1 Introduction

For many years, communication systems based on optical fiber were worked with concern for polarization effects such as polarization-dependent loss (PDL) [1–3], polarization-dependent gain (PDG) [2, 4], and polarization-mode dispersion (PMD) [5, 6]. PDL that two polarizations undergo different rates of loss in the fiber generates the optical power variation due to polarization fluctuations [7, 8]. PMD is one of the major problems to fiber communication systems, causing severe signal impairments and bandwidth limiting problems for long haul and high bit rate fiber transmission systems. In addition, PMD combined with PDL can accelerate the system performance degradation in comparison with their separate effects [2, 3, 9]. To mitigate polarization-related impairments, polarization scrambling that actively changes the state of polarization (SOP) using a polarization modulation method is often utilized. The polarization scrambling can be used at the transmitter as a tool for facilitating PMD measurements [10], reducing signal fluctuations due to PDG or PDL-induced intensity noises in long-haul transmission [11–14], and enhancing some PMD compensation schemes [15]. It is also applied to avoid polarization hole burning in erbium-doped fiber amplifiers [16, 17]. In the course of the signal transmission, when diverse polarization-dependent devices are required for spectral filtering [18–21] and wavelength routing [22–24], repeating optical signals [25, 26], optical signal-to-noise ratio monitoring [27], polarization-division multiplexed or microwave signal processing [28, 29], and PMD monitoring in fiber links, the SOPs of optical signals should be controlled using some in-line polarizing components or polarization attractors. In other words, the polarization-dependent wavelength-selective filters cannot be utilized in the above-mentioned optical processing of scrambled signals without a light-polarizing process. However, the polarizing process makes the light scrambling in the fiber link meaningless. In this case, an apparatus, which can perform the above operations with the depolarized nature of light maintained, is expected to increase the effectiveness of the entire transmission system.

In this paper, we propose a novel scheme that can make depolarized or unpolarized light respond to polarization-dependent optical elements such as a polarization-dependent wavelength-selective filter. A switching device to realize the proposed scheme was fabricated using a polarization beam splitter (PBS) for a polarization-diversity loop configuration (PDLC), two Faraday rotators (FRs) for irreciprocal polarization transformation, and four waveplates. The PDLC that can form a Sagnac interferometer loop with a PBS has been used for achieving input polarization independence in non-linear optical switching applications [30, 31] or wavelength switching in polarization-independent fiber comb filters [32, 33]. We could make unpolarized light selectively excite one of the two principal axes of a polarization-dependent element and its output polarization remain unpolarized, by utilizing the polarization decomposition/superposition property of the PDLC and the irreciprocity of optical Faraday rotation. The principle of operation of this switching device was theoretically analyzed through the investigation of the polarization variation of light passing through the optical elements comprising the device. Then, its polarization-selective feature was experimentally verified by employing a long-period fiber grating (LPG) inscribed on polarization-maintaining fiber (PMF), which was used as a polarization-dependent element in the polarization-diversity loop. It was confirmed from the experiments that unpolarized input light could behave like polarized one when it passed through the LPG written on PMF (PM-LPG), which had two polarization-dependent spectral dips with different resonance wavelengths. One of the two spectrally separated resonances of the PM-LPG could be freely chosen by properly controlling the waveplates contained in the proposed switching apparatus.

2 Principles of operation

Figure 1a shows a schematic diagram of the proposed apparatus that consists of a PBS for realizing a polarization-diversity loop, two FRs for irreciprocal polarization alteration, and two sets of rotatable waveplates comprised of a quarter-wave plate (QWP) and a half-wave plate (HWP) for controlling the SOP of light propagating through the polarization-diversity loop. As an exemplificative filtering device that can be used in the midst of the signal transmission, a polarization-dependent wavelength-selective device is located between the two sets of waveplates. Input light entering the PBS, which can split input light into two orthogonal polarization components or combine them into one output fiber, is decomposed into two orthogonal linearly polarized components such as linear horizontal polarization (LHP) and linear vertical polarization (LVP) ones. The LHP and LVP components that come out of ports 3 and 4 of the PBS rotate along the loop in the clockwise (CW) and counterclockwise (CCW) directions, respectively. In the proposed apparatus, one of the two principal axes of the polarization-dependent device can be chosen for excitation by properly rotating the four waveplates.

Fig. 1
figure 1

a Schematic diagram of proposed switching apparatus and b light propagation paths within proposed apparatus

Full size image

Figure 1b shows light propagation paths when input light passes through the proposed apparatus from port 1 to port 2 of the PBS. The input beam introduced into port 1 of the PBS is divided into LHP and LVP components. Let us designate horizontal and vertical axes of the PBS as x- and y-axes for convenience, respectively. The LHP component sequentially propagates through the x-axis polarizer (horizontally polarized), the FR 1, the QWP 1 (with its fast axis oriented at θ q1), the HWP 1 (with its fast axis oriented at θ h1), the polarization-dependent device as a device under test (DUT), the QWP 2 (with its fast axis oriented at θ q2), the HWP 2 (with its fast axis oriented at θ h2), the FR 2, and the x-axis analyzer (horizontally polarized), rotating along the CW path. Similarly, the LVP component travels the filter along the CCW path, propagating through the y-axis polarizer (vertically polarized), the FR 2, the HWP 2 (−θ h2 oriented), the QWP 2 (−θ q2 oriented), the DUT, the HWP 1 (−θ h1 oriented), the QWP 1 (−θ q1 oriented), the FR 1, and the y-axis analyzer (vertically polarized) in turn. F and S displayed above the waveplates indicate their fast and slow axes, respectively. In both CW and CCW paths (corresponding to LHP and LVP components, respectively), the same output spectrum is obtained in every path, except for the insertion loss (IL) difference that depends on input polarization orientation. This is supported by the mathematical formulation based on Jones matrices, which is addressed later. As the two output beams from both CW and CCW paths have orthogonal polarization states at port 2 of the PBS, the resulting output of the apparatus is obtained by the arithmetic sum of the two output spectra. Thus, there is no interference between these two output beams, and the resulting output beam is kept unpolarized only if the input beam is unpolarized. Moreover, as an arbitrary SOP can always be represented by the superposition of two bases such as LHP and LVP, the output spectrum of the apparatus becomes the power superposition of the two output spectra due to LHP and LVP input beams and thus is independent of input polarization.

Waveplates such as QWPs and HWPs are polarization controllers that can modulate the SOP of light entering the DUT. Using the combination of a QWP and a HWP, a linearly polarized input beam can be transformed into any desired SOP on the Poincare sphere. But, the use of only reciprocal polarization control devices cannot excite the same principal axis of the DUT in both the CW and the CCW paths. This is because light propagating along the two paths is directed to not port 2 but port 1 of the PBS when its SOP is aligned along the same principal axis of the DUT in both paths through the waveplates. That is, in this situation, the polarization direction of light just before the analyzer is perpendicular to the polarizing direction of the analyzer at each path. Irreciprocal polarization change can tackle this issue. An FR can rotate the polarization direction of polarized light passing through it using irreciprocal Faraday rotation. Faraday rotation is a magneto-optic effect in which the polarization plane of polarized light is caused to rotate by passage through a magneto-optic material to which an external magnetic field is applied. The rotation angle β of the FR is given by VBd where V, B, and d are the Verdet constant of the FR material, the magnetic flux density applied to the material along the direction of light propagation, and the path length where light and magnetic field interact, respectively [34]. In our apparatus, β is 45° for both the FR 1 and the FR 2. Due to the irreciprocity of the FR, the plane of polarization of light undergoing these two FRs is rotated by totally 90° in each path, regardless of the incident direction, and the polarization direction of light just before the analyzer becomes parallel to the polarization plane of the analyzer at each path in the above mentioned situation.

The theoretical discussion on the principle of operation can be facilitated through the investigation of the SOP variation during the propagation of light through the optical elements comprising the proposed apparatus. Let us assume that the FRs rotate the polarization plane of input polarization by 45° in the CW direction, i.e., −45° in the polar coordinate system, and an observer at port 3 of the PBS sees light leaving him in the CW path and approaching him in the CCW path for the determination of polarization ellipses. Figure 2a shows the variation of the SOP during the passage of light through the optical elements comprising the apparatus when the waveplates are arranged for light to propagate through the horizontal axis (x-axis) of the DUT. In the CW path, LHP from the x-axis polarizer is rotated by 45° CW by the FR 1, and the waveplate combination of the QWP 1 and the HWP 1, designated as the WPC 1 from now on, makes −45° LP return to LHP again by rotating it by 45° CCW. Then, the x-axis of the DUT is excited by linear horizontally polarized light. The SOP of light coming out of the DUT is changed into 45° LP by the waveplate combination of the QWP 2 and the HWP 2, designated as the WPC 2 from now on, with LHP rotated by 45° CCW. And, 45° LP is rotated by 45° CW by the FR 2, resulting in LHP. Finally, linear horizontally polarized light is directed into port 2 of the PBS, when meeting the analyzer. In the case of the CCW path, LVP from the y-axis polarizer is rotated by 45° CW by the FR 2, and the WPC 2 makes 45° LP become LHP by rotating it by 45° CW because the QWP 2 and the HWP 2 are reversed in comparison with those in the CW path as seen by propagation light. The following situation is identical to the case of the CW path. Linear horizontally polarized light passes through the x-axis of the DUT. As the QWP 1 and the HWP 1 are also reversed compared with those in the CW path, the output SOP of their combination (WPC 1) becomes −45° LP with the output SOP of the DUT, or LHP, rotated by 45° CW. Then, it is rotated by 45° CW by the FR 1, resulting in LVP. In the end, linear vertically polarized light is directed into port 2 of the PBS, when meeting the analyzer. In other words, if the WPC 1 and the WPC 2 are set for −45° LP and LHP to be LHP and 45° LP in the CW path, rotating input polarization by 45° CCW, respectively, propagation light can be coupled into only the x-axis of the DUT in both paths.

Fig. 2
figure 2

SOP variation during passage of light through optical elements comprising proposed apparatus when the waveplates are arranged for light to propagate through the a horizontal axis (x axis), b vertical axis (y axis), and c arbitrary axis of the DUT

Full size image

Figure 2b shows the SOP variation during the passage of light through the optical elements comprising the apparatus when the WPC 1 and the WPC 2 are set for light to propagate through only the vertical axis (y-axis) of the DUT. In the CW path, the SOP evolution before the WPC 1 is identical to that shown in the CW path of Fig. 2a, but the WPC 1 makes −45° LP become LVP by rotating it by 45° CW. Then, the y-axis of the DUT is excited by linear vertically polarized light. The SOP of light coming out of the DUT is changed into 45° LP by the WPC 2 with LVP rotated by 45° CW. The SOP evolution after the WPC 2 is the same as in the CW path of Fig. 2a, and the FR 2 output comes out of port 2 of the PBS. Similarly, in the case of the CCW path, the SOP evolution before the WPC 2 is identical to that shown in the CCW path of Fig. 2a, but the WPC 2 makes 45° LP become LVP by rotating it by 45° CCW as it is reversed compared with that in the CW path. Then, the same thing happens like the CW path with the y-axis of the DUT excited by linear vertically polarized light. The SOP of light coming out of the DUT is changed into −45° LP by the WPC 1 with LVP rotated by 45° CCW. The SOP evolution after the WPC 1 is the same as in the CCW path of Fig. 2a, and the FR 1 output comes out of port 2 of the PBS like in the case of the CW path. In short, if the WPC 1 and the WPC 2 are set for −45° LP and LVP to be LVP and 45° LP in the CW path, respectively, rotating input polarization by 45° CW, i.e., −45° CCW, propagation light can be coupled into only the y-axis of the DUT in both paths.

In particular, the proposed apparatus can make light passing through the DUT be coupled into even the arbitrary axis of the DUT, as shown in Fig. 2c. Figure 2c shows the variation of the SOP of light propagating through the DUT when the WPC 1 and the WPC 2 are set for this operation. In the CW path, the WPC 1 and the WPC 2 make −45° LP and LP with an arbitrary orientation angle of θ d become θ d -oriented LP and 45° LP through the CCW rotation of them by (45° + θ d ) and (45° − θ d ), respectively. In the CCW path, the reciprocal SOP change is occurred by them, that is, the WPC 1 and the WPC 2 transform θ d -oriented LP and 45° LP into −45° LP and θ d -oriented LP by rotating them by (45° + θ d ) and (45° − θ d ) CW, respectively. All other SOP variation mediated by the FRs and the polarizers are the same as in the above two cases shown in Fig. 2a, b. If the WPC 1 and the WPC 2 are set for −45° LP and θ d -oriented LP to be θ d -oriented LP and 45° LP in the CW path, rotating input polarization by (45° + θ d ) and (45° − θ d ) CCW, respectively, therefore, propagation light can be coupled into only the θ d -oriented axis of the DUT in both paths. In addition, when it comes to the WPC, it can be replaced with just one HWP from a theoretical point of view. In the proposed apparatus, a QWP was added to an HWP for the WPC to increase the degree of freedom in controlling the SOP in experiments. Moreover, this apparatus has a capability of unique bidirectional operation. If the apparatus makes input light introduced into port 1 of the PBS excite one of two orthogonal principal axes of the DUT, input light entering its port 2 is coupled into the other principal axis. That is, the apparatus can allow bidirectionally propagating optical signals to excite different orthogonal principal axes of the DUT according to the propagation direction. This can be readily understood through the analysis on the SOP variation with the polarizers and the analyzers shown in Fig. 2 rotated by 90°.

This physical discussion can be supported with the help of Jones matrix formulation [35]. The theoretical power transmittance t of the proposed apparatus can be obtained by using two transfer matrices T CW and T CCW, shown in (1) and (2), which indicate Jones transfer matrices when light propagates along the CW and CCW paths, respectively

$${{T}_{\text{CW}}}=\left[ \begin{matrix} 1 & 0 \\ 0 & 0 \\\end{matrix} \right]{{T}_{\text{FR2}}}\left( \frac{\pi }{4} \right){{T}_{H2}}\left( {{\theta }_{h2}} \right){{T}_{Q2}}\left( {{\theta }_{q2}} \right){{T}_{\text{DUT}}}{{T}_{H1}}\left( {{\theta }_{h1}} \right){{T}_{Q1}}\left( {{\theta }_{q1}} \right){{T}_{\text{FR1}}}\left( \frac{\pi }{4} \right)\left[ \begin{matrix} 1 & 0 \\ 0 & 0 \\\end{matrix} \right]$$
(1)
$${{T}_{\text{CCW}}}=\left[ \begin{matrix} 0 & 0 \\ 0 & 1 \\\end{matrix} \right]{{T}_{\text{FR1}}}\left( -\frac{\pi }{4} \right){{T}_{Q1}}\left( -{{\theta }_{q1}} \right){{T}_{H1}}\left( -{{\theta }_{h1}} \right){{T}_{\text{DUT}}}{{T}_{Q2}}\left( -{{\theta }_{q2}} \right){{T}_{H2}}\left( -{{\theta }_{h2}} \right){{T}_{\text{FR2}}}\left( -\frac{\pi }{4} \right)\left[ \begin{matrix} 0 & 0 \\ 0 & 1 \\\end{matrix} \right]$$
(2)

where T Q1, T Q2, T H1, and T H2 are the Jones matrices of the QWP 1, the QWP 2, the HWP 1, and the HWP 2 that have orientation angles of θ q1, θ q2, θ h1, and θ h2, respectively. T FR1, T FR2, and T DUT indicate the Jones matrices of the FR 1, the FR 2, and the DUT, respectively. The orientation angle of the DUT is assumed as 0° here. The power transmittance t can be derived from T CW and T CCW through following relations (3) and (4)

$$\left[ \begin{matrix} {{E}_{\text{out},x}} \\ {{E}_{\text{out},y}} \\\end{matrix} \right]={{T}_{\text{CW}}}\left[ \begin{matrix} {{E}_{\text{in},x}} \\ {{E}_{\text{in},y}} \\\end{matrix} \right]+{{T}_{\text{CCW}}}\left[ \begin{matrix} {{E}_{\text{in},x}} \\ {{E}_{\text{in},y}} \\\end{matrix} \right]$$
(3)
$$t = {{\left( {{{\left| {{E_{{\rm{out}},x}}} \right|}^2} + {{\left| {{E_{{\rm{out}},y}}} \right|}^2}} \right)} \mathord{\left/ {\vphantom {{\left( {{{\left| {{E_{{\rm{out}},x}}} \right|}^2} + {{\left| {{E_{{\rm{out}},y}}} \right|}^2}} \right)} {\left( {{{\left| {{E_{{\rm{in}},x}}} \right|}^2} + {{\left| {{E_{{\rm{in}},y}}} \right|}^2}} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {{{\left| {{E_{{\rm{in}},x}}} \right|}^2} + {{\left| {{E_{{\rm{in}},y}}} \right|}^2}} \right)}}\;$$
(4)

where E in,x and E in,y indicate x- and y-axis components of an input field, respectively, and E out,x and E out,y are those of an output field. It can be found by reducing (4) that the normalized output power, i.e., the transmittance t, is identical to p|T CW(1,1)|2 + q|T CCW(2,2)|2 = |T CW(1,1)|2 = |T CCW (2,2)|2 where T CW(1,1) and T CCW(2,2) are an element of T CW in row 1 and column 1 and an element of T CCW in row 2 and column 2, respectively. |T CW(1,1)|2 and |T CCW(2,2)|2 are |E out,x |2/|E in,x |2 and |E out,y |2/|E in,y |2, i.e., transmittances along the CW and CCW paths for input SOPs of LHP and LVP, and are designated as t CW and t CCW, respectively. p and q, which are determined by input polarization, indicate portions of input power coupled to the x- and y-axes of the PBS, respectively, and are real values ranging from 0 to 1 with p + q = 1 satisfied. For example, t = t CW (p = 1 and q = 0) for an input SOP of LHP, t = 0.5(t CW  + t CCW ) (p = q = 0.5) for an input SOP of 45° LP, and t = t CCW (p = 0 and q = 1) for an input SOP of LVP. The difference between p and q means the output power difference between light components propagating along the CW and CCW paths. But, the two normalized output power components, or \(\text{p}{{\text{t}}_{\text{cw}}}\ \text{and}\ \text{q}{{\text{t}}_{\text{ccw}}}\), have the same spectral shape except for the IL difference, because t CW = t CCW. Consequently, \(t\left( =\text{p}{{\text{t}}_{\text{cw}}}+\text{q}{{\text{t}}_{\text{ccw}}} \right)\) is independent of input polarization. The derived transmittance t is given as follows.

$$t=\frac{1}{4}\left( \text{a}{{\text{t}}_{x}}+\text{b}{{\text{t}}_{y}}+2c\sqrt{{{t}_{x}}{{t}_{y}}} \right)$$
(5)
$$a = \left( {\sin \theta _{{t1}} \sin \theta _{{t2}} + \sin \theta _{{t3}} \cos \theta _{{t4}} } \right)^{2} + \left( {\cos \theta _{{t2}} \cos \theta _{{t3}} + \sin \theta _{{t4}} \cos \theta _{{t1}} } \right)^{2}$$
(6)
$$b = \left( {\sin \theta _{{t1}} \sin \theta _{{t2}} - \sin \theta _{{t3}} \cos \theta _{{t4}} } \right)^{2} + \left( {\cos \theta _{{t2}} \cos \theta _{{t3}} - \sin \theta _{{t4}} \cos \theta _{{t1}} } \right)^{2}$$
(7)
$$c = - \sin ^{2} \theta _{{t1}} \sin ^{2} \theta _{{t2}} + \sin ^{2} \theta _{{t3}} \cos ^{2} \theta _{{t4}} + \cos ^{2} \theta _{{t2}} \cos ^{2} \theta _{{t3}} - \sin ^{2} \theta _{{t4}} \cos ^{2} \theta _{{t1}}$$
(8)

where t x and t y indicate the transmittances of the DUT when the DUT is excited by horizontally and vertically (x- and y-) polarized light, respectively. In transmittance coefficients a, b, and c in (6)–(8), θ t1 = 2θ h1 − θ q1 + θ q2, θ t2 = 2θ h2 + θ q1 − θ q2, θ t3 = 2θ h1 − θ q1 − θ q2, and θ t4 = 2θ h2 − θ q1 − θ q2. In this formulation, any IL of the optical components comprising the apparatus was not considered, and the phase retardation differences of the four waveplates were assumed to be independent of wavelength. If the four orientation angles of the WPC 1 and the WPC 2, or θ q1, θ h1, θ q2, and θ h2, are selected as −π/4, −π/8, 0, and π/8, respectively, t = t x , that is, the x-axis of the DUT can be selectively excited. If these angle sets are chosen as 3π/4, 5π/8, π/2, and 3π/8, the y-axis of the DUT is excited, resulting in t = t y . In particular, when θ q1, θ h1, θ q2, and θ h2 are −π/4, θ d /2 − π/8, θ d , and θ d /2 + π/8, respectively, t = [cos2 θ d (t x )1/2 + sin2 θ d (t y )1/2]2, which means that a polarization plane whose orientation angle is θ d with respect to the x-axis of the DUT can be selectively excited. This implies that the proposed apparatus can allow the incident beam to excite any arbitrary axis of the DUT whether it is polarized or unpolarized. It can also be considered that there always exists a WPC angle set that makes the principal axes of the DUT selectively illuminated even if it is arbitrarily oriented.

In this theoretical prediction, an FR was assumed to be independent of wavelength. Actually, the FR has a rotation angle of 45° at a center wavelength, and this angle slightly deviates from 45° due to the dispersion of its rotation angle as the operating wavelength moves away from the center wavelength. FRs used in our experiments are centered at 1550 nm. An angle deviation from 45° is proportional to the wavelength detuning from 1550 nm and becomes approximately ±1.5° at a wavelength detuning of 25 nm. When broadband light with a bandwidth over 50 nm is used as a light source, this rotation angle dispersion can affect the selective excitation operation of the proposed apparatus at wavelength regions far from 1550 nm in two aspects, that is, an IL and the orientation angle of the SOP of light exciting the DUT. For example, if it is assumed that the output power of the apparatus is I 0 at 1550 nm and the SOP remains unchanged during the passage of light through the DUT, this output power becomes cos2(3°)I 0 = ~0.9973I 0 at 1575 nm, resulting in an IL of ~0.012 dB. And linearly polarized light excites the DUT at ~1.5° off-axis from the original axis excited at 1550 nm.

3 Experimental results and discussion

To verify the theoretical prediction of the axis-selective excitation capability of the proposed apparatus, it was fabricated using a PBS (OZ Optics) for the implementation of the PDLC, two FRs (OZ Optics) for irreciprocal polarization transformation, and two WPCs. Each WPC is composed of a QWP (OZ Optics) and an HWP (OZ Optics). The two WPCs were placed at both ends of a DUT, or a polarization-dependent device, to control the SOP of light propagating through the polarization-diversity loop. A broadband light source (BBS) and an optical spectrum analyzer (OSA), shown in Fig. 1a, were utilized as an unpolarized light source with a low degree of polarization (DOP) and a spectrum monitoring instrument, respectively. The resolution bandwidth of the OSA (Yokogawa AQ6370C) was 0.02 nm in the experiments. A PM-LPG with a spectral PDL was employed as the DUT for checking the selective excitation performance of the fabricated apparatus. A PM-LPG is an LPG inscribed on PMF, and its principal axes are the same as those of PMF in which the grating is written. As the phase matching condition of the PM-LPG is dependent on input polarization, it has different resonance dips according to input polarization, acting as a narrow band polarizer at resonance wavelengths [36].

Figure 3 shows the transmission spectra of the PM-LPG, measured by using polarized light without the fabricated apparatus or using unpolarized light with the PM-LPG contained in the fabricated apparatus. Figure 3a shows the transmission spectra of the PM-LPG with various band rejection ratios (BRRs) at two different resonance wavelengths, i.e., ~1521.76 nm (λ 1) and ~1543.07 nm (λ 2). The BRR of the PM-LPG depends on the input SOP controlled by a polarization control instrument (Agilent 8169 A). That is, its BRR is modulated according to the coupling ratio of input light into its two principal axes. If one of the two principal axes is excited, one of the two resonance dips with the maximum BRRs is chosen. On the contrary, when input light is totally coupled into the other principal axis, the other resonance dip is picked. For the selected input SOPs, BRRs of 10 and 20 dB and the maximum BRR could be obtained at each resonance wavelength. At two orthogonal input SOPs, the two resonance dips with the maximum BRRs of ~26.3 and ~24.4 dB at λ 1 and λ 2, indicated as red inverted triangles and blue squares, respectively, could be found. This resonance dip switching in the PM-LPG can be realized using only polarized light. In case of unpolarized light, this spectral switching is impossible, and it just has a BRR of less than 3 dB at both resonance wavelengths (λ 1 and λ 2) as the optical power of input light is equally coupled into its two principal axes. The IL of the transmission spectra mainly comes from that of the polarization control instrument (~6.5 dB) and that of the PM-LPG (~3.8 dB), which includes the fusion splicing loss between PMF and single-mode fiber (SMF).

Fig. 3
figure 3

Transmission spectra of PM-LPG measured using a polarized light without fabricated apparatus and b unpolarized light with it contained in fabricated apparatus

Full size image

Figure 3b shows the transmission spectra of the fabricated apparatus that contains the PM-LPG as the DUT, which are measured by using unpolarized light. Likewise in the case of Fig. 3a, wavelength-dependent loss spectra with various BRRs are shown at two different resonance wavelengths (λ 1 and λ 2). Amplified spontaneous emission (ASE) light from the BBS (Fiberlabs FL7701) was used as nearly unpolarized input light with a DOP of ~2.5%. For the selected orientation angle sets of the WPC 1 and the WPC 2, or (θ q1, θ h1) and (θ q2, θ h2), BRRs of 10 and 20 dB and the maximum BRR could be obtained at each resonance wavelength. The maximum BRR (~24.1 dB) at λ 1 was attained when (θ q1, θ h1) and (θ q2, θ h2) were (162°, 345°) and (48°, 353°), respectively. In the case of λ 2, the maximum BRR (~24.7 dB) was achieved at (θ q1, θ h1) = (154°, 20°) and (θ q2, θ h2) = (28°, 29°).

The resonance dip with the maximum BRR at λ 1 or λ 2, indicated as red inverted triangles or blue squares, respectively, is obtained only if input light is coupled into one of the two principal axes of the PM-LPG. Thus, these two resonance dips with maximum BRRs prove that even unpolarized light can selectively excite one of the two principal axes of the PM-LPG even if its azimuth is randomly oriented. The resonance dips without the maximum BRR can also be explained using this selective excitation capability. As mentioned earlier in the theoretical analysis, arbitrarily polarized or even unpolarized light is decomposed into two polarization components such as LHP and LVP ones after passing through the PBS. Through the proper control of the WPC 1 and the WPC 2, these two components can be made to align along the same specific axis of the PM-LPG before going through it. If this specific axis is one of the two principal axes, that is, the difference between optical powers coupled into them is maximized, the BRR is also maximized. Meanwhile, if this optical power difference is minimized, so is the BRR. Thus, a lower BRR implies that the selected specific axis is more distant from the principal axes. The BRRs measured in the PM-LPG contained in the fabricated apparatus slightly deviate from those of the PM-LPG only, which seems to result from the finite polarization extinction ratio (PER) and the imperfect power splitting ratio of the PBS and the weak form birefringence of SMF used for connecting optical components comprising the apparatus. The IL of the transmission spectra originates from the ILs of the two FRs (~1.08 and ~0.92 dB), the two WPCs (~1.01 and ~1.21 dB), the PBS (~1.02 dB for one way, totally ~2.04 dB), and the PM-LPG (~3.8 dB).

To investigate the long-term stability of the output spectra of the fabricated apparatus, shown in Fig. 3b, two resonance dips with a BRR of 20 dB at λ 1 and λ 2 were monitored for an hour with an interval of 4 min, as shown in Fig. 4a, b, respectively. During the measurement period, the maximum level and wavelength fluctuations of the resonance dips were measured as ~0.79 dB and ~0.17 nm, respectively. These fluctuations seem to be caused from a slight change in the grating phase-matching condition due to the sensitivity of birefringence in PMF used in the fabrication of the PM-LPG to environmental perturbations. In particular, in level and wavelength fluctuation measurements done for the PM-LPG itself, there was no notable difference in comparison with the above results. Hence, it is regarded that the proposed structure has little effect on its output spectra in case of external disturbance being applied to it. However, in SMF concatenating the optical elements of the apparatus, a temperature-induced change in inherent birefringence or temperature-induced microbending may vary the SOP of light that travels along the polarization-diversity loop of the apparatus. If the ambient temperature variation is within 1–2 °C, this temperature-induced effect will be negligible, but large temperature changes over 10 °C or more can significantly deteriorate the switching operation. In order to protect the fabricated apparatus from environmental temperature perturbations for operation stability, therefore, the SMF segments used in the apparatus should be hermetically sealed except for lead-in and lead-out fibers, or a thermoelectric cooler may be utilized for more robust operation.

Fig. 4
figure 4

Long-term stability of output of fabricated apparatus with PM-LPG contained as DUT, measured for resonance dips at (a) λ 1 and (b) λ 2

Full size image

Moreover, in order to check the DOP of the output of the fabricated apparatus, the polarization extinction of the output of the fabricated apparatus was measured at two WPC sets where the maximum BRRs were obtained, by placing a rotatable linear polarizer followed by a photodetector at port 2 of the PBS instead of the OSA. The DOP was evaluated by using the relation (P max  − P min )/(P max  + P min ) where P max and P min are maximum and minimum power values measured at the photodetector, respectively. The DOPs of the two resonance dips with the maximum BRRs at λ 1 and λ 2 were measured as ~8.9 and ~6.1%, respectively. Although these DOP values were higher than that of the BBS used in our experiments, sufficiently low DOP values, lower than 10%, could be obtained as expected in the above theoretical prediction. In comparison with the DOP of ASE light, this DOP increase is inferred to mainly come from the non-ideal polarization beam splitting of the PBS with the limited PER.

4 Conclusions

In summary, we propose a switching apparatus that can make unpolarized light respond to polarization-dependent optical elements and further exploit their polarization-dependent optical properties such as spectral PDL or PDG as needed by selectively exciting their principal axes. The principle of operation of the proposed apparatus was theoretically analyzed by investigating the SOP variation of light propagating through the optical components comprising the apparatus. For the experimental verification of the predicted polarization-selective feature of the apparatus, it was fabricated by using a PBS, two FRs, two QWPs and two HWPs, and a PM-LPG, which had polarization-dependent spectral dips with different resonance wavelengths, was utilized as the polarization-dependent element. Experimental results showed that we could make unpolarized light be coupled into only one of the two principal axes of the PM-LPG and its output light remain unpolarized by utilizing the polarization decomposition/superposition property of a polarization-diversity loop and the irreciprocity of optical Faraday rotation. Consequently, it was theoretically and experimentally confirmed that unpolarized input light could be made to be sensitive to the polarization-dependent device, while maintaining its unpolarization nature with the help of the proposed apparatus. It is expected that the proposed apparatus can facilitate the use of polarization-dependent optical devices with a variety of spectral filtering and routing capabilities in long-distance optical fiber links with random PMD. Moreover, the proposed apparatus coupled with a polarization-dependent filter [18, 36, 37] can be beneficially utilized to generate bidirectional optical signals that have different spectral contents or provide a bidirectional filtering with different wavelength-selective properties according to the propagation direction.