Characterization of a Tunable Flattened-Pass-band Fiber Comb Filter

Abstract

The optical characteristics of a tunable flattened-pass-band fiber comb filter, based on the polarization-diversified loop configuration, are investigated using the $Poincar{\acute{e}}$-sphere representation. In the design process, the spectral flatness is checked quantitatively, and the tunability of the pass band is demonstrated experimentally. Theoretical calculations show that the filter also exhibits desirable dispersion and polarization properties. The orientation angles of rotatable wave plates for the wavelength tunability of the filter are obtained. Furthermore, we elaborate on the multiple angle loci produced by degeneracies through the combination of optical elements within the loop of the filter.

I. INTRODUCTION

Optical-fiber comb filters have attracted considerable attention for a wide variety of applications in multiwavelength optical systems, such as dense-wavelength-division multiplexing (DWDM) systems, multiwavelength laser sources, and nonlinear optical switching devices [1-6]. They serve as essential components, due to their capability of selecting desired signals and isolating adjacent signals.

To improve the flexibility of optical comb filters, various approaches to implement continuous wavelength tunability have been proposed, using Sagnac birefringence filters (SBFs)based on birefringence combination [7-12], a double-loopMach-Zehnder interferometer (MZI) [4, 13, 14], or a fiber Bragg grating [15, 16]. In particular, extensive investigations on comb filters using the polarization-diversified loop configuration (PDLC) have been carried out, due to their ability to switch or continuously tune the pass bands. The authors have proposed zeroth-order tunable comb filters using a section of polarization-maintaining fiber (PMF) [17, 18]and first-order Solc and Lyot comb filters using [19, 20] two sections of PMF based on PDLC, respectively.

Recently, a continuously tunable polarization-independent pass-band-flattened fiber comb consisting of two sections ofPMF was proposed and demonstrated experimentally [21].The filter transmission and orientation-angle sets of waveplates for wavelength tuning were derived through the Jonesmatrix formulations. The relationship between wavelength tuning and the final state of polarization (SOP) within the PDLC was also discussed. The arbitrary wavelength tunability in the transmission spectrum was verified by theoretical investigation and experimental results. However, an exact analytic expression for a flat-top transmittance function is required to obtain the wave plate’s orientation angles for its continuous wavelength tuning. Besides, the other optical properties of the filter have not been investigated thoroughly.

In this paper, we investigate the characteristics of the tunable pass-band-flattened fiber comb filter. The operating principles of the filter are described, and the orientation-angleloci of the waveplates for wavelength tuning are obtained by the use of the Poincaré sphere. The algorithms for pass-band-shape design and wavelength tuning are presented in detail. The multiple orientation-angle sets of the waveplates are derived using a geometrical method via the thePoincaré sphere. The optical characteristics are also analyzed, including group-velocity dispersion and differential group delay (DGD).

II. POLARIZATION EVOLUTION WITHIN THE PDLC

Figure 1 shows the schematic of the tunable filter based on the PDLC, which consists of a PBS and two birefringent groups of an HWP, a QWP, and a section of PMF, designated as HWP1, QWP1, and PMF1 in the first group andHWP2, QWP2, and PMF2 in the second group. We denote the PBS’s horizontal and vertical axes as the x-axis andy axis respectively. The orientation angle of each optical element is defined as the angle between its slow axis and the x-axis. Arbitrarily polarized light incident from the INport might have x- and y-axis components, which are separated by the PBS. The x component travels in the clockwise (CW) direction, while the y component moves in the counterclockwise (CCW) direction in the PDLC.PMF2 is butt-coupled to the PBS so that the slow axis ofPMF2 is oriented at 22.5° with respect to the x-axis.

FIG. 1. Schematic diagram of the PDLC.

In fiber comb filters based on the PDLC, the filter spectrum is generated by the wavelength-dependent phase retardation Γ = 2πBL/λ between two orthogonal principal states of polarization of the PMF, where B, L, and λ are the birefringence, length of the PMF, and wavelength of light in vacuum respectively. The birefringence and length of both PMFs are 4.166 × 10-4 and 7.2 m respectively, leading to a channel spacing of 0.8 nm.

Generally, a birefringent element allows a point-of-inputSOP (s1,s2,s3) on the Poincaré sphere to be rotated by its phase retardation CCW (looking from its slow axis to its fast axis) around the axis, passing its two eigenpolarization states in the Poincaré-sphere representation [22]. We concentrate our attention here on the x component of the light's polarization vector since the optical characteristics can be investigated simply by analyzing the SOP evolution of light traveling CW within the PDLC [22]. The input SOP is x-polarized and represented by a point (1,0,0) on the Poincaré sphere, and will be converted into a linear polarization with azimuthal angle of 4θh1 by HWP1. If we assume the wave plates to be achromatic, their output SOPs of broadband light will be identical. After passingHWP1, light passes through QWP1, and its output SOPcan be obtained by rotating the SOP around the 2θq1 axisCCW by an angle of π/2. PMF1 moves the SOPs by Γ, which is dependent on wavelength, and the output SOPsbecome a circle centered on the point with an azimuthal angle of 2θPMF1 on the equator, with a radius of the distance between the SOP after QWP1 and the center of the circle. Hence, the broadband light source is dispersed into a circular locus by rotation about the axis lying on the equator with longitude 2θPMF1, and the locus is rotated by successive HWP2 and QWP2 before PMF2, while remaining circular in shape over the FSR.

For convenience, we designate 1548.0, 1548.2, 1548.4,and 1548.6 nm as λ1, λ2, λ3, and λ4, and their corresponding phase retardations of the PMF as Γ1, Γ2, Γ3, and Γ4, respectively. First let us consider the angle combination that produces a transmission spectrum with dip wavelengthλ1. The SOP loci before PMF2 are shown with a transmittance phase shift of 0° (red) and 45° (blue) in Fig. 2(a). The red circular locus represents the SOP for dip wavelength λ1before PMF2. The SOP of λ1 remains unmoved, while that of λ3 moves toward (1,0,0) after PMF2, which corresponds to the center wavelengths of the stopband and passband respectively. For a 0.1-nm shift (ΔΓ = 45°), the circle is rotated around the 2θPMF1 = 45° axis tightly between two green circles, and spins at the same time CCW by 45°, becoming the blue circle shown in Fig. 2(a). Thus the SOPof 1548.1 nm (= (λ1+λ2)/2), which is located simultaneously on the blue and green circles, will move to (-1,0,0) through rotation by 45° CW, and will be extinguished at the output port. Two circular loci (red and blue) are further dispersed after PMF2, but the final loci are the same in shape but different in wavelength location, implying wavelength tuning. The wavelength locations are those at phase shift0° (red) and 45° (blue) in Fig. 2(b).

FIG. 2. SOP loci (a) before and (b) after PMF2. The phase shifts in the transmittance correspond to 0° (red) and 45° (blue) respectively

The corresponding final polarization ellipses after PMF2at the individual wavelengths of light shown in Fig. 2(b)are shown in Figs. 3(a) and 3(b) for the two cases 0° and45° respectively. To see the tunability and flat passband clearly, theSOP loci before (red circles) and after PMF2 (blue circles)of light traveling CW within the PDLC are replotted as world maps in Figs. 4(a), 4(b), 4(c), and 4(d), where the center wavelength of the stopband corresponds to λ1, λ2,λ3, and λ4 respectively. The SOP loci after PMF2 are identical in shape but different in wavelength location, leading to wavelength tunability of the filter. From their contours of the transmission shown in Fig. 4(a), it is obvious that the 2-dB bandwidth is larger than 0.4 nm,since Δλ = λ4 - λ2 = 0.4 nm.

FIG. 3. Polarization ellipses of light traveling CW within the PDLC after PMF2, for phase shifts of (a) 0° and (b) 45°, at λ₁, λ₂, λ₃, and λ₄

FIG. 4. SOP loci before (blue) and after (red) PMF2, in a world-map description, for phase shifts of (a) 0°, (b) 90°, (c) 180°, and (d) 270°

To clearly observe continuous wavelength tunability of the filter, the orientation-angle sets of four rotatable waveplates (θh1, θq1, θh2, θq2) for individual center wavelengthλp of the passband are investigated using the method explained above for θp1 = 0°. The loci of (θh1, θq1) and (θh1, θh2) are shown in Figs. 5(a) and 5(b) respectively. The tuning over the FSR is implemented for the angle ranges-16.4° ≤ θh1 ≤ 16.4°, 67.5° ≤ θq1 ≤ 112.5°, and -56.2° ≤ θh2 ≤34.1° respectively. The projection of (θh1, θq1, θh2, θq2) onto the (θh1, θq1) plane looks like a Lissajous pattern, while that into (θh1, θh2) becomes a spiral. All trajectories have the periodicity of the FSR (0.8 nm), and θq2 is fixed at 67.5°.To investigate the trend, the loci for various values ofθp1 are shown in Fig. 6(a) and 6(b). For a variation of θp1with a fine wavelength-shift step of 0.005 nm, the loci are always obtained, and thus there is no need to delicately align a PMF when splicing, which becomes favorable for implementing the present filter.

FIG. 5. The orientation-angle loci of the waveplates as a function of dip wavelength: (a) (θh1, θq1) and (b) (θh1, θh2). These angles are obtained for a dip wavelength increasing from 1548.0 nm to 1548.8 nm over an FSR with a step of 0.005 nm, with θp1 set to 0°.

FIG. 6. Wave-plate angle loci of (a) (θh1, θq1) and (b) (θh1, θh2), for various values of θp1. The loci are obtained for a dip wavelength increasing from 1548.0 nm to 1548.8 nm over an FSR with a step of 0.005 nm.

III. CHARACTERIZATION OF OPTICAL PROPERTIES

To demonstrate continuous tunability, the filter was constructed using a fiber-pigtailed four-port PBS (OZOpticsTM), two fiber-pigtailed HWPs (OZ OpticsTM), two fiber-pigtailed QWPs (OZ OpticsTM), and two equal-length bow-tie-type PMF segments (FibercoreTM), as shown in Fig. 1. A broadband source (BBS) was amplified with a spontaneous emission source (Fiberlabs FL7701TM), and an optical spectrum analyzer (OSA) (Yokogawa AQ6370CTM)was employed to measure the transmission spectra of the filter. The calculated and measured transmission spectra are shown in Figs. 7(a)~7(d) for dip wavelengths of 1548.0,1548.2, 1548.4, and 1548.6 nm respectively. One can see that the calculated and measured transmission spectra are shifted by 0.2 nm. The insertion loss was measured as5.87 dB, which originates from the PBS, the butt-coupling of PBS and PMF2, inherent insertion losses of HWPs andQWPs, and fusion splicing of PMFs and single-mode fibers for wave-plate pigtails.

FIG. 7. Calculated (black) and measured (red) wavelength-tuned transmission spectra for various dip wavelengths of (a) 1548.0, (b) 1548.2, (c) 1548.4, and (d) 1548.6 nm.​​​​​​​

It is often desirable that comb filters have both a flattened passband and small dispersion in each passband.To validate the optical properties of the filter, further simulations were carried out. The calculated passband and its corresponding group-delay time are shown in Fig. 8(a).The 3-dB bandwidth is calculated to be 0.5125 nm, which is larger than that of a zeroth-order comb filter by 0.4 nm [18].]

FIG. 8. (a) Calculated pass band and group-delay response, (b) group-velocity dispersion and DGD over an FSR.​​​​​​​

The dispersion and differential group delay are also essential parameters for designing wavelength-selective filters in optical networks. The group-velocity dispersion is defined as the derivative of the group-delay time with respect to the wavelength, as follows:

\(D=\frac{d \tau_{g}}{d \lambda}\)      (1)

where \(\tau_{g}\)  is the group-delay time.

The differential group delay (DGD) of a device is defined as the maximum difference in group delay between all polarization states. The calculated group-velocity dispersion and DGD with each maximum value of 15.5 ps/nm and14.2 ps are shown in Fig. 8(b), which features good characteristics, compared to fiber gratings [23].

We will show in this section that forgiven orientation angles of the wave plates, the angle combinations that produce the same transmission spectrum can be deduced by the use of the Poincaré sphere. Let us consider an angle locus that covers the whole FSR, and assume that (θh1, θq1,θh2, θq2) is a point on it. The HWP1 rotates the incident light by π into a point on the equator making an angle of4θh1 with respect to the S1 axis, and thus θh1 has aperiodicity of π/2. Similarly, the HWP2 rotates the SOPcircle after PMF1 by π and locates its center at a point that is apart arc distance 4θh2, also implying a periodicity of π/2. If we assume a new angle set (θh1′, θq1′, θh2′, θq2′), these relations are expressed as follows:

\(\theta_{h 1}^{\prime}=\theta_{h 1}+\pi / 2, \theta_{h 2}^{\prime}=\theta_{n 2}+\pi / 2\)       (2)

The S1-S2 projection planes from the Poincaré sphere for multiple angle sets in a locus that result in the same transmission spectrum through the combination of the respective optical elements are depicted in Fig. 9. Suppose that point A represents the SOP after QWP1, as shown inFig. 9(a). If θq1′ = θq1 + π/2, the condition for the new SOPafter QWP1 to reach point A is such that 4θh1′is symmetric to 4θh1 with respect to 2θq1; that is, θh1′=-θh1 + θq1, as shown in Fig. 9(a).

FIG. 9. (a) QWP1 and HWP1 and (b) QWP1, HWP1, PMF1, QWP2, and HWP2 combinations. S1-S2 projection planes from the Poincaré sphere for multiple angle sets in the locus are depicted. The degeneracies are observed with respect to the combination of optical elements within the PDLC.

Meanwhile, let us consider another case for the combination of HWP1, QWP1, PMF1, HWP2, and QWP2. In Fig. 9(b), if 4θh1′ and 4θh2′ are symmetric to 4θh1 and 4θh2 with respect to 2θp1, and θq2′ = θq2 + π/2, the new angles are as follows:

\(\theta_{h 1}^{\prime}=-\theta_{h 1}+\theta_{p 1}, \theta_{q 1}^{\prime}=-\theta_{q 1}+2 \theta_{p 1}, \text { and } \theta_{q 2^{\prime}}=\theta_{q 2}+\pi / 2\)       (3)

Suppose that B and C represent the centers of circularSOPs after QWP2, whose azimuthal angles are 4θh2 - 2θp1and 4θh2′-2θp1 respectively. For the same circular SOPafter QWP2, B and C must be symmetric with respect toQWP2, and thus the relation for the orientation angles ofHWP2 and the other elements is as follows:

\(\theta_{n 2}^{\prime}=-\theta_{n 2}+\theta_{q 2}+\theta_{p 1}\)       (4)

The multiple loci obtained as explained earlier are shown in Figs. 10(a) and 10(b) for (θh1, θq1) and (θh1, θh2)respectively. Periodic gaps occur and are calculated to beθh1, θq1, and θh2 (Δθh1, Δθq1, Δθh2) as 57.2°, 45°, and 57.2°respectively. It is noteworthy that the locus at the center of the (θh1, θq1) figure consists of two opposite directional traces that are rotating CW and CCW.

FIG. 10. Periodicity of wave-plate angle loci produced by degeneracies through combinations of optical elements within the PDLC, for (a) (θh1, θq1) and (b) (θh1, θq2)

IV. CONCLUSION

We characterize the optical properties of a tunable pass-band-flattened fiber comb filter based on the PDLC, using the Poincaré-sphere representation. The flatness of the passband is checked quantitatively in the design process by visualization of the SOP through a world map.The working principle of the filter is described, and tuning performance is verified experimentally. The passband-shape design and wavelength-tuning algorithms are presented in detail. The orientation-angle loci of the wave plates, and their periodicities through the combination of the respective optical elements, are deduced using a geometrical method via the Poincaré sphere. The optical characteristics are investigated, including transmission, group-velocity dispersion, and DGD. It is found that the 3-dB bandwidth, maximum dispersion, and DGD of the filter are respectively 0.5125nm, 15.5 ps/nm, and 14.2 ps over the FSR of 0.8 nm. The characterization in this work provides a qualitative understanding of the optical properties of the fiber comb filter based on the PDLC, and this filter may find significant applications in multiwavelength optical systems.