Quarter wave retarders for optical communications

M.A. Habli Computer & Communication Engineering

Department Lebanese International University

P.O. Box 146404 Mazraa Beirut, Lebanon

E-mail:mohamad.habli@liu.edu.lb

I. ElSayad Computer & Communication Engineering

Department Lebanese International University

P.O. Box 146404 Mazraa Beirut, Lebanon

E-mail:ismail.sayad@liu.edu.lb ABSTARCT This paper presents the design of quarter-wave retarders for the C and the L bands using two perpendicular reflective metals coated with a single layer thin film. The overall reflection of 81% is achieved for the quarter-wave retarder. Keywords: Phase retardance,

perpendicular metals, C-band, L-band,

single-layer coating.

INTRODUCTION Phase retarders are optical devices that can produce a relative phase shift between two orthogonally polarized components without affecting their relative amplitudes. These devices can be used in optical communication as optical rotary dispersion and wave separation. A number of interesting work addressed quarter-wave retarders that can operate in certain region of the light spectrum [1-8]. In this paper, quarter-wave retarders are designed to operate in the C-band (λ=1520nm; 0.82 ev) and the L-band (λ=1620nm; 0.77 ev), such frequencies are of special interest in optical communications especially for DWDM. Half-wave retardance can be accomplished by using two consecutive quarter wave retarders. PROBLEM STATMENT Consider the device in Fig.1, which consists of two perpendicular reflected metals.

Fig. 1. Retro-reflective quarter wave retarder (RRQWR). M1 is placed so that a horizontal input beam makes an angle of incident φ1=85o with it. The polarization reflection coefficient ρr is given in equation 1.

sprrr RRj /)exp( =Δ= ρρ (1)

Where Rp and Rs, are the parallel and perpendicular reflectance to the plane of incidence, respectively and they are given in equation 2.

)1/()( 12011201 XrrXrrR vvvvv ++= (2) where, rijv are the Fresnel reflection coefficients [12] of the ij interface for the v plarization (v=p or s), and X=exp(-j2πζ) (3) where ζ is the normalized thickness of the film and it is given in equation 4, ζ=d/Dφ, (4) and Dφ=(λ/2)(N1*N1 - sin2φ) -1/2 (5)

Φ1

M1

M2

Light in

Light out

978-1-4673-5820-0/13/$31.00 ©2013 IEEE

The total polarization reflection coefficient

ρrT of the device is given by eq. 6.

)/(*)/(* 221121 spsprrrT RRRR== ρρρ

(6)

where ρr1 and ρr2 are the polarization reflection coefficients due to the reflection of light from M1 and M2 respectively. The total Fresnel coefficient rTρ can be expressed as the following function F:

rTρ = F (N0, N1, ζ1 , N11 , ζ11, N2 , φ) (7)

Where N0=1 is the air index of refraction, N1 and ζ1, are the index of refraction and the normalized thickness of the coating of M1. N11 and ζ11 are the index of refraction and the normalized thickness of the coating of M2. N2 is the index of refraction of the substrate of the metal and φ is the angle of incident.

rTρ is a complex number and by setting its amplitude | rTρ |=1 and its phase Δr= π/2, one can iterate on the two film refractive indices N1 and N11 and their corresponding normalized thicknesses ζ1 and ζ11, respectively, to satisfy the condition for a specific φ and N2. In this paper gold (Au) metals is used. In the C-band and the L-band, the refractive indices for the Au are 0.37-j10.54 and 0.41-j11.24 respectively, [8,9]. RESULTS Setting | rTρ |=1, Δr= π/2, φ1=85o, φ2=5o, N0=1, and N2 as specified in the previous section, in eq. 7, we iterated on N1 and N11 and their corresponding normalized thicknesses ζ1 and ζ11 respectively, and found the values that satisfy eq. 7. Figs. 2 and 3 show 32 different design cases for the device in the C-band. Fig. 2 shows the values of N1 and N11 and Fig. 3 shows the values of ζ1 and ζ11.

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Different design cases

N1

and

N11

Series1 Series2

Fig. 2. N1 and N11 values for different design cases for the C-band.

0.05

0.15

0.25

0.35

0.45

0.55

0.65

0.75

0.85

0.95

1.05

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Different design cases

Z1 a

nd Z

11

Series1 Series2

Fig. 3. ζ1 and ζ11 values for different design cases for the C-band. Fig. 4 shows the total reflectance coefficient R for the device for all 32 different cases. From Fig. 4 the reflectance coefficient R ranges between 30% and 81%. Figs. 5 and 6 show 29 different design cases for the device in the L-band.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Different design cases

R

Fig. 4. Total reflectance R for different design cases for the C-band.

1

1.5

2

2.5

3

3.5

4

4.5

5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Different design cases

N1

and

N11

Series1 Series2

Fig. 5. N1 and N11 values for different design cases for the L-band.

0.05

0.15

0.25

0.35

0.45

0.55

0.65

0.75

0.85

0.95

1.05

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Different design cases

Z1 a

nd Z

11

Series1 Series2

Fig. 6. ζ1 and ζ11 values for different design cases for the L-band. From the obtained results, one can find suitable materials for the thin films for the C and the L-bands. In this paper two thin films ZnTe and SrFe are used in the device. Their indices, their indices of refractions in the L-band are 2.73 and 1.43 respectively [11,12]. Table 1, shows the characteristics for the device in the L-band. The table shows the amplitude and the phase of the total polarization coefficient upon reflection from the device, | rTρ | and Δr respectively, the normalized thin film thickness of the layers for M1 and M2, ζ1 and ζ11 respectively, and the total reflection of the device, RT.

Table 1. Summary of the device characteristics using ZnTe and SrF2 thin films coating on M1 and M2 respectively for L-band. | rTρ | Δr ζ1 ζ11 RT

1.000 90.00

0.3978

0.0935

0.8106

ERROR ANALYSIS Table 2, shows the effect of applying error to the device. The first row in Table 2 shows the results with no error applied. The second row shows a change of one degree in the angle of incident. As shown from the table, the phase shift increased to 110.15o. The third row shows a 5% change on the actual thin film thickness d1. Such an error changed the phase shift from 90o to 134.38o. In addition, the amplitude of the polarization coefficient rTρ has increased from 1.00 to 1.171. The last row in the table shows the results for 5% change on d1 & d11 the two actual thin film thicknesses of the of M1 and M2 layers, respectively. This modification changed the phase shift to 132.27o. Table 2. Summary of error analysis for the device in table 1. | rTρ | Δr (o) ζ1 ζ11 RT

No error

1.000 90.00 0.3978 0.0935 0.8106

φ1 =84o 1.006 110.15 0.3978 0.0935 0.7409 +5% on d1

1.171 134.38 0.4177 0.0935 0.5973

+5% on d1 & d11

1.17 132.27 0.4177 0.0982 0.6022

CONCLUSIONS Quarter-wave retarder that operates in the C and L-bands is presented. The designed device has an overall reflection of 81%. Error analysis shows that a one degree change in the angle of incident will cause a phase shift of 110.15o. It also shows that a 5% change on the actual thin film thicknesses of the M1 and M2 layers will change the phase shift to 132.27o. REFERENCES [1] Habli, MA. ,” Phase Retarders for dense wave division multiplexing using two parallel mirrors coated with single layer thin film“, Optik, Vol 120, Issue 2, 2009, 79-84.

[2] Chakraborty, B.,” Effect of chromaticity on quarter-wave retarder performance “, Optik 116 (1), p.p. 10-14, 2005. [3] Hariharan, P., Ciddor, P.E., “Broad-band superachromatic retarders and circular polarizers for the UV, visible and near infrared “J. of Modern Optics, 51 (15), p.p. 2315-2322, 2004. [4] Azzam, RMA, Spinu, C.L., “Achromatic angle-insensitive infrared quarter-wave retarder based on total internal reflection at the Si-SiO2 interface “ J. Of the optical society of America, A: Optics & image science and vision, 21 (10) p.p. 2019-2022, 2004. [5] Azzam, RMA, Mahmoud, FA, “Symmetrically coated pellicle beam splitters for dual quarter-wave retardation in reflection and transmission “, Applied Optics, 41 (1) p.p. 235-238, 2002. [6] Lee, J., Rovira, P., An, I., and Collins, R. “Alignment and calibration of the MgF2 biplate compensator for applications in rotating-compensator multichannel ellipsometry “, JOSA, Vol. 21, Issue 8 Page 1980, 2001. [7] Nagib, N. “Phase retardometer: A proposed device for measuring phase retardance “, Applied Optics, Vol. 39, Issue 13 Page 2078, 2000

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