Abstract

An optical monitoring method is described to compensate for the thickness error of nonquarterwave layers of dielectric multilayer filters, using optical admittance during deposition. Stability is confirmed by computer simulation of random thickness error generation in layers. In addition, a band split filter consisting of 61 nonquarterwave and nonperiodic layers is deposited using the proposed method, resulting in high spectral performance, as the application requires.

© 2006 Optical Society of America

1. Introduction

In optical telecommunication systems, optical thin film band split filters (BSFs) have been used for separating one band from other bands, such as the 1310 nm, 1490 nm, and 1550 nm bands. To accommodate many channels, a narrower splitting region between passband and stopband, in addition to higher transmittance in the passband, is required and, therefore, some complicated designs consist of nonquarterwave and nonperiodic layers. This design approach is straightforward and provides the advantage of decreasing the number of layers in the design.However, a sophisticated monitoring method is required to implement this approach.

Optical monitoring is used in multilayer deposition, in order to improve optical thickness accuracy [17–5]. In principle, the propagation of thickness error during deposition can be stopped by properly terminating the current layer deposition. Various optical monitoring methods at a single wavelength are used, depending on the structure of the layers. The turning point method is commonly used to control the optical thickness of periodic quarterwave layers accurately, and results in a strong error compensation effect in the region of monitoring wavelength [6]. The level monitoring method can be applied to control the optical thickness of periodic nonquarterwave thin film structures [7, 8]. The error compensation effect is also shown in the region of monitoring wavelength. However, precoating is required to generate the specific level of reflectance or transmittance for layer deposition termination. For periodic nonquarterwave layers an optical monitoring method is reported recently, such that a layer is divided into two sublayers, and the thickness of the second sublayer after the turning point, is kept to compensate for the thickness error of the previous layer [9].

In this study a band split filter consisting of 61 nonquarterwave and nonperiodic layers is designed. Therefore, a new optical monitoring method with an error compensation effect is required, in order to deposit such a complicated multilayer design. In this paper, an optical monitoring method is proposed, in order to control the optical thickness of nonquarterwave and nonperiodic layers at a single wavelength. The basic theory on the error compensation effect is derived using the optical admittance diagram. The stability of the proposed method is verified using computer simulation, and a band split filter consisting of nonquarterwave and nonperiodic layers is deposited using the proposed method.

2. Theory

Assuming that dielectric layers in an optical thin-film multilayer structure are isotropic and nonabsorbing, the optical thin-film growth process can be modeled using an admittance diagram, as presented in Fig. 1. Since admittance circles of layers and isoreflectance contours of the dielectric layers are centered on the real axis, the admittance of points at which the admittance circles intersect the real axis represents the optical monitoring signal at the turning points [10].

A compensation effect on thickness errors in multilayer thin-film deposition can also be analyzed in the admittance diagram. If the admittance locus of the first nH layer starting from nsub in Fig. 1 is altered by a thickness error, it may move along the path instead of representing the multilayer system without thickness error. In this case, the admittance locus of the first layer arrives at A2, rather than A1 due to overshoot thickness error. This affects the remainder admittance locus of the system and leads the second layer nL to start from A2 and pass through the turning point B2. At B2 the thickness error of the previous layer can be detected from the difference in the optical monitoring signal between turning points B1 and B2. Then the compensation of the error can be achieved by terminating the nL layer deposition at C2, located on the admittance locus of the third layer of nH , because this enables the admittance locus of the third layer (nH) to pass through the turning point D2 as the design predicts.

In Fig. 1, an admittance circle (x, y) for a dielectric layer of index n on a substrate or starting admittance nsub can be expressed as [10]

(xn2+nsub22nsub)2+y2=(n2nsub22nsub)2.

Then the admittance circle of ③ for nL layer is given by

(xnL2+nLsub22nLsub)2+y2=(nL2nLsub22nLsub)2.

where nLsub is the admittance at B2 in the circle ③, i.e., nLsub = Y B2. Similarly, the admittance circle of ⑤ for nH layer is

(xnH2+nHsub22nHsub)2+y2=(nH2nHsub22nHsub)2.

where nHsub is the admittance at D1 in the circle ⑤, i.e., nHsub = Y D1.

 

Fig. 1. Admittance diagram: Dotted line refers to the admittance loci of design and solid line to the deviated admittance loci with thickness error on nH layer, where ①,②,⑤, and ⑥ are the loci of nH layer, and ③ and ④ the loci of nL layer.

Download Full Size | PPT Slide | PDF

Then an intersection of two admittance circles for ③ and ⑤ at C2 is the admittance Y C2 = x C2 + iy C2. From Eqs (2) and (3), Y C2 = x C2 + iy C2 can be derived as

xC2=12(α2β2εγ+γ+ε)
yC2=±α2(xC2γ)2oryC2=±β2(xC2ε)2

where

α=nL2nLsub22nLsub,β=nH2nHsub22nHsub,γ=nL2+nLsub22nLsub,andε=nH2+nHsub22nHsub.

The positive value of y C2 is selected when two admittance circles intersect in the 1st quadrant and the negative value in the 4th quadrant. Since the admittance Y C2 is given by Eqs (4)–(6), the reflectance R C2 at C2 can be written as

RC2=1YC21+YC22=(1xC2)2+yC22(1+xC2)2+yC22.

The admittance Y B2, at turning point B2, can be obtained from the measured reflectance using

YB2=[1R1+RforY<11+R1RforY>1

where R is the measured reflectance at turning point B2. The admittance Y D1, at D1, can be obtained using

YD1=YD22nH

where YD2 is the admittance at D2 and nH is the refractive index of the third layer in Fig. 1.

3. Simulation of a band split filter

Figure 2 presents a simulated optical monitoring curve consisting of three layers, when the thickness error is introduced in the first layer, deposited on a glass substrate. It is assumed that the thickness in the first high-index layer increases from 1.367H at A1 to 1.49H at A2 due to an error. The small transmittance difference in the second layer at the turning points B1 and B2 indicates a thickness error in the previous layer. Then, the admittance at C2 and the termination transmittance of the second layer can be calculated using the proposed method. This demonstrates that the third layer passes the same transmittance as the turning point D2 predicts, and terminates at the target transmittance, which is also predicted by the design. This indicates that the proposed method compensates for thickness error originating from the first layer.

The error compensation effect is also simulated for a band split filter (BSF) near 1500 nm. The refractive index profile of the BSF consisting of 61 nonquarterwave and nonperiodic layers is presented in Fig. 3. The edge wavelength at 3 dB loss is 1522.1 nm at normal incident light. The monitoring wavelength is set at 1510 nm in the passband. The high-index layer of BSF is Ta2O5, low-index layer SiO2, and substrate BK7.

The random error of thickness distributed uniformly in the range of 5% is added to each layer. With this 5% random error, the edge position and steepness varies considerably and the ripple appears near the edge, as presented in Fig. 4(a), i.e., the edge wavelength at 3 dB in transmittance is varied by 19 nm and the insertion loss in 1290~1508 nm increases from 0.19 dB of the design to 1 dB. Conversely, in the presence of thickness errors at each layer, the admittance and reflectance (or transmittance) of the termination point for each layer are calculated, in order to compensate for the error propagated from the previous layer. Finally, stable performance is achieved as presented in Fig. 4(b): the edge shift is 0.4 nm and the insertion loss is 0.38 dB.

 

Fig. 2. Simulated optical monitoring signal for thickness error correction: (dashed line) monitoring signal for a design of [air| 1.054H 1.041L 1.367H |sub], and (solid line) modified monitoring signal for compensation of thickness error for [air| 1.159H 0.8331L 1.49H |sub], where the first layer deposited on the substrate has thickness error from 1.367H to 1.49H.

Download Full Size | PPT Slide | PDF

 

Fig. 3. Refractive index distribution of a band split filter, consisting of 61 layers: [Air| 1.558H 0.765L 0.837H 0.983L 1.230H 0.991L 0.883H 0.920L 1.039H 1.059L 0.967H 0.947L 0.961H 1.009L 0.980H 0.989L 0.952H 0.992L 0.989H 0.994L 0.926H 0.979L 0.995H 1.018L 0.942H 0.973L 0.943H 1.009L 0.999H 0.977L 0.933H 0.995L 0.985H 0.986L 0.936H 1.031L 0.948H 0.991L 0.931H 1.057L 0.904H 1.037L 0.930H 1.015L 0.942H 1.058L 0.905H 0.961L 1.086H 0.959L 0.873H 1.134L 0.864H 1.109L 0.971H 0.921L 1.104H 1.037L 1.054H 1.041L 1.369H | BK7] (nL = 1.457, nH = 2.065, λ0 = 1730 nm).

Download Full Size | PPT Slide | PDF

 

Fig. 4. Simulation of thickness error compensation for BSF. (a) 5 % random thickness error (b) 5 % random thickness error is compensated using admittance. The theoretical transmittance curve for the multilayer design (black dotted line) is shown along with the transmittance curves of the simulations (red solid line).

Download Full Size | PPT Slide | PDF

4. Experimental results and discussion

The band split filter (BSF) of 61 nonquarterwave and nonperiodic layers in Fig. 3 was deposited using the proposed method in a plasma-assisted deposition system (APS1104). An optical monitor system was employed in order to measure the transmittance through the multilayer at normal incidence. Four transmittance references of 93.3, 84.7, 10.6, and 33.0 % were used to calibrate the transmitted signal before deposition. The last layer was terminated at the highest transmittance, since the monitoring wavelength exists in the passband.

Figure 5(a) presents the simulated monitoring signal of the design and Fig. 5(b) presents the transmitted monitoring signal recorded during deposition. In Fig. 5(b) the slight difference between the design and the actual coating at turning points is compensated by terminating the deposition of each layer at a new termination transmittance calculated by Eq. (5) during deposition of the multilayer.

In Fig. 6 the transmittance of design and actual coating is compared. The edge wavelength of the coated filter at 3 dB shifts from 1522.1 nm of the design to 1521.8 nm by -0.3 nm, and the insertion loss in 1290~1508 nm increases from 0.19 dB of the design to 0.3 dB. The result demonstrates that the edge wavelength and the transmittance of the actual coating are close to those of the design, as well as of the simulation. This implies that the proposed optical monitoring method is an accurate process when compensating for the optical thickness errors of BSF, consisting of nonquarterwave and nonperiodic layers.

It is important to note from the theoretical and experimental analyses, that when the proposed method is applied, (1) absolute reflectance or transmittance should be measured to retrieve a thickness error at the turning point, and calculate the admittance, and (2) it is required for the thickness of each layer to have at least one turning point in the monitoring wavelength.

 

Fig. 5. Runsheet of (a) design and (b) actual coating. Monitoring wavelength is 1510 nm. Black dot in (a) indicates termination point of each layer.

Download Full Size | PPT Slide | PDF

 

Fig. 6. Transmittance of design and actual coating of BSF.

Download Full Size | PPT Slide | PDF

5. Conclusion

In order to compensate for the optical thickness error of nonquarterwave layers during optical monitoring of multilayer deposition at a single wavelength, optical admittance is employed. The basic theory of the proposed optical monitoring method is described. The simulation and the actual deposition of a band split filter consisting of 61 nonquarterwave and nonperiodic layers, both demonstrate that the optical thickness errors can be compensated effectively. This suggests that the proposed optical monitoring method, using optical admittance, can be used to accurately deposit nonquarterwave layers of multilayer filters.

Acknowledgments

This work was supported by the Korea Science and Engineering Foundation through the Quantum Photonic Science Research Center at Hanyang University.

References and links

1. H. A. Macleod, “Monitoring of optical coatings,” Appl. Opt. 20, 82–88 (1981). [CrossRef]   [PubMed]  

2. B. T. Sullivan and J. A. Dobrowolski, “Deposition error compensation for optical multilayer coatings. I. Theoretical description,” Appl. Opt. 31, 3821–3835 (1992). [CrossRef]   [PubMed]  

3. B. T. Sullivan and J. A. Dobrowolski, “Deposition error compensation for optical multilayer coatings. II. Experimental results-Sputtering system,” Appl. Opt. 32, 2351–2360 (1993). [CrossRef]   [PubMed]  

4. H. A. Macleod and E. Pelletier, “Error compensation mechanisms in some thin film monitoring systems,” Opt. Acta 24, 907–930 (1977). [CrossRef]  

5. B. Vidal and E. Pelletier, “Nonquarterwave multilayer filters: optical monitoring with a minicomputer allowing correction of thickness errors,” Appl. Opt. 18, 3857–3862 (1979). [PubMed]  

6. H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin-film optical filters,” Opt. Acta 19, 1–28 (1972). [CrossRef]  

7. F. Zhao, “Monitoring of periodic multilayer by the level method,” Appl. Opt. 24, 3339–3343 (1985). [CrossRef]   [PubMed]  

8. R. R. Willey, “Improved repeatability in the production of periodic thin film structures by the use of “Steering” with optical monitoring,” Proc. Soc. Vac. Coaters 36, 156–159 (1993).

9. C. Zhang, Y. Wang, and W. Lu, “Single-wavelength monitoring method for optical thin-film coating,” Opt. Eng. 43, 1439–1444 (2004). [CrossRef]  

10. H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (IoP, Bristol, UK, 2001). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. H. A. Macleod, "Monitoring of optical coatings," Appl. Opt. 20, 82-88 (1981).
    [CrossRef] [PubMed]
  2. B. T. Sullivan and J. A. Dobrowolski, "Deposition error compensation for optical multilayer coatings. I. Theoretical description," Appl. Opt. 31, 3821-3835 (1992).
    [CrossRef] [PubMed]
  3. B. T. Sullivan and J. A. Dobrowolski, "Deposition error compensation for optical multilayer coatings. II. Experimental results-Sputtering system," Appl. Opt. 32, 2351-2360 (1993).
    [CrossRef] [PubMed]
  4. H. A. Macleod and E. Pelletier, "Error compensation mechanisms in some thin film monitoring systems," Opt. Acta 24, 907-930 (1977).
    [CrossRef]
  5. B. Vidal and E. Pelletier, "Nonquarterwave multilayer filters: optical monitoring with a minicomputer allowing correction of thickness errors," Appl. Opt. 18, 3857-3862 (1979).
    [PubMed]
  6. H. A. Macleod, "Turning value monitoring of narrow-band all-dielectric thin-film optical filters," Opt. Acta 19, 1-28 (1972).
    [CrossRef]
  7. F. Zhao, "Monitoring of periodic multilayer by the level method," Appl. Opt. 24, 3339-3343 (1985).
    [CrossRef] [PubMed]
  8. R. R. Willey, "Improved repeatability in the production of periodic thin film structures by the use of "Steering" with optical monitoring," Proc. Soc. Vac. Coaters 36, 156-159 (1993).
  9. C. Zhang, Y. Wang, and W. Lu, "Single-wavelength monitoring method for optical thin-film coating," Opt. Eng. 43, 1439-1444 (2004).
    [CrossRef]
  10. H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (IoP, Bristol, UK, 2001).
    [CrossRef]

2004

C. Zhang, Y. Wang, and W. Lu, "Single-wavelength monitoring method for optical thin-film coating," Opt. Eng. 43, 1439-1444 (2004).
[CrossRef]

1993

B. T. Sullivan and J. A. Dobrowolski, "Deposition error compensation for optical multilayer coatings. II. Experimental results-Sputtering system," Appl. Opt. 32, 2351-2360 (1993).
[CrossRef] [PubMed]

R. R. Willey, "Improved repeatability in the production of periodic thin film structures by the use of "Steering" with optical monitoring," Proc. Soc. Vac. Coaters 36, 156-159 (1993).

1992

1985

1981

1979

1977

H. A. Macleod and E. Pelletier, "Error compensation mechanisms in some thin film monitoring systems," Opt. Acta 24, 907-930 (1977).
[CrossRef]

1972

H. A. Macleod, "Turning value monitoring of narrow-band all-dielectric thin-film optical filters," Opt. Acta 19, 1-28 (1972).
[CrossRef]

Dobrowolski, J. A.

Lu, W.

C. Zhang, Y. Wang, and W. Lu, "Single-wavelength monitoring method for optical thin-film coating," Opt. Eng. 43, 1439-1444 (2004).
[CrossRef]

Macleod, H. A.

H. A. Macleod, "Monitoring of optical coatings," Appl. Opt. 20, 82-88 (1981).
[CrossRef] [PubMed]

H. A. Macleod and E. Pelletier, "Error compensation mechanisms in some thin film monitoring systems," Opt. Acta 24, 907-930 (1977).
[CrossRef]

H. A. Macleod, "Turning value monitoring of narrow-band all-dielectric thin-film optical filters," Opt. Acta 19, 1-28 (1972).
[CrossRef]

Pelletier, E.

B. Vidal and E. Pelletier, "Nonquarterwave multilayer filters: optical monitoring with a minicomputer allowing correction of thickness errors," Appl. Opt. 18, 3857-3862 (1979).
[PubMed]

H. A. Macleod and E. Pelletier, "Error compensation mechanisms in some thin film monitoring systems," Opt. Acta 24, 907-930 (1977).
[CrossRef]

Sullivan, B. T.

Vidal, B.

Wang, Y.

C. Zhang, Y. Wang, and W. Lu, "Single-wavelength monitoring method for optical thin-film coating," Opt. Eng. 43, 1439-1444 (2004).
[CrossRef]

Willey, R. R.

R. R. Willey, "Improved repeatability in the production of periodic thin film structures by the use of "Steering" with optical monitoring," Proc. Soc. Vac. Coaters 36, 156-159 (1993).

Zhang, C.

C. Zhang, Y. Wang, and W. Lu, "Single-wavelength monitoring method for optical thin-film coating," Opt. Eng. 43, 1439-1444 (2004).
[CrossRef]

Zhao, F.

Appl. Opt.

Opt. Acta

H. A. Macleod, "Turning value monitoring of narrow-band all-dielectric thin-film optical filters," Opt. Acta 19, 1-28 (1972).
[CrossRef]

H. A. Macleod and E. Pelletier, "Error compensation mechanisms in some thin film monitoring systems," Opt. Acta 24, 907-930 (1977).
[CrossRef]

Opt. Eng.

C. Zhang, Y. Wang, and W. Lu, "Single-wavelength monitoring method for optical thin-film coating," Opt. Eng. 43, 1439-1444 (2004).
[CrossRef]

Proc. Soc. Vac. Coaters

R. R. Willey, "Improved repeatability in the production of periodic thin film structures by the use of "Steering" with optical monitoring," Proc. Soc. Vac. Coaters 36, 156-159 (1993).

Other

H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (IoP, Bristol, UK, 2001).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Admittance diagram: Dotted line refers to the admittance loci of design and solid line to the deviated admittance loci with thickness error on nH layer, where ①,②,⑤, and ⑥ are the loci of nH layer, and ③ and ④ the loci of nL layer.

Fig. 2.
Fig. 2.

Simulated optical monitoring signal for thickness error correction: (dashed line) monitoring signal for a design of [air| 1.054H 1.041L 1.367H |sub], and (solid line) modified monitoring signal for compensation of thickness error for [air| 1.159H 0.8331L 1.49H |sub], where the first layer deposited on the substrate has thickness error from 1.367H to 1.49H.

Fig. 3.
Fig. 3.

Refractive index distribution of a band split filter, consisting of 61 layers: [Air| 1.558H 0.765L 0.837H 0.983L 1.230H 0.991L 0.883H 0.920L 1.039H 1.059L 0.967H 0.947L 0.961H 1.009L 0.980H 0.989L 0.952H 0.992L 0.989H 0.994L 0.926H 0.979L 0.995H 1.018L 0.942H 0.973L 0.943H 1.009L 0.999H 0.977L 0.933H 0.995L 0.985H 0.986L 0.936H 1.031L 0.948H 0.991L 0.931H 1.057L 0.904H 1.037L 0.930H 1.015L 0.942H 1.058L 0.905H 0.961L 1.086H 0.959L 0.873H 1.134L 0.864H 1.109L 0.971H 0.921L 1.104H 1.037L 1.054H 1.041L 1.369H | BK7] (nL = 1.457, nH = 2.065, λ0 = 1730 nm).

Fig. 4.
Fig. 4.

Simulation of thickness error compensation for BSF. (a) 5 % random thickness error (b) 5 % random thickness error is compensated using admittance. The theoretical transmittance curve for the multilayer design (black dotted line) is shown along with the transmittance curves of the simulations (red solid line).

Fig. 5.
Fig. 5.

Runsheet of (a) design and (b) actual coating. Monitoring wavelength is 1510 nm. Black dot in (a) indicates termination point of each layer.

Fig. 6.
Fig. 6.

Transmittance of design and actual coating of BSF.

Equations (9)

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

( x n 2 + n sub 2 2 n sub ) 2 + y 2 = ( n 2 n sub 2 2 n sub ) 2 .
( x n L 2 + n Lsub 2 2 n Lsub ) 2 + y 2 = ( n L 2 n Lsub 2 2 n Lsub ) 2 .
( x n H 2 + n Hsub 2 2 n Hsub ) 2 + y 2 = ( n H 2 n Hsub 2 2 n Hsub ) 2 .
x C 2 = 1 2 ( α 2 β 2 ε γ + γ + ε )
y C 2 = ± α 2 ( x C 2 γ ) 2 or y C 2 = ± β 2 ( x C 2 ε ) 2
α = n L 2 n Lsub 2 2 n Lsub , β = n H 2 n Hsub 2 2 n Hsub , γ = n L 2 + n Lsub 2 2 n Lsub , and ε = n H 2 + n Hsub 2 2 n Hsub .
R C 2 = 1 Y C 2 1 + Y C 2 2 = ( 1 x C 2 ) 2 + y C 2 2 ( 1 + x C 2 ) 2 + y C 2 2 .
Y B 2 = [ 1 R 1 + R for Y < 1 1 + R 1 R for Y > 1
Y D 1 = Y D 2 2 n H

Metrics