## Inverse design of the absorbing layer for detection enhancement in near-infrared range |

Optics Express, Vol. 21, Issue 20, pp. 23220-23230 (2013)

http://dx.doi.org/10.1364/OE.21.023220

Acrobat PDF (1141 KB)

### Abstract

In spite of rapidly increasing demand and various applications of infrared (IR) detectors, their design process for the performance improvement has been mostly dependent on researchers’ intuition and knowledge. We present two-dimensional unit structure design of the absorbing layer in IR detectors. A systematic approach is introduced to enhance the absorbing efficiency of incident beam in the near-infrared wavelength range. We derived a layered structure composed of a silicon nitride (Si_{3}N_{4}) layer and an amorphous silicon (a-Si) one in turn by the so called topology optimization in association with the time variant finite element analysis (FEA). It is confirmed that thickness at each layer is in associated with the IR wavelength so that detail dimensions of each layer are inferred. A prototype of the layered structure was fabricated and its performance has been verified through experimental measurement.

© 2013 Optical Society of America

## 1. Introduction

1. M. Laamanen, M. Blomberg, R. L. Puurunen, A. Miranto, and H. Kattelus, “Thin film absorbers for visible, near-infrared, and short-wavelength infrared spectra,” Sensor Actuator A **162**(2), 210–214 (2010). [CrossRef]

3. A. Rogalski, “Infrared detector: status and trends,” Prog. Quantum Electron. **27**(2-3), 59–210 (2003). [CrossRef]

4. M. Yuan, X. Zhou, and X. Yu, “Study on Infrared Absorption Characteristics of Ti and TiNx Nanofilms,” ECS Trans. **44**, 1429–1435 (2012). [CrossRef]

5. A. Rogalski, “Infrared detectors: an overview,” Infrared Phys. Technol. **43**(3-5), 187–210 (2002). [CrossRef]

6. A. Lin and J. Phillips, “Optimization of random diffraction gratings in thin-film solar cells using genetic algorithms,” Sol. Energy Mater. Sol. Cells **92**(12), 1689–1696 (2008). [CrossRef]

7. P. Campbell and M. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. **62**(1), 243–249 (1987). [CrossRef]

8. C. Haase and H. Stiebig, “Thin-film silicon solar cells with efficient periodic light trapping texture,” Appl. Phys. Lett. **91**(6), 061116 (2007). [CrossRef]

10. H. Soh and J. Yoo, “Texturing design for a light trapping system using topology optimization,” IEEE Trans. Magn. **48**(2), 227–230 (2012). [CrossRef]

11. J. B. Baxter and E. S. Aydil, “Nanowire-based dye-sensitized solar cells,” Appl. Phys. Lett. **86**(5), 053114 (2005). [CrossRef]

14. D. Lockau, T. Sontheimer, C. Becker, E. Rudigier-Voigt, F. Schmidt, and B. Rech, “Nanophotonic light trapping in 3-dimensional thin-film silicon architectures,” Opt. Express **21**(S1Suppl 1), A42–A52 (2013). [CrossRef] [PubMed]

15. H. Soh, J. Yoo, and D. Kim, “Optimal design of the light absorbing layer in thin film silicon solar cells,” Sol. Energy **86**(7), 2095–2105 (2012). [CrossRef]

16. M. P. Bendsøe and N. Kikuchi, “Generating optimal topologies in optimal design using a homogenization method,” Comput. Method Appl. M. **71**(2), 197–224 (1988). [CrossRef]

18. J. Yoo, N. Kikuchi, and J. L. Volakis, “Structural optimization in magnetic devices by the homogenization design method,” IEEE Trans. Magn. **36**(3), 574–580 (2000). [CrossRef]

19. J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide,” J. Opt. Soc. Am. B **22**(6), 1191–1198 (2005). [CrossRef]

22. T. Nomura, S. Nishiwaki, K. Sato, and K. Hirayama, “Topology optimization for the design of periodic microstructures composed of electromagnetic materials,” Finite Elem. Anal. Des. **45**(3), 210–226 (2009). [CrossRef]

19. J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide,” J. Opt. Soc. Am. B **22**(6), 1191–1198 (2005). [CrossRef]

15. H. Soh, J. Yoo, and D. Kim, “Optimal design of the light absorbing layer in thin film silicon solar cells,” Sol. Energy **86**(7), 2095–2105 (2012). [CrossRef]

_{3}N

_{4}, is proposed. Figure 1(a) shows the constitution of the absorbing layer of a detector and the schematic of the model for the analysis and design process is displayed in Fig. 1(b). The Si

_{3}N

_{4}layer is represented as a black part and the a-Si portion is expressed as a white part. The Helmholtz’s equation as a governing equation is solved using the commercial FEA package COMSOL

^{TM}and the time dependent analysis mode is adopted for taking the time varying field into account. As a result of the topology optimization process, the optimal material distribution of Si

_{3}N

_{4}and a-Si can be obtained as a form of layout design. To confirm the optimal design structure, the fabrication of the absorbing layer prototype and its experimental verification are followed. We have measured the reflectance of the prototype using an integrating sphere as well as its transmittance using a power sensor [23

23. D. Bergström, J. Powell, and A. F. H. Kaplan, “The absorptance of steels to Nd:YLF and Nd:YAG laser light at room temperature,” Appl. Surf. Sci. **253**(11), 5017–5028 (2007). [CrossRef]

24. L. Hanssen, “Integrating-sphere system and method for absolute measurement of transmittance, reflectance, and absorptance of specular samples,” Appl. Opt. **40**(19), 3196–3204 (2001). [CrossRef] [PubMed]

6. A. Lin and J. Phillips, “Optimization of random diffraction gratings in thin-film solar cells using genetic algorithms,” Sol. Energy Mater. Sol. Cells **92**(12), 1689–1696 (2008). [CrossRef]

## 2. The absorbing layer modeling

_{3}N

_{4}layer as displayed in the figure. The periodic boundary condition is applied both along the left and the right boundaries to realize a periodic pattern derived from unit structure design. The absorbing layer is composed of Si

_{3}N

_{4}material and a-Si in the other parts. Si

_{3}N

_{4}has almost same optical property with zinc oxide (ZnO) which is widely used for the TCO layer in solar cells [26

26. J. Springer, A. Poruba, L. Müllerova, and M. Vanecek, “Absorption loss at nanorough silver back reflector of thin-film silicon solar cells,” J. Appl. Phys. **95**(3), 1427–1429 (2004). [CrossRef]

_{3}N

_{4}is replaced as a substitute material for the prototype fabrication for the purpose of experimental verification.

*z*-directional component of the field vector is needed for the analysis as follows:where

*c*represents the speed of light.

_{0}20. J. Andkjær, S. Nishiwaki, T. Nomura, and O. Sigmund, “Topology optimization of grating couplers for the efficient excitation of surface plasmons,” J. Opt. Soc. Am. B **27**(9), 1828–1832 (2010). [CrossRef]

**H**

_{o}expresses the field strength of the incident beam and

*ω*is the frequency of the incident IR radiation. In this study,

*ω*becomes 281.95THz because the incident IR wavelength is set to 1064nm.

**H**plot calculated at the measuring domain for the incident beam with 1064nm wavelength. For defining the design objective value, the energy flux expressed by the Poynting vector formulation is employed in this study. On account of

_{z}*y*-directional incident beam, the energy flux can be formulated as follows:where

**H**represents the complex conjugate of the field vector

_{z}***H**.

_{z}*Ω*represents the measuring domain and

_{obj}*A*means its area. Also,

*Γ*and

_{inc}*L*are the incident boundary and its length, respectively. They are designated in Fig. 1(b).

*ψ*and

_{obj}*ψ*are time integration values of the Poynting vector at the measuring domain and the incident boundary, respectively. The time history is displayed in Fig. 2 and the time integration period is marked. The starting point of the time integration is selected as the second peak point of the history plot to avoid the confusion by mixing the incident wave with the reflected wave and also to reduce the total analysis time. The light transmittance which represents the efficiency is defined as the following equation:

_{inc}## 3. Topology optimization process

### 3.1 Problem formulation

_{3}N

_{4}and its density is defined as 1. On the other hand, void region represents the a-Si and its density is determined to 0 in this problem. The material property in the design domain is determined according to the density of each element. Since the design layout of absorbing layer composed of Si

_{3}N

_{4}and a-Si, the dielectric constant

*ε*, i.e., the material property in two phase material case, can be written aswhere

_{r}*γ*means the density of each element in the design domain and

*ε*is the relative permittivity.

_{r}*ε*and

^{’}*ε*represent the real and the imaginary part of the permittivity, respectively. The penalization parameter

^{”}*p*widely used in SIMP method to avoid gray scale element, is selected as 3 in this problem.

### 3.2 Time dependent field analysis and sensitivity calculation

**K**means the coefficient matrix and

**φ**is the state variable and

**f**is the load vector. The state variable

**φ**represents the

*z*-directional magnetic field strength vector

**H**

_{z}in this study. The adjoint variable method is employed for the sensitivity calculation and the final formulation of sensitivity becomeswhere

**is the adjoint variable and**

*λ**γ*is the design variable, i.e., the element density.

**is computed by solving the following adjoint equation.**

*λ*### 3.3 Topology optimization result

7. P. Campbell and M. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. **62**(1), 243–249 (1987). [CrossRef]

9. R. Dewan and D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys. **106**(7), 074901 (2009). [CrossRef]

11. J. B. Baxter and E. S. Aydil, “Nanowire-based dye-sensitized solar cells,” Appl. Phys. Lett. **86**(5), 053114 (2005). [CrossRef]

_{3}N

_{4}while white region is the a-Si part in the patterned layer. It is remarkable that the wave transmittance of the optimal result is much better than the initial wedge shaped case. Figure 4(b) shows the convergence history of the design objective and the shape change from another initial shape where the design domain is filled with Si

_{3}N

_{4}material. The optimal shape defined at 50th iteration is almost same to that from the wedge initial shape. However, the efficiency of the full Si

_{3}N

_{4}model is better than the final optimal model as confirmed in the graph. No gray scale portions are occurred because this process is focused on a specific wavelength.

*λ/4n*where

*λ*is 1064nm of the incident beam wavelength and

*n*is the refractive index of Si

_{3}N

_{4}material. The a-Si layer and the Si

_{3}N

_{4}layer are stacked sequentially with the thickness value of

*λ/2n.*Therefore, thicknesses of the a-Si layer and the Si

_{3}N

_{4}layer become 130nm and 270nm, respectively, due to the refractive index value difference. It is verified that the structure composed of layers with

*λ/2n*thickness gives good transmittance of the light while the first layer thickness value of

*λ/4n*is effective as an anti-reflection coating for a single layer [27, 28]. Therefore, the final model is suggested to have

*λ/4n*thickness at the top layer and

*λ/2n*thickness in following stacked layers. Figure 5 display shapes of two initial models and final optimal model suggested. Efficiencies at each case are computed as 0.0988, 0.3686 and 0.4480 for wedge initial shape, full Si

_{3}N

_{4}initial shape and suggested optimal shape, respectively. For the suggested model, it gives improved transmittance efficiencies as 353.4% and 21.54% compared with the wedge shaped model and full Si

_{3}N

_{4}model, respectively. Figure 6 compares the wave propagation plot for each cases and strong wave plot can be confirmed in the absorbing layer for the optimal case.

## 4. Experiment

### 4.1 Experiment set-up

_{3}N

_{4}mono-layer model was fabricated by the plasma-enhanced chemical vapor deposition (PECVD) process while the multi-layer model stacked of Si

_{3}N

_{4}and a-Si layers was fabricated using the low pressure chemical vapor deposition (LPCVD) process [29, 30]. The multi-layered model stems from the suggested optimal result. SEM image of two models are displayed with detailed thickness of each layer as expressed in Figs. 5(b) and 5(c). We calculate the absorption (A) from measurement of the reflectance (R) and the transmittance (T) for those two prototype models as

*A = 1-R-T*.

31. U. Willamowski, D. Ristau, and E. Welsch, “Measuring the absolute absorptance of optical laser components,” Appl. Opt. **37**(36), 8362–8370 (1998). [CrossRef] [PubMed]

### 4.2 Experiment results

_{3}N

_{4}mono-layer model, the transmittance is measured as 0.751 and the reflectance is measured as the value of 0.157. The absorptance of full Si

_{3}N

_{4}model becomes 0.092 according to the relation of

*A = 1-R-T*. Si

_{3}N

_{4}/a-Si multi-layered model, that is, the optimized model derived from the suggested process shows the value of 0.685 in transmittance and 0.201 in the reflectance; therefore, the absorptance becomes 0.114 as a result.

## 5. Conclusion

_{3}N

_{4}layer and a-Si layer in turn has been obtained and each layer shows

*λ/4n*thickness in the top layer and

*λ/2n*in other layers. It turns out that those thicknesses are effective for anti-reflection and light transmittance, respectively.

_{3}N

_{4}mono-layered one and Si

_{3}N

_{4}/a-Si multi-layered model, were fabricated and the absorptance is measured by measuring the reflectance and the transmittance. Improvement factors up to 23.91% (by experiment) and 21.54% (by simulation) show similar absorption response. The enhancement of the absorptance is pointing out that the suggested design process is valid in absorbing layer design of IR detectors.

## Acknowledgment

## References and links

1. | M. Laamanen, M. Blomberg, R. L. Puurunen, A. Miranto, and H. Kattelus, “Thin film absorbers for visible, near-infrared, and short-wavelength infrared spectra,” Sensor Actuator A |

2. | A. Rogalski, |

3. | A. Rogalski, “Infrared detector: status and trends,” Prog. Quantum Electron. |

4. | M. Yuan, X. Zhou, and X. Yu, “Study on Infrared Absorption Characteristics of Ti and TiNx Nanofilms,” ECS Trans. |

5. | A. Rogalski, “Infrared detectors: an overview,” Infrared Phys. Technol. |

6. | A. Lin and J. Phillips, “Optimization of random diffraction gratings in thin-film solar cells using genetic algorithms,” Sol. Energy Mater. Sol. Cells |

7. | P. Campbell and M. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. |

8. | C. Haase and H. Stiebig, “Thin-film silicon solar cells with efficient periodic light trapping texture,” Appl. Phys. Lett. |

9. | R. Dewan and D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys. |

10. | H. Soh and J. Yoo, “Texturing design for a light trapping system using topology optimization,” IEEE Trans. Magn. |

11. | J. B. Baxter and E. S. Aydil, “Nanowire-based dye-sensitized solar cells,” Appl. Phys. Lett. |

12. | J. Li, H. Yu, S. M. Wong, G. Zhang, G. Lo, and D. Kwong, “Si nanocone array optimization on crystalline Si thin films for solar energy harvesting,” J. Phys. D Appl. Phys. |

13. | E. D. Kosten, E. L. Warren, and H. A. Atwater, “Ray optical light trapping in Silicon microwires: exceeding the 2 |

14. | D. Lockau, T. Sontheimer, C. Becker, E. Rudigier-Voigt, F. Schmidt, and B. Rech, “Nanophotonic light trapping in 3-dimensional thin-film silicon architectures,” Opt. Express |

15. | H. Soh, J. Yoo, and D. Kim, “Optimal design of the light absorbing layer in thin film silicon solar cells,” Sol. Energy |

16. | M. P. Bendsøe and N. Kikuchi, “Generating optimal topologies in optimal design using a homogenization method,” Comput. Method Appl. M. |

17. | M. P. Bendsøe and O. Sigmund, |

18. | J. Yoo, N. Kikuchi, and J. L. Volakis, “Structural optimization in magnetic devices by the homogenization design method,” IEEE Trans. Magn. |

19. | J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide,” J. Opt. Soc. Am. B |

20. | J. Andkjær, S. Nishiwaki, T. Nomura, and O. Sigmund, “Topology optimization of grating couplers for the efficient excitation of surface plasmons,” J. Opt. Soc. Am. B |

21. | R. Matzen, J. S. Jensen, and O. Sigmund, “Topology optimization for transient response of photonic crystal structures,” J. Opt. Soc. Am. B |

22. | T. Nomura, S. Nishiwaki, K. Sato, and K. Hirayama, “Topology optimization for the design of periodic microstructures composed of electromagnetic materials,” Finite Elem. Anal. Des. |

23. | D. Bergström, J. Powell, and A. F. H. Kaplan, “The absorptance of steels to Nd:YLF and Nd:YAG laser light at room temperature,” Appl. Surf. Sci. |

24. | L. Hanssen, “Integrating-sphere system and method for absolute measurement of transmittance, reflectance, and absorptance of specular samples,” Appl. Opt. |

25. | P. Norton, “HgCdTe infrared detectors,” Opto-Electron. Rev. |

26. | J. Springer, A. Poruba, L. Müllerova, and M. Vanecek, “Absorption loss at nanorough silver back reflector of thin-film silicon solar cells,” J. Appl. Phys. |

27. | P. Ye, |

28. | D. W. Driscoll and W. Vaughan, Handbook of optics (McGraw-Hill, New York, 1978) |

29. | D. N. Wang, J. M. White, K. S. Law, and C. Leung, “Thermal CVD/PECVD reactor and use for thermal chemical vapor deposition of silicon dioxide and in-situ multi-step planarized process,” US Patent, 5000113 (1991). |

30. | G. S. Sandhu and T. W. Buley, “Low-pressure chemical vapor deposition process for depositing high-density, highly-conformal titanium nitride films of low bulk resistivity,” US Patent, 5246881 (1993). |

31. | U. Willamowski, D. Ristau, and E. Welsch, “Measuring the absolute absorptance of optical laser components,” Appl. Opt. |

32. | J. M. Palmer, |

**OCIS Codes**

(040.3060) Detectors : Infrared

(220.0220) Optical design and fabrication : Optical design and fabrication

**ToC Category:**

Detectors

**History**

Original Manuscript: July 29, 2013

Revised Manuscript: September 15, 2013

Manuscript Accepted: September 18, 2013

Published: September 24, 2013

**Citation**

Namjoon Heo, Jaeyeol Lee, Hyundo Shin, Jeonghoon Yoo, and Daekeun Kim, "Inverse design of the absorbing layer for detection enhancement in near-infrared range," Opt. Express **21**, 23220-23230 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-23220

Sort: Year | Journal | Reset

### References

- M. Laamanen, M. Blomberg, R. L. Puurunen, A. Miranto, H. Kattelus, “Thin film absorbers for visible, near-infrared, and short-wavelength infrared spectra,” Sensor Actuator A 162(2), 210–214 (2010). [CrossRef]
- A. Rogalski, Infrared Detectors (CRC Press, 2011).
- A. Rogalski, “Infrared detector: status and trends,” Prog. Quantum Electron. 27(2-3), 59–210 (2003). [CrossRef]
- M. Yuan, X. Zhou, X. Yu, “Study on Infrared Absorption Characteristics of Ti and TiNx Nanofilms,” ECS Trans. 44, 1429–1435 (2012). [CrossRef]
- A. Rogalski, “Infrared detectors: an overview,” Infrared Phys. Technol. 43(3-5), 187–210 (2002). [CrossRef]
- A. Lin, J. Phillips, “Optimization of random diffraction gratings in thin-film solar cells using genetic algorithms,” Sol. Energy Mater. Sol. Cells 92(12), 1689–1696 (2008). [CrossRef]
- P. Campbell, M. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. 62(1), 243–249 (1987). [CrossRef]
- C. Haase, H. Stiebig, “Thin-film silicon solar cells with efficient periodic light trapping texture,” Appl. Phys. Lett. 91(6), 061116 (2007). [CrossRef]
- R. Dewan, D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys. 106(7), 074901 (2009). [CrossRef]
- H. Soh, J. Yoo, “Texturing design for a light trapping system using topology optimization,” IEEE Trans. Magn. 48(2), 227–230 (2012). [CrossRef]
- J. B. Baxter, E. S. Aydil, “Nanowire-based dye-sensitized solar cells,” Appl. Phys. Lett. 86(5), 053114 (2005). [CrossRef]
- J. Li, H. Yu, S. M. Wong, G. Zhang, G. Lo, D. Kwong, “Si nanocone array optimization on crystalline Si thin films for solar energy harvesting,” J. Phys. D Appl. Phys. 43(25), 255101 (2010). [CrossRef]
- E. D. Kosten, E. L. Warren, H. A. Atwater, “Ray optical light trapping in Silicon microwires: exceeding the 2n2 intensity limit,” Opt. Express 19(4), 3316–3331 (2011). [CrossRef] [PubMed]
- D. Lockau, T. Sontheimer, C. Becker, E. Rudigier-Voigt, F. Schmidt, B. Rech, “Nanophotonic light trapping in 3-dimensional thin-film silicon architectures,” Opt. Express 21(S1Suppl 1), A42–A52 (2013). [CrossRef] [PubMed]
- H. Soh, J. Yoo, D. Kim, “Optimal design of the light absorbing layer in thin film silicon solar cells,” Sol. Energy 86(7), 2095–2105 (2012). [CrossRef]
- M. P. Bendsøe, N. Kikuchi, “Generating optimal topologies in optimal design using a homogenization method,” Comput. Method Appl. M. 71(2), 197–224 (1988). [CrossRef]
- M. P. Bendsøe and O. Sigmund, Topology optimization: theory, methods, and applications (Springer-Verlag, 2003).
- J. Yoo, N. Kikuchi, J. L. Volakis, “Structural optimization in magnetic devices by the homogenization design method,” IEEE Trans. Magn. 36(3), 574–580 (2000). [CrossRef]
- J. S. Jensen, O. Sigmund, “Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide,” J. Opt. Soc. Am. B 22(6), 1191–1198 (2005). [CrossRef]
- J. Andkjær, S. Nishiwaki, T. Nomura, O. Sigmund, “Topology optimization of grating couplers for the efficient excitation of surface plasmons,” J. Opt. Soc. Am. B 27(9), 1828–1832 (2010). [CrossRef]
- R. Matzen, J. S. Jensen, O. Sigmund, “Topology optimization for transient response of photonic crystal structures,” J. Opt. Soc. Am. B 27(10), 2040–2050 (2010). [CrossRef]
- T. Nomura, S. Nishiwaki, K. Sato, K. Hirayama, “Topology optimization for the design of periodic microstructures composed of electromagnetic materials,” Finite Elem. Anal. Des. 45(3), 210–226 (2009). [CrossRef]
- D. Bergström, J. Powell, A. F. H. Kaplan, “The absorptance of steels to Nd:YLF and Nd:YAG laser light at room temperature,” Appl. Surf. Sci. 253(11), 5017–5028 (2007). [CrossRef]
- L. Hanssen, “Integrating-sphere system and method for absolute measurement of transmittance, reflectance, and absorptance of specular samples,” Appl. Opt. 40(19), 3196–3204 (2001). [CrossRef] [PubMed]
- P. Norton, “HgCdTe infrared detectors,” Opto-Electron. Rev. 10, 159–174 (2002).
- J. Springer, A. Poruba, L. Müllerova, M. Vanecek, “Absorption loss at nanorough silver back reflector of thin-film silicon solar cells,” J. Appl. Phys. 95(3), 1427–1429 (2004). [CrossRef]
- P. Ye, Optical waves in layered media (Wiley, 1998).
- D. W. Driscoll and W. Vaughan, Handbook of optics (McGraw-Hill, New York, 1978)
- D. N. Wang, J. M. White, K. S. Law, and C. Leung, “Thermal CVD/PECVD reactor and use for thermal chemical vapor deposition of silicon dioxide and in-situ multi-step planarized process,” US Patent, 5000113 (1991).
- G. S. Sandhu and T. W. Buley, “Low-pressure chemical vapor deposition process for depositing high-density, highly-conformal titanium nitride films of low bulk resistivity,” US Patent, 5246881 (1993).
- U. Willamowski, D. Ristau, E. Welsch, “Measuring the absolute absorptance of optical laser components,” Appl. Opt. 37(36), 8362–8370 (1998). [CrossRef] [PubMed]
- J. M. Palmer, Handbook of optics, (McGraw-Hill, 1995).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.