Fiber-optic spectral polarimeter using a broadband swept laser source

Optics Communications 249 (2005) 351–356 www.elsevier.com/locate/optcom

Fiber-optic spectral polarimeter using a broadband swept laser source Eunha Kim a

a,*

, Digant Dave b, Thomas E. Milner

a

Department of Biomedical Engineering, University of Texas at Austin, 1 Texas Longhorns, Austin, TX 78712, USA b Biomedical Engineering Program, University of Texas at Arlington, Arlington, TX 76019, USA Received 17 November 2004; accepted 21 December 2004

Abstract We present a novel fiber-optic spectral polarimetry instrument based on optical frequency domain interferometry to provide measurement of the Stokes spectra of collected light. Stokes spectra are encoded into discrete channels in the time delay domain. The instrument consists of a broadband swept laser source, calibrated wavemeter, two segments of polarization maintaining (PM) fiber, an analyzer and photo-receiver. Performance of the instrument is demonstrated by reconstruction of Stokes spectra for a variety of prepared incident polarization states.
2004 Elsevier B.V. All rights reserved. PACS: 07.60; 07.60; 42.25.Ja Keywords: Polarimeters and ellipsometers; Fiber-optic instruments; Polarization

Spectra of polarization components of backscattered light have been used to characterize quantitatively the structures of living cells in biomedical science [1]. Traditional spectral polarimetric instruments utilize polarization control optics, such as adjustable combinations of a retarder and analyzer, continuously rotating polarizer/analyzer or a polarization modulator and require multiple intensity measurements associated with *

Corresponding author. Tel.: +1 5124714703; fax: +1 5124710616. E-mail address: [email protected] (E. Kim).

mechanical or electrical variation of polarization control optics in addition to spectral scanning to measure the spectrally resolved polarization state of collected light [2]. Such approaches can result in long measurement times that can hinder timeresolved measurements and may be difficult to implement with fiber systems. In this paper, we present a novel fiber-optic spectral polarimetry instrument (FOSPI) based on optical frequency domain interferometry [3] that incorporates a broadband swept laser source and a calibrated wavemeter. Although the FOSPI utilizes the principles of channeled spectropolarimetry [4], our

0030-4018/$ - see front matter
2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.12.044

352

E. Kim et al. / Optics Communications 249 (2005) 351–356

all-fiber instrument is more compact than spectral polarimetric instrumentation using bulk optics and may be easily interfaced to wide variety of samples under test. The FOSPI (Fig. 1) consists of a broadband swept laser source, calibrated wavemeter, two segments of polarization maintaining (PM PANDA) fiber spliced at 45 with respect to each other, an analyzer and photo-receiver. PM fiber is a birefringent optical waveguide that has two orthogonal axes with different refractive indices due to internal stress structures [5]. The two PM fiber segments (L1 and L2) are used as sequential linear retarders. Orthogonal oscillating field components of collected light experience different phase delays due to internal birefringence while passing through the first PM fiber segment (L1). At the 45 splice, both oscillating field components are projected equally on fast and slow axes of the second PM fiber segment (L2). Light exiting the second PM fiber segment has four field components with different phase delays depending on the propagation path and passes through an analyzer aligned with the fast axis of the first PM fiber segment. All four field components of light are projected onto the transmission axis of the analyzer and produce interference fringes with characteristic time delay (s) or optical path length difference (cs). Using the spectrally resolved Jones calculus [6] to represent light propagation in the FOSPI, out-

put intensity [Iout(m)] at optical frequency v emerging from the FOSPI is 1 1 I out ðvÞ ¼ S 0 ðmÞ þ S 1 ðmÞ cosðu2 ðmÞÞ 2 2 1 þ jS 23 ðmÞj cos ½ðu1 ðmÞ
u2 ðmÞÞ þ argðS 23 ðmÞÞ 4 1
jS 23 ðmÞj cos ½ðu1 ðmÞ þ u2 ðmÞÞ þ argðS 23 ðmÞÞ; 4 ð1Þ with S0(m), S1(m), and S23(m) = S2(m)
iS3(m) representing Stokes spectra of collected light (i.e., incident on the first PM fiber segment). The laboratory coordinate system utilized to represent the Stokes spectra is oriented so that the EarthÕs gravitational field corresponds to S1 =
1. Phase retardations of light propagating in first and second PM fiber segments are u1(m) and u2(m), respectively, 2pmðk s ðmÞ
k f ðmÞÞ L1;2 c 2pmDnðmÞ L1;2 ; ¼ c

u1;2 ðvÞ ¼

where ks(f) is wave vector of light propagating on the slow (fast) axis of the PM fiber and Dn(m) is internal birefringence of the PM fiber. Output intensity from the FOSPI [Iout(m)] is a superposition of four Stokes spectra [S0(m), S1(m), and S23(m) = S2(m)
iS3(m)] modulated at different carrier frequencies dependent on phase retardations 2.5m PM Fiber

Swept Laser Source (1520-1620nm)

5m PM Fiber 0

45 Input Polarization State Preparation Optics Wavemeter

Optical Clock signal Frequency

ADC

ð2Þ

Analyzer

Photo Receiver

Fig. 1. Schematic of fiber-optic spectral polarimetry instrument (FOSPI).

E. Kim et al. / Optics Communications 249 (2005) 351–356

(u1(m) and u2(m)) in PM fiber segments. Simple Fourier transformation of Iout(m) isolates each Stokes spectral component in the time delay (s) or optical path length difference (cs) domain. Reconstruction of the complete set of Stokes spectra [S0(m), S1(m), S2(m), and S3(m)] requires demodulation of the four Stokes spectral components. The reconstruction process must account for material and waveguide dispersion in the PM fiber that may result in chirping the carrier frequency of each Stokes spectral component. To test operation of the FOSPI, light from the broadband swept laser source (TLSA 1000, Precision Photonics, 1520–1620 nm, 0.4 mW at the spectral line width of 150 kHz, 0.4 pm (50 MHz) spectral resolution) is delivered with a single mode fiber, collimated, directed into polarization optics that allows preparation of a variety of fixed userspecified polarization states, and collected by the first segment of the PM fiber. Lengths of the two PM fiber segments in the FOSPI are fixed at L1 = 2.5 and L2 = 5 m, respectively, so that Fourier transform of the four Stokes spectral components are displaced equally in the optical path length difference domain. Output intensity from the FOSPI is coupled into a photo-receiver (New Focus, 2011) and input into a 12-bit A/D converter that acquires FOSPI data under a LabViewe software interface. A wavemeter with an integrated HCN gas cell provides a real-time digital clock that is used to trigger data acquisition for real-time

353

synchronization of output intensity (Iout) with optical frequency (m). Because material and mode dispersion in PM fiber results in phase retardations u1(m) and u2(m) that are non-linear with optical frequency, calibration is required to remove these effects in reconstruction of Stokes spectra [S0(m), S1(m), S2, and S3(m)]. Phase retardations u1(m) and u2(m) in Eq. (1) are dependent solely on the optical properties of PM fiber segments and can be calibrated by inputting light with a known polarization state into the FOSPI. Linearly polarized light at 22.5 to the horizontal with S3(m) = 0 [S23(m) = S23*(m) = S2(m)] was used to calibrate phase retardations u1(m) and u2(m). Fourier transform magnitude of Iout indicates the four Stokes spectral components are equally displaced in the optical path length difference domain (Fig. 2). Arguments (phases) of the inverse Fourier transform of first, second and third components in the positive optical path length difference domain give u2(m)
u1(m), u2(m) and u2(m) + u1(m), respectively. Calibrated phase retardations u1(m) and u2(m) obtained with linearly polarized light at 22.5 are used to reconstruct Stokes spectra for collected light with an arbitrary polarization state. After calibrating phase retardations, u1(m) and u2(m), the FOSPI was used to record and reconstruct Stokes spectra for a variety of input polarization states (Fig. 3). Although bandwidth of recorded spectra is 12.2 THz (1520–1620 nm), to

Fig. 2. (a) Output intensity [Iout] from the FOSPI versus optical frequency and (b) Fourier transform magnitude of (a) for linearly polarized incident light at 22.5 to the horizontal.

354

E. Kim et al. / Optics Communications 249 (2005) 351–356

Fig. 3. Output intensity [Iout] from FOSPI versus optical frequency and reconstructed Stokes spectra of (a) horizontally, (b) vertically, (c) right circularly, and (d) linearly polarized light at 67.5 to the horizontal.

E. Kim et al. / Optics Communications 249 (2005) 351–356

view fringes and allow comparison between different input polarization states only a small portion (190–192 THz) of the FOSPI output intensity is shown in Fig. 3A. For both horizontally and vertically polarized light, output intensities are modulated at one carrier frequency corresponding to u2(m). As seen in Figs. 3(a) and (b), respective spectral modulations are out of phase with respect to each other and allow reconstruction of Stokes spectra with sign as well as absolute magnitude. For horizontally polarized light, reconstructed normalized Stokes spectra (S1(m)/S0(m), S2(m)/ S0(m), S3(m)/S0(m)) should approach (1, 0, 0) over the source bandwidth, and the standard deviations of reconstructed normalized Stokes spectra from (1, 0, 0) are calculated as r(S1/S0) = 1.19 · 10
2, r(S2/S0) = 3.06 · 10
2, and r(S3/S0) = 2.26 · 10
2, respectively. For vertically polarized light, r(S1/S0) = 1.84 · 10
2, r(S2/S0) = 3.21 · 10
2,
2 and r(S3/S0) = 2.75 · 10 . Errors are greatest near the start and end of the frequency scan and can be attributed to a ringing effect due to abrupt frequency cut off of the swept laser source. As seen in Fig. 3(c), output intensity for right circularly polarized light are modulated at two carrier frequencies corresponding to u2(m)
u1(m) and u2(m) + u1(m). Although both S2(m) and S3(m) components are modulated at the same carrier frequency, phase offset determined by arg(S23(m) = S2(m)
iS3(m)) allows proper reconstruction of Stokes spectra according to the prepared polarization state. For right circularly polarized light, the variances of reconstructed normalized Stokes spectra from (0, 0, 1) are calculated as r(S1/S0) = 2.15 · 10
2, r(S2/S0) = 3.56 · 10
2,
2 and r(S3/S0) = 2.74 · 10 . Fig. 3(d) shows measured output intensity and reconstructed Stokes spectra for linearly (67.5 to the horizontal) polarized light. Although reconstructed Stokes spectra are in good agreement with corresponding prepared polarization states of collected light, reconstructed Stokes spectra for this case contains a nonzero S3 component (r(S3/S0) = 6.98 · 10
2). Inasmuch as S2 and S3 are encoded in the complex quantity S23 as real and imaginary components, respectively, reconstruction of S2 and S3 is more sensitive to errors in phase calibration compared to S1.

355

Although the spectral polarimetry method presented here and that reported previously in [4] is based on encoding the Stokes parameters into the time delay domain, some important differences are apparent. In both approaches, wide channel separation in the time delay domain is desirable to isolate channels. Wide yet flexible channel separation may be particularly important if additional information is encoded into the optical spectrum of light collected by the FOSPI. Channel separation is dependent on two factors: spectral resolution (Dm) of the instrument and choice of retarders. For the FOSPI reported here, channel separation is s = 3.7 ps and is set by lengths of the PM fiber segments. Maximum channel separation (smax) in the time delay domain is inversely related (smax = 1/8Dm) to the spectral resolution (Dm) of the instrument. The broadband swept laser source (Dv = 50 MHz) used here allows smax = 2.5 ns, which is 250· greater than that of an OSA with Dk = 0.1 nm. A simple criterion suggests spectral resolution of the reconstructed Stokes spectra (DmStokes) is inversely related (DmStokes  1/smax) to the channel separation (smax) in the time delay domain. Following that criterion, a spectral resolution of DmStokes = 6.4 pm in the reconstructed Stokes spectra might be achieved in the FOSPI reported here by increasing length of PM fiber segments to L1 = 2.7 km and L2 = 5.4 km. To compare, if quartz retarders are utilized, corresponding lengths (L1 = 75.6 m and L2 = 151.2 m) to achieve an equivalent spectral resolution of the reconstructed Stokes spectra (DmStokes) are impractical. When using long PM fiber segments, care must be taken to minimize variations in phase retardations (u1(m) and u2(m) in Eq. (1)) induced by environmental mechanical and thermal fluctuations. Although data reported here were repeatable and consistent and did not require isolation of the PM fiber segments, use of very long segments may require use of a thermally isolated mechanical enclosure. A novel feature of the FOSPI is that a wide yet flexible range of channel separations is possible by combining the fine spectral resolution of a broadband swept laser source with the flexibility of a PM fiber retarder system. Accurate optical frequency calibration is crucial for successful FOSPI operation, since

356

E. Kim et al. / Optics Communications 249 (2005) 351–356

Fig. 4. Effect of optical frequency sampling errors on reconstructed Stokes spectra for linearly polarized light at 45 (S1 = 0, S3 = 0). Reconstructed Stokes spectra with: (a) accurate frequency sampling; (b) uniform optical frequency offset (10 GHz); (c) random sampling error (normal deviation) with r = 10 GHz.

demodulation of each Stokes spectral component in Eq. (1) requires accurate optical frequency sampling. To demonstrate importance of accurate optical frequency sampling in reconstruction of Stokes spectra, output intensity from the FOSPI was simulated and Stokes spectra were reconstructed for linearly polarized light at 45 with a Gaussian spectral profile (Fig. 4). In Figs. 4(b) and (c), uniform offset (10 GHz) and random optical requency sampling errors (r = 10 GHz) were introduced, respectively. Magnitude of introduced optical frequency sampling errors is 0.08% of total bandwidth (12.2 THz). Uniform offset error in optical frequency sampling degrades reconstructed Stokes spectra over all spectral regions (Fig. 4(b)) and introduces a systematic error. Inaccurate or non-repeatable synchronization of intensity measurement with the optical frequency can cause this type of error in reconstruction of Stokes spectra. Random error in optical frequency sampling introduces intensity noise in reconstructed Stokes spectra despite that simulation data were intensity noise free (Fig. 4(c)). Error in optical frequency sampling is limited fundamentally by spectral width of the swept laser source and introduces intensity noise in reconstructed Stokes spectra. To our knowledge, we present for the first time an instrument using a broadband swept laser

source and PM fiber retarder system to obtain the complete set of Stokes spectra using one spectral measurement. The FOSPI can easily be incorporated into the detection path of a variety of scan-based optical imaging systems. For example, a confocal scanning microscopy system [7,8] using a broadband swept laser source can be transformed into a spectral polarimetric imaging instrument by inserting the FOSPI into the detection path. Results of ongoing studies in our laboratory investigating applications of the FOSPI in various imaging systems will be reported.

References [1] V. Backman, R. Gurjar, K. Badizadegan, I. Itzkan, R.R. Dasari, L.T. Perelman, M.S. Feld, IEEE J. Sel. Top. Quantum Electron. 5 (1999) 1019. [2] P.S. Hauge, Proc. SPIE 88 (1976) 3. [3] L. Mandel, E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press, Cambridge, England, 1995 (Chapter 4). [4] K. Oka, T. Kato, Opt. Lett. 24 (1999) 1475. [5] M. Nakazawa, M. Tokuda, N. Uchida, Opt. Lett. 8 (1983) 130. [6] C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach, Wiley, New York, 1998. [7] R.H. Webb, Rep. Prog. Phys. 59 (1996) 427. [8] S. Kimura, T. Wilson, Appl. Opt. 30 (1991) 2143.