A number of useful fiber optic devices depend on being able to predict and manipulate the radiation field emitted by tilted fiber Bragg gratings. Previously we demonstrated analytically the manner in which this radiation field is directionally dependent on the phase matching characteristics of a grating’s three-dimensional structure as well as the polarization dependent dipole response of the medium itself. In this paper, for the first time, experimental measurements of the out-tapped field are presented which clearly illustrate and confirm the existence of the predicted trends associated with each of these physical mechanisms. Using an infrared camera and commercially available beam profiling software, these findings were gathered from a number of tilted fiber Bragg gratings written with an ultraviolet excimer laser at a variety of blaze angles.
© 2009 OSA
Following the discovery of fiber photosensitivity , application of the side writing technique , and invention of the phase mask grating fabrication method , the use of fiber Bragg grating (FBG) optical components has become increasingly widespread due to their versatility, compact size, low loss and low cost characteristics.
FBGs are photonic crystals, comprised of a waveguide in which the refractive index varies in some sort of periodic manner. Most commonly this periodicity is treated in a one-dimensional fashion with planes of equivalent refractive index crossing the fiber axis at a 90° angle, however there is also a subset of these devices in which the grating planes are skewed with respect to the guided light. Often referred to as tilted, blazed or slanted FBGs, these devices enable significantly greater out-coupling to cladding and non-guided radiation modes, and are frequently observed to possess significant polarization sensitivity [4–11]. As a consequence, such technology is employed by a number of commercially available products including gain flattening filters , polarization dependent loss (PDL) compensators , inline fiber polarimeters , spectrum analyzers , reconfigurable optical add / drop multiplexers (ROADM) , as well as interferometric , and surface plasmon based sensors .
Of particular note is the disclosure by Peupelmann et al , in which it was first reported that for a given wavelength, some tilted FBGs had been observed to possess multiple azimuthally distributed, polarization-dependent tap angles. Based on this interesting observation they proposed a unique fiber-polarimeter design which exploited this phenomenon. There was not however, a clear explanation of the physical mechanisms responsible for this effect, making optimization of such devices difficult and inhibiting the development of other components that might benefit from the precise control and exploitation of a tilted FBG’s radiation field profile.
Recently we addressed this issue with a thorough theoretical analysis [20,21], based on a formulation of the Volume Current Method (VCM) by Li et al . As a result of this study it became clear that the radiation field emitted by a tilted Bragg grating is directionally dependent on the phase matching characteristics of the grating’s three-dimensional structure as well as the polarization dependent dipole response of the medium in which it is written. The manner in which these two quantifiable contributions are manifested was also clearly illustrated along with the calculated trends in azimuthal behavior for various grating geometries.
In this paper we disclose for the first time, experimental evidence that directly supports these theoretical conclusions and include the first reported fabrication of a three-peak device analogous to Peupelmann’s two-peak gratings. Although tilted gratings have been studied quite extensively in recent years, there are few published measurements of their radiation fields, this, despite the importance of such data for understanding and optimizing any number of devices dependent on the predictability and control of this emitted light [14–19].
Over the years a number of modeling methods have been proposed for analyzing the responses of fiber Bragg gratings. In the case of tilted gratings two of the most relevant examples have included Coupled Mode Theory (CMT) and the Volume Current Method.
Coupled Mode Theory is by far one of the most popular and well established methods for modeling fiber Bragg gratings, but although it has been used to examine radiation mode coupling problems [6,23], its prediction of the scattered field outside the fiber is not so straightforward. This is because there is an infinite continuum of unbounded radiation modes, many of which have to be included in the calculation, making the solution cumbersome .
The Volume Current Method is a useful perturbation analysis tool for solving numerous waveguide radiation problems that result from small refractive index fluctuations. Its derivation is rooted in the Huygens-Fresnel Principle and seeks to model Bragg gratings as a distribution of dipoles that essentially re-radiate the energy supplied by an incident electromagnetic wave.
Examples of its successful implementation can be found throughout the literature with its original formulation being attributed to Snyder [24,25], and its extension to tilted Bragg gratings being first made by Holmes et al . Of particular relevance to the analysis of tilted Bragg grating radiation field distributions is a series of papers by Li et al [22,23,27,28], that provide several helpful formulations of this approach and a comprehensive review of its application to such problems.
In essence, Li’s formulations result in parametric expressions for the Poynting vectors associated with a grating’s scattered light, which subject to the formulation assumptions, fully describe the light radiated from such devices. These expressions take the form of Eq. (1):
where Δ and kt are longitudinal and traverse components of the radiated wavevector, while C is a proportionality factor dependent on the observation distance, index modulation strength, fiber properties and characteristics of the guided mode. δ is the polarization angle of the guided electric field, ϕ is the angular cylindrical coordinate of the fiber, a is the fiber core radius, u = U/a is defined in terms of the fiber’s modal parameter U (analogous to the V parameter), Knew is the detuning vector magnitude and Jν is used to denote Bessel functions of the first kind (order ν) .
A detailed examination of these expressions reveals the manner in which a grating's response is generated by two physical processes: a dipole interaction between the guided light and the medium (proportional to f 1), coupled with the interference characteristics of a grating’s three dimensional structure (proportional to f 2) .
More specifically, as illustrated in Fig. 1, the phase matching effects (f 2) determine the potential shape characteristics of a grating’s radiation field, while the dipole response of the medium (f 1) serves to select and magnify that portion at 90° to the guided mode’s state of polarization (SOP). As evidenced by the absence of birefringence from the model, this polarization dependent directionality does not require birefringence, just as the PDL of such devices does not require it.
According to the Poynting vector expression, the f 2 term fully determines the potential field pattern associated with a given device configuration, including such features as the number of azimuthally distributed peaks and the angular separation of any two peaks. In studying the behavior of this parameter mathematically, we demonstrated that as the transverse detuning increases (decreasing ∣Kt/kt∣) f 2’s response has a tendency to cycle from one peak to three to two peaks to one to three peaks and so on as illustrated in Fig. 2 .
Although these previously published findings were based on a well established model, it was difficult to assess the applicability of these insights to actual device fabrication given the limited availability of published radiation field measurements combined with the expected discrepancies between real world devices and the idealized structures analyzed. In particular fiber lensing distortions , Talbot fringe generation , and transverse non-uniformity of the induced index change [30,31], are three considerations that are not necessarily insignificant.
Interestingly, independent assessment of tilted FBG radiation coupling was presented by Kotacka et al , through an extension of the formulation provided in . Strong similarities exist between Kotačka’s and Li’s formulations since they are both ultimately derived from the original work of Snyder. The main difference between the two formulations is that Kotačka’s derivation relies on the introduction of a polarization factor, whereas such polarization dependencies are intrinsically predicted by Li’s derivation process.
In this study we fabricated and examined several tilted FBGs having gradually increased levels of detuning. Direct measurements of the radiation fields were then compared with VCM calculations.
3.1 Grating Fabrication
To strengthen the out-coupled signal, we maximized the induced index change and guided mode overlap with the grating, by writing the devices in a commercially available, highly germanium doped, high NA, step index, single mode fiber having the properties listed in Table 1. The fiber was hydrogen loaded at 2600 psi and room temperature for two weeks to further enhance its photosensitivity to the ultraviolet (UV) laser, then kept frozen at -55°C prior to use.
The fabrication setup for these components is presented in detail elsewhere . The inscription process for the tilted gratings utilized a fused silica phase mask having a period of 1500 nm, along with 25%, 24% and 8% transmission in the +1, -1 and 0 diffractive orders respectively. A stationary, uniform, collimated beam of 248 nm, UV light from a KrF excimer laser was used to expose a 20 mm length of each fiber to an average fluence of 72 mJ/cm2/pulse at a 100 Hz repetition rate for 10 minutes. Identical exposures of non-tilted devices using a 1069 nm mask resulted in index modulations on the order of 2×10-3. Prior to exposure the back-reflection of the silica mask was used to ensure that it was normal to the writing beam path and the azimuthal rotation of the mask relative to the fiber axis was found to be accurate and easily repeatable to within ±0.2°. Following rotation of the mask, the fiber was gently placed in parallel and near contact with it.
Since excimer lasers generally tend to be highly unpolarized and given the induced index change was relatively modest, no additional precautions were taken to avoid the generation of photoinduced birefringence [35–39].
The properties associated with each fabricated device are listed in Table 2, where Ideal and Talbot respectively refer to grating structures based on Ideal or Talbot grating periods. The Ideal period is that expected for gratings generated by an ideal zero-order nulled phase mask (Λ), while the Talbot period is 2Λ, with both arising in the case of poor zero-order nulling .
3.2 Measurement Setup
Measurements of the relative radiated intensity were taken using an infrared (IR) video camera (Model ITC-52 by Ikegami Tsushinki Co. Ltd.) and commercially available beam profiling software.
As shown in Fig. 3(a), to measure the radiation field profiles each FBG was placed in a special rotation jig allowing controllable rotations about the fiber axis in increments of 2.5°. This jig was mounted on top of a turntable enabling the longitudinal tap angles to be measured with a repeatability of ±1.3. The camera was then placed behind a rectangular aperture (1.1 cm high × 7 cm wide) located 25 cm from the fiber to ensure that only 2.5° of azimuthal arc was measured at any given time.
In order to ensure that the guided light was monochromatic and randomly polarized, an Agilent 81640A high power tunable laser source and an Adaptif Photonics polarization scrambler were used. To ensure that the scattered light was sufficiently intense at a radial distance of 25 cm from the fiber an Erbium Doped Fiber Amplifier (EDFA) was also employed to boost the guided power incident on the grating.
For each device, a video monitor was used to visually align the grating’s longitudinal tap direction with the camera by rotating the turntable until a maximum intensity was observed to be incident the camera’s centre. The turntable position was then locked and the beam profiling software used to measure the relative power variation at 2.5° increments as the fiber was rotated azimuthally using the rotation jig. This process was repeated for each longitudinal tap angle observed for a given device.
To confirm that the polarization dependence of the radiation out-tap , was also present in these devices, a similar setup was employed. In this case however, as illustrated in Fig. 3(b), the polarization scrambler was not used and linearly polarized incident light was butt-coupled to the fiber by a polarization maintaining (PM) fiber jumper 100 mm from the grating. With the grating held stationary, the PM fiber was rotated through 360° in 15° increments. After each rotation of the PM fiber the butt-coupling was realigned as necessary to maintain the coupled power. Using the camera and beam profiling software, the radiated power was measured as a function of incident polarization for each azimuthal maximum.
Beginning with the longitudinal tap angle measurements (defined relative to the negative fiber axis), it is evident from Fig. 4 that both the Ideal and Talbot responses of the fabricated gratings are consistent with the simulated results, within the measurement error (±1.3°). Since it is possible and quite common to calculate the longitudinal tap angle vectorially (using conservation of momentum) without need of the VCM, these results confirm that the devices fabricated do in fact resemble the grating structures intended.
In measuring the radiation field, it was noted that in addition to varying directionally, the intensities also differed with position along the fiber axis. Although some fluctuation might be expected due to non-uniformities in the index change it was interesting to observe photographically that such differences could be significant, with both highly periodic and nearly uniform responses possible as illustrated in Fig. 5(a) and (b). The degree and measure of this periodicity varied from device to device and even from one azimuthal angle to another as shown by Fig. 5(c) and (d). It should be noted that Li’s models do not predict this variation, because successful integration of its analytical result necessarily assumes the observation point lies in the center of the grating’s length.
Nevertheless, since the beam profiling software effectively integrated all of the light sampled for each azimuthal measurement, we were still able to collect the data presented in Fig. 6 and Fig. 7 and compare it with values calculated using the VCM. For the sake of comparison all calculated values were averaged over an azimuthal angle of 2.5° to account for the azimuthal integration inherent in the measurements.
In Fig. 6 and Fig. 7, each curve represents the normalized radiated power (from 0 to 1) measured for a given device, and all curves are offset in proportion with the phase mask tilt angle used to write or model each grating. The theoretical results were calculated using two different VCM formulations [22,27]. Although some minor differences are apparent, for our purposes their results may be treated as essentially identical.
In examining Figs. 6 and 7 there are obvious differences between the measured and calculated profiles. The origins of these inconsistencies lie in a number of areas. The model assumes that the grating is strictly one-dimensional with a purely sinusoidal index modulation, although it has been clearly demonstrated that the gratings fabricated here incorporate a slightly two-dimensional Talbot structure. Other physical effects not accounted for by the model include distortions arising from fiber lensing as well as transverse non-uniformities of the photoinduced index change. The fact that many of the model inputs were necessarily based on estimated fiber properties (i.e. core size, core/cladding index etc.) must also be considered as a potential source of discrepancy.
Despite these minor differences however it is apparent that the model has performed quite well. The qualitative characteristic tendencies resulting from increased detuning are present in both cases (one peak to three to two peaks to one etc.), occurring with similar blaze angles and azimuthal spreads to those predicted by the model. Also evident from Figs. 6 and 7 are the first reported examples of the three-peak devices predicted by [20,21].
In terms of the polarization dependence of these devices, the measured values of PDL included in Table 2 appear to be in-line with what’s expected from a review of , with larger values attributable to gratings having stronger phase matching and blaze angles closer to 45°. The results displayed in Fig. 8 indicate that the radiation coupling is also consistent with the dipole behavior described previously, with Fig. 8(b) resembling other published figures such as the PDL response of a tilted FBG probed with linearly polarized light . This likeness is of no surprise since the PDL in such devices results primarily from radiation mode coupling.
Unfortunately, because these gratings have such weakly resonant broadband responses, we were not able measure their photoinduced birefringence directly. However, untilted gratings fabricated with identical exposure conditions, and subject to several weeks of residual hydrogen out-diffusion at room temperature did not exhibit any measurable polarization dependent wavelength (PDλ) shift of their resonances. This indicates that the induced birefringence does not exceed the intrinsic birefringence of the fibers themselves (~10-6).
These experiments support the conclusion that the radiation field emitted by tilted Bragg gratings is directionally dependent on two physical mechanisms: phase matching associated with a grating’s three-dimensional structure combined with the polarization dependent dipole response of the medium itself.
In terms of azimuthal scattering these results clearly demonstrate that three-peak devices can be fabricated in addition to the two-peak structures originally reported by Peuplemann. The fact that these gratings were fabricated by design as a result of their theoretical discovery is a testament to the accuracy of the VCM. They support its usefulness as a tool for analyzing the radiation field of tilted FBGs, and for optimizing their structures to achieve the design requirements of applications dependent on such guided to radiation mode coupling.
The authors would like to acknowledge most appreciatively Joseph Seregelyi and the Satelite Systems group of CRC for contributing the use of essential equipment. Also recognized are the valuable discussions and ongoing support provided by fellow ROCE members Gino Cuglietta, Xiaoli Dai, Huimin Ding and Chris Smelser, as well as Professor Liang Chen of the University of Ottawa.
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