Abstract

A method to extend the spectral range of a tunable optical filter is proposed in this paper. Two identical Fabry-Perot filters and an additional tunable filter with a different free spectral range are cascaded to extend the spectral range and reduce side lobes. Over 400 nm of free spectral range and 4 nm of FWHM of the filter are achieved. The design procedure and simulation are described in detail. An experimental three-stage tunable Fabry–Perot filter with visible and infrared spectra is demonstrated. The experimental results and the theoretical analysis are presented in detail to verify this method. The results reveal that a compact and extended tunable spectral range of Fabry–Perot filters can be easily attainable by this method.

© 2011 OSA

1. Introduction

Tunable optical filters, known for long time, have played an important role in many applications such as remote sensing [1], hyperspectral imaging [2], biomedical imaging [3,4], optical telecommunication [5,6], astronomical observation [7,8], and displays [9,10]. For tunable optical filters, electro-optic crystals (such as KDP and ADP) or liquid crystals (LC) are often used as variable birefringent retarders [1113] to produce a narrow passband. LC tunable filters have been an active research area because of their advantages of continuous tuning, low power consumption, high tuned speed, compactness, and reliable performance without any movable components. LC tunable filters have been demonstrated in a variety of applications based on the Lyot/Solc filter [14,15] as well as the Fabry–Perot filter [1618]. Compared with the Lyot/Solc filter, the Fabry–Perot filter usually has narrow FWHM, a higher transmission, but a small free-spectral range (FSR), which is typically a few tens of nm. The Fabry–Perot filter has been used widely in optical telecommunication because of the narrow FWHM, but it rarely has been used in many applications that need a wide FSR or a wide dynamic range, in particular for biomedical imaging. Much research has been reported to extend the FSR of an LC tunable optical filter by using a tandem technique. Hirabayashi presented a tunable wavelength selective filter at a wavelength of 1.47–1.6 μm that is stacked by two LC Fabry–Perot interferometers [19]. Aharon [20,21] used an additional LC variable retarder to extend the FSR of a Lyot/Solc tunable filter. The tandem technique is also reported for increasing the sharpness of the transmission profile [22]. Some reports have revealed that an improved channel shape [23,24] and flat-top LC tunable filter [25] can be obtained by using coupled Fabry–Perot cavities. The concept of a coupled-resonator filter is also used in silicon-on-insulator technology. Multistage racetrack resonator filters in silicon-on-insulator have been designed and manufactured [2628]. A viable alternative to increase FSR using the theory of a series-coupled racetrack is reported to extend the FSR of a racetrack resonator, wherein 36 nm of FSR can be achieved [28]. For the tandem technique, the simplest case is the two tandem Fabry–Perot interferometers system. In order to minimize the interaction between the two interferometers, the second one is often used to make the separation distance between the two Fabry–Perot interferometers. However, a large FSR and a narrow FWHM are still in great demand to accomplish many applications such as remote sensing, astronomical observation, and biomedical imaging, which usually covers part of the visible range (450–700 nm) and part of the near infrared range (700–1000 nm).

In this paper, a novel concept (to our knowledge) for extending the spectral range of a tunable Fabry–Perot filter is proposed by cascading three-stage Fabry–Perot filters with an interleaving order. Two identical tunable Fabry–Perot filters are placed in tandem to extend the FSR by interleaving only one order of the transmission peak. The FSR can be extended to maximum because of using one order of difference between the first and second filters. Then an additional Fabry–Perot filter with a different FSR (with one order of difference, too) is cascaded to reduce the side lobes. A three-stage Fabry–Perot filter is achieved with 400 nm of FSR and 4 nm of FWHM. The results reveal that an extended tunable spectral range of a Fabry–Perot filter can be easily attained by this method.

2. Concept and design

A Fabry–Perot LC tunable filter can be achieved by enclosing a plane-parallel plate of the LC, shown in Fig. 1(a). The transmission of the LC Fabry–Perot filter has the form Fig. 1 (a) . The transmission of the LC Fabry–Perot filter has the form

T=I(t)I(i)=11+Fsin2δ2,
where, I(t)is the intensity of output light, and I(i) is the intensity of input light. Finesse F has the form F=4R(1R)2; R is the reflectivity of two distributed Bragg reflectors (DBRs); δ is the phase in passing through the Fabry–Perot filter δ=4πλnd2δDBR, where n is the equivalent refractive index of liquid crystal; d is the thickness of LC layer; and δDBR is the reflective phase of two DBRs and can be considered as a constant value. The equivalent refractive index of the LC has the form
n=1dd2d2no[1(1no2ne2)sin2θ]12dz,
where ne is the extraordinary index of refraction, which depends on the tilt angle of the LC molecules, θ, no is the ordinary index of refraction, and d is the LC layer thickness. The tilt angle profile θ(z) depends on the external voltage and on the surface anchoring conditions.

 

Fig. 1 (a) Fabry–Perot LC tunable filter; (b) layout of three-stage LC tunable Fabry–Perot filter.

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The FWHM and FSR of the Fabry–Perot filter are given by

λpeak=2ndm;FSR=λpeak22nd=2ndm2=λpeakm;FWHM=2λmπ1F,
where m = 1, 2, 3,…is the order of the transmission peak and λpeak is the peak wavelength of the filter. From Eq. (2), the FSR of the filter is in inverse proportion to the order m. The FWHM is in inverse proportion to the order m2. Different FSRs and FWHMs can be achieved at the fixed λpeak when different orders of m are used. Then different peak wavelengths and FSRs can be achieved when the equivalent index of the LC is changed by adjusting the applied voltage of the LC layer.

The structure of a three-stage Fabry–Perot filter is shown in Fig. 1 (b). Two identical Fabry–Perot tunable filters and an additional tunable filter with a different FSR are cascaded to extend the tunable spectral range and reduce the side lobes. The first Fabry–Perot filter and the second filter have the same thickness of LC layer and are made of the same LC material (E44, purchased from Merck).

The transmission function of a three-stage Fabry–Perot filter has

T=11+Fsin2δ1211+Fsin2δ2211+Fsin2δ32=11+Fsin2(2πλn1d)11+Fsin2(2πλn2d)11+Fsin2(2πλn3d3),
where, n1, n2, and n3 are the equivalent indices of the first, second, and third LC layers, respectively; d is the thickness of the first and second LC layers; and d3 is the thickness of the third LC layer. Since a three-stage filter uses the same DBR layer, Finesse F has the same merit:

F=4R(1R)2.

When {2πλn1d=mπ2πλn2d=(m+1)π,2πλn3d3=(m1)π  the total transmission of the three-stage cascading filter is 1. Then, FSR of each filter is

FSR1=λpeakm;FSR2=λpeakm+1;FSR3=λpeakm1.

Three filters are working in different orders and have different FSRs after being cascaded, and the interval wavelength of next order is

λinterval=λpeakmλpeakm+1=λpeakm(m+1).

So, the adjacent peak wavelength of the three-stage filter will be

λpeak'=2n1dm+FSR1λinterval=2n1d2m+1=λpeakm2m+1,
where, λpeak is the peak wavelength of the filter, λpeak ’ is the adjacent peak wavelength, and m is the order of transmission peak.

So, the free spectral range of the whole three-stage filter is

FSR=λpeakm+12m+1,

The first, second, and third Fabry–Perot filters are working at m, m + 1, and m-1 order, respectively; we simply called this the “jump order” filter. Equation (3) shows the transmission of the filter, and the FWHM can be determined exactly. Since the order difference of a three-stage filter is small, the phases of the filters have similar merit, then

T(11+Fsin2δ12)3.

It is easy to show that the finesse will be determined with a good approximation when the transmission function decreases to 50% of its maximum value when its phase is 2π/3.

Hence, the FWHM is approximately

FWHM232λpeakmπ1F.

From Eqs. (5) and (6), the FSR of the whole filter is extended to m+12m+1λpeakand the FWHM improves almost 30% . Moreover, the side lobes of a three-stage Fabry–Perot LC filter are reduced because of the different FSRs by interleaving one order of the transmission peak.

The transmission spectra of a designed three-stage Fabry–Perot tunable filter are shown in Fig. 2 . Figure 2(a) shows the transmission of the first filter (pink) and second filter (blue). The thickness of the LC layer (E44, purchased from Merck) of two filters is exactly the same (3μm). The peak wavelength is tuned to 850 nm. The optical phase of the filter can be varied by adjusting the voltage of the LC layer. A different order of the first and second filters is used, and m = 11 for the first filter and m + 1 = 12 for the second filter. The total transmission of the two cascaded filters is shown in Fig. 2(b). We can see that the FSR is extended by interleaving only one order of two filters. To reduce the side lobes of the two cascaded filters, an additional filter is used. Figure 2(c) shows the transmission of the third filter in which the thickness of the LC is 2.7 μm, and m-1 = 10 is used by using different thicknesses and adjusting the voltage of the LC layer. The total output of the three-stage LC Fabry–Perot tunable filter is shown in Fig. 2(d). By using the method of cascading the three-stage filter, the FSR is extended to over 400 nm, and the FWHM is less than 4 nm and has lower-level side lobes.

 

Fig. 2 (a) Transmission spectra for the first (pink, d = 3000nm, m = 11) and second (blue, d = 3000 nm, m + 1 = 12) Fabry–Perot filter. (b) Transmission spectra of cascaded first and second filters. (c) Transmission spectra for the third (d = 2700nm, m-1 = 10) filter. (d) Total output of three-stage LC Fabry–Perot tunable filter.

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3. Experimental and results

A single LC tunable Fabry–Perot filter was built on glass substrates with an area of 20×20mm and a thickness of 2 mm. The two pieces of flat glass were coated with transparent electrically conducting electrodes made of indium tin oxide (ITO) and DBR. Then they were cleaned and spin coated with an alignment layer. The material of the alignment layer is polyimide (PI-5, purchased from Shanghai Jiaotong University). The spinner was set to 5000 rpm for 60 s to form 100 nm of uniform thickness. Then the polymer was baked in a vacuum oven at a temperature of 80°C for 30 min and then at a temperature of 180°C for 2 h. A rubbing method was used for the alignment of LC molecules. After rubbing, the two plates were celled together by a spacer with a fixed gap. The LC (E44, purchased from Merck) was filled in and then sealed with glue. The three stages of the LC Fabry–Perot filter were cascaded together, as shown in Fig. 3 . The measured transmission of the experimental three-stage filter is shown in Fig. 4 . The total optical loss was about 65%. The thicknesses we built were d1 = d2 = 3 μm for the first- and second-stage filters, and the thickness of the additional stage as the order eliminator was d3 = 2.7 μm. The transmission spectrum can be changed according to the design by adjusting the voltage on the LC layer. The loading voltages changed from 0v–20 V with a 2 K square wave signal.

 

Fig. 3 Experimental three-stage LC Fabry–Perot filter.

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Fig. 4 Five examples of measured spectra of three-stage LC Fabry–Perot tunable filter: the peak wavelength of the filter at 848 nm, 750 nm, 695nm, 625 nm and 490 nm when the loading voltages for the three stages were: {2.03V, 5.75V, 2.12V}, {8.49V, 12.58V, 7.86V}, {12.85V, 16.21V, 13.72V}, {8.23V, 15.45V, 9.16V}, {13.25V, 6.15V, 3.05V}, correspondingly.

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4. Conclusion

A method to extend the spectral range of tunable optical filters is demonstrated by cascading a three-stage Fabry–Perot filter. Two identical tunable Fabry–Perot filters and an additional tunable filter with a different FSR and order are cascaded. The design procedure and simulation are described. Over 400 nm of FSR and 4 nm of FWHM were achieved. An example tunable optical filter with visible and infrared spectrum from 450–850 nm is demonstrated. It is even possible to use our method with other types of filters and other spectra. Tunable Fabry–Perot filters with narrow FWHM and large FSR will play an important role in many applications such as remote sensing, biomedical imaging, and astronomical observation.

Acknowledgments

This work is partially supported by the National Basic Research Program of China (973 Program) (No. 2009CB320803) and the State Key Laboratory of Modern Optical Instrumentation Funding Program.

References and links

1. H. Kurosaki, H. Koshiishi, T. Suzuki, and K. Tsuchiya, “Development of tunable imaging spectro-polarimeter for remote sensing,” Adv. Space Res. 32(11), 2141–2146 (2003). [CrossRef]  

2. A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005). [CrossRef]   [PubMed]  

3. S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6(12), 929–938 (2007). [CrossRef]   [PubMed]  

4. N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE 4056, 50–64 (2000). [CrossRef]  

5. K. Hirabayashi and T. Kurokawa, “Liquid crystal devices for optical communication and information processing systems,” Liq. Cryst. 14(2), 307–317 (1993). [CrossRef]  

6. A. Sneh and K. M. Johnson, “High-speed continuously tunable liquid crystal filter for WDM networks,” J. Lightwave Technol. 14(6), 1067–1080 (1996). [CrossRef]  

7. G. A. Kopp, M. J. Derks, D. F. Elmore, D. M. Hassler, J. C. Woods, J. L. Streete, and J. G. Blankner, “Tunable liquid-crystal filter for solar imaging at the He i 1083-nm line,” Appl. Opt. 36(1), 291–296 (1997). [CrossRef]   [PubMed]  

8. P. J. Miller, “Tunable narrowband birefringent filters for astronomical imaging,” Proc. SPIE 1235, 466–473 (1990). [CrossRef]  

9. S. Saeed and P. J. Bos, “Multispectrum, spatially addressable polarization interference filter,” J. Opt. Soc. Am. A 19(11), 2301–2312 (2002). [CrossRef]  

10. D. D. Huang, X. J. Yu, H. C. Huang, and H. S. Kwok, “Design of polarizing color filters with double-liquid-crystal cells,” Appl. Opt. 41(22), 4638–4644 (2002). [CrossRef]   [PubMed]  

11. H. A. Tarry, “Electrically tunable narrowband optical filter,” Electron. Lett. 11(19), 471–472 (1975). [CrossRef]  

12. C. Ye, “Low-loss birefringent spectral filters comprising three identical retarders,” Appl. Opt. 45(31), 8044–8051 (2006). [CrossRef]   [PubMed]  

13. G. Kopp, “Tunable birefringent filters using liquid crystal variable retarders,” Proc. SPIE 2873, 324–327 (1996).

14. B. Lyot, “Optical apparatus with wide field using interference of polarized light,” C.R. Acad. Sci. (Paris) 197, 1593 (1933).

15. I. Šolc, “Birefringent chain filters,” J. Opt. Soc. Am. 55(6), 621–625 (1965). [CrossRef]  

16. A. Frenkel and C. Lin, “Angle-tuned etalon filters for optical channel selection in high density wavelength division multiplexed systems,” J. Lightwave Technol. 7(4), 615–624 (1989). [CrossRef]  

17. B. Pezeshki, F. K. Tong, J. A. Kash, D. W. Kisker, and R. M. Potemski, “Tapered Fabry–Perot waveguide optical demultiplexer,” IEEE Photon. Technol. Lett. 5(9), 1082–1085 (1993). [CrossRef]  

18. T. Niemi, M. Uusimaa, S. Tammela, P. Heimala, T. Kajava, M. Kaivola, and H. Ludvigsen, “Tunable silicon etalon for simultaneous spectral filtering and wavelength monitoring of a DWDM transmitter,” IEEE Photon. Technol. Lett. 13(1), 58–60 (2001). [CrossRef]  

19. K. Hirabayashi, H. Tsuda, and T. Kurokawa, “Tunable wavelength-selective liquid crystal filters for 600-channel WDM system,” IEEE Photon. Technol. Lett. 4(6), 597–599 (1992). [CrossRef]  

20. O. Aharon and I. Abdulhalim, “Liquid crystal Lyot tunable filter with extended free spectral range,” Opt. Express 17(14), 11426–11433 (2009). [CrossRef]   [PubMed]  

21. O. Aharon and I. Abdulhalim, “Tunable optical filter having a large dynamic range,” Opt. Lett. 34(14), 2114–2116 (2009). [CrossRef]   [PubMed]  

22. A. A. M. Saleh and J. Stone, “Two-stage Fabry–Perot filters as demultiplexers in optical FDMA LAN's,” J. Lightwave Technol. 7(2), 323–330 (1989). [CrossRef]  

23. E.-A. Dorjgotov, A. K. Bhowmik, and P. J. Bos, “Switchable polarization-independent liquid-crystal Fabry–Perot filter,” Appl. Opt. 48(1), 74–79 (2009). [CrossRef]  

24. E. Dorjgotov, A. Bhowmik, and P. Bos, “Design of a wide bandwidth switchable mirror based on a liquid crystal etalon,” J. Appl. Phys. 105, 104906 (2009) [CrossRef]  

25. S. A. Alboon and R. G. Lindquist, “Flat top liquid crystal tunable filter using coupled Fabry–Perot cavities,” Opt. Express 16(1), 231–236 (2008). [CrossRef]   [PubMed]  

26. A. H. Atabaki, B. Momeni, A. A. Eftekhar, E. S. Hosseini, S. Yegnanarayanan, and A. Adibi, “Tuning of resonance-spacing in a traveling-wave resonator device,” Opt. Express 18(9), 9447–9455 (2010). [CrossRef]   [PubMed]  

27. Q. Li, M. Soltani, S. Yegnanarayanan, and A. Adibi, “Design and demonstration of compact, wide bandwidth coupled-resonator filters on a siliconon- insulator platform,” Opt. Express 17(4), 2247–2254 (2009). [CrossRef]   [PubMed]  

28. R. Boeck, N. A. Jaeger, N. Rouger, and L. Chrostowski, “Series-coupled silicon racetrack resonators and the Vernier effect: theory and measurement,” Opt. Express 18(24), 25151–25157 (2010). [CrossRef]   [PubMed]  

References

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  1. H. Kurosaki, H. Koshiishi, T. Suzuki, and K. Tsuchiya, “Development of tunable imaging spectro-polarimeter for remote sensing,” Adv. Space Res. 32(11), 2141–2146 (2003).
    [Crossref]
  2. A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
    [Crossref] [PubMed]
  3. S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6(12), 929–938 (2007).
    [Crossref] [PubMed]
  4. N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE 4056, 50–64 (2000).
    [Crossref]
  5. K. Hirabayashi and T. Kurokawa, “Liquid crystal devices for optical communication and information processing systems,” Liq. Cryst. 14(2), 307–317 (1993).
    [Crossref]
  6. A. Sneh and K. M. Johnson, “High-speed continuously tunable liquid crystal filter for WDM networks,” J. Lightwave Technol. 14(6), 1067–1080 (1996).
    [Crossref]
  7. G. A. Kopp, M. J. Derks, D. F. Elmore, D. M. Hassler, J. C. Woods, J. L. Streete, and J. G. Blankner, “Tunable liquid-crystal filter for solar imaging at the He i 1083-nm line,” Appl. Opt. 36(1), 291–296 (1997).
    [Crossref] [PubMed]
  8. P. J. Miller, “Tunable narrowband birefringent filters for astronomical imaging,” Proc. SPIE 1235, 466–473 (1990).
    [Crossref]
  9. S. Saeed and P. J. Bos, “Multispectrum, spatially addressable polarization interference filter,” J. Opt. Soc. Am. A 19(11), 2301–2312 (2002).
    [Crossref]
  10. D. D. Huang, X. J. Yu, H. C. Huang, and H. S. Kwok, “Design of polarizing color filters with double-liquid-crystal cells,” Appl. Opt. 41(22), 4638–4644 (2002).
    [Crossref] [PubMed]
  11. H. A. Tarry, “Electrically tunable narrowband optical filter,” Electron. Lett. 11(19), 471–472 (1975).
    [Crossref]
  12. C. Ye, “Low-loss birefringent spectral filters comprising three identical retarders,” Appl. Opt. 45(31), 8044–8051 (2006).
    [Crossref] [PubMed]
  13. G. Kopp, “Tunable birefringent filters using liquid crystal variable retarders,” Proc. SPIE 2873, 324–327 (1996).
  14. B. Lyot, “Optical apparatus with wide field using interference of polarized light,” C.R. Acad. Sci. (Paris) 197, 1593 (1933).
  15. I. Šolc, “Birefringent chain filters,” J. Opt. Soc. Am. 55(6), 621–625 (1965).
    [Crossref]
  16. A. Frenkel and C. Lin, “Angle-tuned etalon filters for optical channel selection in high density wavelength division multiplexed systems,” J. Lightwave Technol. 7(4), 615–624 (1989).
    [Crossref]
  17. B. Pezeshki, F. K. Tong, J. A. Kash, D. W. Kisker, and R. M. Potemski, “Tapered Fabry–Perot waveguide optical demultiplexer,” IEEE Photon. Technol. Lett. 5(9), 1082–1085 (1993).
    [Crossref]
  18. T. Niemi, M. Uusimaa, S. Tammela, P. Heimala, T. Kajava, M. Kaivola, and H. Ludvigsen, “Tunable silicon etalon for simultaneous spectral filtering and wavelength monitoring of a DWDM transmitter,” IEEE Photon. Technol. Lett. 13(1), 58–60 (2001).
    [Crossref]
  19. K. Hirabayashi, H. Tsuda, and T. Kurokawa, “Tunable wavelength-selective liquid crystal filters for 600-channel WDM system,” IEEE Photon. Technol. Lett. 4(6), 597–599 (1992).
    [Crossref]
  20. O. Aharon and I. Abdulhalim, “Liquid crystal Lyot tunable filter with extended free spectral range,” Opt. Express 17(14), 11426–11433 (2009).
    [Crossref] [PubMed]
  21. O. Aharon and I. Abdulhalim, “Tunable optical filter having a large dynamic range,” Opt. Lett. 34(14), 2114–2116 (2009).
    [Crossref] [PubMed]
  22. A. A. M. Saleh and J. Stone, “Two-stage Fabry–Perot filters as demultiplexers in optical FDMA LAN's,” J. Lightwave Technol. 7(2), 323–330 (1989).
    [Crossref]
  23. E.-A. Dorjgotov, A. K. Bhowmik, and P. J. Bos, “Switchable polarization-independent liquid-crystal Fabry–Perot filter,” Appl. Opt. 48(1), 74–79 (2009).
    [Crossref]
  24. E. Dorjgotov, A. Bhowmik, and P. Bos, “Design of a wide bandwidth switchable mirror based on a liquid crystal etalon,” J. Appl. Phys. 105, 104906 (2009)
    [Crossref]
  25. S. A. Alboon and R. G. Lindquist, “Flat top liquid crystal tunable filter using coupled Fabry–Perot cavities,” Opt. Express 16(1), 231–236 (2008).
    [Crossref] [PubMed]
  26. A. H. Atabaki, B. Momeni, A. A. Eftekhar, E. S. Hosseini, S. Yegnanarayanan, and A. Adibi, “Tuning of resonance-spacing in a traveling-wave resonator device,” Opt. Express 18(9), 9447–9455 (2010).
    [Crossref] [PubMed]
  27. Q. Li, M. Soltani, S. Yegnanarayanan, and A. Adibi, “Design and demonstration of compact, wide bandwidth coupled-resonator filters on a siliconon- insulator platform,” Opt. Express 17(4), 2247–2254 (2009).
    [Crossref] [PubMed]
  28. R. Boeck, N. A. Jaeger, N. Rouger, and L. Chrostowski, “Series-coupled silicon racetrack resonators and the Vernier effect: theory and measurement,” Opt. Express 18(24), 25151–25157 (2010).
    [Crossref] [PubMed]

2010 (2)

2009 (5)

2008 (1)

2007 (1)

S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6(12), 929–938 (2007).
[Crossref] [PubMed]

2006 (1)

2005 (1)

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
[Crossref] [PubMed]

2003 (1)

H. Kurosaki, H. Koshiishi, T. Suzuki, and K. Tsuchiya, “Development of tunable imaging spectro-polarimeter for remote sensing,” Adv. Space Res. 32(11), 2141–2146 (2003).
[Crossref]

2002 (2)

2001 (1)

T. Niemi, M. Uusimaa, S. Tammela, P. Heimala, T. Kajava, M. Kaivola, and H. Ludvigsen, “Tunable silicon etalon for simultaneous spectral filtering and wavelength monitoring of a DWDM transmitter,” IEEE Photon. Technol. Lett. 13(1), 58–60 (2001).
[Crossref]

2000 (1)

N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE 4056, 50–64 (2000).
[Crossref]

1997 (1)

1996 (2)

G. Kopp, “Tunable birefringent filters using liquid crystal variable retarders,” Proc. SPIE 2873, 324–327 (1996).

A. Sneh and K. M. Johnson, “High-speed continuously tunable liquid crystal filter for WDM networks,” J. Lightwave Technol. 14(6), 1067–1080 (1996).
[Crossref]

1993 (2)

B. Pezeshki, F. K. Tong, J. A. Kash, D. W. Kisker, and R. M. Potemski, “Tapered Fabry–Perot waveguide optical demultiplexer,” IEEE Photon. Technol. Lett. 5(9), 1082–1085 (1993).
[Crossref]

K. Hirabayashi and T. Kurokawa, “Liquid crystal devices for optical communication and information processing systems,” Liq. Cryst. 14(2), 307–317 (1993).
[Crossref]

1992 (1)

K. Hirabayashi, H. Tsuda, and T. Kurokawa, “Tunable wavelength-selective liquid crystal filters for 600-channel WDM system,” IEEE Photon. Technol. Lett. 4(6), 597–599 (1992).
[Crossref]

1990 (1)

P. J. Miller, “Tunable narrowband birefringent filters for astronomical imaging,” Proc. SPIE 1235, 466–473 (1990).
[Crossref]

1989 (2)

A. Frenkel and C. Lin, “Angle-tuned etalon filters for optical channel selection in high density wavelength division multiplexed systems,” J. Lightwave Technol. 7(4), 615–624 (1989).
[Crossref]

A. A. M. Saleh and J. Stone, “Two-stage Fabry–Perot filters as demultiplexers in optical FDMA LAN's,” J. Lightwave Technol. 7(2), 323–330 (1989).
[Crossref]

1975 (1)

H. A. Tarry, “Electrically tunable narrowband optical filter,” Electron. Lett. 11(19), 471–472 (1975).
[Crossref]

1965 (1)

1933 (1)

B. Lyot, “Optical apparatus with wide field using interference of polarized light,” C.R. Acad. Sci. (Paris) 197, 1593 (1933).

Abdulhalim, I.

Adibi, A.

Aharon, O.

Alboon, S. A.

Atabaki, A. H.

Bading, J. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
[Crossref] [PubMed]

Bhowmik, A.

E. Dorjgotov, A. Bhowmik, and P. Bos, “Design of a wide bandwidth switchable mirror based on a liquid crystal etalon,” J. Appl. Phys. 105, 104906 (2009)
[Crossref]

Bhowmik, A. K.

Blankner, J. G.

Boeck, R.

Bos, P.

E. Dorjgotov, A. Bhowmik, and P. Bos, “Design of a wide bandwidth switchable mirror based on a liquid crystal etalon,” J. Appl. Phys. 105, 104906 (2009)
[Crossref]

Bos, P. J.

Chaudhari, A. J.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
[Crossref] [PubMed]

Cherry, S. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
[Crossref] [PubMed]

Chrostowski, L.

Conti, P. S.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
[Crossref] [PubMed]

Crawford, G. P.

S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6(12), 929–938 (2007).
[Crossref] [PubMed]

Darvas, F.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
[Crossref] [PubMed]

Derks, M. J.

Dorjgotov, E.

E. Dorjgotov, A. Bhowmik, and P. Bos, “Design of a wide bandwidth switchable mirror based on a liquid crystal etalon,” J. Appl. Phys. 105, 104906 (2009)
[Crossref]

Dorjgotov, E.-A.

Eftekhar, A. A.

Elmore, D. F.

Frenkel, A.

A. Frenkel and C. Lin, “Angle-tuned etalon filters for optical channel selection in high density wavelength division multiplexed systems,” J. Lightwave Technol. 7(4), 615–624 (1989).
[Crossref]

Gat, N.

N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE 4056, 50–64 (2000).
[Crossref]

Hassler, D. M.

Heimala, P.

T. Niemi, M. Uusimaa, S. Tammela, P. Heimala, T. Kajava, M. Kaivola, and H. Ludvigsen, “Tunable silicon etalon for simultaneous spectral filtering and wavelength monitoring of a DWDM transmitter,” IEEE Photon. Technol. Lett. 13(1), 58–60 (2001).
[Crossref]

Hirabayashi, K.

K. Hirabayashi and T. Kurokawa, “Liquid crystal devices for optical communication and information processing systems,” Liq. Cryst. 14(2), 307–317 (1993).
[Crossref]

K. Hirabayashi, H. Tsuda, and T. Kurokawa, “Tunable wavelength-selective liquid crystal filters for 600-channel WDM system,” IEEE Photon. Technol. Lett. 4(6), 597–599 (1992).
[Crossref]

Hosseini, E. S.

Huang, D. D.

Huang, H. C.

Jaeger, N. A.

Jay, G. D.

S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6(12), 929–938 (2007).
[Crossref] [PubMed]

Johnson, K. M.

A. Sneh and K. M. Johnson, “High-speed continuously tunable liquid crystal filter for WDM networks,” J. Lightwave Technol. 14(6), 1067–1080 (1996).
[Crossref]

Kaivola, M.

T. Niemi, M. Uusimaa, S. Tammela, P. Heimala, T. Kajava, M. Kaivola, and H. Ludvigsen, “Tunable silicon etalon for simultaneous spectral filtering and wavelength monitoring of a DWDM transmitter,” IEEE Photon. Technol. Lett. 13(1), 58–60 (2001).
[Crossref]

Kajava, T.

T. Niemi, M. Uusimaa, S. Tammela, P. Heimala, T. Kajava, M. Kaivola, and H. Ludvigsen, “Tunable silicon etalon for simultaneous spectral filtering and wavelength monitoring of a DWDM transmitter,” IEEE Photon. Technol. Lett. 13(1), 58–60 (2001).
[Crossref]

Kash, J. A.

B. Pezeshki, F. K. Tong, J. A. Kash, D. W. Kisker, and R. M. Potemski, “Tapered Fabry–Perot waveguide optical demultiplexer,” IEEE Photon. Technol. Lett. 5(9), 1082–1085 (1993).
[Crossref]

Kisker, D. W.

B. Pezeshki, F. K. Tong, J. A. Kash, D. W. Kisker, and R. M. Potemski, “Tapered Fabry–Perot waveguide optical demultiplexer,” IEEE Photon. Technol. Lett. 5(9), 1082–1085 (1993).
[Crossref]

Kopp, G.

G. Kopp, “Tunable birefringent filters using liquid crystal variable retarders,” Proc. SPIE 2873, 324–327 (1996).

Kopp, G. A.

Koshiishi, H.

H. Kurosaki, H. Koshiishi, T. Suzuki, and K. Tsuchiya, “Development of tunable imaging spectro-polarimeter for remote sensing,” Adv. Space Res. 32(11), 2141–2146 (2003).
[Crossref]

Kurokawa, T.

K. Hirabayashi and T. Kurokawa, “Liquid crystal devices for optical communication and information processing systems,” Liq. Cryst. 14(2), 307–317 (1993).
[Crossref]

K. Hirabayashi, H. Tsuda, and T. Kurokawa, “Tunable wavelength-selective liquid crystal filters for 600-channel WDM system,” IEEE Photon. Technol. Lett. 4(6), 597–599 (1992).
[Crossref]

Kurosaki, H.

H. Kurosaki, H. Koshiishi, T. Suzuki, and K. Tsuchiya, “Development of tunable imaging spectro-polarimeter for remote sensing,” Adv. Space Res. 32(11), 2141–2146 (2003).
[Crossref]

Kwok, H. S.

Leahy, R. M.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
[Crossref] [PubMed]

Li, Q.

Lin, C.

A. Frenkel and C. Lin, “Angle-tuned etalon filters for optical channel selection in high density wavelength division multiplexed systems,” J. Lightwave Technol. 7(4), 615–624 (1989).
[Crossref]

Lindquist, R. G.

Ludvigsen, H.

T. Niemi, M. Uusimaa, S. Tammela, P. Heimala, T. Kajava, M. Kaivola, and H. Ludvigsen, “Tunable silicon etalon for simultaneous spectral filtering and wavelength monitoring of a DWDM transmitter,” IEEE Photon. Technol. Lett. 13(1), 58–60 (2001).
[Crossref]

Lyot, B.

B. Lyot, “Optical apparatus with wide field using interference of polarized light,” C.R. Acad. Sci. (Paris) 197, 1593 (1933).

Miller, P. J.

P. J. Miller, “Tunable narrowband birefringent filters for astronomical imaging,” Proc. SPIE 1235, 466–473 (1990).
[Crossref]

Moats, R. A.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
[Crossref] [PubMed]

Momeni, B.

Niemi, T.

T. Niemi, M. Uusimaa, S. Tammela, P. Heimala, T. Kajava, M. Kaivola, and H. Ludvigsen, “Tunable silicon etalon for simultaneous spectral filtering and wavelength monitoring of a DWDM transmitter,” IEEE Photon. Technol. Lett. 13(1), 58–60 (2001).
[Crossref]

Pezeshki, B.

B. Pezeshki, F. K. Tong, J. A. Kash, D. W. Kisker, and R. M. Potemski, “Tapered Fabry–Perot waveguide optical demultiplexer,” IEEE Photon. Technol. Lett. 5(9), 1082–1085 (1993).
[Crossref]

Potemski, R. M.

B. Pezeshki, F. K. Tong, J. A. Kash, D. W. Kisker, and R. M. Potemski, “Tapered Fabry–Perot waveguide optical demultiplexer,” IEEE Photon. Technol. Lett. 5(9), 1082–1085 (1993).
[Crossref]

Rouger, N.

Saeed, S.

Saleh, A. A. M.

A. A. M. Saleh and J. Stone, “Two-stage Fabry–Perot filters as demultiplexers in optical FDMA LAN's,” J. Lightwave Technol. 7(2), 323–330 (1989).
[Crossref]

Smith, D. J.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
[Crossref] [PubMed]

Sneh, A.

A. Sneh and K. M. Johnson, “High-speed continuously tunable liquid crystal filter for WDM networks,” J. Lightwave Technol. 14(6), 1067–1080 (1996).
[Crossref]

Šolc, I.

Soltani, M.

Stone, J.

A. A. M. Saleh and J. Stone, “Two-stage Fabry–Perot filters as demultiplexers in optical FDMA LAN's,” J. Lightwave Technol. 7(2), 323–330 (1989).
[Crossref]

Streete, J. L.

Suzuki, T.

H. Kurosaki, H. Koshiishi, T. Suzuki, and K. Tsuchiya, “Development of tunable imaging spectro-polarimeter for remote sensing,” Adv. Space Res. 32(11), 2141–2146 (2003).
[Crossref]

Tammela, S.

T. Niemi, M. Uusimaa, S. Tammela, P. Heimala, T. Kajava, M. Kaivola, and H. Ludvigsen, “Tunable silicon etalon for simultaneous spectral filtering and wavelength monitoring of a DWDM transmitter,” IEEE Photon. Technol. Lett. 13(1), 58–60 (2001).
[Crossref]

Tarry, H. A.

H. A. Tarry, “Electrically tunable narrowband optical filter,” Electron. Lett. 11(19), 471–472 (1975).
[Crossref]

Tong, F. K.

B. Pezeshki, F. K. Tong, J. A. Kash, D. W. Kisker, and R. M. Potemski, “Tapered Fabry–Perot waveguide optical demultiplexer,” IEEE Photon. Technol. Lett. 5(9), 1082–1085 (1993).
[Crossref]

Tsuchiya, K.

H. Kurosaki, H. Koshiishi, T. Suzuki, and K. Tsuchiya, “Development of tunable imaging spectro-polarimeter for remote sensing,” Adv. Space Res. 32(11), 2141–2146 (2003).
[Crossref]

Tsuda, H.

K. Hirabayashi, H. Tsuda, and T. Kurokawa, “Tunable wavelength-selective liquid crystal filters for 600-channel WDM system,” IEEE Photon. Technol. Lett. 4(6), 597–599 (1992).
[Crossref]

Uusimaa, M.

T. Niemi, M. Uusimaa, S. Tammela, P. Heimala, T. Kajava, M. Kaivola, and H. Ludvigsen, “Tunable silicon etalon for simultaneous spectral filtering and wavelength monitoring of a DWDM transmitter,” IEEE Photon. Technol. Lett. 13(1), 58–60 (2001).
[Crossref]

Woltman, S. J.

S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6(12), 929–938 (2007).
[Crossref] [PubMed]

Woods, J. C.

Ye, C.

Yegnanarayanan, S.

Yu, X. J.

Adv. Space Res. (1)

H. Kurosaki, H. Koshiishi, T. Suzuki, and K. Tsuchiya, “Development of tunable imaging spectro-polarimeter for remote sensing,” Adv. Space Res. 32(11), 2141–2146 (2003).
[Crossref]

Appl. Opt. (4)

C.R. Acad. Sci. (Paris) (1)

B. Lyot, “Optical apparatus with wide field using interference of polarized light,” C.R. Acad. Sci. (Paris) 197, 1593 (1933).

Electron. Lett. (1)

H. A. Tarry, “Electrically tunable narrowband optical filter,” Electron. Lett. 11(19), 471–472 (1975).
[Crossref]

IEEE Photon. Technol. Lett. (3)

B. Pezeshki, F. K. Tong, J. A. Kash, D. W. Kisker, and R. M. Potemski, “Tapered Fabry–Perot waveguide optical demultiplexer,” IEEE Photon. Technol. Lett. 5(9), 1082–1085 (1993).
[Crossref]

T. Niemi, M. Uusimaa, S. Tammela, P. Heimala, T. Kajava, M. Kaivola, and H. Ludvigsen, “Tunable silicon etalon for simultaneous spectral filtering and wavelength monitoring of a DWDM transmitter,” IEEE Photon. Technol. Lett. 13(1), 58–60 (2001).
[Crossref]

K. Hirabayashi, H. Tsuda, and T. Kurokawa, “Tunable wavelength-selective liquid crystal filters for 600-channel WDM system,” IEEE Photon. Technol. Lett. 4(6), 597–599 (1992).
[Crossref]

J. Appl. Phys. (1)

E. Dorjgotov, A. Bhowmik, and P. Bos, “Design of a wide bandwidth switchable mirror based on a liquid crystal etalon,” J. Appl. Phys. 105, 104906 (2009)
[Crossref]

J. Lightwave Technol. (3)

A. A. M. Saleh and J. Stone, “Two-stage Fabry–Perot filters as demultiplexers in optical FDMA LAN's,” J. Lightwave Technol. 7(2), 323–330 (1989).
[Crossref]

A. Frenkel and C. Lin, “Angle-tuned etalon filters for optical channel selection in high density wavelength division multiplexed systems,” J. Lightwave Technol. 7(4), 615–624 (1989).
[Crossref]

A. Sneh and K. M. Johnson, “High-speed continuously tunable liquid crystal filter for WDM networks,” J. Lightwave Technol. 14(6), 1067–1080 (1996).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Liq. Cryst. (1)

K. Hirabayashi and T. Kurokawa, “Liquid crystal devices for optical communication and information processing systems,” Liq. Cryst. 14(2), 307–317 (1993).
[Crossref]

Nat. Mater. (1)

S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6(12), 929–938 (2007).
[Crossref] [PubMed]

Opt. Express (5)

Opt. Lett. (1)

Phys. Med. Biol. (1)

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
[Crossref] [PubMed]

Proc. SPIE (3)

N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE 4056, 50–64 (2000).
[Crossref]

P. J. Miller, “Tunable narrowband birefringent filters for astronomical imaging,” Proc. SPIE 1235, 466–473 (1990).
[Crossref]

G. Kopp, “Tunable birefringent filters using liquid crystal variable retarders,” Proc. SPIE 2873, 324–327 (1996).

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Figures (4)

Fig. 1
Fig. 1

(a) Fabry–Perot LC tunable filter; (b) layout of three-stage LC tunable Fabry–Perot filter.

Fig. 2
Fig. 2

(a) Transmission spectra for the first (pink, d = 3000nm, m = 11) and second (blue, d = 3000 nm, m + 1 = 12) Fabry–Perot filter. (b) Transmission spectra of cascaded first and second filters. (c) Transmission spectra for the third (d = 2700nm, m-1 = 10) filter. (d) Total output of three-stage LC Fabry–Perot tunable filter.

Fig. 3
Fig. 3

Experimental three-stage LC Fabry–Perot filter.

Fig. 4
Fig. 4

Five examples of measured spectra of three-stage LC Fabry–Perot tunable filter: the peak wavelength of the filter at 848 nm, 750 nm, 695nm, 625 nm and 490 nm when the loading voltages for the three stages were: {2.03V, 5.75V, 2.12V}, {8.49V, 12.58V, 7.86V}, {12.85V, 16.21V, 13.72V}, {8.23V, 15.45V, 9.16V}, {13.25V, 6.15V, 3.05V}, correspondingly.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

T = I ( t ) I ( i ) = 1 1 + F sin 2 δ 2 ,
n = 1 d d 2 d 2 n o [ 1 ( 1 n o 2 n e 2 ) sin 2 θ ] 1 2 d z ,
λ p e a k = 2 n d m ; F S R = λ p e a k 2 2 n d = 2 n d m 2 = λ p e a k m ; F W H M = 2 λ m π 1 F ,
T = 1 1 + F sin 2 δ 1 2 1 1 + F sin 2 δ 2 2 1 1 + F sin 2 δ 3 2 = 1 1 + F sin 2 ( 2 π λ n 1 d ) 1 1 + F sin 2 ( 2 π λ n 2 d ) 1 1 + F sin 2 ( 2 π λ n 3 d 3 ) ,
F = 4 R ( 1 R ) 2 .
F S R 1 = λ p e a k m ; F S R 2 = λ p e a k m + 1 ; F S R 3 = λ p e a k m 1 .
λ int e r v a l = λ p e a k m λ p e a k m + 1 = λ p e a k m ( m + 1 ) .
λ p e a k ' = 2 n 1 d m + F S R 1 λ int e r v a l = 2 n 1 d 2 m + 1 = λ p e a k m 2 m + 1 ,
F S R = λ p e a k m + 1 2m+1 ,
T ( 1 1 + F sin 2 δ 1 2 ) 3 .
F W H M 2 3 2 λ p e a k m π 1 F .

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