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Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 2, Iss. 12 — Jun. 8, 1998
  • pp: 471–482
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Nonlinear optical liquid cored fiber array and liquid crystal film for ps-cw frequency agile laser optical limiting application

I. C. Khoo, M. V. Wood, B. D. Guenther, Min-Yi Shih, P. H. Chen, Zhaogen Chen, and Xumu Zhang  »View Author Affiliations


Optics Express, Vol. 2, Issue 12, pp. 471-482 (1998)
http://dx.doi.org/10.1364/OE.2.000471


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Abstract

The molecular nonlinear photonic absorption processes of two nonlinear fiber core liquids are discussed in the context of nonlinear propagation and optical limiting of short pulses. These fiber arrays are capable of limiting threshold and clamped output below 1 μJ for picosecond and nanosecond pulses. We also discuss the observation of perhaps the largest optical nonlinearity in some dye-doped nematic liquid crystal films. These films will provide limiting action with a threshold power of 100 nWatt and limited transmission of ≪ 1 microJoule for ms - cw laser.

© Optical Society of America

1. Introduction

Various nonlinear- optical materials [1

1. See, for exampleL. Tutt and T. Boggess, Prog. Quantum Electron.17, 299–338 (1993). [CrossRef]

] and devices have been investigated to meet the challenge of protecting the eye or optical sensors from laser radiation of wide spectral and temporal ranges. In most devices, the nonlinear material has to be placed in the focal plane of the optical system in order to utilize the increased laser energy fluence to achieve the desired limiting performance characteristics. Because of diffraction, the interaction length of the focused laser in the material is rather short, and thus the performance of the material/device is limited. We have proposed [2

2. I. C. Khoo, M. V. Wood, and Brett D. Guenther, Opt. Lett.21, 1625–1627 (1996) and references therein. [CrossRef] [PubMed]

,3

3. I. C. Khoo and H. Li, J. Appl. Phys.B59, 573 (1994).

] using a thin nonlinear fiber array, c.f Figure 1, to circumvent this limitation.

Fig. 1. Optical limiting setup using a nonlinear fiber array.

In this paper, we present the essential molecular photonics of the nonlinear fiber core liquid for optical limiting actions against picosecond - nanosecond laser pulses. We also discuss how a recently discovered extremely nonlinear response of specially doped nematic liquid crystal film may be integrated with the fiber array (c.f figure 2) to extend the limiting action to longer pulse - cw lasers.

2. Nonlinear fiber core liquid molecular photonics and pulse propagation.

Figure 2 depicts the various nonlinear optical processes that occur in the fiber core. Among the various core liquids we have studied, a liquid L34 synthesized at Penn State is found to possess highly promising optical limiting characteristics. L34 is a single constituent liquid with the molecular structure shown in figure 3. Its refractive index is 1.61. The refractive indices of the fiber cladding used range from 1.45 to 1.53, so the liquid core behaves as a waveguide. Figure 3 also shows the linear (single-photon) absorption spectrum of L34. In the visible regime, the liquid, which is very faintly yellowish in appearance, is quite transparent; the linear absorption constant at 532 nm of L34 is 2 cm-1.

Fig. 2. Nonlinear optical processes occurring at the entrance region and the fiber core that limit the transmission of a laser pulse through the fiber.
Fig. 3 Linear absorption spectrum and molecular structure of L34

2.1 Molecular nonlinear photonics

A possible model for the relevant molecular photonic absorption processes is depicted in Figure 4. In these transparent liquids, the ground state |1> is very weakly connected to the intermediate state |i>. The ground state is connected by a two-photon transition to the excited state |2>. The excited state |2> is connected to other high lying excited state manifolds by single photon transition. In similar liquids, studies [4–6

4. F. W. Deeg and M. D. Feyer, J. Chem. Phys.91, 2269 (1989) [CrossRef]

] have shown that the excited state absorption rate can be much larger than the ground - intermediate absorption, giving rise to the so - called excited state absorption (ESA) effect.

The intermediate states are made up of the high lying ro-vibrational manifold of the ground state. In some molecular systems such as Fullerene [7

7. For Fullerene systems, see for example,K. M. Nashold and D. P. Walter, J. Opt. Soc.Am. B.12, 1228–1237 (1995) and references therein [CrossRef]

], the single photon transition from the intermediate state to the excited two-photon state is characterized by a much larger transition cross-section σi than the ground to intermediate state transition σg, giving rise to the so-called Reverse-Saturable-Absorption (RSA) effect.

Fig. 4. Schematic depiction of two-photon, sequential intermediate state, and excited-state absorption processes, intersystem crossing, and other processes occurring in the core molecule.

The actual molecular level structures are of course much more complex. The photo-excited states, for example, could undergo intersystem crossing, cis-trans or other conformational changes, and form isomers or charge transfer complexes. These processes become important at much longer time scales [8

8. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena, (Wiley Interscience, New York, 1994) chap. 2, p. 21 and references therein.

], but could be neglected in the nano- and pico-second time scale.

Accounting for these linear and nonlinear absorption processes, the rate equations for the level population densities are given as follows [9

9. I. C. Khoo, M. V. Wood, B. D. Guenther, Min-Yi Shih, and P. H. Chen, J. Opt. Soc. Am. B,1533–1540, (1998)

]:

dN2dt=σ(2)I22h2υ2N1N2τ21N2τ2iN2σexcI+NiσiI
(1)

and similarly for N1 and Ni.

αg=N0σg;αexc=N0σexc;αi=N0σi;β=N0σ(2)
(2)

If the intermediate and excited states are not significantly populated, i.e., N1~No, N2/No≪1, and Ni/No≪1, analytical expressions for the population densities and the optical intensity could be obtained, and allow us to qualitatively sort out the various contributing mechanisms and their explicit roles in the nonlinear absorption and limiting processes.

Studies [6

6. R. J. McEwan and R. C. Hollins, J. Nonlinear Opt. Phys. Mater.4, 245–260 (1995). [CrossRef]

] of molecules similar to ILC have shown that σexc can be orders of magnitude (~105 times) larger than σg; also τ2 given by 1/τ2 = 1/τ21 +1/τ2i ~ 30 ns. Other studies [4

4. F. W. Deeg and M. D. Feyer, J. Chem. Phys.91, 2269 (1989) [CrossRef]

] of other RSA molecules, such as C60, show that the intermediate state relaxes in τi of about 1.2 ns sec, and that σi ~ 3σg. Since the laser pulse lengths τp’s used in our experimental studies are 60 ps and 20 ns, respectively, they clearly fall into two distinct time scales: (i) picosecond regime, where τp≪ τ2, τI, and (ii) nanosecond regime, where τp≥ τ2, τi. We will discuss these two regimes in the context of nonlinear propagation in the fiber.

2.2 Nonlinear propagation and limiting -picosecond regime

For simplicity in analysis, the laser pulses are assumed to be square pulses of duration τp. Retaining only the largest terms manifesting the effect of the molecular level excitation, the solutions of equations (1) –(2) are as follow:

N1~N0e(B+C)t~N0[1(B+C)t]
N2~[BB+CN0[1e(B+C)t]]~BN0t
Ni~CB+CN0[1e(B+C)t]~CN0t
(3)

where

B=βI2N02
C=σgI=αgIN0
(4)

Note that both Bt and Ct are ≪1 since N1≫ N2, Ni.

Consider the propagation of the laser pulse through the fiber core. The rate of absorption in the fiber is described by an equation of the form:

dIdz=αgN1N0IαiNiN0IβN1N0I2αexcN2N0I
(5)

Following photo-absorptions in the core molecules, thermal and density change effects will create negative index changes in the core, and will therefore also lower the core transmission by channeling the guided modes into the cladding region. Fortunately, these nonlinear absorption processes take place with different rates for different time scales and therefore can be separately treated. More specifically, in the picosecond time scale, thermal/density effects are absent, and we need to consider only nonlinear absorption processes.

Inserting the solutions for N(t;I)’s into the R.H. S. of the propagation equation (5) gives:

dIdz=αgI(αiαg)ICtβI2(αexcαg)IBt
(6a)

Using equation (4), we can rewrite equation (6a) as:

dIdz=αgI[β+(αiαg)σgtI2(αexcαg)I3N02
=αgIβeffI2γI3
(6b)

In the second term on the R.H. S. of equation (6b), (αi - αggt/hν is the contribution from the intermediate state absorption, and it gives rise to an effective two-photon absorption coefficient βeff = β+ (αi - αggt/hν. The last term, varying as I3, arises from excited state absorption. In other words, if ESA and RSA effects are present in the molecular transitions, the laser will incur increased nonlinear absorptions in its propagation through the fiber core, and therefore exhibit enhanced limiting action. This is further illustrated as follows.

Equation (6b) can be cast into analytical form relating the input intensity I(0) with the output intensity I(z). For β2 > 4αγ we have:

2αz=[lnI2(z)α+βI(z)+γI2(z)lnI02α+βI0+γI02]
ββ24αγ[ln2γI(z)+ββ24αγ2γI(z)+β+β24αγln2γI0+ββ24αγ2γI0+β+β24αγ]
(7a)

For β2 < 4αγ we have

2αz=[lnI2(z)I02(α+βI(z)+γI2(z))(α+βI0+γI02)]
2β4αγβ2[tan12γI(z)+β4αγβ2tan12γI0+β4αγβ2]
(7b)

Figures 5(a) and 5(b) illustrate these results for the cases β2 > 4αγ and β2 < 4αγ, respectively. In these figures, the optical intensities are in units of GW/cm2, β = 2.5 cm/GW, z = 0.5 cm and α = 2 cm-1. These are experimentally measured values for the liquid ILC in conjunction with the picosecond laser pulses (τp = 66 ps). Note that a 1 μJ, 66 ps laser pulse in a 30 μm fiber core gives an intensity of 1.6 GW/cm2. In both figures, note that as γ increases, the “clamped” output intensities are progressively lowered. Since γ depends on the excited state population N2, which builds up in time as shown in equation (3), we expect its contribution to become significant for longer (for example, nanoseconds) laser pulses. Similar observation may be made regarding the intermediate state contribution, c.f. equations (3) and (6b), which effectively give rise to a larger β coefficient.

Fig. 5a. Output intensity versus input intensity with different values of γ for β2 > 4αγ, α = 2 cm-1, β = 2.5 cm/GW, z = 0.5 cm.
Fig. 5b. Output intensity versus input intensity with different values of γ for β2 < 4αγ, α = 2 cm-1, β = 2.5 cm/GW, z = 0.5 cm.

One could gain further insight by considering the purely two - and single ground state - photon absorption processes, i.e. setting γ = 0 and βeff = β. In this case, equation (7b) gives for z = L:

I(L)=αI(0)αgeαLβI(0)(1αgeαL)
(8)

where I(0) is the input laser intensity. Notice the interesting feature that for large I, such that βI2≫αI, the transmitted intensity is held at a constant value Iclamped(L) given by:

Iclamped=1βL
(9)

This “clamping” behavior is similar to those depicted in figures 5(a) when excited and intermediate state absorptions are involved.

2.3 Nonlinear propagation and limiting -nanosecond regime, thermal/density effects and propagation mode loss.

In case (ii), where τp ≫ τ2, the intermediate and excited state population will build up and play an increasing role in the nonlinear absorption and optical limiting effect. Thermal and density changes in the liquids following photo - absorption also come into play in this time regime, further complicating the analysis. The latter gives rise to several effects on the fiber core transmission.

In reference (2b), we have treated the problem of core guiding mode → cladding mode loss due to uniform lowering of the core refractive index resulting from the thermal/density changes. The main point in the analysis is that if the core index varies negatively with intensity, the index difference between the core and the cladding will tend towards 0; the fractional power transmitted in the core will thus diminish as the various guided modes evolved into lossy modes.

In general, owing to the presence of propagating density waves, multiple reflections at the core-cladding interface and multi-dimensional thermal diffusion processes, these thermal/density effects also cause inhomogeneous index changes within the core. These index inhomogeneity gives rise to wide angle scatterings of the light out of the guiding cores, a process that is practically indistinguishable from the core → cladding propagation mode loss due to uniform changes in the core index.

Besides intermediate and excited state absorptions, and the thermal/density effects, other processes such as singlet/triplet state crossing and the concommitant relaxation processes will all come into play. This demands more molecular states to be included, and self - consistent solutions of the multi - parameter nonlinear propagation/interaction equations. This is clearly outside the scope of this paper. In the context of optical limiting application, it is interesting and fortuitous that these intermediate and excited state absorptions, as well as the thermal effects, all contribute positively to achieving the low limiting threshold and clamped transmission that are otherwise impossible with two - photon absorption processes alone.

3. Analysis of experimental optical limiting results in fiber.

The experimental setup used to evaluate the optical limiting characteristics of these fibers is similar to reference 2b. Both ILC and L34 nonlinear liquids we have studied exhibit sufficiently large TPA in the picosecond regime to limit the transmitted laser energies to < 1 μJ. Figure 6 shows the results for picosecond laser pulses in L34- and ILC-cored fibers. Theoretical modeling of this data, c.f section 2, shows that the “effective” two-photon absorption coefficients βeff for these fibers are 2.5 cm/GW and 10 cm/GW for ILC and L34, respectively.

Consider now optical limiting action in the nanosecond time scale. For the same laser fluence [energy per unit area], the laser intensity is lower if the pulse duration is longer. The nonlinear absorption processes, which vary as I2 and I3, are thus correspondingly lower. Consider equation (9) for the clamped transmitted intensity. For β =2.5 cm/GW and a fiber length L of 5mm, Iclamp is ~0.8 GW/cm2. This corresponds to a laser fluence of 16 J/cm2 for a 20 ns laser pulse, or a laser energy of 144μJ over the fiber cross-sectional area [diameter of 30 μm]. In other words, the 5 mm long ILC cored fiber will not be able to limit the transmission to <1 μJ. Neither will the L34 core liquid (with β = 10 cm/GW) be able to do the job. To obtain comparable optical limiting, other nonlinear mechanisms, such as the excited state absorption, and the intermediate state absorption, and/or the thermal/density effects must come into play. Alternately, one could employ longer (but impractical) fiber length.

Fig. 6. Transmission and transmitted laser pulse energies versus the input picosecond laser pulse energy through fibers. Fiber length = 5 mm. Core diameter=30 μm. F6 optics.

Figure 7 depicts the experimentally observed limiting curves for nanosecond laser pulses [λ= 532 nm, pulse duration: 20 ns] for ILC and L34. Clearly, the transparent non-absorbing ILC cored fibers are poor optical limiters in this time regime for reasons stated above although the “clamped” transmission of ~9 μJ is much smaller than the above estimate of 144 μJ for a core liquid with β = 2.5 cm/GW. Since ILC is transparent, i.e. small thermal effect, the low clamped transmission value is most likely due to the excited state contribution. In order for the ILC cored fibers to give a clamped transmission below 1 μJ, we found it necessary to dope it slightly with the reverse saturable absorber C60, c.f reference 2 and the following section. In figure 7 we also show the experimental results obtained with L34. A clamped output of ~ 1 μJ, corresponding to a fluence value of 0.1 J/cm2 for a fiber core diameter of 30 μm is obtained. Since L34 is slightly absorbing, it is likely that thermal/density effects play a larger role in this case in addition to excited state absorption.

4. High laser energy, f#s optics and opaque cladding effects

We have also investigated the limiting action of the fiber at higher energy laser pulses and with different input/collection optics. Figure 8 shows the output vs. input curves for C60-doped ILC cored fibers. Similar results are obtained with L34 cored fibers. Generally, the output remains clamped to below or around 1 μJ. At an input laser energy of around 55 μJ, it is observed that the transmission drops off substantially. Visual inspection of the liquid layer at the focal plane of the input laser reveals that a bubble is formed at the entrance region of the fiber. The bubble allows very little transmission of the laser through the fiber, and it remains in place for a fairly long time [several minutes]. By elevating the temperature of the sample, it could be made to float away in much shorter time [~ a few seconds]. For laser energy above 280 μJ (fluence of 39 J/cm2), a pin-prick damage spot is created on the entrance glass window; the spot is highly scattering and also allows very little transmission (≪ 1μJ) through the fiber. Since both the bubble and the damage spot are of the pinprick nature, they do not severely affect the image transmission quality of the fiber array. In other words, the effective operational dynamic range of such fiber array optical limiting device is as large as practically desirable.

Fig. 7. Output versus input energies for nanosecond laser pulses [λ = 0.532 μm; pulse width = 20 ns]. Fiber length = 5 mm; core diameter = 30 μm, F6 optics
Fig. 8. Output versus input energies for nanosecond laser pulses [λ==0.532 nm; pulse width: 2 ns] for different F# optics. Fiber length: 5 mm; fiber core diameter: 30 μm; core material: C60-doped ILC.

We have repeated these limiting experiments for different collection optics ranging from F3 to F6. The F3 optics corresponding to the largest collection aperture gives the largest clamped transmission. The increase in the detected output is due to the reception of more side-scattered or leaky/cladding modes by the larger collection aperture.

If the cladding is made of light absorbing material, as indicated in figure 1, these spurious side scatterings will not be channeled into downstream optics, and the clamped transmission will be lower than the clear-cladding case. Another advantage of opaque or light absorbing cladding is the enhancement of the thermal/density effect through the heating effect at the core-cladding boundary, but this remains to be quantitatively determined.

Experimentally, we have simulated the scattering blocking effect of opaque cladding by using a glass capillary that has an absorbing polymer coating layer. The core of the glass capillary is filled with L34. The polymer coating absorbs light that “leaks” out of the core into the glass cladding region. Figure 9 shows nanosecond laser pulse limiting results obtained with a 5 mm long, 30 μm diameter L34 cored fiber. Although the thresholds for the onset of limiting are the same, as expected, the transmitted output is clamped at a much lower level with the help of the “opaque cladding”. The limiting results with bulk sample of the same thickness and input laser focal plane location are also plotted in figure 9 for comparison. In general, we observe that more effective limiting action is provided by the fiber than the bulk. This is simply due to the longer interaction length in the waveguiding fiber compared to the Rayleigh range of focused laser beam.

Fig. 9. Measured single nanosecond pulse transmitted versus input laser energy through a nonlinear fiber. Fiber length: 5 mm; fiber core diameter: 30 mm; core material: L34. Solid triangles are for transparent glass cladding [no coating], while open diamonds are for ‘simulated’ opaque cladding [with absorbing coating]. Also shown are results with bulk sample of the same thickness and input laser focal plane location

5. Optical limiting of cw - long pulse laser at sub-microwatt power using extremely nonlinear nematic liquid crystal film.

Following the preceding analysis, we can conclude that for longer time scale (millisecond - cw regime), nonlinear absorption processes will no longer be efficient limiting mechanisms. In this section, we describe a non-thermal mechanism for refractive index change in dye-doped nematic liquid crystal films. As reported in a recent publication [9

9. I. C. Khoo, M. V. Wood, B. D. Guenther, Min-Yi Shih, and P. H. Chen, J. Opt. Soc. Am. B,1533–1540, (1998)

], the nonlinear refractive index change coefficient obtainable from these films can be as large a 6 cm2/Watt, as a result of optically induced reorientation of the birefringent nematic crystal’s director axis. The readers are referred to reference 9 for details concerning the basic mechanisms.

Such large nonlinearity enables us to observe self-defocusing and optical limiting effect at very low laser power. Figure 10 shows a typical optical limiting set up using external self-defocusing effect [11

11. I.C. Khoo, J.Y. Hou, T.H. Lui, P.Y. Yan, R.R. Michael, and G.M. Finn, J. Opt. Soc. Am. B,4, 886–891, (1987). [CrossRef]

]. A linearly polarized laser [beam diameter 3 mm] is focused by a 15 cm focal length input lens to a spot diameter of 125 μm onto a 25 μm thick liquid crystal film placed just behind the focal plane of the input lens. The nematic film is tiled so that the incident beam makes an angle of 45 degrees with the normal to the cell; this enhances the nonlinear refractive index change experienced by the extraordinary incident ray [8

8. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena, (Wiley Interscience, New York, 1994) chap. 2, p. 21 and references therein.

]. An aperture of 5 mm diameter is placed at 40 cm behind the sample to monitor the central region of the transmitted beam. The insert in figure 10 is a photograph of the intensity distribution at the onset of limiting [input power ≥~100nanoWatt]; the central region becomes darkened, while the beam divergence increases dramatically.

Fig. 10. Experimental set up for optical limiting action using external self-defocusing effect. The insert is a photograph of the transmitted laser beam at the aperture showing self-defocusing effect.

Figure 11 shows an output versus input curve for cw input laser clearly demonstrating a typical limiting behavior. The threshold is around 0.1 μWatt. This is about 3 orders of magnitude lower than all the previously obtained limiting threshold value [6

6. R. J. McEwan and R. C. Hollins, J. Nonlinear Opt. Phys. Mater.4, 245–260 (1995). [CrossRef]

] in nematic liquid crystals using the so-called giant optical nonlinearities associated with various director axis reorientational processes. The response time is dependent on the speed of space charge field formation [9

9. I. C. Khoo, M. V. Wood, B. D. Guenther, Min-Yi Shih, and P. H. Chen, J. Opt. Soc. Am. B,1533–1540, (1998)

] and is inversely proportional to the optical intensity. At an input intensity of 3 mW/cm2, we have measured a response time of ~100 ms, whereas the response time at 0.5mW/cm2 is about 0.5 sec. Insert in Figure 11 is an oscilloscope trace of a typical detected central region of the output for an input laser power of 0.1 μWatt. Because of self-defocusing, the output decreases progressively to almost vanishing value in a time of ~ 1.5 sec. In other words, less than 0.15 μJoule will be transmitted through the limiter, which is well below the sensor/eye damage level. At higher input power/intensity, the response time is correspondingly shortened, with the net effect that ≪ 1 μJoule of the input laser energy will reach the detector/sensor.

Fig. 11. Plot of detected output power versus input laser power. Insert is an oscilloscope trace of the detected output for an input step-on cw laser.

6. Conclusion

We have presented a physical model for the nonlinear molecular photonic processes occurring in the fiber core liquid molecules, and demonstrated good limiting results for ps and ns laser pulses. We have also demonstrated the feasibility of optical limiting with sub-microWatt laser power at milliseconds speed with a thin nematic liquid crystal film. Because of their thin film nature, these films can be integrated onto the nonlinear liquid core fiber array, c.f. figure 2, to fabricate devices that will provide protection against frequency agile picosecond -cw lasers throughout the entire visible spectrum. These studies are currently in progress in our laboratory.

Acknowledgements

This work is supported by the Army Research Office, the Joint Services Agile Program and the Air Force Phillips Laboratory. X. Zhang is an ONR Young Investigator

References and links

1.

See, for exampleL. Tutt and T. Boggess, Prog. Quantum Electron.17, 299–338 (1993). [CrossRef]

2.

I. C. Khoo, M. V. Wood, and Brett D. Guenther, Opt. Lett.21, 1625–1627 (1996) and references therein. [CrossRef] [PubMed]

3.

I. C. Khoo and H. Li, J. Appl. Phys.B59, 573 (1994).

4.

F. W. Deeg and M. D. Feyer, J. Chem. Phys.91, 2269 (1989) [CrossRef]

5.

H. J. Eichler, R. Macdonald, and B. Trosken, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A.231, 1 (1993) [CrossRef]

6.

R. J. McEwan and R. C. Hollins, J. Nonlinear Opt. Phys. Mater.4, 245–260 (1995). [CrossRef]

7.

For Fullerene systems, see for example,K. M. Nashold and D. P. Walter, J. Opt. Soc.Am. B.12, 1228–1237 (1995) and references therein [CrossRef]

8.

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena, (Wiley Interscience, New York, 1994) chap. 2, p. 21 and references therein.

9.

I. C. Khoo, M. V. Wood, B. D. Guenther, Min-Yi Shih, and P. H. Chen, J. Opt. Soc. Am. B,1533–1540, (1998)

10.

I.C. Khoo, S. Slussarenko, B. D. Guenther, Min-Yi Shih, P. Chen, and M. V. Wood, Opt. Lett.23, 253–255 (1998) [CrossRef]

11.

I.C. Khoo, J.Y. Hou, T.H. Lui, P.Y. Yan, R.R. Michael, and G.M. Finn, J. Opt. Soc. Am. B,4, 886–891, (1987). [CrossRef]

OCIS Codes
(160.3710) Materials : Liquid crystals
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(230.3720) Optical devices : Liquid-crystal devices

ToC Category:
Focus Issue: Nonlinear and photorefractive fibers and waveguides

History
Original Manuscript: January 14, 1998
Revised Manuscript: December 9, 1997
Published: June 8, 1998

Citation
Iam-Choon Khoo, Michael Wood, Brett Dean Guenther, Min-Yi Shih, Pao Chen, Zhaogen Chen, and Xumu Zhang, "Nolinear optical liquid cored fiber array and liquid crystal film fo ps-cw frequency agile laser optical limiting application," Opt. Express 2, 471-482 (1998)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-2-12-471


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References

  1. See, for example, L. Tutt and T. Boggess, Prog. Quantum Electron. 17, 299-338 (1993). [CrossRef]
  2. I. C. Khoo, M. V. Wood and Brett D. Guenther, Opt. Lett. 21, 1625-1627 (1996) and references therein. [CrossRef] [PubMed]
  3. I. C. Khoo and H. Li, J. Appl. Phys. B59, 573 (1994).
  4. F. W. Deeg and M. D. Feyer, J. Chem. Phys. 91, 2269 (1989) [CrossRef]
  5. H. J. Eichler, R. Macdonald and B. Trosken, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A. 231, 1 (1993) [CrossRef]
  6. R. J. McEwan and R. C. Hollins, J. Nonlinear Opt. Phys. Mater. 4, 245-260 (1995). [CrossRef]
  7. For Fullerene systems, see for example, K. M. Nashold and D. P. Walter, J. Opt. Soc.Am. B. 12, 1228-1237 (1995) and references therein [CrossRef]
  8. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena, (Wiley Interscience, New York, 1994) chap. 2, p. 21 and references therein.
  9. I. C. Khoo, M. V. Wood, B. D.Guenther, Min-Yi Shih and P. H. Chen, J. Opt. Soc. Am. B, 1533-1540, (1998)
  10. I. C. Khoo, S. Slussarenko, B. D. Guenther, Min-Yi Shih, P. Chen and M. V. Wood, Opt. Lett. 23, 253-255 (1998) [CrossRef]
  11. I. C. Khoo, J. Y. Hou, T. H. Lui, P. Y. Yan, R. R. Michael and G. M. Finn, J. Opt. Soc. Am. B, 4, 886-891, (1987). [CrossRef]

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