- Email: [email protected]
Sub-nanometer metrology of chirped phase masks by optical Moiré
1 November 1999
Optics Communications 170 Ž1999. 175–179 www.elsevier.comrlocateroptcom
Sub-nanometer metrology of chirped phase masks by optical Moire´ F. Barnier a , P.E. Dyer
a,)
, H.V. Snelling a , R.M. De la Rue
b
a
b
Department of Physics, UniÕersity of Hull, Hull HU6 7RX, UK Department of Electronic and Electrical Engineering, UniÕersity of Glasgow, Glasgow G12 8LT, UK Received 8 June 1999; received in revised form 17 August 1999; accepted 18 August 1999
Abstract Optical Moire´ fringe formation between a linear and chirped phase mask has been investigated theoretically and experimentally and used to determine the chirp rate. Period difference determination down to ; 0.4 nm is demonstrated using a 1080 nm period linear grating and a nominally 1 nmrmm chirped grating. Direct optical diffraction is also used to independently assess the chirp rate. q 1999 Elsevier Science B.V. All rights reserved.
During the past few years there has been a dramatic growth of interest in the development and application of in-fibre Bragg gratings for telecommunications and sensor use. Laser side-writing w1x by means of specially designed phase masks that produce the requisite interference pattern in the fibre core provides a particularly effective approach to fabricating these gratings w2–4x. E-beam lithographic techniques can now be used to fabricate phase masks with a range of characteristics including small chirp rates needed for fibre gratings in dispersion compensation applications w5x. As the fidelity of the master mask determines the performance of the in-fibre gratings it is necessary to develop suitable means for evaluating and validating these masks. One approach is the use of optical metrology based on Moire´
) Corresponding author. Fax: q44-1482-465606; e-mail: [email protected]
fringes produced by a master and test grating and we have recently shown its suitability for identifying stitch-errors in e-beam fabricated phase masks w6x. The use of a high accuracy fibre interferometer technique for characterising in-fibre chirped Bragg gratings has been reported w7x but this is not applicable to the master masks where a non-guided wave approach is necessary. Here we report the use of optical Moire´ for assessing properties of chirped phase masks with a centre period of ; 1080 nm and demonstrate the capability for resolving period differences down to ; 0.4 nm by this method. Direct optical diffraction from these masks has also been used to independently estimate the chirp rate. The basis of the method is the well-known fact w8,9x that a large Moire´ magnification is produced when two gratings are disposed with a small angle a between their grooves. In the present experiments the ratio of grating period, dX , to wavelength, l, is
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 4 6 1 - 7
F. Barnier et al.r Optics Communications 170 (1999) 175–179
176
relatively small Ž dXrl ; 1.6–2.6.. With this condition a theoretical analysis of the emergent irradiance distribution from the grating pair can be carried out by retaining only three diffracted beams for each grating Ž0, "1 orders.. Under low microscope magnification where the Moire´ fringes are formed by those beams making small angles to the axis Ži.e. only low spatial frequencies are imaged., the irradiance distribution of the grating pair in transmission or in reflection has the form w6x: I s A q B cos 2 Ž V y V X . q C cos Ž V y V X .
Ž 1.
Here the coefficients A, B and C are determined by the amplitudes and phases of the various diffracted orders and C is also dependent on the spacing between the gratings. The argument of the cosine terms is given by:
V y V X s 2 p x Ž 1 y t . cos ar2 yy Ž 1 q t . sin ar2 4 rdX where t s dXrd f 1 and dX and d are the periods of the first and second gratings which are oriented at angles yar2 and qar2 respectively to y ŽFig. 1.. The Moire´ fringes make an angle of f with respect to the x axis given by: d yrd x s tan f s 1 y t 4 r Ž 1 q t 4 tan ar2 .
Ž 2.
governed by their period difference Žif t s 1, f s 0 and the fringes are perpendicular to the bisector of a i.e. to the y axis.. The fundamental Moire´ period is: ym s dXr Ž sin f cos ar2 1 y t 4 qcos f sin ar2 1 q t 4 .
Ž 3.
and, from Eq. Ž1., there is also a term at half this period. Either of these periods may dominate or both may co-exist depending on the grating properties w6x. Suppose now that dX is constant and d is linearly chirped with: d s dX q r Ž x cos ar2 q y sin ar2 . where r is the rate of change of period with distance. For small r and a and if y is not too large, this can be approximated as d s dX q rx and Eq. Ž2. can be integrated to yield fringe contours defined by: y s r Ž x 2 y rx 3r3 dX . r2 dXa q constant Ž rx < 2 dX .
For the experiments described below with dX s 1080 nm, r ; 1 nmrmm and < x < F 15 mm, the term in x 3 can be neglected and the fringes to a high degree of accuracy are described by a parabolic form: y s rx 2r2 dXa q constant.
Ž 4.
The Moire´ fringes can thus be used to determine the chirp rate through use of Eqs. Ž2. or Ž4.. Experiments were carried out using a master grating with a constant period of dX s 1080 nm Ždimensions 30.2 mm = 2 mm. and a chirped grating with a centre period of 1080 nm and nominal linear chirp of 1 nmrmm Ždimensions 30 mm = 1 mm.. Both were fabricated in fused silica by e-beam etching. A Nikon Optiphot microscope with an epi-illuminator attachment that allowed viewing in reflection in addition to the usual transmission mode was used in the experiments. The gratings were placed in contact with their grooves facing, mounted on the microscope stage and Moire´ fringe formation observed under white light Koehler illumination with a tungsten halogen source. The fringes were recorded using a 35 mm camera and also a CCD camera to allow subsequent digital image processing to enhance the fringe contrast. Moire´ fringes were observed in both transmission and in reflection from the grating pair and found to have the same period. Initially the grating angle a was set to a relatively large value Ž; 42 mrad. so it could be measured accurately and used to calculate the Moire´ period. Near the centre of the chirped grating where d s dX and f s 0, the measured Moire´ period was 25 mm in close agreement with dXra s 25.5 mm deduced from Eq. Ž3.. This established the fringe system as being the fundamental-period Moire. ´ On this basis in subsequent experiments where considerably smaller values of a were used to enhance the sensitivity to chirp ŽEq. Ž4.., the angle was determined from the Moire´ period rather than the boundary zones of the gratings. This avoided possible errors arising through non-orthogonality of the grooves and grating boundary. The Moire´ fringe system was recorded over the full length of the chirped grating and the local fringe slope ŽEq. Ž2.. used to determine the period differ-
F. Barnier et al.r Optics Communications 170 (1999) 175–179
ence between the master and the chirped grating. A value of a s 4.7 mrad was used as determined from the Moire´ period in the central region of the gratings
177
where f s 0. Fig. 1 shows sections of the parabolic fringe system at several locations along the mask. The variation of d d s d y dX with x is shown in
Fig. 1. Moire´ fringe geometry for chirped phase mask, G1 , overlaying linear grating, G2. The groove directions, designated by g 1 and g 2 , make an angle a to one another, y is the bisector of a and the fringe orientation f is measured with respect to the x-axis. Fringes recorded at the centre and at the ends of the 30 mm long, 1 mm wide chirped grating using optical microscopy Ž=12.5 magnification. are shown for a s 4.7 mrad.
178
F. Barnier et al.r Optics Communications 170 (1999) 175–179
Fig. 2, a linear fit to the data giving a chirp rate of r s 0.95 " 0.1 nmrmm. From the fringes in the central region of Fig. 1 it can be established that fringe curvature can be detected and quantified beyond a distance of about 400 mm from the minima of the fringe system. With r s 0.95 nmrmm this indicates a capability for resolving differences in grating period down to ; 0.4 nm. An independent assessment of the chirp was made using optical diffraction with a HeNe laser beam Ž l s 632.8 nm.. The chirped grating was illuminated at an angle of incidence i s 63.38 and the change of the m s 2 order diffracted beam angle, d r, recorded as the grating was translated across the beam ŽFig. 3.. The average period of the grating over the probed region is given by d s m lrŽsin i y sin r . where r is the angle of diffraction and for small d r the period change d d is:
d d s d 2 cos rd rrm l where m is the order. To eliminate spurious angular deflections arising from lack of flatness in the substrate or tilt in the translation stage the zero-order beam was simultaneously monitored and adjustments made as necessary to keep this beam centralised on the detector. The limiting resolution, d d o , is defined by a combination of the beam divergence set by diffrac-
Fig. 2. Variation of period difference between chirped and linear gratings as a function of position on the chirped mask as derived from Moire´ fringe angle. The linear fit to the data yields a chirp rate of 0.95"0.1 nmrmm.
Fig. 3. Angle of second-order diffracted 632.8 nm laser beam as a function of position on chirped mask Žangle of incidence is63.38.. A linear fit to the data gives a chirp rate of 0.98"0.05 nmrmm.
tion and that produced by the chirp across the probe beam with: 2
d d o s 0.707 d 2 cos irmp v o 4 q r v o 4
ž
2
0.5
/
Here vo is the Gaussian beam waist Žfield. radius at the grating and the minimum resolvable angle of the diffracted beam is taken at the ey1 irradiance. With vo s 0.4 mm and m s 2, a theoretical resolution of d d o s 0.32 nm is realised. In the experiments an angular resolution of d r ( 1 min gave d d o G 0.26 nm which is consistent with this value. Fig. 3 shows the variation of d r with position on the chirped grating, the data yielding a chirp rate of r s 0.98 " 0.05 nmrmm in close agreement with the Moire´ measurement. In conclusion, it has been demonstrated that Moire´ mapping of a chirped phase mask provides a useful method for evaluating the grating chirp. It is remarkable that a resolution of period differences down to ; 0.4 nm can be accomplished in this way using only low resolution optical microscopy. This can be attributed to the high magnification provided by the Moire´ technique. A potential problem of the method with incoherent illumination is the need for near-contact between the masks for effective Moire fringe formation w6x with the possible risk of damage. The use of coherent illumination could overcome this by allowing use of a finite mask spacing albeit at some
F. Barnier et al.r Optics Communications 170 (1999) 175–179
increase in experimental complexity. Direct probing of the grating by optical diffraction provides an alternative non-contact technique, with a theoretical resolution of period difference at the subnanometer level. Acknowledgements P.E.D. and F.B. gratefully acknowledge the continued support of Nortel and thank Mr. H. Rourke of Nortel, Harlow, for helpful discussions. We are also grateful to Mr. G. Robinson in Engineering for use of the microscopy facilities. R.M.D. acknowledges the support of the Engineering and Physical Sciences Research Council and the contributions of the groups at Glasgow and Aston Universities which led to the production of the chirped phase masks.
179
References w1x G. Meltz, W.W. Morey, W.H. Glenn, Opt. Lett. 14 Ž1989. 823. w2x K.O. Hill, B. Malo, F. Bilodeau, D.C. Johnson, J. Albert, Appl. Phys. Lett. 62 Ž1993. 1035. w3x P.E. Dyer, R.J. Farley, R. Giedl, Opt. Commun. 115 Ž1995. 327. w4x J.S. Aichison, R.M. De La Rue, Opt. Lett. 22 Ž1997. 1473. w5x X. Liu, J.S. Aitchison, R.M. De La Rue, S. Thoms, L. Zhang, J.A.R. Williams, I. Bennion, Micro. Eng. 35 Ž1997. 345. w6x F. Barnier, P.E. Dyer, G.A. Steigmann, Opt. Commun. 162 Ž1999. 299. w7x S. Barcelos, M.N. Zervas, R.I. Laming, D.N. Payne, L. Reekie, J.A. Tucknott, R. Kashyap, P.F. McKee, F. Sladen, B. Wojciechowicz, Electron. Lett. 31 Ž1995. 1280. w8x J. Guild, The Interference Systems of Crossed Diffraction Gratings: Theory of Moire´ Fringes, Clarendon Press, Oxford, 1956. w9x B. Hubner, H.W.P. Koops, J. Vac. Sci. Technol. B 10 Ž1992. ¨ 2648.
Optics Communications 170 Ž1999. 175–179 www.elsevier.comrlocateroptcom
Sub-nanometer metrology of chirped phase masks by optical Moire´ F. Barnier a , P.E. Dyer
a,)
, H.V. Snelling a , R.M. De la Rue
b
a
b
Department of Physics, UniÕersity of Hull, Hull HU6 7RX, UK Department of Electronic and Electrical Engineering, UniÕersity of Glasgow, Glasgow G12 8LT, UK Received 8 June 1999; received in revised form 17 August 1999; accepted 18 August 1999
Abstract Optical Moire´ fringe formation between a linear and chirped phase mask has been investigated theoretically and experimentally and used to determine the chirp rate. Period difference determination down to ; 0.4 nm is demonstrated using a 1080 nm period linear grating and a nominally 1 nmrmm chirped grating. Direct optical diffraction is also used to independently assess the chirp rate. q 1999 Elsevier Science B.V. All rights reserved.
During the past few years there has been a dramatic growth of interest in the development and application of in-fibre Bragg gratings for telecommunications and sensor use. Laser side-writing w1x by means of specially designed phase masks that produce the requisite interference pattern in the fibre core provides a particularly effective approach to fabricating these gratings w2–4x. E-beam lithographic techniques can now be used to fabricate phase masks with a range of characteristics including small chirp rates needed for fibre gratings in dispersion compensation applications w5x. As the fidelity of the master mask determines the performance of the in-fibre gratings it is necessary to develop suitable means for evaluating and validating these masks. One approach is the use of optical metrology based on Moire´
) Corresponding author. Fax: q44-1482-465606; e-mail: [email protected]
fringes produced by a master and test grating and we have recently shown its suitability for identifying stitch-errors in e-beam fabricated phase masks w6x. The use of a high accuracy fibre interferometer technique for characterising in-fibre chirped Bragg gratings has been reported w7x but this is not applicable to the master masks where a non-guided wave approach is necessary. Here we report the use of optical Moire´ for assessing properties of chirped phase masks with a centre period of ; 1080 nm and demonstrate the capability for resolving period differences down to ; 0.4 nm by this method. Direct optical diffraction from these masks has also been used to independently estimate the chirp rate. The basis of the method is the well-known fact w8,9x that a large Moire´ magnification is produced when two gratings are disposed with a small angle a between their grooves. In the present experiments the ratio of grating period, dX , to wavelength, l, is
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 4 6 1 - 7
F. Barnier et al.r Optics Communications 170 (1999) 175–179
176
relatively small Ž dXrl ; 1.6–2.6.. With this condition a theoretical analysis of the emergent irradiance distribution from the grating pair can be carried out by retaining only three diffracted beams for each grating Ž0, "1 orders.. Under low microscope magnification where the Moire´ fringes are formed by those beams making small angles to the axis Ži.e. only low spatial frequencies are imaged., the irradiance distribution of the grating pair in transmission or in reflection has the form w6x: I s A q B cos 2 Ž V y V X . q C cos Ž V y V X .
Ž 1.
Here the coefficients A, B and C are determined by the amplitudes and phases of the various diffracted orders and C is also dependent on the spacing between the gratings. The argument of the cosine terms is given by:
V y V X s 2 p x Ž 1 y t . cos ar2 yy Ž 1 q t . sin ar2 4 rdX where t s dXrd f 1 and dX and d are the periods of the first and second gratings which are oriented at angles yar2 and qar2 respectively to y ŽFig. 1.. The Moire´ fringes make an angle of f with respect to the x axis given by: d yrd x s tan f s 1 y t 4 r Ž 1 q t 4 tan ar2 .
Ž 2.
governed by their period difference Žif t s 1, f s 0 and the fringes are perpendicular to the bisector of a i.e. to the y axis.. The fundamental Moire´ period is: ym s dXr Ž sin f cos ar2 1 y t 4 qcos f sin ar2 1 q t 4 .
Ž 3.
and, from Eq. Ž1., there is also a term at half this period. Either of these periods may dominate or both may co-exist depending on the grating properties w6x. Suppose now that dX is constant and d is linearly chirped with: d s dX q r Ž x cos ar2 q y sin ar2 . where r is the rate of change of period with distance. For small r and a and if y is not too large, this can be approximated as d s dX q rx and Eq. Ž2. can be integrated to yield fringe contours defined by: y s r Ž x 2 y rx 3r3 dX . r2 dXa q constant Ž rx < 2 dX .
For the experiments described below with dX s 1080 nm, r ; 1 nmrmm and < x < F 15 mm, the term in x 3 can be neglected and the fringes to a high degree of accuracy are described by a parabolic form: y s rx 2r2 dXa q constant.
Ž 4.
The Moire´ fringes can thus be used to determine the chirp rate through use of Eqs. Ž2. or Ž4.. Experiments were carried out using a master grating with a constant period of dX s 1080 nm Ždimensions 30.2 mm = 2 mm. and a chirped grating with a centre period of 1080 nm and nominal linear chirp of 1 nmrmm Ždimensions 30 mm = 1 mm.. Both were fabricated in fused silica by e-beam etching. A Nikon Optiphot microscope with an epi-illuminator attachment that allowed viewing in reflection in addition to the usual transmission mode was used in the experiments. The gratings were placed in contact with their grooves facing, mounted on the microscope stage and Moire´ fringe formation observed under white light Koehler illumination with a tungsten halogen source. The fringes were recorded using a 35 mm camera and also a CCD camera to allow subsequent digital image processing to enhance the fringe contrast. Moire´ fringes were observed in both transmission and in reflection from the grating pair and found to have the same period. Initially the grating angle a was set to a relatively large value Ž; 42 mrad. so it could be measured accurately and used to calculate the Moire´ period. Near the centre of the chirped grating where d s dX and f s 0, the measured Moire´ period was 25 mm in close agreement with dXra s 25.5 mm deduced from Eq. Ž3.. This established the fringe system as being the fundamental-period Moire. ´ On this basis in subsequent experiments where considerably smaller values of a were used to enhance the sensitivity to chirp ŽEq. Ž4.., the angle was determined from the Moire´ period rather than the boundary zones of the gratings. This avoided possible errors arising through non-orthogonality of the grooves and grating boundary. The Moire´ fringe system was recorded over the full length of the chirped grating and the local fringe slope ŽEq. Ž2.. used to determine the period differ-
F. Barnier et al.r Optics Communications 170 (1999) 175–179
ence between the master and the chirped grating. A value of a s 4.7 mrad was used as determined from the Moire´ period in the central region of the gratings
177
where f s 0. Fig. 1 shows sections of the parabolic fringe system at several locations along the mask. The variation of d d s d y dX with x is shown in
Fig. 1. Moire´ fringe geometry for chirped phase mask, G1 , overlaying linear grating, G2. The groove directions, designated by g 1 and g 2 , make an angle a to one another, y is the bisector of a and the fringe orientation f is measured with respect to the x-axis. Fringes recorded at the centre and at the ends of the 30 mm long, 1 mm wide chirped grating using optical microscopy Ž=12.5 magnification. are shown for a s 4.7 mrad.
178
F. Barnier et al.r Optics Communications 170 (1999) 175–179
Fig. 2, a linear fit to the data giving a chirp rate of r s 0.95 " 0.1 nmrmm. From the fringes in the central region of Fig. 1 it can be established that fringe curvature can be detected and quantified beyond a distance of about 400 mm from the minima of the fringe system. With r s 0.95 nmrmm this indicates a capability for resolving differences in grating period down to ; 0.4 nm. An independent assessment of the chirp was made using optical diffraction with a HeNe laser beam Ž l s 632.8 nm.. The chirped grating was illuminated at an angle of incidence i s 63.38 and the change of the m s 2 order diffracted beam angle, d r, recorded as the grating was translated across the beam ŽFig. 3.. The average period of the grating over the probed region is given by d s m lrŽsin i y sin r . where r is the angle of diffraction and for small d r the period change d d is:
d d s d 2 cos rd rrm l where m is the order. To eliminate spurious angular deflections arising from lack of flatness in the substrate or tilt in the translation stage the zero-order beam was simultaneously monitored and adjustments made as necessary to keep this beam centralised on the detector. The limiting resolution, d d o , is defined by a combination of the beam divergence set by diffrac-
Fig. 2. Variation of period difference between chirped and linear gratings as a function of position on the chirped mask as derived from Moire´ fringe angle. The linear fit to the data yields a chirp rate of 0.95"0.1 nmrmm.
Fig. 3. Angle of second-order diffracted 632.8 nm laser beam as a function of position on chirped mask Žangle of incidence is63.38.. A linear fit to the data gives a chirp rate of 0.98"0.05 nmrmm.
tion and that produced by the chirp across the probe beam with: 2
d d o s 0.707 d 2 cos irmp v o 4 q r v o 4
ž
2
0.5
/
Here vo is the Gaussian beam waist Žfield. radius at the grating and the minimum resolvable angle of the diffracted beam is taken at the ey1 irradiance. With vo s 0.4 mm and m s 2, a theoretical resolution of d d o s 0.32 nm is realised. In the experiments an angular resolution of d r ( 1 min gave d d o G 0.26 nm which is consistent with this value. Fig. 3 shows the variation of d r with position on the chirped grating, the data yielding a chirp rate of r s 0.98 " 0.05 nmrmm in close agreement with the Moire´ measurement. In conclusion, it has been demonstrated that Moire´ mapping of a chirped phase mask provides a useful method for evaluating the grating chirp. It is remarkable that a resolution of period differences down to ; 0.4 nm can be accomplished in this way using only low resolution optical microscopy. This can be attributed to the high magnification provided by the Moire´ technique. A potential problem of the method with incoherent illumination is the need for near-contact between the masks for effective Moire fringe formation w6x with the possible risk of damage. The use of coherent illumination could overcome this by allowing use of a finite mask spacing albeit at some
F. Barnier et al.r Optics Communications 170 (1999) 175–179
increase in experimental complexity. Direct probing of the grating by optical diffraction provides an alternative non-contact technique, with a theoretical resolution of period difference at the subnanometer level. Acknowledgements P.E.D. and F.B. gratefully acknowledge the continued support of Nortel and thank Mr. H. Rourke of Nortel, Harlow, for helpful discussions. We are also grateful to Mr. G. Robinson in Engineering for use of the microscopy facilities. R.M.D. acknowledges the support of the Engineering and Physical Sciences Research Council and the contributions of the groups at Glasgow and Aston Universities which led to the production of the chirped phase masks.
179
References w1x G. Meltz, W.W. Morey, W.H. Glenn, Opt. Lett. 14 Ž1989. 823. w2x K.O. Hill, B. Malo, F. Bilodeau, D.C. Johnson, J. Albert, Appl. Phys. Lett. 62 Ž1993. 1035. w3x P.E. Dyer, R.J. Farley, R. Giedl, Opt. Commun. 115 Ž1995. 327. w4x J.S. Aichison, R.M. De La Rue, Opt. Lett. 22 Ž1997. 1473. w5x X. Liu, J.S. Aitchison, R.M. De La Rue, S. Thoms, L. Zhang, J.A.R. Williams, I. Bennion, Micro. Eng. 35 Ž1997. 345. w6x F. Barnier, P.E. Dyer, G.A. Steigmann, Opt. Commun. 162 Ž1999. 299. w7x S. Barcelos, M.N. Zervas, R.I. Laming, D.N. Payne, L. Reekie, J.A. Tucknott, R. Kashyap, P.F. McKee, F. Sladen, B. Wojciechowicz, Electron. Lett. 31 Ž1995. 1280. w8x J. Guild, The Interference Systems of Crossed Diffraction Gratings: Theory of Moire´ Fringes, Clarendon Press, Oxford, 1956. w9x B. Hubner, H.W.P. Koops, J. Vac. Sci. Technol. B 10 Ž1992. ¨ 2648.