- Email: [email protected]
Nonlinear refractive index change of photoactive yellow protein
15 October 1998
Optics Communications 155 Ž1998. 327–331
Nonlinear refractive index change of photoactive yellow protein J. Vanhanen b
a,)
, V.P. Leppanen a , T. Haring a , V. Kettunen a , T. Jaaskelainen a , S. Parkkinen b, J.P.S. Parkkinen b
a Department of Physics, Vaisala ¨ ¨ ¨ Laboratory, UniÕersity of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland Department of Information Technology, Lappeenranta UniÕersity of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finland
Received 5 May 1998; accepted 14 July 1998
Abstract The nonlinear refractive index change of photoactive yellow protein ŽPYP. was examined by measuring the shape of an originally Gaussian-shaped laser beam after it had propagated through a PYP-film. An unique reshaping of the beam profile was observed. By this data the nonlinear part of the refractive index was calculated by applying optical map transformation. The result was verified by reconstructing the far-field pattern of the beam with the calculated nonlinear refractive index and the Rayleigh–Sommerfeld diffraction formula. The results show that PYP exhibits much stronger nonlinearity than Kerr-like materials. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Nonlinear refractive index; Optical map transform; Ectothiorhodospira halophila
1. Introduction Photochromic properties of Photoactive Yellow Protein ŽPYP. are nowadays under increasing interest. This watersoluble protein isolated from the Eubacterium Ectothiorhodospira halophila acts as a blue-light photoreceptor with a ground state absorption spectrum centered at 446 nm w1x. Its optical properties resemble those of better known bacteriorhodopsin ŽBR. in spite of the different structure w2x. Because of the similar optical behaviour, PYP is a possible alternative for BR in certain optical applications. ˚ resolution w3x. The structure of PYP is known at 1.4 A It has an arb fold, which is formed by an antiparallel b-sheet with six strands. The chromophore is p-coumaric acid linked via thioester bond to amino-acid Cys69 w4x. The absorption of light induces a sequence of structural changes triggered by the trans–cis isomerization of the chromophore w5x. At room temperature this reversible photocycle is usually claimed to include a ground state and
)
Corresponding author. E-mail: [email protected]
two intermediate states w1,6x. The ground state is photochemically converted into the red-shifted intermediate ŽpR., which absorbs maximally at 465 nm. This intermediate is rapidly, in millisecond time scale, transformed into the blue-shifted intermediate ŽpB. with absorption maximum at 355 nm. Finally, the molecule is slowly, in seconds, recovered back into the ground state. The photocycle includes a proton uptake and release w7,8x. In addition to the dark-adapted state pG, the conformation of the long˚ lived intermediate pB has also been resolved at 1.9 A resolution w9x. Optical properties of PYP can be modified by several means for special purposes. Photocycle kinetics and spectral characteristics are influenced by environmental changes like altering pH, temperature or by adding chemicals w10,11x. Strong effect is achieved through genetic modifications w12,13x or by substituting the chromophore with an analogue structure w14x. In addition to these absorption spectrum studies of PYP, its intensity dependent transmittance behaviour has been investigated, as well w15x. An important property of an optical material is also its nonlinear refraction. The refractive index of a nonlinear material is intensity dependent, expressed as nŽ I . s n 0 q
0030-4018r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 8 . 0 0 3 9 5 - 2
328
J. Vanhanen et al.r Optics Communications 155 (1998) 327–331
D nŽ I ., where n 0 is the refractive index without illumination and D nŽ I . is the light induced change in the refractive index. Among photoactive proteins experiments related to this property have been done only to BR w16–18x. Because the population distribution of PYP between the different photointermediates is intensity dependent and each intermediate has a distinct absorption spectrum, the material has intensity dependent refractive index change based on the anomalous dispersion. This paper includes studies of the nonlinear behaviour of PYP introducing simultaneously a novel experiment technique for that purpose. The refractivity of PYP was approached by measuring the shape of the originally Gaussian-shaped laser beam after it had propagated to the far-field through a PYP film. An extraordinary effect, beam reshaping was observed. Top of the beam became flat and the lower intensity part became broader. The measured data was used to determine the nonlinear intensity dependent refractive index change D n of the material. The method to calculate D n was derived by applying the theory of optical map transformations w19–21x. This theory is used for reshaping a laser beam profile and is applied, e.g., designing holograms for such a purpose w21–24x. In case of an uniform output, the analytical formula for the required phase is available w22x. The verification of the results was done by calculating the far-field beam pattern by using the obtained D n-values and Rayleigh–Sommerfeld diffraction formula w25x. The purpose of this study was to examine the nonlinearity of PYP. Unique properties of PYP under Gaussian illumination will be presented. Nonlinear refractive index change of the material was calculated and the correctness of the results is illustrated. According to the results, this protein exhibits stronger nonlinearity than a traditional Kerr-material.
2. Methods PYP was used in a polyacrylamide ŽPAA.-matrix. The protein was heterogously expressed as histidine tagged apoprotein and was reconstituted with the p-coumaric aldehyde chromophore w26x. The 7.5% PYP-PAA-gel at pH 7 was spread between two glass plates. The film was very sensitive to drying so that it had to be stored in water. However, the variation of the humidity causes changes in the absorption of the film. Thus, the transmittance of the PYP-films measured previously w15x may have been different in these experiments. This possible variation will be taken into account later. The sample was illuminated by argon laser beam, which wavelength was 457 nm and the waist diameter was 1.6 mm. The intensity of the incident beam was regulated by an adjustable filter. The shape of the propagated beam was measured by a logarithmic photodiode mounted in a goniometer. The scanning angle was "38. To avoid detection
of scattered light, two apertures were placed between the sample and the detector. The measurements were done in the far-field. Restricted to a one dimensional case, a map transformation between two planes is defined as u s uŽ x ., where x and u are the coordinates of the input plane and the output plane, respectively w19,20x. The direction of the wavefront at the point x is Ž1rk .ŽEfrE x ., where f Ž x . is the phase and k s 2prl w19x. According to geometrical optics, the light ray from x reaches the output plane at usxq
D z Ef k Ex
,
Ž1.
where D z is the distance between the planes w21x. The phase f Ž x . is then
fŽ x. s
k
x
X
X
X
H Ž uŽ x . y x . d x . Dz 0
Ž2.
The complex amplitude of the Gaussian beam in one dimension is expressed as U Ž x , z . s A0
W0 WŽ z.
ž
exp y
x2 W 2Ž z.
/
,
Ž3.
where z is the propagation distance, A 0 a constant, W Ž0. the beam radius at z s 0 and W Ž z . the beam radius in the propagation direction. Due to the energy conservation, the area of the incident intensity profile I I Ž x, z . and the measured, transformed intensity profile I T Ž u. is the same, i.e., x
X
u
X
H0 I Ž x . d x s KH0 I I
T
Ž uX . d uX .
Ž4.
K is a constant, which is added to ensure the equality of both sides. Thus, it neutralizes the error caused by the possible transmittance inconsistency as discussed above. The incident intensity profile has n subdivisions, where n denotes the number of data points. From Eq. Ž4., it follows that the area of each subdivision at the input plane is the same as the corresponding area at the output plane, i.e., I I j Ž x j y x jy1 . s KIT j Ž u j y u jy1 .. The constant K is obtained from Eq. Ž4.. The coordinates u are then calculated as ujs
1 I I j Ž x j y x jy1 . K
IT j
q u jy1 ,
Ž5.
where u 0 s 0. The integral of Eq. Ž2. is written as
fŽ x. s
k Dz
n
ž
Ý w u j y x j x Ž x j y x jy1 . js1
/
.
Ž6.
Finally, f Ž x . is obtained as
fŽ xj. s
k Dz
Ž u j y x j .Ž x j y x jy1 . q f Ž x ny1 . ,
Ž7.
J. Vanhanen et al.r Optics Communications 155 (1998) 327–331
329
Fig. 1. The beam profiles after propagating through photoactive yellow protein-film as a function of the scanning angle. The vertical axis corresponds to the logarithmic detector output. Intensities are in Wrcm2 .
where f Ž x 0 . s 0. The nonlinear part of the refractive index follows from the equation
f Dns
kd
,
Ž8.
where d denotes the thickness of the film.
3. Results The far-field laser beam shape after propagation through the PYP-film was measured with five intensities: 0.0038,
0.01, 0.02, 0.03 and 0.038 Wrcm2. The distance from the laser to the sample was 592 mm and between the sample and the detector 454 mm. The measured data is shown in Fig. 1 as a function of the scanning angle. The vertical axis corresponds to the output of the photodetector. Due to the logarithmic response of the detector, the shapes of the lower parts of the beam profiles are strengthened showing the broadening. The flattening will be seen better in Fig. 4 Žsolid curves., where the scale of the vertical axis is linear. The values of this axis were converted by the information of the intensity dependent transmittance of the PYP-film measured in Ref. w15x.
Fig. 2. The nonlinear refractive index change as a function of radial distance. Intensity is 0.02 Wrcm2 .
330
J. Vanhanen et al.r Optics Communications 155 (1998) 327–331
Fig. 3. The reconstructed far-field beam profiles Ždashed curves. versus the measured ones Žsolid lines. as a function of radial distance. Intensities are in Wrcm2 .
Since the original measured data is rather uneven, super-Gaussian fittings to the profiles were formed and used as the far-field intensities I T . The incident intensity I I was generated using Eq. Ž3. and by multiplying this intensity by the transmittance function of the material derived from the data in Ref. w15x by curve fitting. The intensity dependent refractive index D n was calculated by Eqs. Ž5. and Ž8. for each of the intensities. The calculation gives curves similar to that presented in Fig. 2 as a function of
radial distance. Based on the anomalous dispersion properties and the negative lensing effect shown in Fig. 1, the sign of D n was concluded to be negative. After the D n-values were determined, they were verified. First the beam profiles just after the material were reconstructed by using the corresponding D n-values. Then the profiles were shifted to the far-field by the Rayleigh– Sommerfeld diffraction formula. The resulting profiles are shown in Fig. 3 Ždashed curves.. They are in good agree-
Fig. 4. The average of the nonlinear refractive index changes as a function of intensity.
J. Vanhanen et al.r Optics Communications 155 (1998) 327–331
ment with the measured ones supporting the correctness of the calculated D n-behaviour. Fig. 4 shows the average of the D n-curves as a function of intensity.
4. Conclusions The nonlinear behaviour of PYP was investigated with a novel experimental technique. An interesting reshaping of the Gaussian-shaped laser beam was observed at five incident intensities. The simple experimental setup was found to be applicable to examine nonlinear refractivity of PYP and to determine the nonlinear refractive index. The protein exhibits strong nonlinearity and the nonlinear part of the refractive index cannot be approximated to be quadratic as in Kerr-type materials. However, the sensitivity of the presented method towards experimental problems is restricted because of the super-Gaussian fittings used to replace the measured data.
Acknowledgements The authors are grateful to Professor K.J. Hellingwerf for providing the photoactive yellow protein. The authors will also thank Professor J. Turunen for his interest and help in the work. This research was supported by the Academy of Finland.
References w1x W.D. Hoff, I.H.M. van Stokkum, H.J. van Ramesdonk, M.E. van Brederode, A.M. Brouwer, J.C. Fitch, T.E. Meyer, van Grondelle, K.J. Hellingwerf, Biophys. J. 67 Ž1994. 1691. w2x T.E. Meyer, E. Yakali, M.A. Cusanovich, G. Tollin, Biochemistry 26 Ž1987. 418. w3x G.E.O. Borgstahl, D.R. Williams, E.D. Getzoff, Biochemistry 34 Ž1995. 6278. w4x W.D. Hoff, P. Dux, ¨ K. Hard, ˚ B. Devreese, I.M. NugterenRoodzant, W. Grielaard, R. Boelens, R. Kaptein, J. van Beeumen, K.J. Hellingwerf, Biochemistry 33 Ž1994. 13959.
331
w5x R. Kort, H. Vonk, X. Xu, W.D. Hoff, W. Grielaard, K.J. Hellingwerf, FEBS Lett. 382 Ž1996. 73. w6x I. Schlichting, J. Berendzen, Structure 5 Ž1997. 735. w7x M. Kim, R.A. Mathies, W.D. Hoff, K.J. Hellingwerf, Biochemistry 34 Ž1995. 12669. w8x A. Xie, W.D. Hoff, A.R. Kroon, K.J. Hellingwerf, Biochemistry 35 Ž1996. 14671. w9x U.K. Genick, G.E.O. Borgstahl, K. Ng, Z. Ren, C. Praderˇ vand, P.M. Burke, V. Srajer, T.Y. Teng, W. Schildkamp, D.E. McRee, K. Moffat, E.D. Getzoff, Science 275 Ž1997. 1471. w10x T.E. Meyer, G. Tollin, J.H. Hazzard, M.A. Cusanovich, Biophys. J. 56 Ž1989. 559. w11x W.D. Hoff, B. Devreese, R. Fokkens, I.M. Nugteren-Roodzant, J. van Beeumen, N. Nibbering, K.J. Hellingwerf, Biochemistry 35 Ž1995. 1274. w12x U.K. Genick, S. Devanathan, T.E. Meyer, I.L. Canestrelli, E. Williams, M.A. Cusanovich, G. Tollin, E.D. Getzoff, Biochemistry 36 Ž1997. 8. w13x K. Mihara, O. Hisatomi, Y. Imamoto, M. Kataoka, F. Tokunaga, J. Biochem. 121 Ž1997. 876. w14x A.R. Kroon, W.D. Hoff, H.P.M. Fennema, J. Gijzen, G.J. Koomen, J.W. Verhoeven, W. Grielaard, K.J. Hellingwerf, J. Biol. Chem. 271 Ž1996. 31949. w15x J. Vanhanen, V.P. Leppanen, T. Jaaskelainen, S. Parkkinen, J.P.S. Parkkinen, Optics Comm. 153 Ž1998. 289. w16x Q.W. Song, C. Zhang, R.B. Gross, R.R. Birge, Optics Comm. 112 Ž1994. 296. w17x Q.W. Song, C.Y. Ku, C. Zhang, R.B. Gross, R.R. Birge, R. Michalak, J. Opt. Soc. Am. 12 Ž1995. 797. w18x Q. Wang, C. Zhang, R. Gross, R.R. Birge, Optics Lett. 18 Ž1993. 775. w19x O. Bryngdahl, Optics Comm. 10 Ž1974. 164. w20x O. Bryngdahl, J. Opt. Soc. Am. 64 Ž1974. 1092. w21x N.C. Roberts, Appl. Optics 28 Ž1989. 31. w22x C.C. Aleksoff, K.K. Ellis, B.D. Neagle, Optics Eng. 30 Ž1991. 537. w23x N.C. Roberts, Appl. Optics 31 Ž1992. 3198. w24x C.Y. Han, Y. Ishii, K. Murata, Appl. Optics 22 Ž1983. 3644. w25x L. Mandel, E. Wolf, Optical Coherence and Quantum Optics, Pergamon, Oxford, 1980. w26x R. Kort, W.D. Hoff, M. van West, A.R. Kroon, S.M. Hoffer, K.H. Vlieg, W. Crielaard, J.J. van Beeumen, K.J. Hellingwerf, EMBO J. 15 Ž1996. 3209.
Optics Communications 155 Ž1998. 327–331
Nonlinear refractive index change of photoactive yellow protein J. Vanhanen b
a,)
, V.P. Leppanen a , T. Haring a , V. Kettunen a , T. Jaaskelainen a , S. Parkkinen b, J.P.S. Parkkinen b
a Department of Physics, Vaisala ¨ ¨ ¨ Laboratory, UniÕersity of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland Department of Information Technology, Lappeenranta UniÕersity of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finland
Received 5 May 1998; accepted 14 July 1998
Abstract The nonlinear refractive index change of photoactive yellow protein ŽPYP. was examined by measuring the shape of an originally Gaussian-shaped laser beam after it had propagated through a PYP-film. An unique reshaping of the beam profile was observed. By this data the nonlinear part of the refractive index was calculated by applying optical map transformation. The result was verified by reconstructing the far-field pattern of the beam with the calculated nonlinear refractive index and the Rayleigh–Sommerfeld diffraction formula. The results show that PYP exhibits much stronger nonlinearity than Kerr-like materials. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Nonlinear refractive index; Optical map transform; Ectothiorhodospira halophila
1. Introduction Photochromic properties of Photoactive Yellow Protein ŽPYP. are nowadays under increasing interest. This watersoluble protein isolated from the Eubacterium Ectothiorhodospira halophila acts as a blue-light photoreceptor with a ground state absorption spectrum centered at 446 nm w1x. Its optical properties resemble those of better known bacteriorhodopsin ŽBR. in spite of the different structure w2x. Because of the similar optical behaviour, PYP is a possible alternative for BR in certain optical applications. ˚ resolution w3x. The structure of PYP is known at 1.4 A It has an arb fold, which is formed by an antiparallel b-sheet with six strands. The chromophore is p-coumaric acid linked via thioester bond to amino-acid Cys69 w4x. The absorption of light induces a sequence of structural changes triggered by the trans–cis isomerization of the chromophore w5x. At room temperature this reversible photocycle is usually claimed to include a ground state and
)
Corresponding author. E-mail: [email protected]
two intermediate states w1,6x. The ground state is photochemically converted into the red-shifted intermediate ŽpR., which absorbs maximally at 465 nm. This intermediate is rapidly, in millisecond time scale, transformed into the blue-shifted intermediate ŽpB. with absorption maximum at 355 nm. Finally, the molecule is slowly, in seconds, recovered back into the ground state. The photocycle includes a proton uptake and release w7,8x. In addition to the dark-adapted state pG, the conformation of the long˚ lived intermediate pB has also been resolved at 1.9 A resolution w9x. Optical properties of PYP can be modified by several means for special purposes. Photocycle kinetics and spectral characteristics are influenced by environmental changes like altering pH, temperature or by adding chemicals w10,11x. Strong effect is achieved through genetic modifications w12,13x or by substituting the chromophore with an analogue structure w14x. In addition to these absorption spectrum studies of PYP, its intensity dependent transmittance behaviour has been investigated, as well w15x. An important property of an optical material is also its nonlinear refraction. The refractive index of a nonlinear material is intensity dependent, expressed as nŽ I . s n 0 q
0030-4018r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 8 . 0 0 3 9 5 - 2
328
J. Vanhanen et al.r Optics Communications 155 (1998) 327–331
D nŽ I ., where n 0 is the refractive index without illumination and D nŽ I . is the light induced change in the refractive index. Among photoactive proteins experiments related to this property have been done only to BR w16–18x. Because the population distribution of PYP between the different photointermediates is intensity dependent and each intermediate has a distinct absorption spectrum, the material has intensity dependent refractive index change based on the anomalous dispersion. This paper includes studies of the nonlinear behaviour of PYP introducing simultaneously a novel experiment technique for that purpose. The refractivity of PYP was approached by measuring the shape of the originally Gaussian-shaped laser beam after it had propagated to the far-field through a PYP film. An extraordinary effect, beam reshaping was observed. Top of the beam became flat and the lower intensity part became broader. The measured data was used to determine the nonlinear intensity dependent refractive index change D n of the material. The method to calculate D n was derived by applying the theory of optical map transformations w19–21x. This theory is used for reshaping a laser beam profile and is applied, e.g., designing holograms for such a purpose w21–24x. In case of an uniform output, the analytical formula for the required phase is available w22x. The verification of the results was done by calculating the far-field beam pattern by using the obtained D n-values and Rayleigh–Sommerfeld diffraction formula w25x. The purpose of this study was to examine the nonlinearity of PYP. Unique properties of PYP under Gaussian illumination will be presented. Nonlinear refractive index change of the material was calculated and the correctness of the results is illustrated. According to the results, this protein exhibits stronger nonlinearity than a traditional Kerr-material.
2. Methods PYP was used in a polyacrylamide ŽPAA.-matrix. The protein was heterogously expressed as histidine tagged apoprotein and was reconstituted with the p-coumaric aldehyde chromophore w26x. The 7.5% PYP-PAA-gel at pH 7 was spread between two glass plates. The film was very sensitive to drying so that it had to be stored in water. However, the variation of the humidity causes changes in the absorption of the film. Thus, the transmittance of the PYP-films measured previously w15x may have been different in these experiments. This possible variation will be taken into account later. The sample was illuminated by argon laser beam, which wavelength was 457 nm and the waist diameter was 1.6 mm. The intensity of the incident beam was regulated by an adjustable filter. The shape of the propagated beam was measured by a logarithmic photodiode mounted in a goniometer. The scanning angle was "38. To avoid detection
of scattered light, two apertures were placed between the sample and the detector. The measurements were done in the far-field. Restricted to a one dimensional case, a map transformation between two planes is defined as u s uŽ x ., where x and u are the coordinates of the input plane and the output plane, respectively w19,20x. The direction of the wavefront at the point x is Ž1rk .ŽEfrE x ., where f Ž x . is the phase and k s 2prl w19x. According to geometrical optics, the light ray from x reaches the output plane at usxq
D z Ef k Ex
,
Ž1.
where D z is the distance between the planes w21x. The phase f Ž x . is then
fŽ x. s
k
x
X
X
X
H Ž uŽ x . y x . d x . Dz 0
Ž2.
The complex amplitude of the Gaussian beam in one dimension is expressed as U Ž x , z . s A0
W0 WŽ z.
ž
exp y
x2 W 2Ž z.
/
,
Ž3.
where z is the propagation distance, A 0 a constant, W Ž0. the beam radius at z s 0 and W Ž z . the beam radius in the propagation direction. Due to the energy conservation, the area of the incident intensity profile I I Ž x, z . and the measured, transformed intensity profile I T Ž u. is the same, i.e., x
X
u
X
H0 I Ž x . d x s KH0 I I
T
Ž uX . d uX .
Ž4.
K is a constant, which is added to ensure the equality of both sides. Thus, it neutralizes the error caused by the possible transmittance inconsistency as discussed above. The incident intensity profile has n subdivisions, where n denotes the number of data points. From Eq. Ž4., it follows that the area of each subdivision at the input plane is the same as the corresponding area at the output plane, i.e., I I j Ž x j y x jy1 . s KIT j Ž u j y u jy1 .. The constant K is obtained from Eq. Ž4.. The coordinates u are then calculated as ujs
1 I I j Ž x j y x jy1 . K
IT j
q u jy1 ,
Ž5.
where u 0 s 0. The integral of Eq. Ž2. is written as
fŽ x. s
k Dz
n
ž
Ý w u j y x j x Ž x j y x jy1 . js1
/
.
Ž6.
Finally, f Ž x . is obtained as
fŽ xj. s
k Dz
Ž u j y x j .Ž x j y x jy1 . q f Ž x ny1 . ,
Ž7.
J. Vanhanen et al.r Optics Communications 155 (1998) 327–331
329
Fig. 1. The beam profiles after propagating through photoactive yellow protein-film as a function of the scanning angle. The vertical axis corresponds to the logarithmic detector output. Intensities are in Wrcm2 .
where f Ž x 0 . s 0. The nonlinear part of the refractive index follows from the equation
f Dns
kd
,
Ž8.
where d denotes the thickness of the film.
3. Results The far-field laser beam shape after propagation through the PYP-film was measured with five intensities: 0.0038,
0.01, 0.02, 0.03 and 0.038 Wrcm2. The distance from the laser to the sample was 592 mm and between the sample and the detector 454 mm. The measured data is shown in Fig. 1 as a function of the scanning angle. The vertical axis corresponds to the output of the photodetector. Due to the logarithmic response of the detector, the shapes of the lower parts of the beam profiles are strengthened showing the broadening. The flattening will be seen better in Fig. 4 Žsolid curves., where the scale of the vertical axis is linear. The values of this axis were converted by the information of the intensity dependent transmittance of the PYP-film measured in Ref. w15x.
Fig. 2. The nonlinear refractive index change as a function of radial distance. Intensity is 0.02 Wrcm2 .
330
J. Vanhanen et al.r Optics Communications 155 (1998) 327–331
Fig. 3. The reconstructed far-field beam profiles Ždashed curves. versus the measured ones Žsolid lines. as a function of radial distance. Intensities are in Wrcm2 .
Since the original measured data is rather uneven, super-Gaussian fittings to the profiles were formed and used as the far-field intensities I T . The incident intensity I I was generated using Eq. Ž3. and by multiplying this intensity by the transmittance function of the material derived from the data in Ref. w15x by curve fitting. The intensity dependent refractive index D n was calculated by Eqs. Ž5. and Ž8. for each of the intensities. The calculation gives curves similar to that presented in Fig. 2 as a function of
radial distance. Based on the anomalous dispersion properties and the negative lensing effect shown in Fig. 1, the sign of D n was concluded to be negative. After the D n-values were determined, they were verified. First the beam profiles just after the material were reconstructed by using the corresponding D n-values. Then the profiles were shifted to the far-field by the Rayleigh– Sommerfeld diffraction formula. The resulting profiles are shown in Fig. 3 Ždashed curves.. They are in good agree-
Fig. 4. The average of the nonlinear refractive index changes as a function of intensity.
J. Vanhanen et al.r Optics Communications 155 (1998) 327–331
ment with the measured ones supporting the correctness of the calculated D n-behaviour. Fig. 4 shows the average of the D n-curves as a function of intensity.
4. Conclusions The nonlinear behaviour of PYP was investigated with a novel experimental technique. An interesting reshaping of the Gaussian-shaped laser beam was observed at five incident intensities. The simple experimental setup was found to be applicable to examine nonlinear refractivity of PYP and to determine the nonlinear refractive index. The protein exhibits strong nonlinearity and the nonlinear part of the refractive index cannot be approximated to be quadratic as in Kerr-type materials. However, the sensitivity of the presented method towards experimental problems is restricted because of the super-Gaussian fittings used to replace the measured data.
Acknowledgements The authors are grateful to Professor K.J. Hellingwerf for providing the photoactive yellow protein. The authors will also thank Professor J. Turunen for his interest and help in the work. This research was supported by the Academy of Finland.
References w1x W.D. Hoff, I.H.M. van Stokkum, H.J. van Ramesdonk, M.E. van Brederode, A.M. Brouwer, J.C. Fitch, T.E. Meyer, van Grondelle, K.J. Hellingwerf, Biophys. J. 67 Ž1994. 1691. w2x T.E. Meyer, E. Yakali, M.A. Cusanovich, G. Tollin, Biochemistry 26 Ž1987. 418. w3x G.E.O. Borgstahl, D.R. Williams, E.D. Getzoff, Biochemistry 34 Ž1995. 6278. w4x W.D. Hoff, P. Dux, ¨ K. Hard, ˚ B. Devreese, I.M. NugterenRoodzant, W. Grielaard, R. Boelens, R. Kaptein, J. van Beeumen, K.J. Hellingwerf, Biochemistry 33 Ž1994. 13959.
331
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