c) show that once polymer viscosity is above a certain point, further increases in viscosity cause the thickness of the polymer in the groove and on the flat to increase at the same rate.
The transmission loss of the approximately 2 cm long polymer waveguides shown in Figs. (a) - (c) were measured at a wavelength of 1550 nm to be respectively 1.6 dB, 36 dB, and too high to measure. Experiments demonstrated that waveguides with a thick layer of polymer on the flat surface of the fiber have high loss. Of the three samples shown in Fig. 4, only sample (a) is suitable for many applications because of the high loss of the other two.
3. Loss analysis
Several factors affect transmission loss as light travels through the polymer waveguide section. First, the electro-optic polymer has a higher bulk absorption coefficient than the germania-doped glass. In particular, DR1-azo dye doped PMMA has a bulk absorption coefficient of about 1 dB/cm at a wavelength of 1300 nm [8]. Light scattering along the length of the polymer waveguide is another source of loss. This source of loss can be avoided by keeping fibers free of contamination between the core removal step and the polymer application step.
Fig. 4. Cross-sectional SEM images of polymer waveguides with polymer viscosities increasing from (a) to (c). The white lines were added to show the interface between the glass and polymer.
As noted above there is a strong relationship between the polymer thickness on the flat surface of the fiber and transmission loss. This loss is attributed to the excitation of slab modes in the polymer on the flat side of the fiber. Also, there is transmission loss associated with the mismatch between the mode supported by the unetched fiber section and that supported by the polymer waveguide. Such losses can be reduced by forming a gradual transition to and from the polymer waveguide section. We performed numerical simulations to analyze these sources of loss.
All numerical simulations of waveguides were performed at a wavelength of 1550 nm using the beam propagation method (BPM) in the commercial software package BeamPROP™. BPM is based on the paraxial approximation to the Helmholtz equation [9]. To simulate three-dimensional propagation, the fundamental mode of the unetched fiber is computed via the imaginary distance beam propagation method and then launched into the fiber. BeamPROP™then simulates the propagation of light through the polymer waveguide. The computed electric field distribution at regular intervals along the propagation axis is stored and used to calculate loss in the waveguide as a function of propagation distance.
3.1. Slab modes
Experiments consistently demonstrate that waveguides with thick polymer layers on the flat surface of the fiber have high transmission loss. These thick polymer layers on the flat result in high loss because they behave like slab waveguides, allowing light to couple out of the polymer waveguide in the core region and into slab modes on the flat side of the fiber.
BeamPROP™’s three-dimensional simulation capabilities model light propagation through the transition from the unetched fiber core to the polymer waveguide. Figure 5(a) shows a model of a waveguide with a thin layer of polymer on the flat surface of the fiber, similar to the cross-sectional image shown in Fig. 4(a). Figure 5(b) shows a waveguide with a thick layer of polymer similar to the cross-section shown in Fig. 4(c). All indices of refraction are given at a wavelength of 1550 nm and absorption loss in the polymer has been neglected in these models. If thick enough, polymer layers on the flat surface of the fibers behave as asymmetric slab waveguides. The polymer layer on the flat of the fiber in Fig. 5(a) is too thin to support a slab mode, but that in Fig. 5(b) does support a slab mode [6]. The full three-dimensional model assumes a butt-coupled transition between the unetched section of optical fiber and the polymer waveguide sections illustrated in Fig. 5.
Fig. 6. Top view of the three-dimensional simulation of light propagating from unetched fiber into polymer waveguide for thin (a) and thick (b) polymer layers.
Figure 6 shows the top view of the simulations of light propagating from the unetched core into the polymer waveguide section. The abrupt transitions from unetched core to polymer waveguide occur at the longitudinal position of z=10µm. At the transition, any power that is not coupled into the polymer layer quickly radiates away from the core. In addition to this loss from mode mismatch, a thick layer of polymer also results in continuous radiation of light away from the core region along the length of the fiber. Even though more power is coupled from the unetched fiber into the polymer waveguide when the polymer is thicker, the total transmission loss is substantially higher because the power that couples into slab modes does not couple back into the optical fiber core. Figure 7 shows full simulations of light propagating through the abrupt transition from unetched fiber to polymer waveguide. The green ellipse in the figure shows the location of the elliptical core (before etching). The top half of Fig. 7 is a simulation of the thin-polymer waveguide in Fig. 4(a) and the bottom half is a simulation of a thick-polymer waveguide as in Fig. 4(c). Power continuously couples out of the core region along the length of the waveguide in the simulation of the thick polymer waveguide. The simulated thick polymer waveguide loses about 1.5 dB/mm to slab modes, whereas the thin polymer waveguide loses no power to slab modes.
The cutoff thickness for different polymer indices gives an estimate of the upper bound on the thickness of the polymer on the flat side of the optical fiber. The cutoff thickness is defined as the point where the effective index of refraction of the fundamental mode falls below the index of the substrate. To ensure that no slab modes were supported, the thickness of the polymer on the flat needs to be kept below 0.4 µm [6].
3.2. Transition loss
The mode supported by the unetched optical fiber is different than the mode supported by the polymer waveguide. This mode mismatch contributes to the transmission loss of the device. Butt-coupled transitions can result in a total transmission loss of about 3 dB [6]. The loss associated with mode mismatch is decreased by a gradual transition between the unetched core and the polymer waveguide [10].
Fig. 7. (1.27 MB) Simulations of light propagating through a transition from unetched fiber to thin (top) and thick (bottom) polymer waveguides.
Light propagation through transitions from fiber core to polymer waveguide and back into the fiber core was modeled using BeamPROP™. The transition length was varied in order to quantify its effect on transmission loss. The model consists of a short unetched length of fiber followed by a transition region, a 2500 µm section of polymer waveguide, another transition, and a final length of unetched fiber 2500 µm long. Figure 8 is a movie of a cross-sectional view of the fiber along the z-direction. This movie shows the transitional geometry from the unetched fiber into the polymer waveguide.
Fig. 8. (322 KB) Video of the index profile of the fiber with 110 µm long transition regions as a function of z.
Figure 9 shows the relationship between loss and propagation distance for waveguides with different transition lengths. The 1100 µm transition fiber performs best, having only 0.5 dB of loss. The plot shows that the overall loss is approximately evenly divided between the transitions to and from the polymer waveguide.
4. Summary and conclusions
Insertion of a polymer that is contiguous with an optical fiber presents a new means of launching into and guiding light in a variety of materials. Using experiment and numerical simulations, we have designed and analyzed a low-loss in-fiber polymer waveguide.
The simulations and experiments discussed above provide bounds on the waveguide dimensions in order to achieve low transmission loss. An in-fiber polymer waveguide must have a very thin layer of polymer on the flat side of the fiber for the waveguide to have low loss. Numerical results indicate that a polymer waveguide of index 1.54 must have a flat thickness less than 0.4 µm to avoid excitation of slab modes. The transition length from unetched fiber to polymer waveguide should also be greater than 1 mm to ensure low loss.
References and links
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