Multiband retardation control using multi-twist retarders

Transcription

1 Multiband retardatin cntrl using multi-twist retarders Kathryn J. Hrnburg, Ravi K. Kmanduri, and Michael J. Escuti Department f Electrical and Cmputer Engineering, Nrth Carlina State University, Raleigh, Nrth Carlina 27695, USA ABSTRACT We intrduce and demnstrate an apprach t create highly chrmatic retardatin spectra acrss varius wavelengths. The design apprach is based n Multi-Twist Retarder (MTR) principle where multiple liquid crystal plymer layers are cated n tp f each ther n a single substrate. Previus MTRs have been applied t develp bradband achrmatic retarders, but here we shw that MTRs are quite flexible, and their retardatin spectrum can be tuned t create arbitrary prfiles. As a representative example, we shw this tailrability by creating a retarder which prduces apprximately zer retardatin in visible (5-9 nm) and half-wave retardatin in near-infrared (1-2.7 µm) wavelength regin. This wuld prvide enhancement in remte sensing, telecm, and spectrscpy systems where it is advantageus t have an ptical element which affects nly ne band, but is largely transparent therwise. Keywrds: Multi-Twist Retarders, retardatin cntrl, half-wave retarders, liquid crystals, MTR, chrmatic 1. INTRODUCTION Precise retardatin cntrl is a imprtant when dealing with measurement f elements r within a filtering setting such as with remte sensing, telecm, r spectrscpy systems. Previus attempts which allwed fr multiple bands f different utput retardatin, bth in the achrmatic and chrmatic schemes, resulted in cmplex elements that had cmplicated assembly requirements, such as Slc; Lyt-Ohman; and a hybrid f these tw designs, Evans. These designs, called birefringent chain filters by their creatrs, can be thught f as multiband r narrwband cntrllers due t the passband like nature f the resulting transmissin spectrum. 1 These bands have a cmplex cntrlled effect n the utput retardatin. New fabricatin methds have been develped t simplify the element alignment and thus assembly prcess by cating birefringent phtalignable materials n a single substrate. Initially, these new fabricatin methds were used t create passive achrmatic elements. 2 Here we shw that it is pssible t use these methds t develp chrmatic Multi-Twist Retarders (MTR) with similar prperties t the achrmatic MTRs intrduced previusly. With chrmatic MTRs, the Stkes vectr at the utput f the retarder can vary acrss wavelength, allwing fr bands with different, precisely tunable retardatin. 2. BACKGROUND 2.1 Traditinal Appraches t Chrmatic Retardatin Cntrl In the past, birefringent chain filters were develped t allw narrw bandwidths f transmitted signal t pass thrugh a system f waveplates, birefringent plates, and plarizers. These clr filters fall int tw main categries: Lyt-Ohman and Slc. 1, 3 With Slc-type filters, there are multiple retarders in series with a plarizer n bth ends f the stack. The tw types f Slc filters, shwn in Fig.1(a-b), describe the methds t align the rientatin angle thrughut the system. Flded Slc filters have the ptical axes f the retardatin plates s that they vary ±ρ, where ρ is defined as π/4n and N is the number f plates in the system. 4 Fan Slc filters have retardatin plates ptical axes that increase with each additinal element and rtate arund frm t 2π, with all the elements in the system. 3, 4 Crrespndence shuld be sent t: mjescuti@ncsu.edu, Telephne: Plarizatin: Measurement, Analysis, and Remte Sensing XI, edited by David B. Chenault, Dennis H. Gldstein, Prc. f SPIE Vl. 999, 999Z 214 SPIE CCC cde: X/14/$18 di: / Prc. f SPIE Vl Z-1 Dwnladed Frm: n 8/29/214 Terms f Use:

2 Lyt-Ohman systems have a series f birefringent elements each separated by a plarizer. 3 This separatatin f the birefringent stack makes it different than ur grups wrk. A derivative f the Lyt-Ohman, the Evans filter, which has several sets f thick waveplates and quarter waveplates (QWP) separated by plarizers is shwn in Fig.1(c). Althugh the filter designs can have high transmissin, 86% as shwn by Evans, 5 there is still the prblem with the thickness f the design, alignment f each element in the stack, and small useable aperture. 1 In additin, all these designs depend n the use f plarizers which act t reduce the signal utput. Anther apprach studied was the use f bi-layer plarizatin gratings fr ptical filters which had the advantage f remving the lssy plarizers in the stack, but still had the limitatin that each cmpnent had t be aligned precisely. 6 (a) 9 ρ ρ -ρ -ρ (b) ρ ρ ρ 1 2 ρ 3 (c) QWP QWP Figure 1. Tw Types f Slc Filters: (a) Flded and (b) Fan and (c) Evans filter with QWPs aligned t. retardatin cntrller is a unique set f individual plarizers and waveplates. We see that each 2.2 Multi-Twist Retarders MTRs are passive birefringent retarders created with dped liquid crystals cated nt a single prepared substrate. The substrate itself is prepared with Light Plymerizable Plymer (LPP) ROP-18 (Rlic Technlgies Ltd.) t align the liquid crystals t the apprpriate angle φ. Each liquid crystal layer has the parameters f twist φ m and thickness d m, which allw fr the generatin f distinct transmissin prfiles as illustrated in Fig.2. 2 The parameter M specifies the number f individual transfrm matrices that are part f the full MTR transfrmatin matrix. A higher M equates t mre layers each with individual twists and thicknesses. The ttal number f defined parameters fr the system is 2M + 1. The twist f the layer is generated by dping nematic liquid crystal with small amunts f chiral liquid crystal in slvent at specific cncentratins. Fr this test, we used the experimentally verified Liquid Crystal Plymer (LCP) RMS3-1c (Merck Chemicals Ltd.) with a birefringence prfile f n(λ) = /λ 2. Dping f the LCP was accmplished using CB15 (Merck Chemicals Ltd.) and C45S (LC Matter Crp). Each chrmatic design begins with a set f transfrmatin matrices riginally design fr twisted nematic cells. 2, 7 One transfrmatin matrix, T m describes an individual layer f the full design with the individual parameters fr each layer f nrmalized phase retardatin ζ m, magnitude f nrmalized retardatin and twist χ m, and mean f the twist φ. Each f these cmpnents have the prperties: ζ m = Γ m (λ)/2 = π n(λ)d m /λ (1) Prc. f SPIE Vl Z-2 Dwnladed Frm: n 8/29/214 Terms f Use:

3 LPP χ m = ζ 2 m + φ 2 m (2) m φ = 1/m φ i + π/2 (3) i= The series f transfrm matrices becme a full MTR design when multipled tgether, T MTR = T M... T 2 T 1. (a) (b)... S i (λ) Substrate S (λ) Φ m... y y Φ z Φ 1 Φ 2 Φ... m d 1 d 2 d m Substrate x Figure 2. A chrmatic MTR as viewed frm (a) its side and (b) tp view. In (a), each subsequent layer is aligned t the twist beneath it. Frm the tp, the light passes thrugh and fllws the cmbined twist thrugh the MTR. 3.1 Apprach 3. HIGHLY CHROMATIC MTR THEORY We use traditinal linear algebra t represent the utput Stkes vectr such that S (λ) = T MTR S i (λ), where S (λ) is the Stkes vectr at the utput. With the chrmatic MTR system, S is a functin f wavelength, thus cmplex chrmatic retardatin schemes can be achieved. A specific MTR cst functin f = 1 S (λ) S t (λ) is used in designing the prper parameters f twist and thickness fr a MTR. This cst functin when applied t the slutins f the S (λ) helps determine hw accurate the S is t the target Stkes prfile S t by taking the mean f the Stkes vectr deviatin frm the target acrss all wavelengths. A gd slutin has been achieved when the f is minimized. T test the chrmatic MTR thery, a retarder was designed and built fr S 3 input that is prduces zer retardatin in visible (VIS, 5-9 nm) and half-wave retardatin in near-infrared (NIR, µm). This retarder cnverts frm ne circular plarizatin t anther acrss the wavelengths f interest classifying it as a circular t circular halfwave retarder as seen in Fig.3. These retarders can be useful because their catings culd be applied t mre cmplex patterned ptics, such as plarizatin grating r q-plates which act n S 3 input. Three different designs fr this circular t circular retarder were generated using the cst functin fr three different M values. The resulting designs are listed in Table 1. Prc. f SPIE Vl Z-3 Dwnladed Frm: n 8/29/214 Terms f Use:

4 Table 1. The twist and thicknesses f 3 different circular t circular chrmatic half waveplate retarder slutins fund with varius different M s. φ ( ) φ 1 ( ) d 1 (µm) φ 2 ( ) d 2 (µm) φ 3 ( ) d 3 (µm) φ 4 ( ) d 4 (µm) 2TR TR TR Retardatin (waves).4.3 NIR.2 Zer Wave Band Transitin Regin.1 VIS Half Wave Band 1% f Peak Retardatin 9% f Peak Retardatin Figure 3. Circular t Circular Retarder with 3 bands f interest: zer wave, where the S 3 input is preserved, transitin regin, and a half wave regin, where the S 3 input switches handedness. The 1% and 9% lines indicate the retarder shuld have high cntrast t distinguish between the zer and half wave bands. 3.2 Impact f M Generally, as the number f M is increased the design matches the specificatin mre precisely. The designs fr a circular t circular chrmatic half waveplate retarder with M=2, 3, and 4 are shwn with S 3 input in Fig.4. Bth the 2TR and 3TR fail at making accurate matches t the desired target prfile. This is mst prfund in the VIS regin where bth f these designs d nt match the shape f the target prfile and als intrduce additinal peaks. We selected the 4TR versin f the circular t circular chrmatic halfwave retarder fr fabricatin because it quickly changed between the zer wave and half wave bands and had the best cntrast between the VIS and NIR bands. Prc. f SPIE Vl Z-4 Dwnladed Frm: n 8/29/214 Terms f Use:

5 (a) TR 3TR 2TR Target (b) T // T 4 2 4TR 3TR 2TR Target (c) S3 ( ) TR 3TR 2TR Target Retardatin (waves) TR.1 3TR 2TR Target (d) Figure 4. M=2,3,and 4 designs are cmpared with S 3 input. (a) Transmissin with parallel plarizers, T // (b) Transmissin with crssed plarizers T (c) Effect n S 3, and (d) Retardatin. The M=4 design matches all the target spectra mst accurately. Prc. f SPIE Vl Z-5 Dwnladed Frm: n 8/29/214 Terms f Use:

6 4. CIRCULAR TO CIRCULAR CHROMATIC HALFWAVE RETARDER 4.1 Fabricatin Fabricatin f the halfwave retarder is accmplished in the same way as fr achrmatic MTR, where an alignment layer is applied t a substrate and plymerized. Catings f differently dped liquid crystal are applied t the aligned substrate and plymerized between layers. 2 The recipe and mixtures needed t create the final part are listed in Tables 2 and 3 respectively. Table 2. LCP mixtures fr the circular t circular chrmatic halfwave retarder. Mix Materials wt:wt Rati Net Chiral: LCP-Slids: Slvent Raw LCP Set by Manufacturer Set by Manufacturer :.3:.7 A CB15(+):PGMEA.2 :.98.2 : :.98 B C45S(-):PGMEA.2 :.98.2 : :.98 C Mix-A:Raw LCP.3 : 1.462:.231:.765 D Mix-A:Raw LCP.2 : 1.392:.294:.75 E Mix-B:Raw LCP.22 : 1.431:.294:.76 F Mix-A:Raw LCP.17 : 1.291:.256:.741 Table 3. The recipe fr the circular t circular chrmatic halfwave retarder. Layer 1 Layer 2 Layer 3 Layer 4 4TR Mix-C, 116 rpm Mix-D, 585 rpm Mix-E, 7 rpm Mix-F, 965 rpm 4.2 Results Fr the first measurement, the final waveplate was measured using a in-huse Full-Stkes Plarimetry system with S 1 input plarizatin with a wavelength band f 425 t 8nm. 8 Frm the Stkes utput f the retarder, the unique parameters f twist and thickness were fitted t the data. This fit, displayed in Table 4, was used as the best mdel f the data s that it is pssible t mdel what wuld be like with a S 3 input plarizatin, since bradband creatin f S 3 input was nt feasible. The fit, alng with the data and the design fr S 1 are shwn in Fig. 5. Table 4. The fit fund fr the circular t circular retarder frm in-huse Full-Stkes Plarimetry system. φ ( ) φ 1 ( ) d 1 (µm) φ 2 ( ) d 2 (µm) φ 3 ( ) d 3 (µm) φ 4 ( ) d 4 (µm) 4TR A Varian Cary 5E was used t get a bradband transmissin spectrum view f the retarder t shw that this retarder has a cntrlled bradband effect with the S 1 input available in the lab, shwn in Fig. 6. The transmissin captured was between parallel linear plarizers. The design and fit are verlayed nt this data. With the Cary 5E data, we see the fit is mre accurate in the VIS than in NIR. This fit discrepancy likely is due t the fit being calculated fr 425 t 8 nm and nt the entire 5 t 27 nm spectrum. Acrss the entire spectrum, the data matches the general shape f the design, but des nt reach the same level f cntrast. Mdeling the fit using S 3 input, seen in Fig. 7, shws a VIS regin that des nt cnvert the S 3 input and a NIR regin that is apprximately halfwave. In NIR, the cntrast is lwer than the design and transmissin data frm Cary 5E suggest. This culd be due t the errr in fit mdel seen fr S 1 input. Prc. f SPIE Vl Z-6 Dwnladed Frm: n 8/29/214 Terms f Use:

7 1.5 Data S1 ( ) Figure 5. Final retarder measured and fit with Full-Stkes Plarimetry system with linear surce and a 425 t 8 nm wavelength band. The resulting fit was used t mdel the retarder s respnse t S 3 input T // 4 2 Data Figure 6. Bradband transmissin measurement f retarder with Varian Cary 5E, a S 1 input tl. Prc. f SPIE Vl Z-7 Dwnladed Frm: n 8/29/214 Terms f Use:

8 (a) (b) 6 6 T // 4 T (c) 1.5 (d).4.5 S3 ( ) Retardatin (waves) Figure 7. and fit f circular t circular chrmatic halfwave retarder are cmpared with S 3 input. parallel plarizers T // (b) Transmissin with crssed plarizers T (c) Effect n S 3, and (d) Retardatin. (a) Transmissin with Prc. f SPIE Vl Z-8 Dwnladed Frm: n 8/29/214 Terms f Use:

9 5. CONCLUSION We have develped and demnstrated chrmatic MTRs that have specific bands with different chrmatically cntrlled retardatins. Previusly MTRs were designed t augment the retardatin achrmatically, nw we can generate chrmatic designs that can precisely tailr the retardatin spectrum f a waveplate acrss the wavelengths f interest. T shw this in practice a representative sample, a circular t circular halfwave retarder, was created t test the chrmatic thery. This circular t circular retarder shws it is pssible t create bands f different distinct retardatin with MTRs. The chrmatic branch f MTRs pens up a variety f new elements where the chrmatic cating culd be applied t cmplex patterned ptical elements that wrk with S 3 input, i.e. plarizatin gratings and q-plates, fr additinal cntrl f the retardatin spectrum and bandwidth prperties. Acknwledgments The authrs f this paper greatly acknwledge the supprt f the Natinal Science Fundatin (CAREER award ECCS ) fr this wrk. REFERENCES [1] Šlc, I., Birefringent chain filters, J. Opt. Sc. Am. 55(6), (1965). [2] Kmanduri, R. K., Lawler, K. F., and Escuti, M. J., Multi-twist retarders: bradband retardatin cntrl using self-aligning reactive liquid crystal layers, Opt. Express 21(1), (213). [3] Evans, J. W., Slc birefringent filter, J. Opt. Sc. Am. 48(3), (1958). [4] Hdgkinsn, I. J. and Qi-Hng, W., [Birefringent Thin Films and Plarizing Elements], , Wrld Scientific (1997). [5] Evans, J. W., A birefringent mnchrmatr fr islating high rders in grating spectra, Appl. Opt. 2(2), (1963). [6] Niclescu, E. and Escuti, M. J., Plarizatin-independent tunable ptical filters using bilayer plarizatin gratings, Applied Optics 49(2), (21). [7] Tang, S. T. and Kwk, H. S., Mueller calculus and perfect plarizatin cnversin mdes in liquid crystal displays, Jurnal f Applied Physics 89(1), (21). [8] Gldstein, D. H., [Plarized Light], CRC Press, 3 ed. (211). Prc. f SPIE Vl Z-9 Dwnladed Frm: n 8/29/214 Terms f Use: