Tuneable liquid crystal Fabry-Perot filters

Transcription

1 Tuneable liquid crystal Fabry-Perot filters Wolfgang Vogel *a, Manfred Berroth **a a Institute for Electrical and Optical Communication Engineering, University of Stuttgart ABSTRACT In this paper tuneable optical filters based on liquid crystal Fabry-Perot interferometers (LCFPI) are presented. Liquid crystal (LC) devices are lightweight and suitable for compact arrays with a large number of pixels, as shown in high resolution flat panel displays. The fabricated filters offer a high finesse (9) and a wide tuning range (> 6 nm). The devices are coupled to standard single mode fibers by fiber collimators. For all filters the layer structure of a standard passive LC display is used, adding only two reflective layers. Dielectric mirrors (R =.98) are used to achieve high finesse and low insertion losses (-4.8 db). The cost can be further reduced by using thin gold layers, acting as electrodes and mirrors (R =.9) at the same time. The finesse of the Gold-FPIs is about 3 and the measured insertion loss is - db. Additionally, a twisted nematic (TN) structure is investigated. Using this orientation, the polarization dependence of the device is reduced with increasing tuning voltage. Keywords: Liquid crystal, Fabry-Perot interferometer, tuneable optical filter, polarization, WDM transmission systems, metropolitan area networks. INTRODUCTION For long haul transmission systems as well as in metropolitan area networks (MAN) the demand for high transmission capacities will grow further. Therefore the wavelength division multiplexing (WDM) technique is transferred more and more to metropolitan networks. A characteristic of the MAN is the need for rapid provisioning of new services and free configurable data streams, combined with a guarantee for the quality of services. So, the topology and maintenance of those networks is more complex compared to a long haul point to point data highway. In such networks, tuneable optical filters are key components for wavelength channel selection and monitoring. A large number of optical devices will be required for both fixed and portable instruments, so there is a demand for filters which are cheap and easy to manufacture. The used liquid crystal materials are transparent from the visible to the infrared wavelength range. Thus, with appropriate mirrors, the devices can be applied for all fiber optic transmission windows. A large number of filters can be realized by using an array of pixels. The power consumption of the devices is extremely low, which is already exploited by battery powered instruments with LC displays. The combination of the well established LC display fabrication process with optical filters results in compact devices with low manufacturing cost and mass production capability.. FABRY-PEROT THEORY Since the invention of the Fabry-Perot filter by the French scientists Charles Fabry and Alfred Perot, numerous publications have been released on theory and applications of the Fabry-Perot filter. However, a summary of the most important properties is given in this section, in order to understand the influence of the liquid crystal material inside the resonator as well as the surface defects of the substrates and the mirror losses. The mirrors of an ideal Fabry-Perot resonator are flat and parallel, their power reflection and transmission coefficients are R i and T i respectively (i =, ). Although the mirror surface is ideal, there are losses by scattering or absorption of the mirror material itself, represented by the absorption A i. Due to conservation of energy, R i +T i +A i = has to be * w.vogel@int.uni-stuttgart.de, phone , fax , University of Stuttgart, Pfaffenwaldring 47, 755 Stuttgart, Germany ** berroth@int.uni-stuttgart.de, phone , fax , University of Stuttgart, Pfaffenwaldring 47, 755 Stuttgart, Germany Copyright Society of Photo-Optical Instrumentation Engineers.

2 satisfied. The resonator cavity is filled by a material with the refractive index n and the intensity absorption constant α. Because of the multiple reflections of the electromagnetic field inside the cavity, the absorption constant α will affect the field at each round trip. The round trip phase δ is given by the optical path length n d in respect to the free space wavelength λ, which depends on the light frequency f and the speed of light c in vacuum. π πf δ = nd cosθ = nd cosθ. () λ c A simple model of the Fabry-Perot resonator described above is shown in Fig.. Losses are indicated by vertical arrows, transmitted and reflected power travels perpendicular to the mirror surfaces. In general the propagation direction of the wave is tilted by the angle θ in respect to the surface normal, but for this paper, always θ = is assumed. mirror # resonator mirror # A e -αd A incident power P in transmitted power P t T R e -jδ R T reflected power P r device reflection: R FPI e -αd device transmission: T FPI Fig. : Model of a Fabry-Perot filter with mirror losses A i and absorption losses α To calculate the transmission of the device, an incoming monochromatic plane wave E is assumed. For the electrical field, the complex amplitude reflection and transmission coefficients r i and t i are used. The coefficient α/ is the absorption factor of the field amplitude. jδ () E t = E t e e t. The other fractions of the wave are reflected back and forth inside the cavity. With each reflection, the wave is partially coupled out of the resonator. The m th roundtrip contributes to the transmission with: E tm jδ m mjδ mαd = E tt e e ( r r ) e e with m =,...,. (3) The total transmitted field results of the superposition of all transmitted parts, i.e. the transmitted field E t in respect to the incoming field E is: E E t jδ = tt e e m= jδ ( r r e e ) m. (4) Copyright Society of Photo-Optical Instrumentation Engineers.

3 Using the expression can be simplified: m x = = x m for x < (5) E t jδ = tt e e. (6) jδ E r r e e The intensity transmission is the square of the absolute value of the amplitude transmission, i.e. T FPI = (E t /E ) (E t /E ) *. Taking into account R i = r i and T i = - R i - A i = t i, the superposition of all multiple reflections in consideration of the mirror and resonator losses leads to the total device transmission T FPI, given in Eq. (7). This is a periodic function with resonance frequencies f m (or resonance wavelengths λ m respectively) at δ m = m π (m =,,,...). T FPI = ( R A ) ( R A ) ( R R e ) e + 4 RR e ( R R e ) sin. δ (7) Device reflection properties are not considered in detail but can be deduced in a similar way. For completeness the total reflection R FPI of the device is given in Eq. (8). RFPI ( R R ( A ) e ) + 4 R R ( A ) e sin δ =. (8) ( R R e ) + 4 R R e sin δ The whole device has to satisfy the conservation of energy too, i.e. R FPI + T FPI + A FPI =. The total device loss A FPI is also a periodic function with resonant peaks at the phases δ = δ m. The distance between two transmission peaks is called the free spectral range (FSR). In the frequency range, the peaks are equidistant and the FSR depends only on the optical path length n d of the resonator. c FSR =. (9) nd In terms of wavelength, the FSR is given by Eq. (), assuming that λ >> FSR. λ is the mean wavelength of two neighboring transmission peaks. Note that the unit of the term in Eq (9) is Hz, whereas the unit of Eq. () is m. The latter definition is commonly used in WDM systems, where the channel positions are given in wavelength units rather than in frequency units. λ FSR =. () nd To simplify Eq. (7), the maximum transmission T max and the filter finesse F is introduced. This leads to Eq. (). T FPI = Tmax. F + sin δ π () Copyright Society of Photo-Optical Instrumentation Engineers.

4 For further investigations a symmetric filter is assumed, i.e. R = R = R, A = A = A, T = T = T. Then, Eq. (7) results in: ( R A) e Tmax =. () ( R e ) T max is influenced by both the mirror losses A and the resonator losses αd. Thus for high transmission in the pass band, low loss dielectric mirrors are mandatory and the material absorption inside of the resonator is to be kept as low as possible. The filter finesse F affects both the width of the transmission peaks and the contrast of the filter. For an ideal filter, the total filter finesse F is equal to the reflection finesse F R. The reflection finesse F R is defined by the mirror intensity reflection coefficient R and the resonator losses αd. F R = π R e ( R e ). (3) F R increases with the mirror reflectivity, as indicated in Eq. (3). Without cavity losses, F R becomes infinite for R. The cavity loss limits the reflection finesse and therefore restricts the width of the transmission peaks even for R. In real devices, the mirrors are deposited on glass substrates with an inherent roughness and curvature. During the assembly process or due to spacer aberrations the mirrors might be tilted. Those surface defects can be expressed in terms of a surface finesse F S. This also restricts the total finesse of the filter and was introduced therefore by Chabbal as limiting finesse. Further details of the correlation between surface defects and surface finesse can be found e.g. in 3. The total filter finesse F is now composed of the reflection finesse F R and the surface finesse F S. F FR FS =. (4) FR + FS It is evident that surface defects not only influence the FWHM but also the maximum power transmission, because the surface has an impact on the superposition of the multiple reflections inside the cavity. The maximum transmission factor including the surface finesse is given in Eq. (5). 4 FS FR Tmax, F = Tmax arctan. (5) F F R The contrast C of the filter is the ratio of maximum to minimum transmission and depends on the mirror reflectivity and the cavity losses, assuming ideal mirrors. A more general definition uses the total filter finesse including the surface finesse to calculate the contrast. The terms given in Eq. (6) are deduced from Eq. (7) and Eq. () respectively. S C = T T max + R e 4F = = + R e π ( δ = π ). (6) Using the filters in WDM transmission systems requires a pass band small enough to select the channels of the WDM grid. In the frequency domain, all peaks have the same width, so it is sufficient to determine the width of the first pass band, which is centered at f =. A measure for the pass band is the full width at half maximum (FWHM) of a transmission peak. The first point of T FPI /T max = ½ is located at the frequency f /. Due to the symmetry of the curve at f =, f / is half the width of the pass band and can be calculated by resolving Eq. (7). Copyright Society of Photo-Optical Instrumentation Engineers.

5 This results in: With FWHM = f /, this leads to: T FPI = =. Tmax F π f (7) + sin nd π c f FWHM = c π = arcsin. (8) πnd F c arcsin πnd π F. (9) For a high finesse, i.e. F > 3 and thus arcsin(x) x, Eq. (9) is approximated by the well known relation FSR FWHM =. () F In WDM transmission systems, the cross talk from a neighboring channel to the selected channel is an important factor. To estimate the cross talk, a section of the periodic transmission function of the Fabry-Perot filter (see Eq. ()) can be approximated by a non-periodic Lorentzian shaped function centered at the selected resonance wavelength λ m. T = Tmax. 4 ( λ λ m ) + FWHM () The cross talk C cr = T/T max at a wavelength λ, which is close to the resonance wavelength λ m, i.e. (λ - λ m ) << FSR, can then be estimated in units of db by Eq. (). C cr = log + 4 λ λ m FWHM. () This concludes the basics of Fabry-Perot interferometers. In the next section, the properties of liquid crystals (LC) and the tunability of the liquid crystal Fabry-Perot interferometer (LCFPI) will be discussed. 3. LIQUID CRYSTAL FABRY-PEROT INTERFEROMETER (LCFPI) The liquid crystal materials consist of optical uniaxial molecules represented by a refractive index ellipse with the axes n e (extraordinary index, slow axis), and n o (ordinary index, fast axis). The birefringence of the molecules is n = n e - n o. In the so called nematic phase the molecules show an orientational order, but no positional order. The mean direction of the long axes of the molecules is represented by a vector n, called director. In a liquid crystal cell, the nematic material is bottled between two parallel glass substrates coated with transparent Indium Tin Oxide (ITO) electrodes. The gap between the substrates in the order of µm to 5 µm is maintained by spacers. This is the standard layer stack of a passive matrix LC display. To get a liquid crystal Fabry-Perot interferometer, this display structure is extended with an additional mirror layer on each substrate. Because losses inside of the resonator have to be kept low, the ITO-electrodes are placed between the glass substrate and the mirror, i.e. outside of the resonator. Fig. shows a cross section of the LCFPI device. The mirrors are made up of commercially available dielectric layer stacks. For low cost/low finesse filters, the ITO-electrodes and the dielectric mirrors can be replaced by thin gold layers. Copyright Society of Photo-Optical Instrumentation Engineers.

6 The resonator cavity is filled with the liquid crystal material. The orientational order of the molecules inside the cavity is determined by alignment layers on the mirror surface. Without applied control voltage, in the vertically aligned nematic (VAN-) cell, the director n is perpendicular to the substrate surface. In the parallel aligned nematic (PAN-) cell the director is uniformly parallel to the surface. Both alignments are suitable for phase only modulation of the passing light, when a linear input polarization parallel to the alignment layer is used (see e.g. 5 ). The most common alignment for displays is the twisted nematic 6 (TN) configuration. Here the director is also parallel to the substrate surfaces, but the second substrate is rotated by 9 degrees in respect to the first one. The molecules at each surface are fixed by the alignment layers so they are forced to twist also by 9 degrees along the distance d. incident power substrate LC substrate transmitted power mirror d Fig. : LCFPI device ITO-elektrode Due to the dielectric anisotropy ε = ε - ε the molecules rotate when an external electrical field is applied. The balance of the material s elastic restoring forces and the torque of the induced dipole momentum caused by the external electric field results in a rotation angle < Θ < 9 of the director. The power consumption is very low, because the device is field controlled. The rotation of the molecules is independent of the field polarity, so both DC and AC voltages may be applied. To prevent the material from electrolytic disruption, an AC control voltage is preferred. The voltage dependence of Θ for the VAN- and PAN orientation is given in Eq. (3). 7 Θ = U < U th π U U. th (3) arctan exp U > U th U U is the applied rms control voltage, U th the threshold voltage and U is a device specific constant. We now assume linear polarized light with its electrical field component parallel to the alignment direction. The effective refractive index n eff, VAN of a vertically aligned cell is then given by Eq. (4). no ne n eff, VAN ( Θ) =. (4) n sin Θ + n cos Θ o With no field applied, the tilt angle Θ is zero and the effective refractive index of the cavity is n o, which results in the resonance wavelength λ m,o. For high voltages the tilt angle Θ is 9 and the effective index becomes n e and the resonance wavelength is λ m,e. In a PAN-cell, it starts with n e at zero volts and ends up with n o for high voltages. For both cells, this results in a wavelength shift λ of the resonance wavelength. The wavelength shift for a resonance of the order m is given in Eq. (5). e n n n λ = λm, o = λm, e λ. (5) ne no n Copyright Society of Photo-Optical Instrumentation Engineers.

7 Assuming a typical birefringence of n. and a mean refractive index n.6 a tuning range of λ 97 nm is expected. Note that the tuning range is independent of the resonator length d. Because of n e > n o, the resonance wavelength of a VAN-cell increases, whereas in a PAN-cell the resonance wavelength decreases with high voltage. With the change of the effective refractive index and the optical path length of the cavity respectively also the free spectral range is changed. FSRe n λ o m, e FSR = = =. (6) FSRo n λ e m, o The relative change FSR of the FSR is inverse proportional to the ratio of the ordinary and the extraordinary index, n e and n o, and directly proportional to the ratio of the resonance wavelengths λ m,e and λ m,o. 4. EXPERIMENTAL SETUP AND RESULTS In Fig. 3 the experimental setup is shown. A tunable laser source (Anritsu MG9637A) was used, providing a constant incident optical power. The light is guided to the tunable filter by a standard single mode fiber (SSMF) with a collimator at its end, generating a parallel beam with approximately.4 mm diameter. The transmitted power is collected by another collimator and measured with an optical power meter (Agilent HP85A with HP85B optical head). The filter is controlled by a low frequency (LF) voltage of about khz, provided by an Hameg HM83 signal generator. All instruments are controlled by a personal computer (PC) via the general purpose interface bus (GPIB). fiber collimator LCFPI fiber collimator tunable laser source LF signal generator optical power meter PC GPIB Fig. 3: Measurement setup For the VAN filter, Merck s MLC 669 mixture 8 is used. At a temperature of C and a wavelength of 589 nm (Na-D and -D emission lines) the refractive index is n o =.4737 and n e =.554. The dielectric constants at f = khz are ε = 7. and ε = 3.4 respectively, resulting in a negative dielectric anisotropy of ε = The filter is fabricated with standard fused silica substrates of 5.4 mm diameter and a thickness of 6.35 mm. ITO electrodes are deposited by RF sputtering. Then, commercially available dielectric mirrors with R =.98 (specified from 5 nm to 58 nm) are deposited. Fig. 4 shows on the left hand side the measured result of the filter transmission at U = V together with the simulated curve. The noise like oscillations of the measured curve are due to Fresnell reflections at the glass surface. The resonator length is d = 5 µm, resulting in a measured FSR of 3.7 nm. The peak transmission is T max = -4.8 db and a contrast of C = 37 db is achieved. The total filter finesse is F = 9 and the width of the peaks is FWHM =.7 nm. For the simulation, a material absorption of α =.5 cm -, A =.5 and F S = is assumed. On the right hand of Fig. 4 the tuned device is shown at different voltages. All voltages are rms values. A voltage of 4 V is sufficient to shift the peak wavelength within one FSR. The total tuning range of the VAN-device is λ = 6 nm as shown in Fig. 5. According to Eq. (5), this indicates a reduced infrared birefringence of n.6 at λ =55 nm ( n =.777 at 589 nm). Copyright Society of Photo-Optical Instrumentation Engineers.

8 V.5 V 3 V 3.5 V - db - meas. calc. - db T FPI -4 T FPI nm nm 58 wavelength wavelength Fig. 4: Transmission of VAN-LCFPI at U = V and tuned device Using a liquid crystal with positive dielectric anisotropy (MLC -) 8 with a PAN-alignment, leads to similar filter performance. Due to its larger optical anisotropy ( n =.876 at 589 nm) the tuning range is increased to λ = 87 nm. The measured and calculated tuning range of the PAN-filter is shown in Fig. 5. The mirrors and electrodes of this filter are deposited on thin (. mm) glass substrates. Therefore the surface finesse is reduced to F S = resulting in F = 84 and T max = -6.3 db. The contrast is C = 34.6 db and the width of the peaks is slightly increased to FWHM =.38 nm. Because the alignment of the PAN-cell is inverse to the VAN-cell, the peak wavelength of the VAN-cell is decreased with increasing voltage, which is expressed in a negative sign of n. With the achieved FWHM of this filter, a DWDM channel at λ - λ m =.8 nm ( GHz grid) has a cross talk of C cr = -5.6 db. For 5 GHz cannel spacing, the cross talk is C cr = -9.9 db. The fabrication cost can be reduced significantly by using thin (5 nm) gold layers, acting both as mirrors and electrodes. The reflection coefficient of the used layers is R =.9. Due to absorption in the metal (A gold =.8), the maximum transmission of this gold-fpi is T max = - db. The finesse is 8.3 and the FWHM is.5 nm with a FSR of 4 nm. The resonator length is µm. Filled with the MLC 669, the tuning range is 6 nm, which is also displayed in the left part of Fig. 5. Increasing the gold layer thickness results in higher reflectance and finesse, but will also increase the absorption A, thus leading to poor transmission of the device. So the gold mirror filters are suitable for low cost/low resolution applications, e.g. channel power monitors in coarse WDM (CWDM) systems. 8 nm 6 µm, gold 5 µm, diel. calculated nm - -4 MLC - PAN λ 4 VAN MLC 669 λ -6-8 measured calculated - 4 6V V voltage voltage Fig. 5: Tuning range of (on the left) VAN- and (on the right) PAN-LCFPI Copyright Society of Photo-Optical Instrumentation Engineers.

9 Note that in the left diagram of Fig. 5 the different length of the two resonators result in the same tuning range, as predicted in Eq. (5). For filters with dielectric mirrors, the threshold voltage is slightly larger than with gold mirrors because the field is weakened by the dielectric layers. This also explains the deviations of measured and calculated curves at medium voltages. The introduced filter types with VAN- and PAN-orientation are polarization dependent. For tuning, a linear input polarization parallel to the alignment layer, called p-polarization, is required. The s-polarization is perpendicular to the alignment layer. Due to the uniaxial molecules, the refractive index for s-polarized light is always n o, independent of the rotation angle Θ of the molecules. Therefore no wavelength tuning is achieved. The transmitted power measured a constant wavelength keeps unmodified for s-polarized light and changes for p-polarized light, as shown on the left diagram of Fig. 6. The measurement was taken at a constant wavelength and controlled polarization. To avoid the polarization dependence, dynamic control or polarization diversity approaches (e.g. with polarization beam splitters) are necessary. Using a twisted nematic alignment of the liquid crystal material in the resonator cavity, an intrinsic polarization independent region is achieved 9. Without applied field, the input polarization is rotated by the twisted liquid crystal and there are two resonator modes. As the molecules are twisted, the modes are called ordinary (o-) resonance and extraordinary (e-) resonance rather than s- or p-resonances. db -5 - s-polarized circular polarized db -5 - TN TFPI VAN p-polarized V T FPI e-resonance o-resonance V voltage voltage Fig. 6: Comparison of polarization dependence of (on the left) VAN- and (on the right) TN-filter Both resonances are tuned in a different way by applying a voltage. Increasing the field dissolves the twisted structure and for high fields the cell becomes isotropic. In the transition and high field region the resonance is polarization independent. A detailed mathematical deduction can be found in and. The right diagram of Fig. 6 shows a measurement of the transmission of a TN-FPI at constant wavelength over voltage. The resonance wavelength at high voltage is selected for this purpose. With a polarization controller the input polarization is set to have pure e- or o-resonance respectively for the two measurements. For voltages U <.5 V the transmission characteristics are different for the two modes. A further increase of the voltage leads to an identical transmission for both input polarization states, i.e. the device is polarization independent. The tuning range is decreased to about nm, because not the complete voltage range can be used to tune the device polarization independently. 5. CONCLUSION Using standard LC display technology with only two additional reflecting layers, high finesse tuneable Fabry-Perot filters can be fabricated. The presented devices with PAN- or VAN-orientation offer a high finesse (up to 9) and a wide tuning range (up to 84 nm). Using a TN-orientation, the polarization dependence of the device is reduced with increasing tuning voltage. A polarization independent tuning range of about nm was achieved. The large FSR and wide tuning range covers the amplification bandwidth of erbium doped fiber amplifiers (EDFAs). By using appropriate Copyright Society of Photo-Optical Instrumentation Engineers.

10 dielectric mirrors, filters for other fiber optic transmission windows can be achieved without modifying the fabrication process. ACKNOWLEDGEMENTS The authors would like to thank their colleagues of the Flat Panel Display Laboratory of the University of Stuttgart for producing the LC modules, and the Deutsche Forschungsgemeinschaft DFG for financial support. REFERENCES. Joseph F. Mulligan, Who Were Fabry and Pérot?, American Journal of Physics, 66, no. 9, pp , 998. Robert Chabbal, Finesse Limite d un Fabry-Pérot Formé de Lames Imparfaites, Le journal de physique et le radium, 9, pp. 95-3, J. V. Ramsay, Aberrations of Fabry-Perot Interferometers When Used as Filters, Applied Optics, 8, no. 3, pp , Katsuhiko Hirabayashi, Hiroyuki Tsuda, Takashi Kurokawa, New Structure of Tunable Wavelength-Selective Filters with a Liquid Crystal for FDM Systems, IEEE Photonics Technology Letters, 3, no. 8, pp , R. A. Soref, M. J. Rafuse, Electrically Controlled Birefringence of Thin Nematic Films, Journal of Applied Physics, 43, no. 5, pp. 9-37, M. Schadt, W. Helfrich, Voltage-Dependent Optical Activity of a Twisted Nematic Crystal, Applied Physics Letters, 8, no. 4, pp. 7-8, B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics, Wiley, New York, Merck KG, Germany, Liquid Crystal Mixtures for Electro-Optic Displays, LC data sheets 9. Hiroyuki Tsuda, Tetsuo Yoshizawa, Katsuhiko Hirabayashi, Takashi Kurokawa, Polarization-Independent Tunable Liquid-Crystal Fabry-Perot Interferometer Filters, Japanese Journal of Applied Physics, 35, part, no. 4A, pp , 996. H. Yoda, Y. Ohtera, O. Hanaizumi, S. Kawakami, Analysis of Polarization-Insensitive Optical Filter using Liquid Crystal: Connection Formula and Apparent Paradox, Optical and Quantum Electronics, 9, pp , 999. Y. Ohtera, H. Yoda, S. Kawakami, Analysis of Twisted Nematic Liquid Crystal Fabry-Perot Interferometer (TN- FPI) Filter Based on the Coupled Mode Theory, Optical and Quantum Electronics, 3, pp , Copyright Society of Photo-Optical Instrumentation Engineers.