## Abstract

We present a simple and efficient technique for evaluating the optical losses of a planar film by use of a quasi-waveguide configuration and a prism film coupler configuration. The technique can separate two contributions to optical loss: that from the surface scattering caused by the roughness of surface and that from volume losses including volume scattering and volume absorption.

© 2002 Optical Society of America

Studies of various dielectric films are always attractive because of their important applications in fields such as integrated optics and optoelectronics. Films with very high optical quality and low loss are required, because the performance of the film device is critically affected by optical loss. The optical loss of a planar film arises from three kinds of loss: (i) surface scattering (S-Sc) due to the surface roughness of the film; (ii) volume scattering (V-Sc) due to problems such as defects, inhomogeneity, and doped clusters; and (iii) volume absorption (V-Ab) due to impurities or/and intrinsic absorption. The method for measuring and evaluating the optical loss of the film is important for practical applications. Up to now, three methods have been developed. The first is a system consisting of lenses, filter, slit, and detector, which collects the light scattered into a synchronously movable detector with an adjustable slit [1]. The second is the technique of transmission measurement [2], in which two coupling prisms are used, one to excite a light streak in the film and the other to couple out the light wave of the film; the loss could thus be evaluated through measuring the output at different points along the light streak by movement of the output prism and with the input prism kept simultaneously intact. The third approach is a slightly crude method based on the sensitivity of the human eye [2]. The probable loss in the film should be 27/*x* dB/cm if the length of the light streak as observed by the naked eye is *x* cm, because the sensitivity of the eye covers a range of ~27 dB. In addition to these methods, total-internal-reflection microscopy was used to inspect the surface of transparent films or bulk materials [3,4], and the size and position of scattering sites at or near the surface of the sample could be determined by examining the evanescent waves.

In the present paper, we suggest a technique for measuring the optical loss of a planar film. Two configurations are considered here: one involves a dielectric film spin-coated/deposited directly on a high-refraction-index prism, forming a planar quasi-waveguide (QWG) [5–7]; in the other, we first have a dielectric film spin-coated/deposited on a substrate constructing a planar film waveguide, then a high-refraction-index prism is placed above the thin-film guide, and finally a prism film coupler (PFC) is formed [8,9]. Since the laser light spot that we use in the following experiment is quite large (approximately 1–2 mm in diameter) compared with the imperfections on the interfaces, the volume scattering and absorption centers in the film, and the thickness of the film, we can take into account macroscopic effects in dealing with the problem and also use the multiple-wave interference. The technique is not only simple and efficient but also can separate the contribution of S-Sc and volume attenuation (V-At) including V-Sc and V-Ab from the entire optical attenuation.

First, we consider a planar QWG structure formed by the prism (a right-angled and isosceles prism), the film (with a thickness *W*), and air. They are successively defined as layers 2, 1, and 0; the refractive indices are *n*
_{2}, *n*
_{1}, and *n*
_{0}; and it is required that *n*
_{2} > *n*
_{1} > *n*
_{0} [see Fig. 1(a)]. A linearly polarized wave (we use the TE-polarized light beam in our following simulation) at wavelength *λ*. enters the prism through its input face at an angle *α* to become the wave *A*
_{2}. At interface 2–1, *A*
_{2} is divided into the reflected wave *B*
^{20} (=*r*
_{21}
*A*
_{2}) and the transmitted wave. In the film, the transmitted wave propagates along the zigzag path; and within a zigzag path the wave will experience these five processes: S-Sc at two interfaces, V-At (including V-Sc and V-Ab), pure propagation, total internal reflection (TIR) at interface 1–0, and partial internal reflection (PIR) at interface 1–2. Finally, all the waves in the film will return to the prism and then produce a series of reflected waves (*B*
_{21}, *B*
_{22},…, *B*
_{2v},…) because the wave is leaky at interface 2–1 only. We introduce *C*_{V}
and *C*_{S}
to describe the properties of optical losses of the film. The former represents the ratio between the energy attenuated by V-At (V-Sc and V-Ab) and the incident energy per unit propagation distance. The latter one, *C*_{S}
, is a nominal parameter representing the whole S-Sc effect in one zigzag path. Since the presence of S-Sc gives rise to the loss of incident energy, according to the Rayleigh criterion [2], the ratio of the residual energy to the incident energy after one zigzag path should be exp(-${{C}_{S}}^{2}$ cos^{2}
*θ*
_{1}); here *C*_{S}
and *θ*
_{1} correspond to *K* and *θ* in Eqs. (16) and (18) of Ref. 2. *C*_{S}
is dimensionless, and *C*_{V}
has the dimension of *m*
^{-1}. If all the reflected waves *B*
_{2v} (including *B*
_{20}) are superimposed, the theoretical complex reflectivity *r*
_{QWG} can be easily obtained as

where *r*_{ij}
and *t*_{ij}
are the Fresnel reflection and transmittance coefficients at interface *i*-*j*, *ϕ*_{W}
is the phase shift within one zigzag path due to the pure propagation in the film, *h*_{S}
= exp(-${{C}_{S}}^{2}$ cos ${\theta}_{1}^{2}$/2) and *h*_{V}
= exp(-*C*_{V}*W* sec *θ*
_{1}), where *θ*
_{1} is the angle formed by the wave vector and the normal of the film in the film. The mode equation of the QWG is given by

where *ϕ*
_{10} is the phase shift due to TIR at interface 1–0 and *ϕ*
_{12} = - *π* is the phase shift due to PIR at interface 1–2 from the optical loose film to optical dense prism.

Next, a very practical case is that a planar film has already been spin-coated or deposited on the substrate of low refractive index. How to measure the optical loss of the planar film is an interesting problem. If a PFC configuration is used, the aim can be achieved, in which a prism of high refractive index is placed above the planar film and is separated from it by a small air gap with thickness of *D*, forming a four-layer structure composed of the prism, the air gap, the film, and the substrate. Their refractive indices are *n*
_{3}, *n*
_{2}, *n*
_{1}, and *n*
_{0}, and the structure requires *n*
_{3} > *n*
_{1} > *n*
_{0} > *n*
_{2} [see Fig. 1(b)]. We treat this problem similarly as in the above QWG; however, both the prism and the air gap must be dealt with as an equivalent “monolayer.” The coefficients *r*
_{12}, *r*
_{21}, *t*
_{12}, and *t*
_{21} in Eq. (1) must be replaced with *r*
_{123}, *r*
_{321}, *t*
_{123}, and *t*
_{321} of the equivalent “monolayer,” respectively. The complex reflectivity of PFC is thus

Here *r*
_{123} = (*r*
_{12}+*q*
^{2}
*r*
_{23})/(1+*q*
^{2}
*r*
_{32}
*r*
_{21}), *r*
_{321} = (*r*
_{32}+*q*
^{2}
*r*
_{21})/(1+*q*
^{2}
*r*
_{32}
*r*
_{21}), *t*
_{123} = *q*
^{2}
*t*
_{12}
*t*
_{23}/(1+*q*
^{2}
*r*
_{32}
*r*
_{21}), and *r*
_{321} = *q*
^{2}
*t*
_{21}
*t*
_{32}/(1+*q*
^{2}
*t*
_{32}
*t*
_{21}), where *q* = exp[*i*2*π*(${{n}_{2}}^{2}$ - ${{n}_{1}}^{2}$ sin *θ*
_{1})^{1/2}
*D*/*λ*] is a dimensionless coupling strength, where *θ*
_{1} is still the angle between the wave vector and the normal of the film in the film and *α* is still the incident angle at the input face of the prism. Since the light cannot be leaky at boundary 1–0 for the PFC, in the PFC case the mode equation is given by

The unique difference between Eqs. (2) and (4) is that *ϕ*
_{12} in Eq. (2) is replaced with *ϕ*
_{123} in Eq. (4).

Note that in the case of no absorbent and ideal optical film, the reflectivity in both QWG and PFC is identically equal to unity for any incident angle, i.e., *R*
_{QWG} = ∣*r*
_{QWG}∣^{2} = 1 and *R*
_{PFC}=∣*r*
_{PFC}∣^{2} = 1 for *C*_{V}
= *C*_{S}
= 0; shown as the four thick solid lines in Figs. 2 and 3. If not, both *R*
_{QWG} and *R*
_{PFC} will be oscillating functions of the incident angle *α* or *θ*
_{1}, as depicted with the green, blue and red lines in Figs. 2 and 3; there exist some resonant valleys (dips) representing the modes of the QWG and the PFC, and the positions of the modes are determined by the solutions of the mode equations of Eq. (2) for the QWG configuration and Eq. (4) for the PFC configuration, respectively.

It is obvious from Figs. 2 and 3 that the V-At (*C*_{V}
) and S-Sc (*C*_{S}
) have different effects on the reflectivity spectra *R*
_{QWG} (*θ*
_{1} or *α*) and RPFC (*θ*
_{1} or *α*). Only in the presence of S-Sc is the intensity of the higher order modes obviously stronger than that in the presence of V-At only. Therefore, from the reflectivity spectrum measured experimentally, the values of *C*_{S}
and *C*_{V}
can be estimated. For a QWG configuration, first the refractive index *n*
_{1} and thickness *W* of the film can be determined through measuring the positions of the modes by using the method of *m*-lines [6] and then *C*_{S}
and *C*_{V}
can be obtained by measuring the reflectivity spectrum *R*
_{QWG} (*θ*
_{1} or *α*) to fit Eq. (1). For a PFC configuration, first, we have to measure the positions of the modes (see the perpendicular dash-dot lines in Fig. 3) under the condition of extremely weak coupling (i.e., the thickness *D* of the air gap is considered as infinity) by using the method of *m*-lines [9], thus the refractive index *n*
_{1} and the thickness *W* of the film can be obtained; second, under the strong coupling situation (i.e., *D* is small) we measure again the positions of the modes (which have the shifts due to the extremely weak coupling case shown in Fig. 3, because the positions of the modes in PFC are altered by the difference of *D*, see the mode equation Eq. (4)), then the value of *D* can be estimated through the shifts; third, we retain the coupling situation and measure the reflectivity spectrum *R*
_{PFC} (*θ*
_{1} or *α*) simultaneously: finally, *C*_{S}
and *C*_{V}
can be figured by fitting *R*
_{PFC} (*θ*
_{1} or *α*) with Eq. (3).

In order to confirm our technique, as an example, we prepared a QWG sample that a HEACNA-doped PMMA [7] polymer film is spin-coated on a prism of high refractive index (*n*
_{2} = 1.64564 at *λ* = 610nm). The refractive index and thickness of the film are measured to be *n*
_{1} = 1.50384 ± 0.00002 at *λ* = 610nm and *W* = 1.5368 ± 0.0004 μm by use of the method of the *m*-lines [6]. The measured reflectivity spectrum (as circles in Fig. 4) was not understood until we suggested the current technique. When we use the previous theory (V-At due to V-Sc only was considered) developed by us [7] to fit the experiment and obtain *C*_{V}
= 0.0122 μm^{-1} (when *C*_{S}
= 0), we found that the fitted curve as shown with the red line in Fig. 4 has a large deviation from the experiment. When we employ the present theory that considers simultaneously both V-At and S-Sc to fit the experiment, it is obvious that the fitted curve (blue line in Fig. 4) is in good agreement with the experiment, giving that *C*_{V}
= 0.0095 μm^{-1} and *C*_{S}
= 1.07. At the same time, considering only S-Sc, as shown with green line in Fig. 4, we obtain *C*_{S}
= 1.94 (*C*_{V}
= 0). It can be seen that there is also large deviation between that fitted curve and the experiment.

Now, if the same film as the QWG used above is spin-coated on a fused quartz substrate, a planar waveguide can be formed. This waveguide, with the parameters of *C*_{V}
= 0.0095 μm^{-1}, *C*_{S}
= 1.07, *n*
_{1} = 1.50384 at *λ*= 610nm and *W* = 1.5368 μm, can support two waveguide modes. According to the above argument, for the *m*th-order waveguide mode, the losses from S-Sc and V-At per unit propagation distance along the film are inversely proportion to tg *θ*_{m}
and sin *θ*_{m}
, respectively; where *θ*_{m}
is an angle formed by the wave vector of the *m*th-order mode allowed and the normal of the film in the film. We estimate the results as follows: the losses caused by S-Sc are respectively 34dB/cm for *m* = 0 mode and 275dB/cm for *m* = 1 mode, while the losses caused by V-At are respectively 417dB/cm for *m* = 0 mode and 427dB/cm for *m* = 1 mode. We find that the volume loss of the *m* = 1 mode is merely 2.4% larger than that of the *m* = 0 mode, while the surface loss of the *m* = 1 mode is 8 times of that of the *m* = 0 mode. Consequently, the loss from S-Sc has significant influence on the higher order modes. Although the losses of the film in our experiments are too large for use in integrated optics, the film with low loss can be fabricated when the appropriate preparation condition is found; unfortunately we cannot actualize it until now. In principle, this way is also valid even for the case when the film has low losses. Of course, compared with the three methods mentioned above, the technique developed by us is more reasonable in dealing with the case when the losses in the film are relatively high, for the above three methods will not be effective if the light propagation distance in the film is too short. Thus when some films made with new kinds of materials are investigated and the preparation technique is not good enough for the perfect films to be made, our method will be useful in discussing the losses in this situation and will give useful results of the loss levels in these films for the purpose of improving the films’ quality. So our simple yet efficient method can be valuably complement to those conventional methods.

Of course, this way can also be used to characterize the losses of a planar film on a low refractive index substrate by use of the PFC configuration. Although we did not do the experiment, it doesn’t mean that our method is invalid in the PFC case.

In summary, a simple yet efficient technique for evaluating the optical losses of a planar film on a low- or high-refractive-index substrate has been developed and demonstrated, and it can separate the contributions of the losses from the surface scattering and from volume attenuation; however, it cannot further separate the volume scattering and the volume absorption from the entire volume attenuation. A practical example is also given to prove this technique and confirm that surface scattering has a stronger influence on higher orders of modes than does volume attenuation. In addition, our technique provides the opportunity to evaluate the optical losses in the films with high loss levels.

## Acknowledgements

This work has been supported by the National Natural Science Foundation of China under Grant No. 60178015 and No. 90101030, and by a grant for the State Key Program for Basic Research of China.

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