We present detailed investigations of chromatic polarization effects, caused by fiber spools used in FDML lasers and buffering spools for rapidly wavelength swept lasers. We introduce a novel wavelength swept FDML laser source, specially tailored for polarization sensitive optical coherence tomography (OCT) which switches between two different linear polarization states separated by 45°, i.e. 90° on the Poincaré sphere. The polarization maintaining laser cavity itself generates a stable linear polarization state and uses an external buffering technique in order to provide alternating polarization states for successive wavelength sweeps. The design of the setup is based on a comprehensive analysis of the polarization output from FDML lasers, using a novel 150 MHz polarization analyzer. We investigate the fiber polarization properties related to swept source OCT for different fiber delay topologies and analyze the polarization state of different FDML laser sources.
© 2012 OSA
Polarization effects in optical single mode (SM) fibers have been studied extensively for a variety of applications. Optical “single mode” (SM) fibers permit the propagation of two orthogonal polarization modes. Due to optical birefringence in the fiber, different polarization states travel at different group velocities. A varying optical birefringence along the fiber causes coupling between the polarization modes. In telecommunication systems, this is well-known as polarization mode dispersion (PMD) [1–3], a review is given in . External stress, like fiber bends , fiber twists , transverse pressure and axial tension  affect birefringence and hence polarization. The stress-optic effect  can be used to suppress coupling between the two orthogonal polarization modes and allows to make various types of polarization maintaining (PM) fiber as reviewed in .
Recently, with the introduction of swept-source optical coherence tomography (SS-OCT) [10-11], also called optical frequency domain imaging (OFDI) , a new application for single mode fiber in the km range has emerged featuring a new set of parameters: In contrast to telecom applications, the optical fiber is used primarily as a means to introduce a time delay in order to multiply the sweep rate of various rapidly wavelength swept light sources used for SS-OCT. This time-multiplexing technique has been termed “buffering” [13-14] and enabled fastest OCT imaging speeds [15–18]. For space efficiency, it is always held in spools introducing bending birefringence. The length is usually around ~1 km and mostly below 4 km. Yet, the spectral width of interest is typically at least 100 nm centered around 1310 nm or 1550 nm, and at least 70 nm around 1050 nm. Since birefringence depends on wavelength  and the wavelength of the light sweeps quickly over a wide spectral span with repetition rates from below 50 kHz into the low MHz range, rapidly changing polarization states are generated.
Optical delay lines for SS-OCT are used primarily in two classes of light sources: (a) Inside the resonator of Fourier domain mode locked (FDML) lasers , and (b) for time-interleaving, also called buffering, in FDML [13-14, 17-18, 21] as well as in conventional wavelength swept light sources to increase the sweep repetition rate available for imaging [15-16]. In this paper, we investigate the fiber polarization properties related to SS-OCT for different fiber delay topologies, analyze the polarization state of different FDML laser sources and analyze the physical mechanisms behind FDML lasers with fixed polarization output as described in [22–27].
OCT  is not only a powerful technique to map optical scattering properties of biological tissue in three dimensions with micron scale resolution, but recently, OCT has been extended beyond imaging of tissue morphology to visualize tissue function. The main approaches of functional OCT (F-OCT) are polarization-sensitive OCT (PS-OCT) [29–32] to visualize tissue birefringence, Doppler OCT (D-OCT) to investigate blood flow [33-34] and spectroscopic OCT (S-OCT) for molecular contrast . Especially for polarization sensitive SS-OCT [36–38], the polarization properties of the swept laser source are of interest.
Information about tissue birefringence in PS-OCT can provide valuable, additional information in OCT application for dermatology , dentistry  and ophthalmology [32,41] and there is great interest to combine this imaging modality with high speed frequency domain OCT techniques. The first bulk optic implementations of PS-OCT used circularly polarized light  incident on the sample. For use with fiber based beam delivery systems, like endoscopes, it is difficult to prepare a well defined and stable circular polarization state of the light impinging on the sample, due to changing birefringence in the fiber. Bending during examination and the rotation of the fiber based OCT endoscope continuously change the output polarization. This problem can be overcome by using two different polarization states at the input of the fiber endoscope, preferentially with a 90° separation on the Poincaré sphere. For polarization sensitive SS-OCT systems with a conventional wavelength swept laser source, the polarization switching can be realized with an external, active component, like an electro optic polarization modulator [36, 41].
The application of FDML lasers for PS-OCT instead of conventional wavelength swept lasers appears attractive, because of the better performance of FDML lasers with respect to many operation parameters. Usually, standard rapidly wavelength swept lasers are limited in the maximum achievable sweep rate by the buildup time for lasing  and the non-stationary operation leads to loss in coherence and increased intensity noise . The introduction of Fourier Domain Mode Locking (FDML)  has helped to overcome these physical limitations and they have proven superior performance in a series of biomedical imaging, spectroscopy and sensing applications [13, 20-21, 44–51].
In FDML, a tunable optical bandpass filter is driven in resonance to the optical roundtrip time of light in a several kilometer long laser cavity. Typically, the tunable optical bandpass filter is either a fiber Fabry-Pérot tunable filter (FFP-TF) [20, 47, 52] or a grating based scanner with a rotating polygon mirror [53-54]. The maximum tuning rate of these filters determines the maximum sweep frequency of FDML lasers. Because today the filter tuning rates are limited to several 100 kHz, resonator lengths of ~1 km are required. Such long cavities are realized by long optical single mode fibers. Since these fibers do not maintain polarization, they exhibit significant birefringence due to internal stress and residual inhomogenities, and they are susceptible to acoustic distortions. Therefore it was unclear up to now, if FDML lasers exhibit a stable, a slowly drifting or a completely random state of output polarization. The problem of polarization in FDML lasers will be investigated and an FDML laser based swept source will be presented that passively switches between two stable and defined polarization states, separated by 90° on the Poincaré sphere. We analyze the polarization state of the FDML laser for various operation conditions with a homemade polarization analyzer at a bandwidth of 150 MHz, and quantify the influence of the different optical components.
2. Experimental setup
2.1 The high speed polarization analyzer
In order to perform the polarization measurements presented here, a special high speed polarization analyzer was set up. This analyzer is built in free-space optics and measures the full state of polarization (SOP) with an electronic bandwidth of 150 MHz. The bandwidth was chosen to be ~3000 times faster than the sweep repetition rate so that even fast fluctuations of the SOP can be detected in case they exist. A schematic is shown in Fig. 1 . The incident light is attenuated and then split into 4 beams of equal intensity by use of three 50/50 beam splitters (BS). Care was taken to use achromatic and polarization independent splitters (Thorlabs Inc.) and small incident light angles. 3 of these 4 beams pass wire grid polarizers (Codixx ColorPol) oriented in 0°, 45° and 90°, respectively, and are then focused onto photo diodes (PD) for detection. The fourth beam passes a quarter wave plate (1200 – 1650 nm, Thorlabs Inc.) followed by a 0° wire grid polarizer and leads into the fourth photo diode. The photo diodes have a bandwidth of 150 MHz and the 4 signals are acquired simultaneously by use of a 4-channel digital storage oscilloscope (Tektronix DPO7104, 1 GHz). The oscilloscope is controlled and continuously read out via network by a PC in which the data is processed to calculate the time evolution of the polarization state.
The 4 photo diodes PD1 to PD4 measure intensities I0°, I45°, I90°, Iσ, respectively, representing the linear polarization in 0°, 45° and 90° as well as the left circular polarization. These measurements are used to reconstruct the polarization state of the incident light by computing the 4 component Stokes vector :Fig. 1, right)  providing a graphic visualization of the polarization state. For a quantitative comparison, we will map the Poincaré sphere in cylindrical projection: Angle θ (longitude 0…360°) represents the linear polarization orientation (0…180°), so the linear orientation of the electrical field is θ/2. Angle φ denotes the circular part where ± 90° corresponds to (left/right) circular polarization and angles in between are elliptic states. The distance from the origin (r = 0…1) represents the degree of polarization which is not represented on the cylindrical projection. The spherical representation is computed from the Stokes vector as follows:
One such calibration was performed for all measurements around 1310 nm and one for measurements around 1550 nm. For the calibration, the formula above can be written as
Figure 2 (left) shows 4 measurements performed with the polarization analyzer: Using bulk optical components, 3 linear input polarizations (0°, 45°, 90°) as well as a left circular polarization were prepared from an FDML source sweeping over 135 nm centered around 1307 nm. The measurements show the values for forward (red dots) and backward (black dots) wavelength sweep of the FDML laser. Due to residual chromatic dependence of the wavelength split ratios in the beam splitters, the measurements exhibit a systematic error of ~5° and consequently, the observed measurement points are slightly spread out. For the circular polarization, this spread is stretched, because at the poles the longitude angle θ is not defined. Figure 2 (right) shows 36 measurements of ASE covering two full circles of elliptic states on the Poincaré sphere.
3. FDML laser polarization
FDML lasers typically use many meters of single-mode fiber within their cavity. This fiber is usually bent and laid out in circles on a spool for reasons of space efficiency. Bent fibers introduce a wavelength-dependent birefringence and hence alter the polarization state of the guided light introducing different retardation for different wavelengths and different incident polarization orientations. This immediately raises the question whether the FDML laser output shows a repetitive polarization pattern over consecutive sweeps or whether the polarization continuously twists over several sweeps or if there is simply random fluctuation.
In order to address these questions, several single-sweep polarization measurements at the output of two FDML lasers at 1550 nm were performed: Both lasers were built in sigma-ring configuration without any polarization dependent components except for the SOA (see Fig. 3 left): The first laser (L1) incorporates a Covega BOA-6066 (type: 1004) which only amplifies one linear polarization direction. The second laser (L2) makes use of a polarization-independent Covega SOA-4057 (type: 1084) with 2 dB polarization dependent gain (PDG). The polarization analyzer was attached at the output of the FDML laser with ~5 m fiber with only few bends. The ~3 m fiber between the SOA and the output coupler was laid in circles of ~10cm diameter as typically used within an FDML laser.
3.1 FDML laser with polarization dependent SOA (L1)
Our measurement results show that the FDML laser with polarization dependent SOA (L1) generates a nearly constant polarization over the whole sweep range of 140 nm around 1557 nm. We acquired polarization data for several non-averaged single-sweep traces within ~1 minute as well as an average over many sweeps and could not find significant difference between these measurements. All polarization measurements show a degree of polarization of nearly 1.0 (typically >0.95 average over the whole sweep) with the slight deviation attributed to measurement errors. The situation at the laser output does not change when replacing the FRM with a conventional mirror (see Fig. 3, right) which introduces a much larger change of SOP over the sweep within the cavity (see section 3.3). The only difference is that the polarization controllers have to be adjusted much more carefully in the latter case to achieve lasing over the whole sweep range of 140 nm. The polarization controllers were adjusted only by looking at the spectrum on the OSA. Each time a good polarization controller state was found (i.e. lasing over the whole sweep range), a SOP trace was acquired with the polarization analyzer. Several different angles of the polarization controller resulted in good lasing and all of them were found to show nearly identical output SOP. We also find that the observed polarization is neither dependent on the sweep range and the center wavelength nor on slight detuning of the filter drive frequency. In Fig. 3 (right), the small deviation from a linearly polarized state is caused by birefringence in the fiber path between the SOA and the polarization analyzer.
This indicates that in an FDML laser with polarization dependent SOA, the SOA fixes the SOP within the cavity. Of course, at positions in the cavity further away from the SOA, especially after the delay fiber, the situation will generally look different and the SOP trace will have a larger extent. The effect of the delay line and polarization controllers is described in sections 3.3 and 3.4.
3.2 FDML laser with polarization independent SOA (L2)
The situation is completely different when a polarization independent SOA is used (L2). Due to a different gain profile of the SOA, this laser swept over 130 nm with a center wavelength of 1511 nm. We find that the laser shows a good output spectrum for nearly all possible states of the polarization controller. Tilting the controller paddles mainly reduces the output power by 1 – 2 dB which is expected from a polarization dependent gain of 2 dB. Measuring the SOP, we find 2 main differences to the former case L1 as shown in Fig. 4 : First, the SOP is no longer stable but changes significantly over the sweep generating an SOP trace with huge extent. Second, the polarization shows pronounced shot-to-shot fluctuations. These fluctuations are not completely random: On average (over many sweeps as well as when averaging neighboring wavelength bins), the SOP at the laser output follows a certain path. However, high frequency noise-like deviations from this path are clearly visible. Individual photo diode traces in the analyzer show noise much larger than intensity noise present on the laser output. It is also interesting to note that the two sweep directions show different SOP traces in the averaged graphs.
The large extent of the SOP and the fluctuations make an FDML laser with polarization insensitive SOA less suitable for a lot of applications where the polarization matters and especially for cases where a certain polarization is required.
3.3 Influence of different delay spool implementations
Considering birefringence in the FDML laser cavity, the long delay spool clearly provides the major contribution: A typical delay line for a 50 kHz laser has a length of 3.6 km. Bending-induced birefringence in the fiber spool causes retardation between the polarization axes parallel and perpendicular to the spool’s plane. For a fiber diameter d and a spool diameter D, the bending-induced difference in the refractive index between the two axes is Δn ≈0.133 (d/D)2 . For a fiber of length L, this translates into a retardation of L▪Δn. For a spool diameter of 20 cm, this corresponds to a 150 λ (120 λ) waveplate at 1310 nm (1550 nm). In order to investigate the influence on polarization caused by different delay lines, we constructed the following setup: Light from a 50 kHz FDML laser at 1550 nm is sent through a fiber polarizer and coupled into PM fiber. The output after the polarizer is verified to show clean linear polarization. This linearly polarized light is then sent into a 2 km delay fiber spool in 3 different ways: First, with the polarization axis in the spool plane, next with the polarization axis perpendicular to the spool plane and third at the intermediate angle of 45°. Several different layouts for the delay line were investigated: (D1) A traditional 2 km delay spool (diameter of all spools: 23 cm), (D2) a sigma ring delay with a 1 km spool traversed two times and a Faraday rotation mirror, (D3) the same setup but with a normal mirror instead of the Faraday mirror and (D4) two 1 km delay spools oriented 90° with respect to each other (see Fig. 5 , right bottom). The same measurements were repeated at 1310 nm, however in this case a PM-FDML laser providing linearly polarized light in a PM fiber output  (see also section 4) was used so an additional polarizer was not necessary. The results are shown in Figs. 5 and 6 .
First, we find that the orientation of the incident light polarization has little influence on the extent of the polarization traces, just moves/rotates them around on the Poincaré sphere. This seems counterintuitive since birefringence generally retards the polarization perpendicular to the spool plane relative to the polarization in the spool plane. Hence, 0° and 90° polarization should pass unaffected while the 45° state should see the most severe distortion. However, at a length of 1 km, standard single mode fiber does not keep light at 0° or 90° throughout the whole spool due to PMD, slight random fluctuations of birefringence along the fiber. Hence, coupling between the two polarization modes occurs and the polarization changes gradually within the length of fiber. In effect, the orientation of the polarization axis when entering the spool is rendered rather irrelevant. This also explains why replacing a single 2 km spool with two 1km spools oriented in right angle relative to each other (D4) does not provide much improvement.
Secondly, as qualitatively expected we find that the least distortion is introduced by a sigma ring configuration. In this configuration, the light enters a circulator, travels through a 1 km delay, is reflected by a Faraday rotation mirror (FRM), travels back the same spool and leaves through the third port of the circulator. The crucial idea behind this concept is as follows: The polarization axes 0° and 90° (relative to the spool plane) find a certain amount of retardation while traveling towards the mirror. The FRM then rotates the polarization state by 90° effectively exchanging the 0° and 90° states (180° and 0° polarization have their electrical fields in the same plane). Hence, on the return path through the fiber, the 0° axis sees the same retardation as the 90° axis saw on the forward run and vice versa. Since both axes get treated effectively the same way, no change in the polarization state occurs except for a rotation of 90°. Of course, residual effects remain, such as the 2 x 2 m fiber spools before and after the circulator (bending diameter ~7 cm) as well as imperfections of the FRM.
3.4 The effect of polarization controllers in the FDML cavity
The main reason for the formation of different polarizations in an FDML laser is fiber-induced birefringence which introduces a wavelength dependent phase shift. The major contribution for birefringence is provided by the fiber spool of the delay line. A typical delay line for a 50 kHz laser has a length of 3.6 km. At a spool diameter of 20 cm, this corresponds to a 150 λ waveplate at 1310 nm. Since usual polarization paddles provide zero order waveplates, these cannot compensate the retardation introduced by the fiber spool over all wavelengths simultaneously. Yet, the polarization paddles within the laser cavity play a crucial role for FDML laser activity, especially for polarization dependent SOAs. When not adjusted properly, the FDML laser output power drops and/or lasing only builds up for a subset of wavelengths. This holds especially true for FDML lasers with a direct delay line while a sigma ring configuration is less susceptive to paddle misalignment. Our findings suggest the following model:
We find that the major influence provided by polarization paddles is that they allow positioning the incoming light anywhere on the Poincaré sphere. However, since they cannot compensate for the retardation of the cavity, they only provide little influence on the extent of the polarization trace. To demonstrate this, we prepared a linearly polarized sweep which is sent into a 460 m long delay spool followed by a usual 3-paddle polarization controller (λ/4, λ/2, λ/4). The resulting SOP for different paddle positions is shown in Fig. 7 (left). For SOAs with high polarization dependence of the gain, only a certain (linear) orientation of the polarization is amplified (gain axis). Hence, the effective gain of the SOA for a certain incoming polarization is given by the magnitude A of the projection onto this gain axis.
Figure 7 (right) shows a contour plot of the normalized magnitude A for an SOA with a linear gain axis with 0° orientation. Proper adjustment of the polarization paddles brings all wavelengths of the incident light onto the SOA near the gain axis. As described in section 3.4, sigma-ring configuration shows a much smaller extent on the Poincaré sphere than a traditional direct delay spool. Hence, slight detuning of the polarization paddles in sigma ring configuration has little influence on a running FDML laser. In contrast, for traditional direct delay lines, the polarization changes so much over the sweep range that only careful alignment of the polarization controllers allows lasing over the whole range. In agreement with this model, we find that delay spools with smaller diameter and lasers at shorter wavelengths (1310 nm and especially 1060 nm) make polarization controller adjustment more difficult or even make lasing over a wavelength range >100 nm (>60 nm) impossible to achieve for a 1310 nm (1060 nm) center wavelength .
4. Polarization maintaining FDML laser
We developed an FDML laser with polarization maintaining (PM) cavity. This PM-FDML laser runs in the 1310 nm region and offers two main benefits: First, the laser output is linearly polarized and delivered via PM fiber ensuring that the polarization is not affected by bending the fiber. Second, there are no polarization paddles to be adjusted within the laser cavity. The laser presented here was used in [22–26].
A schematic of the PM-FDML laser is shown in Fig. 8 . It consists of an SOA with integrated isolators and PM fiber pigtails (Covega type 1132), a PM output coupler and a special PM pigtailed fiber Fabry-Pérot tunable filter (FFP-TF, LambdaQuest LLC). Since km long PM fiber is both expensive and degrades the linear polarization state due to slight coupling between the fast and the slow axis , a usual single mode fiber (SMF) delay line is much more attractive. This was implemented by use of a polarization beam splitter (PBS) attached to an SMF delay spool with an FRM at the end.
We found that FC/APC fiber couplers introduce coupling between fast and slow axis of the PM fiber and introduce intensity modulations in the laser output. These modulations are due to interference between the light from the fast axis and the retarded light from the slow axis. To minimize this effect, all connections in the PM fiber cavity were fusion spliced. Residual intensity modulations from polarization crosstalk cause ghost signals in OCT separated from the primary image by the frequency of the modulation. By keeping the pigtails short (~10 cm), the ghost images are kept within one resolution element of the OCT system.
The FDML laser is followed by a single buffer stage built analogous to the sigma ring delay fiber within the laser cavity. The current of the SOA stays on during one sweep direction of the filter and is switched off during the other sweep direction by means of a high speed laser diode controller (WL-LDC10D, wieserlabs.com). The laser cavity hence produces ~10 µs laser output followed by 10 µs with no output which is subsequently filled up by the buffer stage with a delayed copy of the previous sweep.
4.2 Performance and polarization switching
The laser runs at 54.58 kHz fundamental frequency and provides a tuning range of up to 136 nm around 1312 nm. The output polarization was measured by observing the transmitted power through a rotating wire grid polarizer and is better than 100:1. The two outputs of the buffer stage can be combined by a PBS. This results in a buffered swept laser which delivers sweeps with 90° alternating polarization at a repetition rate of 109 kHz. Unlike conventional buffer stages with 50/50 couplers, this one has only one output that delivers all the power instead of two outputs with half the power.
However, for certain polarization sensitive OCT applications, it is desirable to prepare two alternating polarizations which are 90° spaced apart on the Poincaré sphere, so the swept source has to deliver e.g. linear polarizations 0° and 45°. Such polarization states cannot be combined using a PBS. Furthermore, when coupling a 45° state into PM fiber, different propagation times of the slow and the fast axis of the PM fiber complicate or impede SS-OCT imaging due to interference. One possible solution is to combine the two linearly polarized outputs of the buffer stage using a regular (non-PM) fused fiber coupler. To keep birefringence introduced by the SMF to a minimum, the fiber length of the coupler was cut down to <10cm. Rotatable FC/PC connectors allow to turn the two PM fibers under a 45° angle relative to each other. We found that slight bending of the short SM fiber ends of the coupler can be used to compensate for elliptic polarization components generated in the fiber and the coupler itself. Figure 8 (right) shows the resulting SOP behind the 50/50 coupler for sweeps over 130 nm around 1310 nm. The two alternating linear polarization states are separated by 90° on the Poincaré sphere; the spread in the diagram is caused mainly by chromatic imperfections in the polarization analyzer.
5. Conclusion and outlook
In summary we demonstrate a detailed analysis of the polarization evolution of light in km long fiber spools as used in OCT for FDML lasers and for buffering of conventional light sources. A polarization analyzer with a bandwidth of 150 MHz can measure the full state of polarization with a temporal resolution better than 10 ns.
In fiber spools, the wide relative tuning range of more than 10% of the center wavelength causes a pronounced wavelength dependent rotation of the polarization state. This effect cannot be compensated by standard polarization controllers, as they affect all wavelengths components in the same way. If fiber loop polarization controller paddles are used, the extent of the wavelength sweep on the Poincaré sphere may be even increased because such paddles represent only zero order wave plates.
In FDML lasers an analysis of the polarization shows fundamentally different behavior between FDML lasers with polarization dependent SOAs and with polarization independent SOAs. FDML lasers with polarization independent SOAs show random and quickly-changing polarization fluctuations between sweeps and deliver similar performance independent of the polarization controller states. Polarization sensitive SOAs in FDML lasers fix the polarization state of the FDML cavity. These lasers operate best when the delay spool topology is chosen in a way that the wavelength dependent SOP change is kept small, favoring a sigma-ring configuration. Furthermore, a careful adjustment of the polarization controllers is required. The SOP at the laser output changes over the sweep due to wavelength dependent retardation introduced by birefringence of the fiber after the SOA. The situation generally stays stable as long as temperature and mechanical fiber layout are not changed. This can be overcome by setting up a polarization maintaining laser cavity. Such a PM-FDML laser delivers constant linear polarization over the complete sweep; polarization crosstalk can be minimized by keeping fiber pigtails short.
Based on the finding, the PM FDML laser was combined with an external buffering stage to generate a rapidly wavelength swept laser source which switches between two different linear polarization states separated by 45°, i.e. 90° on the Poincaré sphere. The wavelength sweeps with the alternating polarization state may be used for future endoscopic PS–OCT  where changing birefringence caused by bending of the endoscope can be numerically compensated.
We would like to acknowledge the support from Prof. W. Zinth at the Ludwig-Maximilians-University Munich. This research was sponsored by the Emmy Noether program of the German Research Foundation (DFG – HU 1006/2-1), the European Union project FUN-OCT (FP7 HEALTH, contract no. 201880) and FDML-Raman (FP7 ERC, contract no. 259158).
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