Widely tunable electro-optic distributed Bragg reflector in liquid crystal waveguide

doi:10.1364/OE.18.011524

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Widely tunable electro-optic distributed Bragg reflector in liquid crystal waveguide

Giovanni Gilardi, Rita Asquini, Antonio d’Alessandro, and Gaetano Assanto »View Author Affiliations

Optics Express, Vol. 18, Issue 11, pp. 11524-11529 (2010)
http://dx.doi.org/10.1364/OE.18.011524

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– Abstract
1. Introduction
2. Device geometry and physics
3. Design and analysis
4. Conclusions
– References and links

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Abstract

We propose and numerically investigate a versatile and easy-to-realize configuration for a guided-wave voltage-tunable distributed feedback grating based on reorientation in nematic liquid crystal and coplanar comb electrodes. The device has a wide tuning range exceeding 100 nm and covers C and L bands for wavelength division multiplexing.

1. Introduction

Bragg reflectors are key elements for a variety of applications such as spectral filtering [1

T. E. Murphy, J. T. Hastings, and H. I. Smith, “Fabrication and Characterization of Narrow-Band Bragg-Reflection Filters in Silicon-on-Insulator Ridge Waveguides,” J. Lightwave Technol. 19(12), 1938–1942 (2001). [CrossRef]

K. J. Kim, J. K. Seo, and M. C. Oh, “Strain induced tunable wavelength filters based on flexible polymer waveguide Bragg reflector,” Opt. Express 16(3), 1423–1430 (2008). [CrossRef] [PubMed]

], tunable lasers [3

G. Jeong, J. H. Lee, M. Y. Park, C. Y. Kim, S. H. Cho, W. Lee, and B. W. Kim, “Over 26-nm wavelength tunable external cavity laser based on polymer waveguide platforms for WDM access networks,” Photon. Technol. Lett. 18(20), 2102–2104 (2006). [CrossRef]

], polarization dispersion compensation and manipulation [4

M. Kumar, T. Sakaguchi, and F. Koyama, “Giant birefringence and tunable differential group delay in Bragg reflector based on tapered three dimensional hollow waveguide,” Appl. Phys. Lett. 94(6), 061112 (2009). [CrossRef]

], multi/demultiplexing [5

J. Brouckaert, W. Bogaerts, S. Selvaraja, P. Dumon, R. Baets, and D. Van Thourhout, “Planar concave grating demultiplexer with high reflective Bragg reflector facets,” Photon. Technol. Lett. 20(4), 309–311 (2008). [CrossRef]

], spectrometry [6

R. G. DeCorby, N. Ponnampalam, E. Epp, T. Allen, and J. N. McMullin, “Chip-scale spectrometry based on tapered hollow Bragg waveguides,” Opt. Express 17(19), 16632–16645 (2009). [CrossRef] [PubMed]

], and sensing [7

V. Maselli, J. R. Grenier, S. Ho, and P. R. Herman, “Femtosecond laser written optofluidic sensor: Bragg Grating Waveguide evanescent probing of microfluidic channel,” Opt. Express 17(14), 11719–11729 (2009). [CrossRef] [PubMed]

]. Among the waveguides employed to date we mention those in polymers [2

K. J. Kim, J. K. Seo, and M. C. Oh, “Strain induced tunable wavelength filters based on flexible polymer waveguide Bragg reflector,” Opt. Express 16(3), 1423–1430 (2008). [CrossRef] [PubMed]

H. Zou, K. W. Beeson, and L. W. Shacklette, “Tunable planar polymer Bragg gratings having exceptionally low polarization sensitivity,” J. Lightwave Technol. 21(4), 1083–1088 (2003). [CrossRef]

S. Aramaki, G. Assanto, G. I. Stegeman, and M. Marciniak, “Realization of integrated Bragg reflectors in DANS-polymer waveguides,” J. Lightwave Technol. 11(7), 1189–1195 (1993). [CrossRef]

], silicon-on-insulator (SOI) [1

,10

I. Giuntoni, A. Gajda, M. Krause, R. Steingrüber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express 17(21), 18518–18524 (2009). [CrossRef]

,11

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsuitsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett. 43(11), 630-631 (2007). [CrossRef]

], hollow capillaries [4

,12

M. Kumar, T. Sakaguchi, and F. Koyama, “Wide tunability and ultralarge birefringence with 3D hollow waveguide Bragg reflector,” Opt. Lett. 34(8), 1252–1254 (2009). [CrossRef] [PubMed]

], lithium niobate [13

F. Heismann, L. L. Buhl, and R. Alferness, “Electro-optically tunable, narrowband Ti:LiNbO₃ wavelength filter,” Electron. Lett. 23(11), 572–574 (1987). [CrossRef]

–15

F. Tian, C. Harizi, H. Herrmann, V. Reimann, R. Ricken, U. Rust, W. Sohler, F. Wehrmann, and S. Westenhofer, “Polarization-independent integrated optical, acoustically tunable double-stage wavelength filter in LiNbO3,” J. Lightwave Technol. 12(7), 1192–1197 (1994). [CrossRef]

], silica [16

A. Iocco, H. G. Limberger, R. Salathe, L. A. Everall, K. Chisholm, J. Williams, and I. Bennion, “Bragg gratings fast tunable filter for wavelength division multiplexing,” J. Lightwave Technol. 17(7), 1217–1221 (1999). [CrossRef]

–18

C. S. Goh, M. R. Mokhtar, S. A. Butler, S. Y. Set, K. Kikuchi, and M. Ibsen, “Wavelength tuning of fiber Bragg gratings over 90nm using a simple tuning package,” Photon. Technol. Lett. 15(4), 557–559 (2003). [CrossRef]

], metal-insulator-metal [19

A. Hosseini and Y. Massoud, “A low-loss metal-insulator plasmonic Bragg reflector,” Opt. Express 14(23), 11318–11323 (2006). [CrossRef]

,20

Y. Gong, L. Wang, X. Hu, X. Li, and X. Liu, “Broad-bandgap and low-sidelobe surface plasmon polariton reflector with Bragg-grating-based MIM waveguide,” Opt. Express 17(16), 13727–13736 (2009). [CrossRef] [PubMed]

] and liquid crystals [21

I. Fujieda, O. Mikami, and A. Ozawa, “Active optical interconnect based on liquid-crystal grating,” Appl. Opt. 42(8), 1520–1525 (2003). [CrossRef] [PubMed]

–25

A. d’Alessandro, D. Donisi, L. De Sio, R. Beccherelli, R. Asquini, R. Caputo, and C. Umeton, “Tunable integrated optical filter made of a glass ion-exchanged waveguide and an electro-optic composite holographic grating,” Opt. Express 16(13), 9254–9260 (2008). [CrossRef] [PubMed]

Bragg tuning has been proposed/implemented thermo-optically [3

H. Zou, K. W. Beeson, and L. W. Shacklette, “Tunable planar polymer Bragg gratings having exceptionally low polarization sensitivity,” J. Lightwave Technol. 21(4), 1083–1088 (2003). [CrossRef]

,10

,11

], mechanically [2

K. J. Kim, J. K. Seo, and M. C. Oh, “Strain induced tunable wavelength filters based on flexible polymer waveguide Bragg reflector,” Opt. Express 16(3), 1423–1430 (2008). [CrossRef] [PubMed]

,12

M. Kumar, T. Sakaguchi, and F. Koyama, “Wide tunability and ultralarge birefringence with 3D hollow waveguide Bragg reflector,” Opt. Lett. 34(8), 1252–1254 (2009). [CrossRef] [PubMed]

,16

,18

], acousto-optically [14

A. d’Alessandro, D. A. Smith, and J. E. Baran, “Polarisation-independent low power integrated acousto-optic tunable filter/switch using APE/Ti polarisation splitters on lithium niobate,” Electron. Lett. 29(20), 1767–1769 (1993). [CrossRef]

,15

], electro-optically [13

F. Heismann, L. L. Buhl, and R. Alferness, “Electro-optically tunable, narrowband Ti:LiNbO₃ wavelength filter,” Electron. Lett. 23(11), 572–574 (1987). [CrossRef]

,17

B. Srinivasan and R. K. Jain, “First demonstration of thermally poled electrooptically tunable fiber Bragg gratings,” Photon. Technol. Lett. 12(2), 170–172 (2000). [CrossRef]

,24

F. R. M. Adikan, J. C. Gates, A. Dyadyusha, H. E. Major, C. B. E. Gawith, I. J. G. Sparrow, G. D. Emmerson, M. Kaczmarek, and P. G. R. Smith, “Demonstration of 100 GHz electrically tunable liquid-crystal Bragg gratings for application in dynamic optical networks,” Opt. Lett. 32(11), 1542–1544 (2007). [CrossRef] [PubMed]

,25

] and opto-optically [26

G. Assanto and G. I. Stegeman, “Optical bistability in nonlocally nonlinear periodic structures,” Appl. Phys. Lett. 56(23), 2285–2287 (1990). [CrossRef]

–29

C. Conti, G. Assanto, and S. Trillo, “Excitation of self-transparency Bragg solitons in quadratic media,” Opt. Lett. 22(17), 1350–1352 (1997). [CrossRef]

]. The largest thermo-optic tunings were obtained in SOI rib guides (18 nm) [11

] and in polymeric gratings (between 20 and 30 nm) [3

H. Zou, K. W. Beeson, and L. W. Shacklette, “Tunable planar polymer Bragg gratings having exceptionally low polarization sensitivity,” J. Lightwave Technol. 21(4), 1083–1088 (2003). [CrossRef]

]. Wavelength shifts of about 45 nm were reported by tensile strain on a flexible polymeric waveguide [2

K. J. Kim, J. K. Seo, and M. C. Oh, “Strain induced tunable wavelength filters based on flexible polymer waveguide Bragg reflector,” Opt. Express 16(3), 1423–1430 (2008). [CrossRef] [PubMed]

] and of more than 90 nm in silica via mechanical beam-bending [18

]. Tuning over 76 nm was achieved acoustically in LiNbO₃ [15

], and over 160 nm by piezoelectric actuators in hollow waveguides [12

M. Kumar, T. Sakaguchi, and F. Koyama, “Wide tunability and ultralarge birefringence with 3D hollow waveguide Bragg reflector,” Opt. Lett. 34(8), 1252–1254 (2009). [CrossRef] [PubMed]

]. Tunable Bragg gratings were also realized with liquid crystals exploiting their large electro-optic response [24

,25

In this paper we propose and numerically investigate an electro-optically tunable integrated Bragg reflector in a liquid crystalline cell with coplanar comb electrodes. At variance with previously proposed geometries [30

D. Donisi, R. Asquini, A. d’Alessandro, and G. Assanto, “Distributed feedback grating in liquid crystal waveguide: a novel approach,” Opt. Express 17(7), 5251–5256 (2009). [CrossRef] [PubMed]

], this design allows a transverse electric (TE) mode to undergo distributed feedback with a Bragg wavelength adjustable in the near infrared over more than 100 nm with the application of modest voltages. The latter also ensures bi-dimensional signal confinement in the planar NLC waveguide.

2. Device geometry and physics

The device structure is a planar waveguide as sketched in Fig. 1 . It consists of a nematic liquid crystal (NLC) layer sandwiched between two borosilicate (BK7) glass plates (refractive index 1.50 at λ = 1550 nm). Liquid crystals are mesophase dielectrics with intermediate properties between solids and liquids [31

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471(5-6), 221–267 (2009). [CrossRef]

], their nematic phase featuring orientational order and uniaxial symmetry, with the optic axis along the molecular director

\hat{n}

and a dielectric tensor with two eigenvalues ε_|| =

n_{/ /}^{2}

and ε _⊥ =

n_{⊥}^{2}

along and normally to

\hat{n}

, respectively. The inner face of one of the plates is patterned with comb-shaped Indium Tin Oxide (ITO) transparent electrodes as in Fig. 1(b).

Fig. 1 (a) 3D sketch of the Bragg reflector and (inset) molecular director

\hat{n}

, (b) top view of the coplanar comb electrode pattern in ITO.

Both electrodes are periodic along z and symmetric with respect to y = 0. The electrode topology and the NLC parameters need be selected in order to achieve high coupling between an injected transverse electric (TE) optical beam and the voltage induced Bragg grating over a finite propagation distance. Moreover, the applied voltage is intended to increase the index in an NLC finite region along y and so ensure two-dimensional (2D) transverse confinement of the light injected in the thin film slab. We considered the commercial NLC mixture E7 (supplied by Merck). In order to obtain single mode operation at λ = 1550nm we designed an NLC thickness h = 1µm and electrode dimensions a = b = 500nm, c = 250nm, t = 250 nm and T = 500nm. An NLC layer with molecular director in the plane yz can support the propagation of transverse electric (TE) waves in the guide. We also assumed a pre-twist angle φ₀ of about 4° with respect to z in order to eliminate the Fréedericks threshold [31

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471(5-6), 221–267 (2009). [CrossRef]

], and ITO electrodes 100 nm thick, with complex refractive index 1.3 + i0.1 at λ = 1550nm.

The desired pre-twist condition can be obtained by using a thin (≈50nm) film of Nylon 6 for the alignment, rubbing it along z. In the regime of strong anchoring, the rubbed layer determines the boundary conditions for the molecular director in x = 0 and x = 1μm. The external voltage forces the rotation of the director in the bulk, yielding the formation of a periodic grating defined by the electrode topology. Nylon 6 has a refractive index of 1.52 (at λ = 1550nm); hence, it does not affect the propagation of light in the higher index NLC.

Figure 2 displays molecular reorientation without and with applied voltage. At V = 0V the director is aligned along z because of the anchoring. An applied voltage can induce reorientation. The resulting twist is larger in the regions where the inter-electrode separation is minimum (b) as compared to those where the separation is maximum (b + 2c).

Fig. 2 Sketch of liquid crystal reorientation above the electrode area (in brown) for (a) V = 0 and (b) V > 0V.

The low-frequency voltage applied between the electrodes perturbs the NLC molecular orientation; as anticipated, it creates an average increase of refractive index in a channel finite in y and parallel to z with an additional periodic modulation, as shown in Fig. 2, producing a 2D channel waveguide with a superimposed phase grating for TE propagation along z. The latter can operate as a distributed-feedback guided-wave reflector with voltage-controlled effective index and contrast of the periodic modulation. The electro-optic orientation of the NLC director

\hat{n}

corresponds to the minimum of the free energy, which includes elastic and electrostatic terms:

F = F_{elastic} - ∭ [\frac{1}{2} ε_{0} ε_{⊥} {| \vec{E} |}^{2} + \frac{1}{2} ε_{0} Δ ε {(\vec{E} \cdot \hat{n})}^{2}] d v

(1)

with

\vec{E} = - \vec{\nabla} V

the applied electric field, ε _⊥ = 7 the permittivity for a field perpendicular to the optic axis

\hat{n}

and

Δ ε

the dielectric anisotropy. The elastic (Oseen-Frank) energy can be expressed as:

F_{elastic} = ∭ {\frac{1}{2} K_{11} {(\vec{\nabla} \cdot \hat{n})}^{2} + \frac{1}{2} K_{22} {[\hat{n} \cdot (\vec{\nabla} \times \hat{n})]}^{2} + \frac{1}{2} K_{33} {[\hat{n} \times (\vec{\nabla} \times \hat{n})]}^{2}} d v

(2)

where K ₁₁ = 12pN, K ₂₂ = 7.3pN, K ₃₃ = 17pN are the splay, twist and bend elastic constants determining the restoring torques when an equilibrium configuration is perturbed. The minimization of F is achieved by solving the Euler–Lagrange equation for the free energy density. We couple the problem of a stationary F with the Poisson equation for the electric field distribution:

\vec{\nabla} \cdot [\vec{\nabla} V + Δ ε (\vec{\nabla} V \cdot \hat{n}) \hat{n}] = 0

(3)

Minimization of Eq. (2) and the solution of Eq. (3) yield the spatial distribution of the NLC director tilt (θ) and twist (φ) or, equivalently, its distribution

\hat{n} =

(sinθ, cosθ cosφ, cosθ sinφ) in the reference system of Fig. 1. Due to the particular geometry of the cell and the nonlocal electro-optic response of NLC, the distribution of the refractive index

n_{e} = {(\cos^{2} ϕ / n_{⊥}^{2} + \sin^{2} ϕ / n_{/ /}^{2})}^{- 1 / 2}

for the extraordinarily (e-) polarized electric field of TE modes in the planar waveguide (confinement across x) can be approximated by solving:

K \nabla^{2} φ - \frac{Δ ε_{} {| E_{y} |}^{2}}{2} \sin 2 φ = 0

(4)

with K = K ₁₁≈K ₂₂≈K ₃₃ and E_y = E_y (x,y,z) the dominant component of the applied (low-frequency) electric field. Boundary conditions are dictated by surface anchoring (ϕ₀ ) in x = 0 and x = h.

Equation (4) is derived from Eq. (2) in the frequently used single constant approximation (K ₁₁~K ₂₂~K ₃₃). The latter applies well to the present case as the NLC director undergoes a pure twist-deformation.

3. Design and analysis

Starting with the voltage-dependent molecular reorientation, we obtain the director distribution and finally the profile of the refractive index n_e for extraordinarily (e-) polarized light, i.e. for electric field vectors in the plane xy. In the calculations we neglected the walk-off inherent to extraordinary-wave propagation in uniaxial dielectrics. Figures 3(a) thru 3(f) show the e-index profile for three values of the bias in two transverse sections along z, where the electrode separations are b + 2c (z = 0μm) and b (z = 0.25μm), respectively.

Fig. 3 Refractive index profile for e-polarization in (a,c,e) z = 0μm and (b,d,f) z = 0.25μm. The bias is 2.4V in (a,b), 5V in (c,d) and 13V in (e,f). The electrodes are in white. (g) Intensity profile of the TE₀₀ eigenmode at 1550nm and V = 5V.

A mode solver or, equivalently, a beam propagator can then yield the transverse profile of the guided field distribution at a given wavelength and for each applied voltage. Due to the particular choice of parameters, only the fundamental order TE₀₀ mode propagated in the structure. Figure 3(g) shows the TE₀₀ transverse profile for a bias V = 5V, with an effective index N_TE00 = 1.5474 at λ = 1550nm. The periodic separation between the electrodes yields a modulated strength of E_y and, correspondingly, the sought index grating along z. Figure 4(a) displays the index modulation in a 6-period region along z, evaluated in x = 0.2μm and y = 0 for various biases between 2.8 and 4.5V. As expected, the modulation is sinusoidal with a 0.5μm period, maximum when the electrode spacing is minimum (i.e. equals b). Figure 4(b) graphs the resulting index contrast versus voltage between 0 and 13V. For V = 5V the NLC director is entirely reoriented (//y) in the regions with minimum inter-electrode separation (b), but only partially reoriented where the electrodes are separated by b + 2c. Therefore, by increasing the voltage above 5V only the un-saturated NLC regions can still reorient, resulting in a progressive reduction of the index modulation for V > 5V. For V ≥ 12.4V the whole NLC has reoriented with director //y and a negligible index contrast.

Fig. 4 (a) Refractive index modulation along z for applied voltages between 2.8V (bottom line) and 4.5V (top line) in 0.1V steps, evaluated 200nm above the electrodes and in the symmetry axis between them (y = 0). A video (Media 1) shows a top-view of the index distribution versus applied voltage. (b) Corresponding longitudinal modulation versus applied voltage.

Based on the e-index distribution and using coupled mode theory, we calculated the resonant Bragg wavelength (Fig. 5 ) as well as the back-reflected power for TE light propagating over 3000 periods, i. e. a grating length of 1.5mm (Fig. 6 ).

Fig. 5 Bragg resonant wavelength versus applied voltage.

Fig. 6 Spectral reflectivity for various voltages and propagation over 1.5mm (3000 periods). FWHM from left to right are 0.56nm (1.52076μm), 0.85nm (1.5299μm), 1.3nm (1.54219μm), 1.7nm (1.55394μm), 2.1nm (1.56731μm), 2.3nm (1.58108μm), 2.2nm (1.59565μm), 1.6nm (1.61032μm), 1.0nm (1.62052μm) and 0.60nm (1.6246μm).

The reflected wavelength at resonance red-shifts with applied biases of a few volts, providing an extended tunability of ≈104 nm with a reflectivity R ≥ 50% (98nm for R ≥ 90%) while maintaining good spectral selectivity. Graphs of Bragg reflectivity and spectral selectivity (FWHM) versus bias are visible in Figs. 7(a) , 7(b) for various reflector lengths, from 0.5 to 8.0mm. Furthermore, for a given propagation length, a modest change in bias can alter the reflectivity; for instance, for L = 1.0mm (2.0mm) R increases from 30 to 100% (70 to 100%) as the voltage changes from 2.8 to 4.5V.

Fig. 7 (a) Bragg reflectivity and (b) FWHM versus voltage for a few propagation lengths L in mm: 0.5 (blue), 1.5 (red), 3 (green), 5 (violet), 8 (black).

4. Conclusions

We have proposed, designed and numerically investigated a voltage-tunable distributed feedback grating in a liquid crystal waveguide with coplanar comb-shaped electrodes. The device provides transverse light confinement and periodic index modulation, yielding high reflectivity in a wide tuning range of ≈104nm for voltages between 2.5 and 10.2V. This novel geometry provides ease of fabrication and a simple electro-optic control, while ensuring Bragg reflection and spectral filtering over a wide range of wavelengths in the whole C + L band for optical communications.

References and links

1.	T. E. Murphy, J. T. Hastings, and H. I. Smith, “Fabrication and Characterization of Narrow-Band Bragg-Reflection Filters in Silicon-on-Insulator Ridge Waveguides,” J. Lightwave Technol. 19(12), 1938–1942 (2001). [CrossRef]
2.	K. J. Kim, J. K. Seo, and M. C. Oh, “Strain induced tunable wavelength filters based on flexible polymer waveguide Bragg reflector,” Opt. Express 16(3), 1423–1430 (2008). [CrossRef] [PubMed]
3.	G. Jeong, J. H. Lee, M. Y. Park, C. Y. Kim, S. H. Cho, W. Lee, and B. W. Kim, “Over 26-nm wavelength tunable external cavity laser based on polymer waveguide platforms for WDM access networks,” Photon. Technol. Lett. 18(20), 2102–2104 (2006). [CrossRef]
4.	M. Kumar, T. Sakaguchi, and F. Koyama, “Giant birefringence and tunable differential group delay in Bragg reflector based on tapered three dimensional hollow waveguide,” Appl. Phys. Lett. 94(6), 061112 (2009). [CrossRef]
5.	J. Brouckaert, W. Bogaerts, S. Selvaraja, P. Dumon, R. Baets, and D. Van Thourhout, “Planar concave grating demultiplexer with high reflective Bragg reflector facets,” Photon. Technol. Lett. 20(4), 309–311 (2008). [CrossRef]
6.	R. G. DeCorby, N. Ponnampalam, E. Epp, T. Allen, and J. N. McMullin, “Chip-scale spectrometry based on tapered hollow Bragg waveguides,” Opt. Express 17(19), 16632–16645 (2009). [CrossRef] [PubMed]
7.	V. Maselli, J. R. Grenier, S. Ho, and P. R. Herman, “Femtosecond laser written optofluidic sensor: Bragg Grating Waveguide evanescent probing of microfluidic channel,” Opt. Express 17(14), 11719–11729 (2009). [CrossRef] [PubMed]
8.	H. Zou, K. W. Beeson, and L. W. Shacklette, “Tunable planar polymer Bragg gratings having exceptionally low polarization sensitivity,” J. Lightwave Technol. 21(4), 1083–1088 (2003). [CrossRef]
9.	S. Aramaki, G. Assanto, G. I. Stegeman, and M. Marciniak, “Realization of integrated Bragg reflectors in DANS-polymer waveguides,” J. Lightwave Technol. 11(7), 1189–1195 (1993). [CrossRef]
10.	I. Giuntoni, A. Gajda, M. Krause, R. Steingrüber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express 17(21), 18518–18524 (2009). [CrossRef]
11.	S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsuitsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett. 43(11), 630-631 (2007). [CrossRef]
12.	M. Kumar, T. Sakaguchi, and F. Koyama, “Wide tunability and ultralarge birefringence with 3D hollow waveguide Bragg reflector,” Opt. Lett. 34(8), 1252–1254 (2009). [CrossRef] [PubMed]
13.	F. Heismann, L. L. Buhl, and R. Alferness, “Electro-optically tunable, narrowband Ti:LiNbO₃ wavelength filter,” Electron. Lett. 23(11), 572–574 (1987). [CrossRef]
14.	A. d’Alessandro, D. A. Smith, and J. E. Baran, “Polarisation-independent low power integrated acousto-optic tunable filter/switch using APE/Ti polarisation splitters on lithium niobate,” Electron. Lett. 29(20), 1767–1769 (1993). [CrossRef]
15.	F. Tian, C. Harizi, H. Herrmann, V. Reimann, R. Ricken, U. Rust, W. Sohler, F. Wehrmann, and S. Westenhofer, “Polarization-independent integrated optical, acoustically tunable double-stage wavelength filter in LiNbO3,” J. Lightwave Technol. 12(7), 1192–1197 (1994). [CrossRef]
16.	A. Iocco, H. G. Limberger, R. Salathe, L. A. Everall, K. Chisholm, J. Williams, and I. Bennion, “Bragg gratings fast tunable filter for wavelength division multiplexing,” J. Lightwave Technol. 17(7), 1217–1221 (1999). [CrossRef]
17.	B. Srinivasan and R. K. Jain, “First demonstration of thermally poled electrooptically tunable fiber Bragg gratings,” Photon. Technol. Lett. 12(2), 170–172 (2000). [CrossRef]
18.	C. S. Goh, M. R. Mokhtar, S. A. Butler, S. Y. Set, K. Kikuchi, and M. Ibsen, “Wavelength tuning of fiber Bragg gratings over 90nm using a simple tuning package,” Photon. Technol. Lett. 15(4), 557–559 (2003). [CrossRef]
19.	A. Hosseini and Y. Massoud, “A low-loss metal-insulator plasmonic Bragg reflector,” Opt. Express 14(23), 11318–11323 (2006). [CrossRef]
20.	Y. Gong, L. Wang, X. Hu, X. Li, and X. Liu, “Broad-bandgap and low-sidelobe surface plasmon polariton reflector with Bragg-grating-based MIM waveguide,” Opt. Express 17(16), 13727–13736 (2009). [CrossRef] [PubMed]
21.	I. Fujieda, O. Mikami, and A. Ozawa, “Active optical interconnect based on liquid-crystal grating,” Appl. Opt. 42(8), 1520–1525 (2003). [CrossRef] [PubMed]
22.	Y. J. Liu, Y. B. Zheng, J. Shi, H. Huang, T. R. Walker, and T. J. Huang, “Optically switchable gratings based on azo-dye-doped, polymer-dispersed liquid crystals,” Opt. Lett. 34(15), 2351–2353 (2009). [CrossRef] [PubMed]
23.	D. Donisi, A. d’Alessandro, R. Asquini, R. Beccherelli, L. De Sio, R. Caputo, and C. Umeton, “Realization of an optical filter using POLICRYPS holographic gratings on glass waveguides,” Mol. Cryst. Liq. Cryst . 486, 31/[1073]-37/[1079] (2008)
24.	F. R. M. Adikan, J. C. Gates, A. Dyadyusha, H. E. Major, C. B. E. Gawith, I. J. G. Sparrow, G. D. Emmerson, M. Kaczmarek, and P. G. R. Smith, “Demonstration of 100 GHz electrically tunable liquid-crystal Bragg gratings for application in dynamic optical networks,” Opt. Lett. 32(11), 1542–1544 (2007). [CrossRef] [PubMed]
25.	A. d’Alessandro, D. Donisi, L. De Sio, R. Beccherelli, R. Asquini, R. Caputo, and C. Umeton, “Tunable integrated optical filter made of a glass ion-exchanged waveguide and an electro-optic composite holographic grating,” Opt. Express 16(13), 9254–9260 (2008). [CrossRef] [PubMed]
26.	G. Assanto and G. I. Stegeman, “Optical bistability in nonlocally nonlinear periodic structures,” Appl. Phys. Lett. 56(23), 2285–2287 (1990). [CrossRef]
27.	G. Assanto, “All-optical integrated nonlinear devices,” J. Mod. Opt. 37, 855–863 (1990). [CrossRef]
28.	J. E. Ehrlich, G. Assanto, and G. I. Stegeman, “All-optical tuning of waveguide nonlinear distributed feedback gratings,” Appl. Phys. Lett. 56(7), 602–604 (1990). [CrossRef]
29.	C. Conti, G. Assanto, and S. Trillo, “Excitation of self-transparency Bragg solitons in quadratic media,” Opt. Lett. 22(17), 1350–1352 (1997). [CrossRef]
30.	D. Donisi, R. Asquini, A. d’Alessandro, and G. Assanto, “Distributed feedback grating in liquid crystal waveguide: a novel approach,” Opt. Express 17(7), 5251–5256 (2009). [CrossRef] [PubMed]
31.	I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471(5-6), 221–267 (2009). [CrossRef]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(230.1480) Optical devices : Bragg reflectors
(230.2090) Optical devices : Electro-optical devices
(230.3720) Optical devices : Liquid-crystal devices

ToC Category:
Optical Devices

History
Original Manuscript: February 19, 2010
Revised Manuscript: April 14, 2010
Manuscript Accepted: April 24, 2010
Published: May 14, 2010

Citation
Giovanni Gilardi, Rita Asquini, Antonio d’Alessandro, and Gaetano Assanto, "Widely tunable electro-optic distributed Bragg reflector in liquid crystal waveguide," Opt. Express 18, 11524-11529 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-11-11524

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References

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F. R. M. Adikan, J. C. Gates, A. Dyadyusha, H. E. Major, C. B. E. Gawith, I. J. G. Sparrow, G. D. Emmerson, M. Kaczmarek, and P. G. R. Smith, “Demonstration of 100 GHz electrically tunable liquid-crystal Bragg gratings for application in dynamic optical networks,” Opt. Lett. 32(11), 1542–1544 (2007). [CrossRef] [PubMed]
A. d’Alessandro, D. Donisi, L. De Sio, R. Beccherelli, R. Asquini, R. Caputo, and C. Umeton, “Tunable integrated optical filter made of a glass ion-exchanged waveguide and an electro-optic composite holographic grating,” Opt. Express 16(13), 9254–9260 (2008). [CrossRef] [PubMed]
G. Assanto and G. I. Stegeman, “Optical bistability in nonlocally nonlinear periodic structures,” Appl. Phys. Lett. 56(23), 2285–2287 (1990). [CrossRef]
G. Assanto, “All-optical integrated nonlinear devices,” J. Mod. Opt. 37, 855–863 (1990). [CrossRef]
J. E. Ehrlich, G. Assanto, and G. I. Stegeman, “All-optical tuning of waveguide nonlinear distributed feedback gratings,” Appl. Phys. Lett. 56(7), 602–604 (1990). [CrossRef]
C. Conti, G. Assanto, and S. Trillo, “Excitation of self-transparency Bragg solitons in quadratic media,” Opt. Lett. 22(17), 1350–1352 (1997). [CrossRef]
D. Donisi, R. Asquini, A. d’Alessandro, and G. Assanto, “Distributed feedback grating in liquid crystal waveguide: a novel approach,” Opt. Express 17(7), 5251–5256 (2009). [CrossRef] [PubMed]
I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471(5-6), 221–267 (2009). [CrossRef]

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