## Dielectric multilayer beam splitter with differential phase shift on transmission and reflection for division-of-amplitude photopolarimeter |

Optics Express, Vol. 22, Issue 9, pp. 11011-11020 (2014)

http://dx.doi.org/10.1364/OE.22.011011

Acrobat PDF (3027 KB)

### Abstract

Dielectric multilayer beam splitter with differential phase shift on transmission and reflection for division-of-amplitude photopolarimeter (DOAP) was presented for the first time to our knowledge. The optimal parameters for the beam splitter are *T _{p}* = 78.9%,

*T*= 21.1% and Δ

_{s}*− Δ*

_{r}*= π/2 at 532nm at an angle of incidence of 45°. Multilayer anti-reflection coating with low phase shift was applied to reduce the backside reflection. Different design strategies that can achieve all optimal targets at the wavelength were tested. Two design methods were presented to optimize the differential phase shift. The samples were prepared by ion beam sputtering (IBS). The experimental results show good agreement with those of the design. The ellipsometric parameters of samples were measured in reflection (ψ*

_{t}

_{r}_{,}Δ

*) = (26.5°, 135.1°) and (28.2°, 133.5°), as well as in transmission (ψ*

_{r}*, Δ*

_{t}*) = (62.5°, 46.1°) and (63.5°, 46°) at 532.6nm. The normalized determinant of instrument matrix to evaluate the performance of samples is respectively 0.998 and 0.991 at 532.6nm.*

_{t}© 2014 Optical Society of America

## 1. Introduction

1. H. G. Berry, G. Gabrielse, and A. E. Livingston, “Measurement of the Stokes parameters of light,” Appl. Opt. **16**(12), 3200–3205 (1977). [CrossRef] [PubMed]

5. L. Weller, T. Dalton, P. Siddons, C. S. Adams, and I. G. Hughes, “Measuring the Stokes parameters for light transmitted by a high-density rubidium vapour in large magnetic fields,” J. Phys. At. Mol. Opt. Phys. **45**(5), 055001 (2012). [CrossRef]

6. R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta (Lond.) **29**(5), 685–689 (1982). [CrossRef]

7. R. M. A. Azzam and A. De, “Optimal beam splitters for the division-of-amplitude photopolarimeter,” J. Opt. Soc. Am. A **20**(5), 955–958 (2003). [CrossRef] [PubMed]

8. R. M. A. Azzam and F. F. Sudradjat, “Single-layer-coated beam splitters for the division-of-amplitude photopolarimeter,” Appl. Opt. **44**(2), 190–196 (2005). [CrossRef] [PubMed]

## 2. Design of multilayer beam splitter

6. R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta (Lond.) **29**(5), 685–689 (1982). [CrossRef]

_{0}, D

_{1}, D

_{2}, D

_{3}and the intensity signals i

_{1}, i

_{2}, i

_{3}, i

_{4}were recorded. It can be written as vector

**A**is instrument matrix, usually determined by calibration [9

9. R. M. A. Azzam and A. G. Lopez, “Accurate calibration of the four-detector photopolarimeter with imperfect polarizing optical elements,” J. Opt. Soc. Am. A **6**(10), 1513–1521 (1989). [CrossRef]

**A**is nonsingular, its inverse

**A**

^{−1}exists. By maximizing the absolute value of the determinant of matrix

**A**, the measurement accuracy can be increased. The determinant of matrix

**A**is determined by the optical parameters of the beam splitter and can be expressed by [7

7. R. M. A. Azzam and A. De, “Optimal beam splitters for the division-of-amplitude photopolarimeter,” J. Opt. Soc. Am. A **20**(5), 955–958 (2003). [CrossRef] [PubMed]

*R*and

*T*are the reflectance and transmittance of beam splitter. (ψ

*, Δ*

_{r}*) and (ψ*

_{r}*, Δ*

_{t}*) are the ellipsometric parameters written in reflection and transmission, respectively. ψ is the intensity ratio of p-polarized and s-polarized light in reflection or transmission, and*

_{t}_{2}O

_{5}and SiO

_{2}are employed as high and low refractive index materials, respectively, and the substrate is BK7. The optical constants Nb

_{2}O

_{5}and SiO

_{2}at different wavelengths are listed in Table 1.The refractive index of Nb

_{2}O

_{5}is 2.317 and SiO

_{2}is 1.488 at 532nm, the extinction coefficient of Nb

_{2}O

_{5}is 2.2 × 10

^{−4}, which can be regarded as non-absorption.

### 2.1 Design of the beam splitter

*and Δ*

_{r}*should be π/2 and the fixed values for Δ*

_{t}*and Δ*

_{r}*are not required. In this case, there are two design strategies to optimize the phase shift: I) define Δ*

_{t}*and Δ*

_{r}*separately as the constant values for the optimization targets, II) directly define Δ*

_{t}*− Δ*

_{r}*as the optimization target in a spectral region.*

_{t}*MF*is introduced to evaluate the deviation between the design results and the targets, which allows to convert the design problem to a minimization of merit function. Therefore, there are four optimization targets

*T*,

_{s}*T*, Δ

_{p}*, and Δ*

_{r}*by design method I, and the corresponding merit function can be expressed as:Here*

_{t}*λ*is wavelength in the target region and m = 1, 2,…M are a set of wavelengths.

*T*(

*λ*) is the theoretical transmittance for both p and s polarization light at a specified wavelength, while Δ(

_{m}*λ*) is the theoretical phase shift difference on p- and s-polarized light for both reflection and transmission at a specified wavelength.

_{m}*T*

^{(}

^{m}^{)}and Δ

^{(}

^{m}^{)}are the corresponding target values and

*δT*

^{(}

^{m}^{)},

*δ*Δ

^{(}

^{m}^{)}are the corresponding tolerances.

10. A. V. Tikhonravov and M. K. Trubetskov, OptiLayer Software, http://www.optilayer.com.

11. A. V. Tikhonravov, M. K. Trubetskov, and G. W. Debell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. **35**(28), 5493–5508 (1996). [CrossRef] [PubMed]

^{10}/Glass on the front surface with air and glass as the incident and exit medium. H and L are quarterwave layer of high index material (Nb

_{2}O

_{5}) and low index material (SiO

_{2}) respectively. Sub means a glass substrate which is BK7 glass in this paper.

*and Δ*

_{r}*, have influence on physical thickness and merit function of design results. In order to find a good solution with proper values of Δ*

_{t}*and Δ*

_{r}*, we designed beam splitter with different values of Δ*

_{t}*and set the difference*

_{t}*= 15, 30, 45, 60 degrees are shown in Table 2.The spectral region is from 517nm to 547nm, and the transmittances of p-polarized, s-polarized light are 78.9% and 21.1% respectively. The tolerances of*

_{t}*T*and

_{p}*T*are 0.1%, and the tolerances of Δ

_{s}*, Δ*

_{r}*are 0.1°. For Δ*

_{t}*= 15, 30, 45, 60 degrees, the corresponding merit function*

_{t}*MF1*are 7.7, 6.07, 5.81, and 11.04, and the total physical thickness are 2353nm, 2430nm, 2420nm, and 2675nm. The design with Δ

*= 45 degrees has the lowest merit function. Therefore, we set Δ*

_{t}*= 45 degrees and correspondingly Δ*

_{t}*= 135 degrees as the targets.*

_{r}*is 44.7° at 532nm and Δ*

_{t}*is 135.1° and the value of Δ*

_{r}*− Δ*

_{r}*is 90.4° as seen in Fig. 3(c).*

_{t}*T*,

_{s}*T*, and

_{p}*T*at 532nm are 4.8%, 5.4%, and 4.9%. For the phase difference shift Δ

*and Δ*

_{r}*, the deviations are 4.2° and 3.8°, and the deviation of Δ*

_{t}*− Δ*

_{r}*is 6.5° at 532nm.*

_{t}*and Δ*

_{r}*are separately set as a constant value. In fact, the value of Δ*

_{t}*− Δ*

_{r}*is the final target we require. Therefore it is possible to directly define Δ*

_{t}*− Δ*

_{r}*as an optimization target, not considering the detailed values of Δ*

_{t}*and Δ*

_{r}*. As a result, the merit function contains only three parameters:*

_{t}*T*,

_{p}*T*, and Δ

_{s}*– Δ*

_{r}*. It can be described as Eq. (5):Where*

_{t}*– Δ*

_{r}*in the equation and other parameters are the same as in Eq. (4)*

_{t}*is 45.8° at 532nm and on reflectance Δ*

_{t}*is 135.9°. The value of Δ*

_{r}*– Δ*

_{r}*is 90.05° with a deviation of under ± 0.2° at wavelengths from 517nm to 547nm, and is close to the target in the desired wavelength region.*

_{t}*T*,

_{s}*T*, and

_{p}*T*at 532nm are 5.7%, 5.9%, and 5.4%. For the phase difference shift Δ

*and Δ*

_{r}*, the deviations are 5.4° and 5.8°, and the estimated value of Δ*

_{t}*– Δ*

_{r}*is 81.2°~98.8°, with a deviation of 8.8° at 532nm.*

_{t}*– Δ*

_{r}*by direct optimization. However, according to error analysis with a random thickness deviation of 1nm, the deviations of the transmittance and phase difference shift in design I are lower.*

_{t}### 2.2 Design of anti-reflection coating on the backside

*is minimized as well.*

_{t}*are shown in Fig. 5(b) and 5(c) respectively. P-, s-polarized and the average reflectance are lower than 0.5%, meanwhile the absolute value of Δ*

_{t}*is under 0.2° at 532nm.*

_{t}## 3. Experimental results and analysis

^{−4}Pa. Ar and O

_{2}were introduced into the system during the process and the working pressure was 5 × 10

^{−2}Pa. The deposition rates of Nb

_{2}O

_{5}and SiO

_{2}were respectively 0.12nm/s and 0.1nm/s. Quartz crystal monitoring was used to control the thickness of thin films during the deposition process.

*, Δ*

_{r}*) and (ψ*

_{r}*, Δ*

_{t}*) of the beam splitters were measured by spectroscopic ellipsometer (J. A. Woollam M-2000). The J. A. Woollam M-2000 can measure ellipsometric parameters in reflectance and transmittance, and cover a wavelength range from 193nm to 1690nm with a resolution of 1.6nm in the visible spectral range. So, the values at wavelength of 532.6nm are obtained in fact. The measured ψ*

_{t}*and ψ*

_{r}*of samples are shown in Fig. 7.The measured ψ*

_{t}*and ψ*

_{r}*of sample I are 26.5° and 62.5° at 532.6nm, while 28.2° and 63.5° for sample II. Both their values are very close to the target values of 27.4° and 62.6°, with a deviation of less than 1°.*

_{t}*and Δ*

_{r}*of the samples. For sample I, Δ*

_{t}*and Δ*

_{r}*are respectively 135.1° and 46.1°, while 133.5° and 46° for sample II. The two beam splitters designed by different methods has the similar measured results at 532.6nm.*

_{t}*– Δ*

_{r}*of samples from previous results, as presented in Fig. 9.For sample I, Δ*

_{t}*– Δ*

_{r}*is 89.0° at 532.6nm and the value is 89.0°~91.3° from 526.2nm to 532.6nm. For sample II, Δ*

_{t}*– Δ*

_{r}*is 87.5° at 532.6nm and it is 88.7°~90.1° in 537.4-548.5nm. Phase shift on transmittance of the anti-reflection coating was measured, as shown in Fig. 10.The value of Δ*

_{t}*is −0.3° at 532.6nm while the design value is −0.1°. The results match the theoretical data very well at the interested spectral range. So, the anti-reflection coating can significantly reduce reflection caused by the backside of substrate and very low phase shift is introduced.*

_{t}**A**in DOAP can be used to evaluate the performance of a beam splitter. For a perfect beam splitter, normalized determinant should be equal to 1. Normalized determinants of sample I and II at different wavelengths are shown in Fig. 11. The value of sample I is 0.998 at wavelength of 532.6nm and is larger than 0.98 from 521.4nm to 542.1nm. The value of sample II is 0.991 at 532.6nm and is larger than 0.98 from 519.8nm to 548.5nm.

## 4. Conclusions

*and Δ*

_{r}*as a constant in the targeted spectral range and the other is to define Δ*

_{t}*– Δ*

_{r}*directly as an optimized target.*

_{t}**A**of sample I is 0.998, and the value of sample II is 0.991 at 532.6nm The results demonstrated that the normalized determinant of matrix

**A**of sample II is lower at 532.6nm than sample I, but has a broader wavelength region where the normalized determinant of matrix

**A**is above 0.98. The samples present a very good performance and satisfy the optimal parameters for DOAP. Furthermore, the extensions to different spectral ranges or angles and a broad bandwidth application are also possible.

## Acknowledgments

## References and links

1. | H. G. Berry, G. Gabrielse, and A. E. Livingston, “Measurement of the Stokes parameters of light,” Appl. Opt. |

2. | F. Gori, “Measuring Stokes parameters by means of a polarization grating,” Opt. Lett. |

3. | B. Kanseri, S. Rath, and H. C. Kandpal, “Direct determination of the generalized Stokes parameters from the usual Stokes parameters,” Opt. Lett. |

4. | T. Kihara, “Measurement method of Stokes parameters using a quarter-wave plate with phase difference errors,” Appl. Opt. |

5. | L. Weller, T. Dalton, P. Siddons, C. S. Adams, and I. G. Hughes, “Measuring the Stokes parameters for light transmitted by a high-density rubidium vapour in large magnetic fields,” J. Phys. At. Mol. Opt. Phys. |

6. | R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta (Lond.) |

7. | R. M. A. Azzam and A. De, “Optimal beam splitters for the division-of-amplitude photopolarimeter,” J. Opt. Soc. Am. A |

8. | R. M. A. Azzam and F. F. Sudradjat, “Single-layer-coated beam splitters for the division-of-amplitude photopolarimeter,” Appl. Opt. |

9. | R. M. A. Azzam and A. G. Lopez, “Accurate calibration of the four-detector photopolarimeter with imperfect polarizing optical elements,” J. Opt. Soc. Am. A |

10. | A. V. Tikhonravov and M. K. Trubetskov, OptiLayer Software, http://www.optilayer.com. |

11. | A. V. Tikhonravov, M. K. Trubetskov, and G. W. Debell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. |

**OCIS Codes**

(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry

(230.1360) Optical devices : Beam splitters

(310.6860) Thin films : Thin films, optical properties

(310.4165) Thin films : Multilayer design

(310.5696) Thin films : Refinement and synthesis methods

**ToC Category:**

Optical Devices

**History**

Original Manuscript: March 31, 2014

Revised Manuscript: April 16, 2014

Manuscript Accepted: April 20, 2014

Published: April 30, 2014

**Citation**

Wenjia Yuan, Weidong Shen, Yueguang Zhang, and Xu Liu, "Dielectric multilayer beam splitter with differential phase shift on transmission and reflection for division-of-amplitude photopolarimeter," Opt. Express **22**, 11011-11020 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-9-11011

Sort: Year | Journal | Reset

### References

- H. G. Berry, G. Gabrielse, A. E. Livingston, “Measurement of the Stokes parameters of light,” Appl. Opt. 16(12), 3200–3205 (1977). [CrossRef] [PubMed]
- F. Gori, “Measuring Stokes parameters by means of a polarization grating,” Opt. Lett. 24(9), 584–586 (1999). [CrossRef] [PubMed]
- B. Kanseri, S. Rath, H. C. Kandpal, “Direct determination of the generalized Stokes parameters from the usual Stokes parameters,” Opt. Lett. 34(6), 719–721 (2009). [CrossRef] [PubMed]
- T. Kihara, “Measurement method of Stokes parameters using a quarter-wave plate with phase difference errors,” Appl. Opt. 50(17), 2582–2587 (2011). [CrossRef] [PubMed]
- L. Weller, T. Dalton, P. Siddons, C. S. Adams, I. G. Hughes, “Measuring the Stokes parameters for light transmitted by a high-density rubidium vapour in large magnetic fields,” J. Phys. At. Mol. Opt. Phys. 45(5), 055001 (2012). [CrossRef]
- R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta (Lond.) 29(5), 685–689 (1982). [CrossRef]
- R. M. A. Azzam, A. De, “Optimal beam splitters for the division-of-amplitude photopolarimeter,” J. Opt. Soc. Am. A 20(5), 955–958 (2003). [CrossRef] [PubMed]
- R. M. A. Azzam, F. F. Sudradjat, “Single-layer-coated beam splitters for the division-of-amplitude photopolarimeter,” Appl. Opt. 44(2), 190–196 (2005). [CrossRef] [PubMed]
- R. M. A. Azzam, A. G. Lopez, “Accurate calibration of the four-detector photopolarimeter with imperfect polarizing optical elements,” J. Opt. Soc. Am. A 6(10), 1513–1521 (1989). [CrossRef]
- A. V. Tikhonravov, M. K. Trubetskov, OptiLayer Software, http://www.optilayer.com .
- A. V. Tikhonravov, M. K. Trubetskov, G. W. Debell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35(28), 5493–5508 (1996). [CrossRef] [PubMed]

## 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.