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 n_H layer starting from n_sub 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 n_L 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 n_L layer deposition at C₂, located on the admittance locus of the third layer of n_H , because this enables the admittance locus of the third layer (n_H) 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 n_sub can be expressed as [10]

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

where n_Lsub is the admittance at B₂ in the circle ③, i.e., n_Lsub = Y _B2. Similarly, the admittance circle of ⑤ for n_H layer is

where n_Hsub is the admittance at D₁ in the circle ⑤, i.e., n_Hsub = 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 n_H layer, where ①,②,⑤, and ⑥ are the loci of n_H layer, and ③ and ④ the loci of n_L layer.

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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

where

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

The admittance Y _B2, at turning point B₂, can be obtained from the measured reflectance using

where R is the measured reflectance at turning point B₂. The admittance Y _D1, at D₁, can be obtained using

where Y_D2 is the admittance at D₂ and n_H 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.

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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] (n_L = 1.457, n_H = 2.065, λ₀ = 1730 nm).

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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).

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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.

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

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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.