We demonstrate single-mode uniform and parabolically tapered three-dimensional waveguides fabricated via direct-write lithography in diffusion-based photopolymers. Modulation of the writing power is shown to compensate Beer-Lambert absorption in the single-photon initiator and to provide precise control of modal tapers. A laminated sample preparation is introduced to enable full 3D characterization of these modal tapers without the need for sample polishing which is difficult for this class of polymer. The accuracy and repeatability of this modal characterization is shown to allow precise measurement of propagation loss from single samples. These testing procedures are used to demonstrate single-mode waveguides with 0.147 dB/cm excess propagation loss and symmetrical tapers up to 1:2.5 using 1.5 microwatts of continuous write power.
© 2012 OSA
Traditional optical waveguide circuits are planar devices with uniform thickness and discrete index profiles. In the past decade, there has been growing interest in three-dimensional (3D) waveguides whose path, peak index and cross section can all be controlled along an arbitrary guide path. These additional degrees of freedom enable novel optical circuits and may provide a platform for the interconnection of fiber and other traditional waveguide devices, including mode transformations.
Current approaches to 3D waveguide fabrication can be characterized by the lithography method (direct write vs. “self-written”) and the material photo-response (multiphoton vs. single photon). The most common technique is 3D scanning direct-write lithography with a femtosecond laser which undergoes multiphoton absorption at the focus to locally change the index of refraction of glass or polymer [1–3]. This method is popular because the lithography approach provides programmable 3D control over the waveguide path and the nonlinear absorption confines the response to the focal region. The primary disadvantages are low fabrication speed enforced by the small multiphoton cross section and difficulty in aligning the waveguides to other devices. The second common approach is to “self-write” waveguides in a one-photon sensitized photopolymer. Here, light from a stationary focus or embedded fiber is introduced directly into the photopolymer, forming a waveguide which propagates into the polymer in a soliton-like fashion . The advantages of this approach are its simplicity and the automatic alignment of the self-written waveguide to an embedded or butt-coupled source. However this technique has limited control over the shape and direction of the resulting waveguides and single-mode operation has not yet been demonstrated over millimeter scale [5, 6]. Finally, nearly all studies of 3D waveguides to date have performed limited characterization because the deeply buried, gradient-index guide is not compatible with profilometry, prism coupling or other measurement methods designed for planar devices. This lack of characterization methods is particularly problematic for studies of nonuniform guides such as modal tapers [7–9].
In this work, we investigate the use of direct-write lithography, which provides control over the waveguide path and mode, with a one-photon photopolymer, which requires only a low-power continuous laser source. Specifically, we show that direct-write lithography with a μW laser focused into a one-photon photopolymer can form symmetric, single-mode, 3D waveguides. The power of the writing laser is varied to compensate for absorption and to create precisely controlled modal tapers.
Additionally, we report test procedures for deeply-buried polymer waveguides not compatible with existing techniques. The waveguides written are small (D < 10 μm), weak (δn < 0.01) and deeply embedded in thick (mm) polymers, defeating most index and modal characterization methods. Near-field techniques such as electron microscopy and profilometry can provide precise index shape of ridge planar waveguides, but do not apply to embedded 3D waveguides. Phase microscopy such as differential interference contrast (DIC) microscopy  typically offers a qualitative, but not quantitative, index picture. Quantitative phase microscopy has been reported , but is limited to physically thin objects. Specialized methods for index profiling of 3D waveguides and fiber cores including modified optical diffraction tomography (ODT) , scanning transmission microscopy  and reflection scanning  do not provide a complete 3D measurement of the guide index. This incomplete characterization prevents the calculation of the critical waveguide properties including mode size, shape and loss.
An alternative is to forgo index measurement and instead to directly measure modal properties along the guide length. The prism-coupling method is commonly used for planar waveguides, but it is not applicable for deeply embedded 3D waveguides. The cutback method allows mode characterization of 3D waveguides including tapers but requires an optical-quality polish after each cut. While appropriate for inorganic glasses and crystals, this polishing step is often impossible for polymers, particularly those with low glass transition temperature as used here. This lack of index or modal test methods for 3D glass and polymer waveguides is reflected in virtually no reported characterization beyond total loss and end-facet mode profile.
Here, we introduce a procedure that enables optical-quality cut-back surfaces in polymers that cannot be cut or polished. Thick, optical-quality materials are first fabricated as laminates of a number of thin polymer layers. After waveguide lithography, the layers are separated and independently tested for modal properties. This provides complete characterization of modal properties as a function of distance along the guide.
We use this test procedure to show symmetric 3D tapered and untapered polymer waveguides and confirm that they are single mode over length. Precise characterization of the mode profile allows the total measured loss to be separated into coupling and propagation loss. These measurements are used to verify the repeatability of uniform waveguide fabrication which in turn provides an accurate validation of the propagation loss measured via cutback.
3D waveguides fabricated in diffusion-driven photopolymers
Photopolymer offers several advantages over glass as a material platform for optical waveguides including greater optical sensitivity, widely tunable material properties and lower cost. However, polymers used for 3D waveguides must self-develop an index change in response to light, unlike 2D waveguides in which wet chemistry (e.g. solvents) can be used to develop structure . For example, multiphoton absorption writing uses the increased index of the photopolymerized region at the focus [2, 3]. Unfortunately, the structure is only stable so long as one-photon or thermal processes do not cause the large remaining quantity of initiator and monomer to react. Since this assumption is not applicable for one-photon absorbers, an additional process is required to form permanent structures in 3D one-photon polymers.
Diffusive photopolymers, also referred to as volume or holographic photopolymers, were originally developed for holographic data storage (HDS)  and have recently been adapted for 3D optical interconnection [5, 17, 18]. Typical diffusive photopolymers consist of two chemical systems: one that forms a solid yet flexible matrix and the photo-active components consisting of an initiator that absorbs a fraction of the incident light to form radicals or other initiating species and a monomer that polymerizes by reaction with this photoinitiator. The matrix can be formed from the same monomer as the writing material  or from an initial catalyzed thermal reaction . After this matrix formation, localized illumination of the photo-active components creates a high molecular-weight polymer in the illuminated region via the consumption of low-molecular-weight monomer. This local depletion of monomer causes monomer diffusion into the exposed region, resulting in an area of increased density and refractive index. After this mass transport has locally increased the refractive index, a uniform optical exposure is used to consume all the remaining initiator and monomer, rendering the polymer chemically and optically inert and thus environmentally stable. The diffusive photopolymer used in this work is InPhase Technologies TapestryTM HDS 3000 modified for lower absorption by half the usual photoinitiator concentration
Direct-write lithography for 3D waveguide fabrication can be implemented by moving the polymer sample primarily perpendicular or parallel to the optical axis . Perpendicular writing tends to create asymmetrical guides, however beam shaping has been demonstrated in multiphoton absorption to create symmetrical waveguides [2, 21]. Alternatively, parallel writing automatically creates symmetrical guides from a symmetrical focus . The parallel write geometry is used in this paper, as shown in Fig. 1 . 3D waveguides are formed by focusing several μW of the 50-mW Coherent Compass 315M laser into the moving polymer. Although the cm-thick polymer is optically thin, weak Beer-Lambert absorption naturally tapers the waveguide index if incident power is held constant. This taper can be controlled or eliminated by a logarithmic-variable neutral density (ND) filter, Thorlabs NDL-10C-4, moved synchronously with the sample via Newport PM500 stages. By varying the velocity of the ND filter relative to the velocity of the polymer, the incident writing power can be modulated proportional to, where TEff is the effective material transmittance and z is the material depth to the focus in mm. Beer–Lambert absorption is compensated at the focus when TEff equals the pre-exposure transmittance of 1 mm of material.
Pseudo-cutback method for 3D mode characterization
Tapered and uniform 3D waveguides written into this diffusion-based photopolymer bulk are difficult to characterize as a function of length because polymer materials can be difficult to cut and polish, particularly the rubbery materials required for diffusion of the monomer. This difficulty can be overcome by exploiting the flexible nature of the polymer as shown in Fig. 2 . First, the liquid polymer precursors are cast between flat glass plates separated by 1 mm spacers. Room-temperature thermal polymerization solidifies the material into optical-quality slabs which are then removed from the mold and laminated together to form multi-mm samples. Coherent confocal microscopy verifies that the laminate boundaries have less than 0.1% reflectivity, indicating intimate contact. Glass microscope slides are laminated to the front and back to act as optical windows. After waveguides are written and developed, the laminated stack is easily separated into optically-flat sections, avoiding the need to cut or polish the polymer.
After separation, the individual polymer layers have optical-quality faces and can be individually tested for mode profile to characterize taper performance. Each polymer layer is laminated to a front-surface metal mirror so that testing of the waveguide can be performed in reflection, as shown in Fig. 3 . This reflection test method provides two advantages: the path length is doubled, helping to separate guided from radiation modes and only one alignment is needed, improving the repeatability of coupling loss measurement.
We show below that the measured mode profile enables calculation of coupling efficiency, allowing propagation loss to be extracted from total measured loss. However, this is only true if the guides support only a single mode. Since the mode image shown in Fig. 3 could be the sum of the fundamental and one or more symmetric higher-order modes, an independent test must be used to verify that only a single mode is present. Scanning the incident beam focus across the guide excites the fundamental and possibly higher-order antisymmetric modes. Coupling efficiency versus offset to these multiple modes will be broader than coupling to a single mode. This latter quantity can be calculated via the overlap integral of two displaced Gaussian fields as shown in Fig. 5(a) to be a Gaussian versus offset Δy with a radius. As shown in Fig. 4 , the measured coupling efficiency agrees well with the theoretical prediction. This confirms that the waveguides support only a single mode.
Mode profiles versus thickness for single-mode 3D uniform and tapered waveguides are presented in Fig. 5. These waveguides are written at 1 mm/s using a focused spot of 4.36 μm 1/e2 diameter. The writing power is 1.5 μW at the front surface, modified by three power profiles along the waveguide’s depth. One example of these power profiles is shown as the dash-dot line in Fig. 2. The power profile with TEff = 0.71 yields a uniform waveguide with mode diameter of 5.2 μm, while the modes of waveguides written with TEff = 0.73 and 0.75 are parabolically tapered. The mode profiles are nearly Gaussian (Gaussian fit quality  ≥ 0.92) and symmetrical within measurement limits. The narrow error bars in Fig. 5 demonstrate the ability to write repeatable uniform and tapered waveguides.
The index profile of a waveguide is not uniquely determined by the mode profile. However we can estimate peak index change ∆n by assuming the index shape of the waveguide. For a single-mode waveguide with a Gaussian-shaped index profile , the field radius of the guided mode can be expressed as :Eq. (1) differs from reference  due to different definitions of the mode filed. In reference , the mode field is defined as, while in the mode profiler measurement it is defined as. Sublinear kinetics of radical photoinitiation  result in an index change proportional to Iα, where I is the writing beam intensity and α is a single fit parameter . We have previously shown the sub-linear kinetic parameter α to be ~0.75 for this material . Given , where w0 is the 1/e2 radius of the writing beam, the index profile is, resulting. Therefore, the calculated NA for the uniform waveguide shown in Fig. 5 is estimated to be 0.12. Since NA of a single-mode waveguide can be approximated as, where n0 = 1.481, the estimated peak index change ∆n is 4.64 × 10−3, which is consistent with holographic recordings in the same material .
Loss measurement for uniform single-mode polymer waveguides
This mode characterization along the guide length enables simple and accurate measurement of propagation loss of a single waveguide via calculation and subtraction of coupling loss. To confirm the accuracy of this measurement, we exploit the repeatability demonstrated in Fig. 5 to test individual waveguides with different lengths, shown in Fig. 6(a) . Uniform waveguides are written with an exposure power of 1.5 μW and power profile TEff = 0.71 in three polymer slabs of thickness L = 1, 5, and 10 mm, respectively. Each slab is tested as shown in Fig. 3 to obtain propagation loss for length 2L and coupling efficiency. Excess propagation loss was obtained by fitting the results of four experiments at each length to a line, as is standard for the cutback method, shown in Fig. 6(b). Excess propagation loss of four samples of each length yields 0.147 ± 0.009 dB/cm waveguide loss. The y intercept from the linear fit Eq. (0).393 ± 0.124 dB, close to the calculated coupling loss 0.413 ± 0.056 dB. This accuracy enables propagation loss measurement from a sample of a single length by subtracting the coupling loss calculated from the mode measurement from the total loss. For a 10-mm waveguide this yields an excess propagation loss of0.140 ± 0.043 dB/cm. This loss is in addition to bulk material absorption of 0.141 ± 0.038 dB/cm due primarily to incomplete initiator bleaching. The characterization of mode size and single-mode condition versus length enables precise knowledge of the coupling loss even for tapered guides, which in turn permits measurement of propagation loss from a single sample length, avoiding the need for cutback loss measurement.
We have demonstrated uniform and parabolically tapered single-mode 3D waveguides in diffusion-based photopolymers and introduced methods to accurately measure mode profile and propagation loss along the guide length. Single-photon holographic photopolymers developed for data storage are shown to be an attractive platform for 3D photonics due to their high sensitivity and self-developing index change. A logarithmic ND filter synchronized to the sample motion is shown to be a natural external modulator to compensate for Beer-Lambert absorption in order to fabricate uniform and tapered single-mode waveguides. A laminated sample fabrication method is shown to provide optical-quality surfaces for direct measurement of the evolution of the single-mode profile along the taper length. This precise and repeatable characterization enables coupling loss to be accurately calculated to find propagation loss from single sample measurements. The accuracy and repeatability of both the fabrication procedure and testing methods are verified by loss measurements for guides of 1 to 10 mm length which show excellent agreement. These results demonstrate single-mode waveguides with 0.147 dB/cm excess propagation loss and symmetrical tapers up to 1:2.5 using 1.5 μW of continuous write power.
This article is based upon work supported by the National Science Foundation under Grant Numbers ECCS 0636650 and IIP 0750506 and Intel Corporation under the University Research Grant Program. Fellowship support for graduate studies is gratefully acknowledged including from DoED GAANN (K.K.) and CDM Optics, Inc. (C.Y.). Research equipment donated by JDS Uniphase Corporation is gratefully acknowledged. The authors would also like to thank InPhase Technologies for sample preparation and materials expertise.
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