Weimin Liu, Yuqiao Liu, John Zhang, Kevin Shirk, and Wei-Shin Tsay
Managing the effects of polarization is an important consideration in telecom system performance. Passive fiber-ring depolarizers can control or modify these effects.
Many lightwave applications involve polarization-dependent processing of light with an arbitrary state of polarization (SOP). For optical amplifiers, coherent optical fiber systems, and fiberoptic sensors, the stability of SOP of the guided light is an important parameter in determining the overall system performance.1, 2, 3 Because of inherent gain-polarization dependence, for example, it is desirable to depolarize the pump light source to reduce polarization-dependent gain (PDG) in Raman amplifiers for long-haul transmission systems.4 Also, depolarizers reduce the noise in fiber sensors created by polarization instability.
The usefulness of a light source in a particular application may depend upon its degree of polarization (DOP). Light produced by a diode laser is almost completely polarized, giving both benefits and challenges when designing telecommunication systems and sensors. The light from a light-emitting diode (LED) can be polarized from 10% to 20%. When a light is traveling through free space, the DOP will be maintained. However, in many cases, a transmission medium can change the DOP of the light passing through it. Managing these effects is an important consideration in telecom system performance, and depolarizers offer a method to control or modify these effects.
When light passes through a standard low-birefringence optical fiber, the random fluctuations of the SOP caused by birefringence changes in the fiber affect the performance of the device connected to the fiber. In principle, we can solve this problem in two ways: by maintaining SOP or by randomizing it. Although one solution to polarization sensitivity is to replace standard low-birefringence fibers with polarization-maintaining fibers (PMF), which will preserve the initial SOP of the light, this approach is costly and often impractical. Thus, depolarizers are commonly used to randomize the polarized light coming from the source to solve the polarization-dependent problem.
DEGREE OF POLARIZATION
Polarized light propagating in fiber or in free space is represented by an electric field vector lying in the plane perpendicular to the direction of propagation. Polarization is defined as the pattern traced by this vector in the transverse plane as a function of time.
However, it is not always possible to describe light in terms of a predictable electric field vector. Unpolarized light can be represented as an electric field vector that takes random orientations in the transverse plane as time passes. Partially polarized light can be viewed as the superposition of a fully polarized component and completely unpolarized light. The DOP is defined as the power ratio of polarized light to total light:
The DOP can also be expressed in terms of the normalized Stokes parameters:
In the case of fully polarized light, DOP = 1; in the case of unpolarized light, DOP = 0.
Depolarizers lower the DOP of the light source. This effect is equivalent to having two orthogonal polarized beams of substantially equal amplitude added incoherently. In other words, the phase shift between their instantaneous electric fields varies randomly and quickly on the time scale of the measurement.
Depolarizers can be classified as active and passive. Active depolarizers use some external modifier of the index of refraction to alter the SOP. Passive devices use the inherent effects of the material or component to alter the SOP. Active devices may not offer true depolarization, but rather deliver a pseudo state of depolarization. The electro-optic pseudo-depolarizer, in which the refractive index within a waveguide is changed by an electric field generated by an electrodes positioned on either side of the waveguide, is one such device (see Fig. 1).5 The SOP of the light passing through the waveguide varies with refractive index. By cycling the index of refraction, the time-averaged light comes out to be depolarized because no single SOP is preferred during the averaging time.
This form of depolarizer can be used with narrowband sources such semiconductor lasers, which are less expensive than superfluorescent broadband sources. However, its disadvantage is that light exiting the active depolarizer has a high DOP within a narrow time interval. Therefore, a high-speed detector will receive light with a high DOP when the light is time-averaged over this narrow time interval. This active system requires both a power supply and driving circuit, which increases costs and complexity compared to passive depolarizers. Additionally, there will be a high DOP when any of these active components fails.
Another active pseudo method is to modulate the birefringence of the fiber.6 The acoustic depolarizer incorporates a length of fiber coiled on a driving speaker. The vibrating speaker alters the refractive index in the fiber, which varies the DOP at the vibrating frequency. Narrowband sources can be used with this form of depolarizer. Although the acoustic depolarizer reduces DOP, the output light still retains a significant DOP within a narrow time interval. The problems of high cost and complexity exist as they do with the electro-optic pseudo-depolarizer.
Several designs for passive fiberoptic depolarizers have been reported. A well-known example of such a device is the traditional Lyot depolarizer, which comprises two plates of quartz crystal with optical axes orientated at 45° to each other. The crystals must have high retardation effect. When broadband light enters the depolarizer with a given degree of polarization, the different wavelengths in the spectrum experience different amounts of retardation as they pass through the device. As no one state of polarization dominates, the source light can be considered depolarized. The 45° optical axes orientation ensures that the depolarizer is effective for input light of any polarization state.
From its operating principle, we know that the Lyot depolarizer is inefficient for narrowband light sources. Also, the component cost is high. Because chromatic dispersion increases with bandwidth of light source, many fiberoptic communication systems require narrowband sources, limiting the usefulness of Lyot depolarizer.
The fiber version of the traditional Lyot depolarizer is formed by splicing two lengths of PM fiber with optical axes rotation of 45°. The fiber Lyot depolarizer functions the same way as a traditional Lyot depolarizer. Again, for narrowband sources, this approach is not practical because of the long length of PM fiber required.
A simpler design is based on a fiber-ring structure built with cascading directional couplers. This all-fiber passive depolarizer can be used for narrowband laser sources. In a single-ring recirculating depolarizer constructed from a standard 2 x 2 fiber coupler, the fiber recirculating delay line is made by connecting one of the input ports to one of the output ports (see Fig. 2). As light enters the depolarizer, it will split into a direct output beam and a recirculating beam, which will be split again and again. The total output beam is a combination of the direct output beam and the multiple recirculating beams, with random polarization states. When the recirculating beams are incoherent, the DOP is lowered and the output beam is depolarized. In practice, the same structure can be cascaded to further lower DOP (see Fig. 3). In some cases, DOP of 5% can be obtained.
In designing the depolarizer, the fiber recirculating delay line is treated as the birefringence medium. The output DOP is determined by retardation, length of delay line, coupling ratio, the number of cascading stages, and the relationship among the delay lines.
The common simulation approaches include very complicated calculations associated with many parameters. For practical purposes, the design can be simplified. Assume the direct coupling ratio of the coupler is k. The intensity of each of the recirculating beam can be written as a series: k, (1-k)2, (1-k)2k,
(1-k)2k2, . . .,(1-k)2kn-2.... Because the intensity of recirculating beams in this series decreases rapidly with the number of beam cycles (n), it is sufficient to consider only the first few cycling beams in the design. The optimization of the coupling ratio of the 2 x 2 depolarizer is straightforward, and that of the depolarizer becomes greatly simplified (see Fig. 4). DOP is minimized when the coupling ratio k = 0.38.
To obtain incoherent beams, the length of the recirculating delay line, L, must be much longer than the coherence length (Lc) of the light source. This condition can be easily satisfied in practice when a narrow band laser source is used. Fig. 5 shows our calculated result of the coherence length as a function of the bandwidth of a laser source at 1480 nm, the typical value for Raman lasers. The coherence length is less than 25 mm as bandwidth varies from 0.1 to 3 nm. This value is much smaller than the length (1 m) of the coupler pigtails that are connected to form the recirculating delay line. There is almost no bandwidth limit in practice for this depolarizer. For a laser source with bandwidth of 10-4 nm, the coherence length is 10 m, which is not too long for the fiber to be assembled in the depolarizer. For bandwidth of 0.75 nm, coherence length is in the range of 2 to 3.5 mm, when wavelength varies from 1200 to 1600 nm.
As the single-ring structure is cascaded, beams from different cascading stages may interfere, which can increase and destabilize DOP. Therefore, in order to efficiently lower and stabilized DOP, the lengths of recirculating delay lines should be specially designed to eliminate coherence effects coming from recirculating beams from the cascading stages. To be incoherent, beams in each stage have to be delayed by a length much larger than the coherence length of the light source. Furthermore, the first few cycling beams of each stage have to be designed to avoid coherent overlapping and interference while the remaining ones are neglected because of negligible intensity. Under these conditions, beams from different cascading stages can avoid severe interference, and the output light will be effectively depolarized.
With the cascaded fiber-ring structure, the averaged DOP decreases with the increasing number of fiber-ring stages. The stage number cannot be too large (>10), however, due to accumulating insertion losses. As a result, there is always a trade-off between DOP and insertion loss in the design. Theoretically, a 3 x 3 structure should be more suitable for depolarization. However, since the designed coupling ratios are rarely repeatable, the 2 x 2 structure is chosen in practice.
The fiber-ring passive depolarizer is low-cost, simple, and reliable. It requires no precise alignment of the polarization axes, no expensive PM fiber, no extra active elements, and no external power. It can be used with narrowband sources typically used in telecommunication systems, and it can be easily assembled and modified for a particular application or source. Most important, low DOP (5%) can be achieved in a totally passive component.
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Weimin Liu is an optical engineer, Yuqiao Liu is chief scientist and acting director of component development, John Zhang is product manager, Kevin Shirk is director of advanced technology platforms, and Wei-Shin Tsay is senior vice president of product/business development at Alliance Fiber Optic Products Inc., 735 N. Pastoria Ave., Sunnyvale, CA 94085. Wei-Shin Tsay can be reached at firstname.lastname@example.org.