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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 21 — Oct. 21, 2013
  • pp: 24566–24573
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Linear photonic frequency discriminator on As2S3-ring-on-Ti:LiNbO3 hybrid platform

Jaehyun Kim, Won Ju Sung, Ohannes Eknoyan, and Christi K. Madsen  »View Author Affiliations


Optics Express, Vol. 21, Issue 21, pp. 24566-24573 (2013)
http://dx.doi.org/10.1364/OE.21.024566


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Abstract

We report a photonic frequency discriminator built on the vertically integrated As2S3-ring-on-Ti:LiNbO3 hybrid platform. The discriminator consists of a Mach Zehnder interferometer (MZI) formed by the optical path length difference (OPD) between polarization modes of Ti-diffused waveguide on LiNbO3 substrate and a vertically integrated As2S3 race-track ring resonator on top of the substrate. The figures of merit of the device, enhancement of the signal-to-3rd order intermodulation distortion (IMD3) power ratio and corresponding 3rd order intercept point (IP3) over a traditional MZI, are demonstrated through device characterization.

© 2013 Optical Society of America

1. Introduction

In this paper, we present the design, fabrication and characterization of a photonic frequency discriminator utilizing a birefringent MZI and an As2S3 race-track, long feedback path resonator [11

11. Y. Zhou, X. Xia, W. T. Snider, J. Kim, Q. Chen, W. C. Tan, and C. K. Madsen, “Two-Stage Taper Enhanced Ultra-High Q As2S3 Ring Resonator on LiNbO3,” IEEE Photon. Technol. Lett. 23(17), 1195–1197 (2011). [CrossRef]

, 12

12. M. E. Solmaz, D. B. Adams, W. C. Tan, W. T. Snider, and C. K. Madsen, “Vertically integrated As2S3 ring resonator on LiNbO3,” Opt. Lett. 34(11), 1735–1737 (2009). [CrossRef] [PubMed]

]. for which FSR is comparable to the bandwidth (BW) of the discriminator. Unlike the RAMZI filter, the BW of the discriminator is solely determined by the long path ring resonator, as it has relaxed design and fabrication tolerances on the MZI. The device is electrically tunable using high electro-optic coefficients of the LiNbO3 substrate. The impact of linearized ramp on distortion, particularly for IMD3 will be demonstrated through characterization of the fabricated devices.

2. Operating Principle

Figure 1(a)
Fig. 1 (a) Schematic of the linear frequency discriminator and (b) intensity response for bar state of the discriminator with C = 0.87 and ϕ0 = π/2 versus frequency normalized to one FSR of the APF. The nonlinear relative phase between the two arms results in the linear intensity ramp.
shows a schematic of the discriminator. The intensity ramp for frequency discrimination is formed by interference of the MZI, which is dependent on the relative phase between the two arms. An ideal ring resonator is an all-pass filter (APF) which has a unity gain but induces a nonlinear phase advance, ϕNL. The interference pattern is then determined by Δϕ = ϕNL0, where ϕ0 is the initial phase of the MZI. The OPD of the MZI is so small that the FSR of the MZI (FSRMZI) is much wider than that of the APF (FSRAPF). Under this condition, ϕ0 is considered to be constant over one FSRAPF and the ramp is formed as ϕNL sweeps a full-2π range. The transfer matrix of the discriminator is written as
H¯¯=12[1jj1][HAPF00exp(jφ0)][1jj1],HAPF=tγexp(jβL)1tγexp(jβL)
(1)
where t2 = 1-C, γ = exp(-αL), β is the propagation constant of the ring waveguide, L is the ring circumference, C is the power coupling ratio between the ring and bus waveguide, and αL is the ring roundtrip loss (RTL) [13

13. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, Wiley series in microwave and optical engineering (John Wiley, 1999).

]. The matrix element H11 and H21 represent the transfer function for the bar and cross state of the discriminator, respectively. The relative phase between the two arms with ϕ0 = π/2 and the corresponding intensity of the bar state with C = 0.87 is plotted in Fig. 1(b). The intensity ramp is fit to be a linear line for which slope is 3/2 × FSRAPF. This corresponds to a discriminator with a BW of 2/3 × FSRAPF.

3. Design and Fabrication

Figure 2
Fig. 2 Schematic of the As2S3 ring-on-Ti:LiNbO3 frequency discriminator
shows a schematic of the discriminator built on the As2S3-ring-on-Ti:LiNbO3 platform. Titanium diffusion on an x-cut, y-propagation LiNbO3 substrate (Ti:LiNbO3) creates a graded index waveguide for which mode field diameter is comparable to that of a standard single-mode fiber, minimizing fiber coupling loss as low as 0.5 dB/facet [11

11. Y. Zhou, X. Xia, W. T. Snider, J. Kim, Q. Chen, W. C. Tan, and C. K. Madsen, “Two-Stage Taper Enhanced Ultra-High Q As2S3 Ring Resonator on LiNbO3,” IEEE Photon. Technol. Lett. 23(17), 1195–1197 (2011). [CrossRef]

]. High birefringence between the quasi-TE and quasi-TM mode of the waveguide also provides an OPD and corresponding ϕ0 of the MZI. However, implementing a ring resonator with the Ti:LiNbO3 waveguide is not trivial due to relatively large bending loss of a weakly-guiding diffused waveguide. Vertical integration of a high-index-contrast As2S3 ridge waveguide on LiNbO3 enables an APF with low roundtrip loss [11

11. Y. Zhou, X. Xia, W. T. Snider, J. Kim, Q. Chen, W. C. Tan, and C. K. Madsen, “Two-Stage Taper Enhanced Ultra-High Q As2S3 Ring Resonator on LiNbO3,” IEEE Photon. Technol. Lett. 23(17), 1195–1197 (2011). [CrossRef]

]. Another important feature of the hybrid platform is polarization-selective coupling between the waveguides. Owing to the high birefringence, only the TM mode of the bus waveguide couples with the ring resonator and hence experiences ϕNL, while the TE mode propagates through the bus waveguide without interacting with the vertically integrated ridge waveguide. This is equivalent to an MZI with an APF on only one arm.

A simulation (FIMMWAVE mode solver) result suggests that the effective index of a 3.5 μm-wide, 0.47 μm-thick As2S3 ridge waveguide covered with SiO2 cladding is nTM = 2.2144. A 17 mm-long feedback path corresponds to an FSR of 7.25 GHz at C band. The effective index of each polarization mode for the bus waveguide is calculated to be nTE = 2.1402 and nTM = 2.2114, respectively. Relatively high coupling ratio between the two asymmetric bus and ring waveguides, required for a linear ramp shown in Fig. 1(b), is achieved by two back-to-back, two-stage taper enhanced adiabatic couplers [11

11. Y. Zhou, X. Xia, W. T. Snider, J. Kim, Q. Chen, W. C. Tan, and C. K. Madsen, “Two-Stage Taper Enhanced Ultra-High Q As2S3 Ring Resonator on LiNbO3,” IEEE Photon. Technol. Lett. 23(17), 1195–1197 (2011). [CrossRef]

, 14

14. X. Xia, Y. Zhou, and C. K. Madsen, “Analysis of As2S3-Ti: LiNbO3 Taper Couplers Using Supermode Theory,” Optics and Photonics Journal 2, 344–351 (2012). [CrossRef]

].

With this polarization-selective ring resonator, the simplest form of the discriminator is to rotate the chip by 45þ with respect to the input polarization as a traditional bulk birefringent crystal discriminator [1

1. I. P. Kaminow, “Balanced optical discriminator,” Appl. Opt. 3(4), 507–510 (1964). [CrossRef]

, 2

2. S. E. Harris, “Coversion of FM light to AM light using birefringent crystals,” Appl. Phys. Lett. 2(3), 47–49 (1963). [CrossRef]

]. Taking the polarization dependent loss (PDL) of the waveguides into account, however, the input rotation angle needs to be adjustable. A wave plate can be cascaded on either side of the chip as a polarization coupler. The TE↔TM coupling ratio can be tuned by rotating the input wave plate. Another approach is to implement electro-optically tunable, on-chip polarization couplers as shown in Fig. 2. An interdigital polarization coupler utilizing r51 of the elector-optic tensor of LiNbO3 [15

15. R. C. Alferness and L. L. Buhl, “High-speed waveguide electro-optic polarization modulator,” Opt. Lett. 7(10), 500–502 (1982). [CrossRef] [PubMed]

] with 21.5um × 250 perturbation periods is used, for which 3-dB bandwidth is calculated to be 560 GHz. The two polarization couplers are separated by 2.4 cm and corresponding FSRMZI is approximately 175 GHz at C band, which is 24 times wider than FSRAPF. The central frequency of the discriminator can be tuned by the phase retarder.

Simulated intensity response of the discriminator with FSRMZI = 24 × FSRAPF is plotted for a half FSRMZI in Fig. 3(a)
Fig. 3 Calculated intensity response of the discriminator versus frequency normalized to the FSR of the MZI: (a) The linear intensity ramp is formed at phase quadrature of the MZI. (b) RTL (γ = 1dB) creates intensity envelope associated with non-uniform ring response and, (c) Ring both with RTL(γ = 1dB) and pole-zero phase difference [17] (∠p-∠z = π/50) result in asymmetric complementary outputs.
. The linear-intensity discriminator appears at phase quadrature (ϕ0 = π/2) of the MZI. Balanced detection [16

16. J. M. Wyrwas and M. C. Wu, “Dynamic Range of Frequency Modulated Direct-Detection Analog Fiber Optic Links,” J. Lightwave Technol. 27(24), 5552–5562 (2009). [CrossRef]

] is possible by using two complementary TE/TM outputs. Figure 3 also shows the effect of non-idealities of the ring resonator. An actual ring resonator has RTL mainly due to the rough sidewall of the ridge waveguide and radiation upon ring-bus coupling. Figure 3(b) illustrates the transfer function of the discriminator in the presence of 1 dB of RTL. A ring resonator with RTL deviates from ideal all-pass behavior as it has a notch on the intensity response at resonance. Due to this non-uniform intensity response of the APF with RTL, the MZI cannot make complete interference between the two arms. As the result, the envelope corresponding to FSRMZI is formed on the output as shown in Fig. 3(b). Despite the intensity envelope, two TE/TM complementary outputs are still symmetric at phase quadrature and hence balanced detection is still possible. If the ring with RTL also has a pole-zero phase difference, the ring shows an asymmetric spectral response [17

17. M. E. Solmaz, Y. Zhou, and C. K. Madsen, “Modeling asymmetric resonances using an optical filter approach,” J. Lightwave Technol. 28(20), 2951–2955 (2010). [CrossRef]

]. This, in turn, results in the asymmetric TE/TM complementary outputs as shown in Fig. 3(c), which produces non-zero even-order distortions even with a balanced detector.

4. Device characterization

We fabricated two samples. Sample #1 is a ring resonator built on a 2 cm-long chip and sample #2 is a ring resonator integrated with two polarization couplers and a phase shifter on a 4 cm-long chip. The wavelength-swept Jones matrix of a device-under-test (DUT) is measured with an optical vector network analyzer (OVNA). However, as shown in Fig. 5
Fig. 5 Experimental setup: The Jones matrix measured with OVNA is a cascade of I/O fiber pigtails and DUT.
, the Jones matrix measured by OVNA is the transfer matrix of a DUT cascaded with I/O fibers which induces random polarization. The fiber-induced random polarization is removed by a DUT Jones matrix extraction algorithm [19

19. J. Kim, D. B. Adams, and C. K. Madsen, “Device-Under-Test Jones Matrix Extraction Algorithm With Device TE/TM Reference Frame,” IEEE Photon. Technol. Lett. 24(1), 88–90 (2012). [CrossRef]

]. Once the TE/TM-resolved transfer matrix of the DUT is found, we multiplied the Jones matrix of a half wave plate on either side of the transfer matrix to find the optimized rotation angle for the input wave plate. Assuming TM mode input, the transfer function for each output polarization is
(HTEHTM)=R(π/8)JDUTR(θ)(01)whereR(θ)=(cos2θsin2θsin2θcos2θ)
(2)
where the subscripts denote the output polarization. Figure 6
Fig. 6 Measured intensity response of TM-to-TM and TM-to-TE transfer function of sample #1.
shows the measured intensity transfer function of sample #1 with θ = 14.7þ. See Appendix for more detailed transfer function measurement procedure.

δIP3=8f1f2|X1|/|X3|
(5)

The two tones are at f1 = 1 GHz and f2 = 1.005 GHz and corresponding IMD3 frequencies are 2f2-f1 = 1.01GHz and 2f1-f2 = 0.995 GHz. Figure 7(a)
Fig. 7 Complex constant ratio (a) versus optical bias frequency with f1 = 1 GHz modulation frequency and (b) versus modulation frequency biased at λc = 1560.117 nm: The discriminator can be biased at λ = 1560.117 nm with balanced detection to maximize the ratio. The ratio for a MZI discriminator is also shown for comparison.
shows |X1|/|X3| versus optical bias frequency for sample #1. That of an MZI discriminator with a BW of 5 GHz is also plotted for comparison. Although each of the two complementary discriminators has the peak complex constant ratio at different bias frequencies, the ratio is maximized at fc = 192.16019 THz (λc = 1560.117nm) with a balanced detector. The corresponding signal-to-IMD3 power ratio at δ = 0.1 GHz is 71.4 dB, and δIP3 is 6.09 GHz, which correspond to 5 dB and 1.5GHz improvement over a baseline MZI discriminator, respectively. Figure 7(b) shows |X1|/|X3| versus modulation frequency of the discriminator biased at fc.

We measured the transfer function of sample #2 which has on-chip polarization couplers. Although a linearized ramp is formed, the RTL of the ring resonator is measured to be as high as 6.2 dB, which results in IMD3 even worse than a MZI discriminator. The difference between the two samples is that sample #1 is aligned with a projection printer whereas sample #2 is exposed under a contact aligner during As2S3 lithography process, which affected the sidewall quality of the As2S3 ridge waveguide. This, in turn, results in a higher propagation loss and coupling radiation than sample #1. The measured transfer function of sample #2 is shown in Fig. 8
Fig. 8 Intensity response of the sample #2 with on-chip I/O polarization couplers: The driving voltage applied to each polarization coupler is Vin = 10V and Vout = 20 V, respectively.
. Despite the high RTL, feasibility of the design is shown by the sample.

5. Conclusion

A linear photonic discriminator built on the As2S3-Ti:LiNbO3 hybrid platform has been demonstrated. The Ti:LiNbO3 birefringent waveguide enables electro-optical tuning and offers design flexibility. The narrow FSR of the APF is achieved by the long race-track As2S3 resonator. A two-tone test shows that δIP3 increased by 1.5 GHz and IMD3 is improved by 5 dB compared to a traditional MZI discriminator at 1GHz modulation frequency.

Although the fabricated discriminator has a BW of 5GHz, discriminators with wider BWs can be achieved by reducing ring circumference. This will enhance the linearity of the discriminator because smaller ring is expected to have reduced RTL. Therefore, the device is highly feasible with integrated photonics.

6. Appendix

The Jones matrix of the ring resonator extracted by an algorithm [19

19. J. Kim, D. B. Adams, and C. K. Madsen, “Device-Under-Test Jones Matrix Extraction Algorithm With Device TE/TM Reference Frame,” IEEE Photon. Technol. Lett. 24(1), 88–90 (2012). [CrossRef]

] is a complete transfer function which includes both of the magnitude and phase response. A time domain plot of the ring resonator is obtained by a Fourier transform of the matrix element J22. Figure 9(a)
Fig. 9 (a) Measured impulse response of the ring resonator and one of the three window functions: Flat-top Gaussian windows are used to separate each pulse. (b) Schematic of the coupling region
is the time domain plot for sample #1. The impulse response of the long feedback path resonator includes a train of pulses delayed by each roundtrip as well as noise components such as Fresnel reflection on either facet, white noise, and fan noise from the equipment. The complete impulse response of the ring resonator in the time domain is
hAPF=n=1hn
(6)
The transfer function of an APF is the sum of an infinite geometric series. The constant ratio of the series is found by using the relation between each pulse shown in Fig. 9(b). The complete transfer function of the measured ring resonator is then
HAPF=HBB+γ˜HBAHAB1γ˜HAA=H1+H21H3/H2
(7)
where H1, H2 and H3 are the Fourier transform of h1, h2 and h3, respectively. The first three pulses are separated by three different window functions which truncate all other parts of the impulse response than each pulse. This will also truncate most noise components. Equation (7) is a complete noise-free transfer function of the IIR ring resonator because it is not limited by the finite time window set by OVNA. The frequency resolution required for the numerical two-tone test is achieved by zero-padding to each window function. Using Eq. (7), non-idealities such as ring roundtrip loss and pole-zero phase difference can be directly calculated.

References and links

1.

I. P. Kaminow, “Balanced optical discriminator,” Appl. Opt. 3(4), 507–510 (1964). [CrossRef]

2.

S. E. Harris, “Coversion of FM light to AM light using birefringent crystals,” Appl. Phys. Lett. 2(3), 47–49 (1963). [CrossRef]

3.

W. V. Sorin, K. W. Chang, G. A. Conrad, and P. R. Hernday, “Frequecy-domain analysis of an optical FM discriminator,” J. Lightwave Technol. 10(6), 787–793 (1992). [CrossRef]

4.

G. Chen, J. U. Kang, and J. B. Khurgin, “Frequency discriminator based on ring-assisted fiber Sagnac filter,” IEEE Photon. Technol. Lett. 17(1), 109–111 (2005). [CrossRef]

5.

X. B. Xie, J. Khurgin, J. Kang, and F. S. Choa, “Ring-assisted frequency discriminator with improved linearity,” IEEE Photon. Technol. Lett. 14(8), 1136–1138 (2002). [CrossRef]

6.

T. E. Darcie, J. Y. Zhang, P. F. Driessen, and J. J. Eun, “Class-B microlwave-photonic link using optical frequency modulation and linear frequency discriminators,” J. Lightwave Technol. 25(1), 157–164 (2007). [CrossRef]

7.

P. F. Driessen, T. E. Darcie, and J. Y. Zhang, “Analysis of a Class-B Microwave-Photonic Link Using Optical Frequency Modulation,” J. Lightwave Technol. 26(15), 2740–2747 (2008). [CrossRef]

8.

D. Marpaung, C. Roeloffzen, A. Leinse, and M. Hoekman, “A photonic chip based frequency discriminator for a high performance microwave photonic link,” Opt. Express 18(26), 27359–27370 (2010). [CrossRef] [PubMed]

9.

J. M. Wyrwas, R. Peach, S. Meredith, C. Middleton, M. S. Rasras, K.-Y. Tu, M. P. Earnshaw, F. Pardo, M. A. Cappuzzo, E. Y. Chen, L. T. Gomez, F. Klemens, R. Keller, C. Bolle, L. Zhang, L. Buhl, M. C. Wu, Y. K. Chen, and R. DeSalvo, “Linear phase-and-frequency-modulated photonic links using optical discriminators,” Opt. Express 20(24), 26292–26298 (2012). [CrossRef] [PubMed]

10.

M. S. Rasras, Y. K. Chen, K. Y. Tu, M. P. Earnshaw, F. Pardo, M. A. Cappuzzo, E. Y. Chen, L. T. Gomez, F. Klemens, B. Keller, C. Bolle, L. Buhl, J. M. Wyrwas, M. C. Wu, R. Peach, S. Meredith, C. Middleton, and R. DeSalvo, “Reconfigurable Linear Optical FM Discriminator,” IEEE Photon. Technol. Lett. 24(20), 1856–1859 (2012). [CrossRef]

11.

Y. Zhou, X. Xia, W. T. Snider, J. Kim, Q. Chen, W. C. Tan, and C. K. Madsen, “Two-Stage Taper Enhanced Ultra-High Q As2S3 Ring Resonator on LiNbO3,” IEEE Photon. Technol. Lett. 23(17), 1195–1197 (2011). [CrossRef]

12.

M. E. Solmaz, D. B. Adams, W. C. Tan, W. T. Snider, and C. K. Madsen, “Vertically integrated As2S3 ring resonator on LiNbO3,” Opt. Lett. 34(11), 1735–1737 (2009). [CrossRef] [PubMed]

13.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, Wiley series in microwave and optical engineering (John Wiley, 1999).

14.

X. Xia, Y. Zhou, and C. K. Madsen, “Analysis of As2S3-Ti: LiNbO3 Taper Couplers Using Supermode Theory,” Optics and Photonics Journal 2, 344–351 (2012). [CrossRef]

15.

R. C. Alferness and L. L. Buhl, “High-speed waveguide electro-optic polarization modulator,” Opt. Lett. 7(10), 500–502 (1982). [CrossRef] [PubMed]

16.

J. M. Wyrwas and M. C. Wu, “Dynamic Range of Frequency Modulated Direct-Detection Analog Fiber Optic Links,” J. Lightwave Technol. 27(24), 5552–5562 (2009). [CrossRef]

17.

M. E. Solmaz, Y. Zhou, and C. K. Madsen, “Modeling asymmetric resonances using an optical filter approach,” J. Lightwave Technol. 28(20), 2951–2955 (2010). [CrossRef]

18.

W. T. Snider, D. D. Macik, and C. K. Madsen, “Electro-Optically Tunable As2S3 Mach-Zehnder Interferometer on LiNbO3 substrate,” IEEE Photon. Technol. Lett. 24(16), 1415–1417 (2012). [CrossRef]

19.

J. Kim, D. B. Adams, and C. K. Madsen, “Device-Under-Test Jones Matrix Extraction Algorithm With Device TE/TM Reference Frame,” IEEE Photon. Technol. Lett. 24(1), 88–90 (2012). [CrossRef]

OCIS Codes
(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems
(060.2630) Fiber optics and optical communications : Frequency modulation
(060.5060) Fiber optics and optical communications : Phase modulation
(130.3120) Integrated optics : Integrated optics devices
(060.5625) Fiber optics and optical communications : Radio frequency photonics

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: August 6, 2013
Revised Manuscript: September 21, 2013
Manuscript Accepted: September 23, 2013
Published: October 7, 2013

Citation
Jaehyun Kim, Won Ju Sung, Ohannes Eknoyan, and Christi K. Madsen, "Linear photonic frequency discriminator on As2S3-ring-on-Ti:LiNbO3 hybrid platform," Opt. Express 21, 24566-24573 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-24566


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References

  1. I. P. Kaminow, “Balanced optical discriminator,” Appl. Opt.3(4), 507–510 (1964). [CrossRef]
  2. S. E. Harris, “Coversion of FM light to AM light using birefringent crystals,” Appl. Phys. Lett.2(3), 47–49 (1963). [CrossRef]
  3. W. V. Sorin, K. W. Chang, G. A. Conrad, and P. R. Hernday, “Frequecy-domain analysis of an optical FM discriminator,” J. Lightwave Technol.10(6), 787–793 (1992). [CrossRef]
  4. G. Chen, J. U. Kang, and J. B. Khurgin, “Frequency discriminator based on ring-assisted fiber Sagnac filter,” IEEE Photon. Technol. Lett.17(1), 109–111 (2005). [CrossRef]
  5. X. B. Xie, J. Khurgin, J. Kang, and F. S. Choa, “Ring-assisted frequency discriminator with improved linearity,” IEEE Photon. Technol. Lett.14(8), 1136–1138 (2002). [CrossRef]
  6. T. E. Darcie, J. Y. Zhang, P. F. Driessen, and J. J. Eun, “Class-B microlwave-photonic link using optical frequency modulation and linear frequency discriminators,” J. Lightwave Technol.25(1), 157–164 (2007). [CrossRef]
  7. P. F. Driessen, T. E. Darcie, and J. Y. Zhang, “Analysis of a Class-B Microwave-Photonic Link Using Optical Frequency Modulation,” J. Lightwave Technol.26(15), 2740–2747 (2008). [CrossRef]
  8. D. Marpaung, C. Roeloffzen, A. Leinse, and M. Hoekman, “A photonic chip based frequency discriminator for a high performance microwave photonic link,” Opt. Express18(26), 27359–27370 (2010). [CrossRef] [PubMed]
  9. J. M. Wyrwas, R. Peach, S. Meredith, C. Middleton, M. S. Rasras, K.-Y. Tu, M. P. Earnshaw, F. Pardo, M. A. Cappuzzo, E. Y. Chen, L. T. Gomez, F. Klemens, R. Keller, C. Bolle, L. Zhang, L. Buhl, M. C. Wu, Y. K. Chen, and R. DeSalvo, “Linear phase-and-frequency-modulated photonic links using optical discriminators,” Opt. Express20(24), 26292–26298 (2012). [CrossRef] [PubMed]
  10. M. S. Rasras, Y. K. Chen, K. Y. Tu, M. P. Earnshaw, F. Pardo, M. A. Cappuzzo, E. Y. Chen, L. T. Gomez, F. Klemens, B. Keller, C. Bolle, L. Buhl, J. M. Wyrwas, M. C. Wu, R. Peach, S. Meredith, C. Middleton, and R. DeSalvo, “Reconfigurable Linear Optical FM Discriminator,” IEEE Photon. Technol. Lett.24(20), 1856–1859 (2012). [CrossRef]
  11. Y. Zhou, X. Xia, W. T. Snider, J. Kim, Q. Chen, W. C. Tan, and C. K. Madsen, “Two-Stage Taper Enhanced Ultra-High Q As2S3 Ring Resonator on LiNbO3,” IEEE Photon. Technol. Lett.23(17), 1195–1197 (2011). [CrossRef]
  12. M. E. Solmaz, D. B. Adams, W. C. Tan, W. T. Snider, and C. K. Madsen, “Vertically integrated As2S3 ring resonator on LiNbO3,” Opt. Lett.34(11), 1735–1737 (2009). [CrossRef] [PubMed]
  13. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, Wiley series in microwave and optical engineering (John Wiley, 1999).
  14. X. Xia, Y. Zhou, and C. K. Madsen, “Analysis of As2S3-Ti: LiNbO3 Taper Couplers Using Supermode Theory,” Optics and Photonics Journal2, 344–351 (2012). [CrossRef]
  15. R. C. Alferness and L. L. Buhl, “High-speed waveguide electro-optic polarization modulator,” Opt. Lett.7(10), 500–502 (1982). [CrossRef] [PubMed]
  16. J. M. Wyrwas and M. C. Wu, “Dynamic Range of Frequency Modulated Direct-Detection Analog Fiber Optic Links,” J. Lightwave Technol.27(24), 5552–5562 (2009). [CrossRef]
  17. M. E. Solmaz, Y. Zhou, and C. K. Madsen, “Modeling asymmetric resonances using an optical filter approach,” J. Lightwave Technol.28(20), 2951–2955 (2010). [CrossRef]
  18. W. T. Snider, D. D. Macik, and C. K. Madsen, “Electro-Optically Tunable As2S3 Mach-Zehnder Interferometer on LiNbO3 substrate,” IEEE Photon. Technol. Lett.24(16), 1415–1417 (2012). [CrossRef]
  19. J. Kim, D. B. Adams, and C. K. Madsen, “Device-Under-Test Jones Matrix Extraction Algorithm With Device TE/TM Reference Frame,” IEEE Photon. Technol. Lett.24(1), 88–90 (2012). [CrossRef]

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