- Email: [email protected]
Broadband spectral shaping using nematic liquid crystal
Results in Physics 12 (2019) 531–534
Contents lists available at ScienceDirect
Results in Physics journal homepage: www.elsevier.com/locate/rinp
Broadband spectral shaping using nematic liquid crystal
T
Bhaskar Kanseri , Gyaprasad, Ateesh Kumar Rathi ⁎
Experimental Quantum Interferometry and Polarization (EQUIP), Department of Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110012, India
ARTICLE INFO
ABSTRACT
Keywords: Birefringence Polarization Spectral switching
We demonstrate what is, to our knowledge, the first implementation of nematic liquid crystal (LC) for spectral shaping of broadband light fields. A LC cell of several microns thickness is placed between a polarizer and an analyzer. By changing the analyzer angle, one can use the combined device as a spectral filter of different types, such as a notch filter, narrow-band filter etc. We also demonstrate that the source spectrum also gets manipulated by changing the LC cell thickness and by tuning the voltage applied across the LC cell, providing another degrees of freedom for shaping the broadband spectrum. Such important effect using liquid crystals can find technological applications in spectral shaping of light fields by making variable spectral filters, and in spectral switching based data communication schemes.
Introduction Spectral shaping of light fields is an active area of research in Physics. Spectral changes in the source spectra may be induced owing to several reasons such as, correlation induced [1–3], polarization induced [4,5], propagation induced [6], scattering induced [7], non-linearity induced [8] etc. These spectral changes find applications in several areas, for instance, in spatial and spectral shaping of optical sources[9,10], spectroscopy [11], data transmission and encoding [4,12] and in spectral imaging [13] etc. Very recently, spectral manipulation using birefringence property of bulk crystals has been proposed theoretically, though the crystal thicknesses were very small (in microns), making the experimental realisation of this scheme very difficult [14]. In our experiment, we implement similar theoretical technique using liquid crystal in place of bulk crystal for these practical reasons. A theoretical work related to LC based spectral manipulations has been reported recently [15]. Over the last several decades, liquid crystal has evolved as a very versatile medium for optical manipulations [16]. Liquid crystals (LCs) are birefringent in nature, though the value of birefringence is generally smaller than the several bulk crystals [17]. Interestingly, the birefringence of LCs can be tuned by applying DC voltage across them offering an advantage over the crystals [18]. The underlying properties of liquid crystals led their applications in various areas such as biology, photonics, electro-optics, optical device fabrication, display, rheology etc [19]. LCs have been used for narrow spectral filtering in several configurations [20–22] (and references therein), and such LC based tunable filters are now commercially available, for instance [23]. Thus
⁎
in a nutshell, compared to birefringent bulk crystals, liquid crystals offer a diverse medium for optical manipulations, and in particular, spectral manipulations, which is the topic of the present study. For a birefringent medium such as bulk crystal or liquid crystal, the phase difference for the light between the fast and slow axes can be expressed as [16,17]
( )=
2
[ne ( )
no ( )] d,
(1)
where d is the thickness of liquid crystal cell and ne and no are the extraordinary and ordinary refractive indices (the difference between ne and no is called birefringence) which are dependent on the wavelength of light . From Eq. (1), one can see that the phase difference can be changed either tuning the birefringence of the medium, or by changing the thickness of the medium. In this paper, for the first time, we demonstrate the application of nematic LC for broadband spectral shaping. Using the birefringence property of LC, we show both theoretically and experimentally spectral manipulations in the broadband source spectrum using a simple scheme involving a LC cell along with two polarizers. We demonstrate that by increasing the LC cell thickness, which is several tens of microns, the modulations in the source spectrum also enhance. Since these spectral changes can be accurately predicted using theoretical modelling, they are precisely controllable and can find potential applications in spectral shaping of the broadband light sources. In addition, we also show that by changing the applied voltage across the LC cell may induce spectral changes. The later approach is non-mechanical and thus faster in implementation providing an additional degree of freedom for achieving
Corresponding author. E-mail address: [email protected] (B. Kanseri).
https://doi.org/10.1016/j.rinp.2018.11.086 Received 27 September 2018; Received in revised form 15 November 2018; Accepted 26 November 2018 Available online 01 December 2018 2211-3797/ © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Results in Physics 12 (2019) 531–534
B. Kanseri et al.
ne2 ( ) = Ae +
Be 2
+
Ce 4
,
(4)
where A0 , B0, C0, Ae , Be , Ce are constants for a given liquid crystal at a given temperature. For 5CB liquid crystal at room temperature 25.1 °C, Ae = 1.6795; Be = the coefficients are given by . 0.0048 × 10 12 m2; Ce = 0.0027 × 10 24 m4; Ao = 1.5187; Bo
spectral manipulation in the source spectrum.
= 0.0016 × 10 12 m2; Co = 0.0011 × 10 24 m4 Since the phase difference acquired by different wavelength components would be different, one could expect different output states of polarization for different wavelength components. The analyzer selects wavelength components having a particular polarization, thus making the spectrum manipulated with respect to the source spectrum. We use the Jones matrix approach for calculating the output spectrum, which involves writing transformation matrix for each of the components and multiply them in sequence to get the final Jones matrix for the whole system [25]. Theoretical simulations are made using the input normalized Gaussian spectral distribution given by Eq. (2) with parameters resembling with the experimental broadband source spectrum after the filter (F), shown in Fig. 1.
Experiment
Results and discussions
The empty glass cell is formed by using two conducting indium titanium oxide (ITO) coated glass plates (1.5 cm × 1 cm) sandwiched together, separated by a set of identical Mylar spacers of desired thickness between them. On the ITO coated side of the glass, thin film of 0.5% solution of nylon was spin coated and was heated at 80 °C for 45 min for stabilization. In order to homogeneously align liquid crystal molecules parallel to the surface of the glass plate (planer cell), micro-grooves were formed on the polymer surface (nylon film) by unidirectional rubbing of good quality velvet cloth (also known as rubbed polyimide technique). The glass cell of appropriate thickness hence formed was filled with 5CB (4-Cyano-4′-pentylbiphenyl) nematic liquid crystal using capillary action. The experimental scheme for demonstrating spectral manipulation using liquid crystal is shown in Fig. 1. Light emanating from a whitelight LED source is collimated using a plano-convex lens with a small aperture placed at its back focal plane, and is filtered using a bandpass filter (central wavelength 550 nm, FWHM 70 ± 10 nm). The resultant broadband light field further passes through a combination of horizontal polarizer and analyzer. A nematic liquid crystal cell is placed between the polarizer-analyzer combination, with its fast axis making 45° angle with the input polarizer axis (see Fig. 1). The light passing through the analyzer is collected by a plano-convex lens and coupled to the fiber patch cable of a spectrometer (Research-India). The spectral changes are quantified using in a computer attached with the spectrometer. The measurements are taken at room temperature ( 25 °C) at which 5CB liquid crystal is at nematic phase.
We place a 25 µm thickness liquid crystal cell in the scheme shown in Fig. 1 and record the output spectra as a function of the analyzer is angle . The resultant output spectra for increasing values of shown in Fig. 2. When x-polarized light passes through a liquid crystal cell it introduces a phase by which the polarization state of each wavelength changes. The birefringent LC cell works as a retardation plate of varying phase for different wavelengths. For central wavelength it works as a half wave plate (for 19 micron thickness cell, c.f. Eq. 1), and rotates the input polarization by 90° owing to the fact that it is placed at 45° with respect to the input polarizer. The polarization rotation for near-central wavelengths is less than 90°. When the analyzer angle = 0° , then according to Malus law [25] spectral components in the vicinity of central wavelengths show a drop in spectral density. Only those wavelengths, for which the polarization would be non-orthogonal following Eq. (1), would pass through the system and one gets a two peak spectrum (notch filter). On increasing the analyzer angle the peaks begin collapsing to each other, i.e., the visibility of peaks decrease, and one gets a flat top spectrum at = 40° (not shown in Fig. 2). Further changing the angle, these peaks completely collapse to one point and the spectrum becomes triangle type at = 45°. More analyzer rotation decreases the spectral bandwidth and the spectrum becomes nipple type at = 50° (not shown in Fig. 2). Further analyzer rotation makes central peak dominate and at = 60°, spectral bandwidth is 31.4 nm and side peaks start emerging. The spectral intensity of these side peaks increase with further increase in the analyzer angle, shrinking the central peak bandwidth, and at analyzer angle , we get central-peak-dominated spectrum with bandwidth of approximately 26.2 nm. Thus it is apparent that a wide range of spectral configurations can be generated by polarization control of liquid crystal. The theoretically predicted results shown in Fig. 2, are found very well in agreement with the experimental results. We emphasize here that the output spectra obtained either theoretically or experimentally in Fig. 2 clearly demonstrate the effect of losses in the intensity of each spectral component, passing through our scheme shown in Fig. 1. In order to study the effect of LC cell thickness on the output spectrum, we made the LC cells of different thicknesses, based on the availability of myler spacers with us: 25 µm , 44 µm , 57 µm , 75 µm and 94 µm . These LC cells were probed using the experimental scheme shown in Fig. 1, keeping relative angle between first polarizer and LC cell same as in the previous study. The analyzer was placed orthogonal to the polarizer. Fig. 3 shows the spectral changes in the input spectrum for different thicknesses of the LC cell. We observe that with increasing
Fig. 1. Experimental scheme to demonstrate spectral manipulation using nematic liquid crystal cell. Notations: A aperture, L lens, F broadband filter, P polarizer and LC liquid crystal cell. Spectrum of light of the LED source and output spectrum of the broadband filter are shown in the inset.
Theoretical analysis For theoretical analysis, the incident broadband light spectrum can be considered to be normalized Gaussian distribution, expressed as
S 0 ( ) = exp
(
0)
2
2
,
(2)
where 0 = c/ is the central frequency, c is speed of light and is the bandwidth of the spectrum. For the liquid crystal, the dependance of ordinary and extraordinary refrective indices on the wavelength of light can be expressed by using the three coefficient (extended) Cauchy equations obtained from the three band model of LC [24]:
no2 ( ) = A0 +
B0 2
+
C0 4
,
(3) 532
Results in Physics 12 (2019) 531–534
B. Kanseri et al.
Fig. 2. Spectral shaping of the output spectra by changing the angle of analyzer ranging from 0° to 90° for a 25 micron thick LC cell placed in the configuration shown in Fig.1. Left plots are theoretical results whereas right ones are experimental results. Dashed line (blue) corresponds to input source spectrum whereas the solid line (red) represents output spectrum.
Fig. 3. Spectral shaping for increasing LC cell thickness. The analyzer is placed orthogonal to the polarizer. Left plots are theoretical results whereas right ones are experimental results. Dashed line (blue) corresponds to input source spectrum whereas the solid line (red) represents output spectrum. Number of spectral peaks increase with cell thickness.
Fig. 1 with analyzer placed at 90° with respect to the input polarizer. Fig. 4 demonstrates the change in input spectra for different applied voltages across the nemetic LC cell of 25 micron thickness. We observe that at 0 V, there is cross-polarization condition, and similar to Fig. 2, a two peak spectrum is obtained. By increasing the voltage, one of the peaks enhances, whereas the other subsides. At 1.4 V, the second peak disappears and a blue-shifted spectrum is obtained. This characteristic voltage at which spectrum is blue-shifted depends on the thickness of the LC cell and the type of liquid crystal (birefringence). On further increase in voltage the effect repeats itself and at 1.8 V we get a redshifted spectrum. On further increase in voltage, the peak starts flatten and the spectral width becomes wider with less visibility of the spectral modulations. These spectral changes occur in a time frame of several microseconds, which is dependent on the relaxation time of the LC molecules.
LC thickness, the spectral peaks (modulations) increase. The number of peaks obtained for the LC thicknesses 25 µm , 44 µm , 57 µm , 75 µm and 94 µm are 3, 4, 6, 8 and 9, respectively. We also infer from the figures that the theoretically predicted spectral changes (peaks) with varying LC thickness are very well in agreement with the experimental results. Slight mismatch in spectral densities in theory and experiment could be due to unavoidable imperfections in LC cell formation, LC filling and losses due to larger thickness of the LC cell. We clearly observe that excellent match between experimental and theoretical results of Figs. 2 and 3 demonstrate a precise control of LC parameters on the spectral shape of broadband light field, advocating the application of this effect on spectral shaping. Since liquid crystals have electro-optical properties, their birefringence can be tuned by applying voltage across the LC cell [18]. Thus one can obtain spectral changes in the transmitting light field by just applying DC voltage across the LC cell placed in the scheme of
533
Results in Physics 12 (2019) 531–534
B. Kanseri et al.
Acknowledgements The authors thank Dr. Swadesh K. Gupta for help in making the liquid crystal cells. Research leading to the results reported in this paper received funding from Science and Engineering Research Board, India through grant YSS/2015/000367, YSS/2015/000743, and from Council for Scientific and Industrial Research, India through grant 03(1401)/ 17/EMR-II. Author Gyaprasad is thankful to University Grant Commission, India for a Junior Research Fellowship. References [1] Pu J, Zhang H, Nemoto S. Spectral shifts and spectral switches of partially coherent light passing through an aperture. Opt Commun 1999;162:57. [2] Kandpal HC, Anand S, Vaishya JS. Experimental observation of the phenomenon of spectral switching for a class of partially coherent light. IEEE J Quant Electron 2002;38:336. [3] Pu J, Cai C, Nemoto S. Spectral anomalies in Young’s double-slit interference experiment. Opt Expr 2004;12:5131. [4] Kanseri B. Polarization assisted data encoding and transmission using coherence based spectral anomalies. J Opt 2013;15:055407 . [5] Han P. Spectral shifts with polarization control. J Opt 2013;15:105710 . [6] Pu J, Korotkova O, Wolf E. Invariance and noninvariance of the spectra of stochastic electromagnetic beams on propogation. Opt Lett 2006;31:2097. [7] Shirai T, Asakura T. Spectral changes of light induced by scattering from spatially random media under the Rytov approximation. J Opt Soc Am A 1995;12:1354. [8] Han P. All optical spectral switches. Opt Lett 2012;37:2319. [9] Krupa K, Labruyre A, Tonello A, Shalaby BM, Couderc V, Baronio F, Acheves AB. Polychromatic filament in quadratic media: spatial and spectral shaping of light in crystals. Optica 2015;2:1058. [10] Labroille G, Pinel O, Treps N, Joffre M. Pulse shaping with birefringent crystals:a tool for quantum metrology. Opt Expr 2013;21:1890. [11] Han P. Lattice spectroscopy. Opt Lett 2009;34:1303. [12] Yadav BK, Raman S, Kandpal HC. Information exchange in free space using spectral switching of diffracted polychromatic light: possibilities and limitations. J Opt Soc Am A 2008;25:2952. [13] Garini Y, Young IT, McNamara G. Spectral imaging: principles and applications. Cytometry 2006;69A:735. [14] Ding P-F, Han P. Spectral manipulation and complementary spectra with birefringence polarization control. J Opt 2017;19:035601 . [15] Ding P-F, Hsu H-C, Han P. Spectral manipulation and tunable optical frequency ruler using liquid crystal birefringence. Optik 2019;179:115. [16] Khoo I-C, Wu S-T. Optics and nonlinear optics of liquid crystals. Singapore: World Scientific; 1993. [17] Wu S-T, Efron U, Hess LD. Birefringence measurements of liquid crystals. Appl Opt 1984;23:21. [18] Michel RE, Smith GW. Dependence of birefringence threshold voltage on dielectric anisotropy in a nematic liquid crystal. J Appl Phys 1974;45:3234. [19] Vicari L. Optical applications of liquid crystals. Boca Raton, Florida: CRC Press; 2003. [20] Abulell M, Abdulhalim I. Narrowband multispectral liquid crystal tunable filter. Opt Lett 2008;41:1957. [21] Gilardi G, Donisi D, Serpengze A, Beccherelli R. Liquid-crystal tunable filter based on sapphire microspheres. Opt Expr 2009;34:3253. [22] Aharon O, Abdulhalim I. Liquid crystal Lyot tunable filter with extended free spectral range. Opt Expr 2009;17:11426. [23] See the link:https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id= 3488. [24] Li J, Wu S-T. Extended Cauchy equations for the refractive indices of liquid crystals. J Appl Phys 2004;95:896. [25] Goldstein DH. Polarized light. Boca Raton, Florida: CRC Press; 2011.
Fig. 4. Spectral manipulation by applying the DC voltage across the 25 micron thick LC cell. Polarizer and analyzer are placed orthogonal to each other, and the liquid crystal director makes 45° (red) with the polarizer axis. Dashed line (blue) corresponds to input source spectrum whereas the solid line represents output spectrum.
Conclusion In conclusion, we have demonstrated both theoretically and experimentally a simple yet effective method for spectral shaping of broadband light field by controlling several parameters of the nematic liquid crystal. We demonstrate spectral manipulation using three ways: a) by polarization control using a set of polarizers with LC, 2) by changing the thickness of LC cell and 3) by tuning the birefringence of LCs by changing the applied DC voltage across it. The output field can have spectral distribution as two peaks, red shifted, blue shifted, notch filter, narrow band, central peak dominated, nipple type etc. These spectral shapes and modulations are theoretically predictable, providing a precise control over the spectral manipulation process. The use of liquid crystal thus offers a versatile medium for spectral manipulation of light fields over a broad spectral range which can find potential applications in spectral shaping, and in synthesis of sources having arbitrary spectral distributions. The polarization and voltage dependent spectral manipulations might find applications in designing achromatic polarization components (such as achromatic retarders) applicable to a wide range of spectrum, providing a tunable and cost-effective solution compared to the crystal based achromatic optical components.
534
Contents lists available at ScienceDirect
Results in Physics journal homepage: www.elsevier.com/locate/rinp
Broadband spectral shaping using nematic liquid crystal
T
Bhaskar Kanseri , Gyaprasad, Ateesh Kumar Rathi ⁎
Experimental Quantum Interferometry and Polarization (EQUIP), Department of Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110012, India
ARTICLE INFO
ABSTRACT
Keywords: Birefringence Polarization Spectral switching
We demonstrate what is, to our knowledge, the first implementation of nematic liquid crystal (LC) for spectral shaping of broadband light fields. A LC cell of several microns thickness is placed between a polarizer and an analyzer. By changing the analyzer angle, one can use the combined device as a spectral filter of different types, such as a notch filter, narrow-band filter etc. We also demonstrate that the source spectrum also gets manipulated by changing the LC cell thickness and by tuning the voltage applied across the LC cell, providing another degrees of freedom for shaping the broadband spectrum. Such important effect using liquid crystals can find technological applications in spectral shaping of light fields by making variable spectral filters, and in spectral switching based data communication schemes.
Introduction Spectral shaping of light fields is an active area of research in Physics. Spectral changes in the source spectra may be induced owing to several reasons such as, correlation induced [1–3], polarization induced [4,5], propagation induced [6], scattering induced [7], non-linearity induced [8] etc. These spectral changes find applications in several areas, for instance, in spatial and spectral shaping of optical sources[9,10], spectroscopy [11], data transmission and encoding [4,12] and in spectral imaging [13] etc. Very recently, spectral manipulation using birefringence property of bulk crystals has been proposed theoretically, though the crystal thicknesses were very small (in microns), making the experimental realisation of this scheme very difficult [14]. In our experiment, we implement similar theoretical technique using liquid crystal in place of bulk crystal for these practical reasons. A theoretical work related to LC based spectral manipulations has been reported recently [15]. Over the last several decades, liquid crystal has evolved as a very versatile medium for optical manipulations [16]. Liquid crystals (LCs) are birefringent in nature, though the value of birefringence is generally smaller than the several bulk crystals [17]. Interestingly, the birefringence of LCs can be tuned by applying DC voltage across them offering an advantage over the crystals [18]. The underlying properties of liquid crystals led their applications in various areas such as biology, photonics, electro-optics, optical device fabrication, display, rheology etc [19]. LCs have been used for narrow spectral filtering in several configurations [20–22] (and references therein), and such LC based tunable filters are now commercially available, for instance [23]. Thus
⁎
in a nutshell, compared to birefringent bulk crystals, liquid crystals offer a diverse medium for optical manipulations, and in particular, spectral manipulations, which is the topic of the present study. For a birefringent medium such as bulk crystal or liquid crystal, the phase difference for the light between the fast and slow axes can be expressed as [16,17]
( )=
2
[ne ( )
no ( )] d,
(1)
where d is the thickness of liquid crystal cell and ne and no are the extraordinary and ordinary refractive indices (the difference between ne and no is called birefringence) which are dependent on the wavelength of light . From Eq. (1), one can see that the phase difference can be changed either tuning the birefringence of the medium, or by changing the thickness of the medium. In this paper, for the first time, we demonstrate the application of nematic LC for broadband spectral shaping. Using the birefringence property of LC, we show both theoretically and experimentally spectral manipulations in the broadband source spectrum using a simple scheme involving a LC cell along with two polarizers. We demonstrate that by increasing the LC cell thickness, which is several tens of microns, the modulations in the source spectrum also enhance. Since these spectral changes can be accurately predicted using theoretical modelling, they are precisely controllable and can find potential applications in spectral shaping of the broadband light sources. In addition, we also show that by changing the applied voltage across the LC cell may induce spectral changes. The later approach is non-mechanical and thus faster in implementation providing an additional degree of freedom for achieving
Corresponding author. E-mail address: [email protected] (B. Kanseri).
https://doi.org/10.1016/j.rinp.2018.11.086 Received 27 September 2018; Received in revised form 15 November 2018; Accepted 26 November 2018 Available online 01 December 2018 2211-3797/ © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Results in Physics 12 (2019) 531–534
B. Kanseri et al.
ne2 ( ) = Ae +
Be 2
+
Ce 4
,
(4)
where A0 , B0, C0, Ae , Be , Ce are constants for a given liquid crystal at a given temperature. For 5CB liquid crystal at room temperature 25.1 °C, Ae = 1.6795; Be = the coefficients are given by . 0.0048 × 10 12 m2; Ce = 0.0027 × 10 24 m4; Ao = 1.5187; Bo
spectral manipulation in the source spectrum.
= 0.0016 × 10 12 m2; Co = 0.0011 × 10 24 m4 Since the phase difference acquired by different wavelength components would be different, one could expect different output states of polarization for different wavelength components. The analyzer selects wavelength components having a particular polarization, thus making the spectrum manipulated with respect to the source spectrum. We use the Jones matrix approach for calculating the output spectrum, which involves writing transformation matrix for each of the components and multiply them in sequence to get the final Jones matrix for the whole system [25]. Theoretical simulations are made using the input normalized Gaussian spectral distribution given by Eq. (2) with parameters resembling with the experimental broadband source spectrum after the filter (F), shown in Fig. 1.
Experiment
Results and discussions
The empty glass cell is formed by using two conducting indium titanium oxide (ITO) coated glass plates (1.5 cm × 1 cm) sandwiched together, separated by a set of identical Mylar spacers of desired thickness between them. On the ITO coated side of the glass, thin film of 0.5% solution of nylon was spin coated and was heated at 80 °C for 45 min for stabilization. In order to homogeneously align liquid crystal molecules parallel to the surface of the glass plate (planer cell), micro-grooves were formed on the polymer surface (nylon film) by unidirectional rubbing of good quality velvet cloth (also known as rubbed polyimide technique). The glass cell of appropriate thickness hence formed was filled with 5CB (4-Cyano-4′-pentylbiphenyl) nematic liquid crystal using capillary action. The experimental scheme for demonstrating spectral manipulation using liquid crystal is shown in Fig. 1. Light emanating from a whitelight LED source is collimated using a plano-convex lens with a small aperture placed at its back focal plane, and is filtered using a bandpass filter (central wavelength 550 nm, FWHM 70 ± 10 nm). The resultant broadband light field further passes through a combination of horizontal polarizer and analyzer. A nematic liquid crystal cell is placed between the polarizer-analyzer combination, with its fast axis making 45° angle with the input polarizer axis (see Fig. 1). The light passing through the analyzer is collected by a plano-convex lens and coupled to the fiber patch cable of a spectrometer (Research-India). The spectral changes are quantified using in a computer attached with the spectrometer. The measurements are taken at room temperature ( 25 °C) at which 5CB liquid crystal is at nematic phase.
We place a 25 µm thickness liquid crystal cell in the scheme shown in Fig. 1 and record the output spectra as a function of the analyzer is angle . The resultant output spectra for increasing values of shown in Fig. 2. When x-polarized light passes through a liquid crystal cell it introduces a phase by which the polarization state of each wavelength changes. The birefringent LC cell works as a retardation plate of varying phase for different wavelengths. For central wavelength it works as a half wave plate (for 19 micron thickness cell, c.f. Eq. 1), and rotates the input polarization by 90° owing to the fact that it is placed at 45° with respect to the input polarizer. The polarization rotation for near-central wavelengths is less than 90°. When the analyzer angle = 0° , then according to Malus law [25] spectral components in the vicinity of central wavelengths show a drop in spectral density. Only those wavelengths, for which the polarization would be non-orthogonal following Eq. (1), would pass through the system and one gets a two peak spectrum (notch filter). On increasing the analyzer angle the peaks begin collapsing to each other, i.e., the visibility of peaks decrease, and one gets a flat top spectrum at = 40° (not shown in Fig. 2). Further changing the angle, these peaks completely collapse to one point and the spectrum becomes triangle type at = 45°. More analyzer rotation decreases the spectral bandwidth and the spectrum becomes nipple type at = 50° (not shown in Fig. 2). Further analyzer rotation makes central peak dominate and at = 60°, spectral bandwidth is 31.4 nm and side peaks start emerging. The spectral intensity of these side peaks increase with further increase in the analyzer angle, shrinking the central peak bandwidth, and at analyzer angle , we get central-peak-dominated spectrum with bandwidth of approximately 26.2 nm. Thus it is apparent that a wide range of spectral configurations can be generated by polarization control of liquid crystal. The theoretically predicted results shown in Fig. 2, are found very well in agreement with the experimental results. We emphasize here that the output spectra obtained either theoretically or experimentally in Fig. 2 clearly demonstrate the effect of losses in the intensity of each spectral component, passing through our scheme shown in Fig. 1. In order to study the effect of LC cell thickness on the output spectrum, we made the LC cells of different thicknesses, based on the availability of myler spacers with us: 25 µm , 44 µm , 57 µm , 75 µm and 94 µm . These LC cells were probed using the experimental scheme shown in Fig. 1, keeping relative angle between first polarizer and LC cell same as in the previous study. The analyzer was placed orthogonal to the polarizer. Fig. 3 shows the spectral changes in the input spectrum for different thicknesses of the LC cell. We observe that with increasing
Fig. 1. Experimental scheme to demonstrate spectral manipulation using nematic liquid crystal cell. Notations: A aperture, L lens, F broadband filter, P polarizer and LC liquid crystal cell. Spectrum of light of the LED source and output spectrum of the broadband filter are shown in the inset.
Theoretical analysis For theoretical analysis, the incident broadband light spectrum can be considered to be normalized Gaussian distribution, expressed as
S 0 ( ) = exp
(
0)
2
2
,
(2)
where 0 = c/ is the central frequency, c is speed of light and is the bandwidth of the spectrum. For the liquid crystal, the dependance of ordinary and extraordinary refrective indices on the wavelength of light can be expressed by using the three coefficient (extended) Cauchy equations obtained from the three band model of LC [24]:
no2 ( ) = A0 +
B0 2
+
C0 4
,
(3) 532
Results in Physics 12 (2019) 531–534
B. Kanseri et al.
Fig. 2. Spectral shaping of the output spectra by changing the angle of analyzer ranging from 0° to 90° for a 25 micron thick LC cell placed in the configuration shown in Fig.1. Left plots are theoretical results whereas right ones are experimental results. Dashed line (blue) corresponds to input source spectrum whereas the solid line (red) represents output spectrum.
Fig. 3. Spectral shaping for increasing LC cell thickness. The analyzer is placed orthogonal to the polarizer. Left plots are theoretical results whereas right ones are experimental results. Dashed line (blue) corresponds to input source spectrum whereas the solid line (red) represents output spectrum. Number of spectral peaks increase with cell thickness.
Fig. 1 with analyzer placed at 90° with respect to the input polarizer. Fig. 4 demonstrates the change in input spectra for different applied voltages across the nemetic LC cell of 25 micron thickness. We observe that at 0 V, there is cross-polarization condition, and similar to Fig. 2, a two peak spectrum is obtained. By increasing the voltage, one of the peaks enhances, whereas the other subsides. At 1.4 V, the second peak disappears and a blue-shifted spectrum is obtained. This characteristic voltage at which spectrum is blue-shifted depends on the thickness of the LC cell and the type of liquid crystal (birefringence). On further increase in voltage the effect repeats itself and at 1.8 V we get a redshifted spectrum. On further increase in voltage, the peak starts flatten and the spectral width becomes wider with less visibility of the spectral modulations. These spectral changes occur in a time frame of several microseconds, which is dependent on the relaxation time of the LC molecules.
LC thickness, the spectral peaks (modulations) increase. The number of peaks obtained for the LC thicknesses 25 µm , 44 µm , 57 µm , 75 µm and 94 µm are 3, 4, 6, 8 and 9, respectively. We also infer from the figures that the theoretically predicted spectral changes (peaks) with varying LC thickness are very well in agreement with the experimental results. Slight mismatch in spectral densities in theory and experiment could be due to unavoidable imperfections in LC cell formation, LC filling and losses due to larger thickness of the LC cell. We clearly observe that excellent match between experimental and theoretical results of Figs. 2 and 3 demonstrate a precise control of LC parameters on the spectral shape of broadband light field, advocating the application of this effect on spectral shaping. Since liquid crystals have electro-optical properties, their birefringence can be tuned by applying voltage across the LC cell [18]. Thus one can obtain spectral changes in the transmitting light field by just applying DC voltage across the LC cell placed in the scheme of
533
Results in Physics 12 (2019) 531–534
B. Kanseri et al.
Acknowledgements The authors thank Dr. Swadesh K. Gupta for help in making the liquid crystal cells. Research leading to the results reported in this paper received funding from Science and Engineering Research Board, India through grant YSS/2015/000367, YSS/2015/000743, and from Council for Scientific and Industrial Research, India through grant 03(1401)/ 17/EMR-II. Author Gyaprasad is thankful to University Grant Commission, India for a Junior Research Fellowship. References [1] Pu J, Zhang H, Nemoto S. Spectral shifts and spectral switches of partially coherent light passing through an aperture. Opt Commun 1999;162:57. [2] Kandpal HC, Anand S, Vaishya JS. Experimental observation of the phenomenon of spectral switching for a class of partially coherent light. IEEE J Quant Electron 2002;38:336. [3] Pu J, Cai C, Nemoto S. Spectral anomalies in Young’s double-slit interference experiment. Opt Expr 2004;12:5131. [4] Kanseri B. Polarization assisted data encoding and transmission using coherence based spectral anomalies. J Opt 2013;15:055407 . [5] Han P. Spectral shifts with polarization control. J Opt 2013;15:105710 . [6] Pu J, Korotkova O, Wolf E. Invariance and noninvariance of the spectra of stochastic electromagnetic beams on propogation. Opt Lett 2006;31:2097. [7] Shirai T, Asakura T. Spectral changes of light induced by scattering from spatially random media under the Rytov approximation. J Opt Soc Am A 1995;12:1354. [8] Han P. All optical spectral switches. Opt Lett 2012;37:2319. [9] Krupa K, Labruyre A, Tonello A, Shalaby BM, Couderc V, Baronio F, Acheves AB. Polychromatic filament in quadratic media: spatial and spectral shaping of light in crystals. Optica 2015;2:1058. [10] Labroille G, Pinel O, Treps N, Joffre M. Pulse shaping with birefringent crystals:a tool for quantum metrology. Opt Expr 2013;21:1890. [11] Han P. Lattice spectroscopy. Opt Lett 2009;34:1303. [12] Yadav BK, Raman S, Kandpal HC. Information exchange in free space using spectral switching of diffracted polychromatic light: possibilities and limitations. J Opt Soc Am A 2008;25:2952. [13] Garini Y, Young IT, McNamara G. Spectral imaging: principles and applications. Cytometry 2006;69A:735. [14] Ding P-F, Han P. Spectral manipulation and complementary spectra with birefringence polarization control. J Opt 2017;19:035601 . [15] Ding P-F, Hsu H-C, Han P. Spectral manipulation and tunable optical frequency ruler using liquid crystal birefringence. Optik 2019;179:115. [16] Khoo I-C, Wu S-T. Optics and nonlinear optics of liquid crystals. Singapore: World Scientific; 1993. [17] Wu S-T, Efron U, Hess LD. Birefringence measurements of liquid crystals. Appl Opt 1984;23:21. [18] Michel RE, Smith GW. Dependence of birefringence threshold voltage on dielectric anisotropy in a nematic liquid crystal. J Appl Phys 1974;45:3234. [19] Vicari L. Optical applications of liquid crystals. Boca Raton, Florida: CRC Press; 2003. [20] Abulell M, Abdulhalim I. Narrowband multispectral liquid crystal tunable filter. Opt Lett 2008;41:1957. [21] Gilardi G, Donisi D, Serpengze A, Beccherelli R. Liquid-crystal tunable filter based on sapphire microspheres. Opt Expr 2009;34:3253. [22] Aharon O, Abdulhalim I. Liquid crystal Lyot tunable filter with extended free spectral range. Opt Expr 2009;17:11426. [23] See the link:https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id= 3488. [24] Li J, Wu S-T. Extended Cauchy equations for the refractive indices of liquid crystals. J Appl Phys 2004;95:896. [25] Goldstein DH. Polarized light. Boca Raton, Florida: CRC Press; 2011.
Fig. 4. Spectral manipulation by applying the DC voltage across the 25 micron thick LC cell. Polarizer and analyzer are placed orthogonal to each other, and the liquid crystal director makes 45° (red) with the polarizer axis. Dashed line (blue) corresponds to input source spectrum whereas the solid line represents output spectrum.
Conclusion In conclusion, we have demonstrated both theoretically and experimentally a simple yet effective method for spectral shaping of broadband light field by controlling several parameters of the nematic liquid crystal. We demonstrate spectral manipulation using three ways: a) by polarization control using a set of polarizers with LC, 2) by changing the thickness of LC cell and 3) by tuning the birefringence of LCs by changing the applied DC voltage across it. The output field can have spectral distribution as two peaks, red shifted, blue shifted, notch filter, narrow band, central peak dominated, nipple type etc. These spectral shapes and modulations are theoretically predictable, providing a precise control over the spectral manipulation process. The use of liquid crystal thus offers a versatile medium for spectral manipulation of light fields over a broad spectral range which can find potential applications in spectral shaping, and in synthesis of sources having arbitrary spectral distributions. The polarization and voltage dependent spectral manipulations might find applications in designing achromatic polarization components (such as achromatic retarders) applicable to a wide range of spectrum, providing a tunable and cost-effective solution compared to the crystal based achromatic optical components.
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