## Simple and efficient technique for evaluating the optical losses from surface scattering and volume attenuation in a thin film

Optics Express, Vol. 10, Issue 25, pp. 1485-1490 (2002)

http://dx.doi.org/10.1364/OE.10.001485

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### 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

1. R. D Stanley, W. M. Gibson, and J. W. Rodgers, “Properties of ion-bombarded fused quartz for integrated optics,” Appl. Opt. **11**, 1313–1316 (1972). [CrossRef]

2. P. K. Tien, “Light waves in thin films and integrated optics,” Appl. Opt. **10**, 2395–2413 (1971). [CrossRef] [PubMed]

2. P. K. Tien, “Light waves in thin films and integrated optics,” Appl. Opt. **10**, 2395–2413 (1971). [CrossRef] [PubMed]

*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

3. P. A. Temple, “Total internal reflection microscopy: a surface inspection technique,” Appl. Opt. **20**, 2656–2664 (1981). [CrossRef] [PubMed]

4. S. N. Jabr, “Total internal reflection microscopy: inspection of surfaces of high bulk scatter materials,” Appl. Opt. **24**, 1689–1692 (1985). [CrossRef] [PubMed]

5. R. Th. Kersten, “A new method for measuring refractive index and thickness of liquid and deposited solid thin films,” Opt. Commun. **13**, 327–329 (1975). [CrossRef]

8. P. K. Tien, R. Ulrich, and R. J. Martin, “Modes of propagating light waves in thin deposited semiconductor films,” Appl. Phys. Lett. **14**, 291–294 (1969). [CrossRef]

9. R. Ulrich and R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. **12**, 2901–2908 (1973). [CrossRef] [PubMed]

*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

2. P. K. Tien, “Light waves in thin films and integrated optics,” Appl. Opt. **10**, 2395–2413 (1971). [CrossRef] [PubMed]

^{2}

*θ*

_{1}); here

*C*

_{S}and

*θ*

_{1}correspond to

*K*and

*θ*in Eqs. (16) and (18) of Ref. 2

**10**, 2395–2413 (1971). [CrossRef] [PubMed]

*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

*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(-

*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

*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.

*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

*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*(

*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

*ϕ*

_{12}in Eq. (2) is replaced with

*ϕ*

_{123}in Eq. (4).

*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.

*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

6. T. N. Ding and E. Garmire, “Measuring refractive index and thickness of thin films: a new technique,” Appl. Opt. **22**, 3177–3181 (1983). [CrossRef] [PubMed]

*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

9. R. Ulrich and R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. **12**, 2901–2908 (1973). [CrossRef] [PubMed]

*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).

7. H. T. Wang, T. Aruga, and P. X. Ye, “Theory and properties of quasiwaveguide modes,” Appl. Phys. Lett. **69**, 611–613 (1996). [CrossRef]

*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

6. T. N. Ding and E. Garmire, “Measuring refractive index and thickness of thin films: a new technique,” Appl. Opt. **22**, 3177–3181 (1983). [CrossRef] [PubMed]

7. H. T. Wang, T. Aruga, and P. X. Ye, “Theory and properties of quasiwaveguide modes,” Appl. Phys. Lett. **69**, 611–613 (1996). [CrossRef]

*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.

*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.

## Acknowledgements

## References and links

1. | R. D Stanley, W. M. Gibson, and J. W. Rodgers, “Properties of ion-bombarded fused quartz for integrated optics,” Appl. Opt. |

2. | P. K. Tien, “Light waves in thin films and integrated optics,” Appl. Opt. |

3. | P. A. Temple, “Total internal reflection microscopy: a surface inspection technique,” Appl. Opt. |

4. | S. N. Jabr, “Total internal reflection microscopy: inspection of surfaces of high bulk scatter materials,” Appl. Opt. |

5. | R. Th. Kersten, “A new method for measuring refractive index and thickness of liquid and deposited solid thin films,” Opt. Commun. |

6. | T. N. Ding and E. Garmire, “Measuring refractive index and thickness of thin films: a new technique,” Appl. Opt. |

7. | H. T. Wang, T. Aruga, and P. X. Ye, “Theory and properties of quasiwaveguide modes,” Appl. Phys. Lett. |

8. | P. K. Tien, R. Ulrich, and R. J. Martin, “Modes of propagating light waves in thin deposited semiconductor films,” Appl. Phys. Lett. |

9. | R. Ulrich and R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. |

**OCIS Codes**

(230.7390) Optical devices : Waveguides, planar

(290.5820) Scattering : Scattering measurements

(290.5880) Scattering : Scattering, rough surfaces

(310.6860) Thin films : Thin films, optical properties

**ToC Category:**

Research Papers

**History**

Original Manuscript: December 4, 2002

Revised Manuscript: December 5, 2002

Published: December 16, 2002

**Citation**

Xi-Jing Zhang, Xi-Zhi Fan, Hui-Tian Wang, Jing-Liang He, and N. Ming, "Simple and efficient technique for evaluating the optical losses from surface scattering and volume attenuation in a thin film," Opt. Express **10**, 1485-1490 (2002)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-25-1485

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### References

- R. D Stanley, W. M. Gibson, and J. W. Rodgers, �??Properties of ion-bombarded fused quartz for integrated optics,�?? Appl. Opt. 11, 1313-1316 (1972). [CrossRef]
- P. K. Tien, �??Light waves in thin films and integrated optics,�?? Appl. Opt. 10, 2395-2413 (1971). [CrossRef] [PubMed]
- P. A. Temple, �??Total internal reflection microscopy: a surface inspection technique,�?? Appl. Opt. 20, 2656-2664 (1981). [CrossRef] [PubMed]
- S. N. Jabr, �??Total internal reflection microscopy: inspection of surfaces of high bulk scatter materials,�?? Appl. Opt. 24, 1689-1692 (1985). [CrossRef] [PubMed]
- R. Th. Kersten, �??A new method for measuring refractive index and thickness of liquid and deposited solid thin films,�?? Opt. Commun. 13, 327-329 (1975). [CrossRef]
- T. N. Ding and E. Garmire, �??Measuring refractive index and thickness of thin films: a new technique,�?? Appl. Opt. 22, 3177-3181 (1983). [CrossRef] [PubMed]
- H. T. Wang, T. Aruga, and P. X. Ye, �??Theory and properties of quasiwaveguide modes,�?? Appl. Phys. Lett. 69, 611-613 (1996). [CrossRef]
- P. K. Tien, R. Ulrich, and R. J. Martin, �??Modes of propagating light waves in thin deposited semiconductor films,�?? Appl. Phys. Lett. 14, 291-294 (1969). [CrossRef]
- R. Ulrich and R. Torge, �??Measurement of thin film parameters with a prism coupler,�?? Appl. Opt. 12, 2901-2908 (1973). [CrossRef] [PubMed]

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