Quarter wave retarders for Dense Wave Division Multiplexing M.A. Habli Electrical & Computer Engineering Department Sultan Qaboos University P.O. Box 33 Muscat 123, Oman Email:Mhabli@squ.edu.om ABSTARCT The design of quarter-wave retarders for the Dense Wave Division Multiplexing using parallel mirrors coated with a single layer is presented. The output light from the device is parallel to the input light and it is displaced by a distance d. The quarter wave retarder overall reflection was in the range of 83%. Error analysis on the design is conducted. The error analysis shows how changes on the angle of incident and the thin film thicknesses effect the design of the retarders. Keywords: Phase retardance, parallel mirrors, C-band, L-band, single layer coating. 1. INTRODUCTION Phase retarders are very essential for optical communication especially for Wave Division Multiplexing (WDM) and Dense Wave Division Multiplexing (DWDM). The frequencies that are usually used in optical communication are in the infrared and far infrared regions. The C-band (1520nm) and the L-band (1620nm) are two frequencies of special interest in optical communication especially for DWDM. In this paper quarter wave phase retarders are designed that can operate in C-band and L-band regions. There has always been an interest in phase retardance and specially in quarter wave. Recently there has been a number of interesting work that addressed quarter wave retarders that can operate in certain region of the light spectrum[1-7]. In this paper, quarter wave retarders are designed using two parallel mirrors, both mirrors are coated with a single layer. The retarders are designed to operate in the C-band and the L-band. Half wave retardance can be accomplished by using two consecutive quarter wave retarders. 2. PROBLEM STATMENT Consider the device in Fig.1. This device consists of two parallel mirrors that are mounted on light metal base. The input and output light from the device are parallel to each other. Both the input and the output light are horizontal and the output is displaced Optical Components and Materials IV, edited by Shibin Jiang, Michel J. F. Digonnet, Proc. of SPIE Vol. 6469, 64690Z, (2007) 0277-786X/07/$18 doi: 10.1117/12.697024 Proc. of SPIE Vol. 6469 64690Z-1
by a distance d. The mirrors are placed in such a way that the input beam makes an angle of incident φ=85 o with M1. The polarization reflection coefficient ρ r due to the change of the polarization of light upon reflection is given by the ratio of the complex amplitude reflectance s R p and R s, which are the parallel and perpendicular to the plane of incidence, the p and s linear polarizations, respectively: ρ = ρ exp( j ) = R / R (1) r r r p s Therefore, the total polarization reflection coefficient ρ rt of the device is given by eq. 2. ρ = ρ ρ (2) rt r1 * r 2 Where ρ r1 and ρ r2 are the polarization reflection coefficients due to the change of polarization upon the reflection of the light from M1 and M2, the first and the second mirror respectively. Using the Fresnel coefficients, ρ can also be expressed as a rt function of: ρ = F (N rt 0, N 1, ζ 1, N 11, ζ 11, N 2, φ) (3) where N 0 =1 for air index of refraction, N 1 and ζ 1, are the index of refraction and the normalized thickness of the thin film layer of M1. N 11 and ζ 11 are the index of refraction and the normalized thickness of the thin film layer of M2. N 2 is the index of refraction of the substrate of the mirror and φ is the angle of incident. By setting ρ =1 and rt r = π/2 in eq. 1 and equating it with the function in eq. 3, one can iterate on the two film refractive indices and their corresponding normalized thicknesses ζ 1 and ζ 11 respectively, to satisfy the condition for a specific φ and N 2. Two materials for the mirrors substrate are considered in this paper which are silver (Ag) and gold (Au). In the C-band the refractive indices for the Ag and Au are 0.46-j9.13 and 0.37-j10.54, respectively[8]. In the L-band the refractive indices for the Ag and Au are 0.5-j9.77 and 0.41-j11.24, respectively [8]. Proc. of SPIE Vol. 6469 64690Z-2
Light IN M1 φ M2 d Light OUT Fig. 1. Parallel mirror quarter wave retarder (PMQWR). 3. RESULTS Table 1&2, summarizes the first set of results for the designed quarter wave retarders. All tables in this section show the amplitude and the phase of the overall polarization coefficient upon reflection from M1 and M2, ρ and rt r respectively. It also shows the normalized thin film thickness of the layers for M1 and M2, ζ 1 and ζ 11 respectively. Finally it shows the overall reflection of the device, R T. In the first set of results that is shown in Table 1, both M1 and M2 were silver (Ag), and the film used on both M1 and M2 was sodium fluoride (NaF). The indices of refractions for NaF in the C-band and the L-band are 1.31932 and 1.31899 respectively [10]. Table 2, shows the results for Gold substrate for both M1 and M2, the film used in Table 2, is also NaF for both M1 and M2. Table 1. Summary of the device characteristics for Gold mirrors and NaF thin film coating on both mirrors Substrate index of refraction for M1 and M2 N 2 =0.46-j9.13 for Ag N 1 =N 11 =1.31932 for NaF N 2 =0.5-j9.77 for Ag N 1 =N 11 =1.31899 for NaF 1.000 90.00 0.0993 0.4023 0.8352 1.000 90.00 0.1045 0.404 0.8359 Proc. of SPIE Vol. 6469 64690Z-3
Table 2. Summary of the device characteristics for Silver mirrors and NaF thin film coating on both mirrors Substrate index of refraction for M1 and M2 N 2 =0.37-j10.54 for Au N 1 =N 11 =1.31932 for NaF N 2 =0.41-j11.24 for Au N 1 =N 11 =1.31899 for NaF 1.000 90.00 0.1129 0.4066 0.840 1.000 90.00 0.1135 0.4069 0.841 Another set of results is shown in Tables 3 and 4. In Table 3, both M1 and M2 were silver (Ag), and the films used on M1 and M2 in the C-band were Indium Phosphide (InP) and Calcium fluoride (CaF 2 ) respectively. The indices of refraction for the InP and CaF 2 in the C-band are 3.151 and 1.42616 respectively [9,10]. For the L-band the films used on M1 and M2 were Silicon (Si) and Barium fluoride (BaF 2 ) respectively. The indices of refraction for the Si and BaF 2 in the L-band are 3.5 and 1.46581 respectively [8,9].Table 4, shows the results for Gold substrate for both M1 and M2, the films used on M1 and M2 in the C-band were Galium Aresinide (GaAs) and Barium fluoride (BaF 2 ) respectively. The indices of refraction for the GaAs and BaF 2 in the C-band are 3.377 and 1.46615 respectively [9,10]. For the L-band the films used on M1 and M2 were Silicon monoxide (SiO) and Sodium fluoride (NaF) respectively. The indices of refraction for the SiO and NaF in the L-band are 1.848 and 1.31899 respectively [9]. Table 3. Summary of the device characteristics for Gold mirror using InP and CaF2 thin film coating on M1 and M2 respectively for C-band and Si and CaF2 thin film coating on M1 and M2 respectively for L-band. Substrate index of refraction for M1 and M2 N 2 =0.46-j9.13 for Ag N 1 =3.151 For InP N 11 =1.42616 for CaF 2 N 2 =0.5-j9.77 for Ag N 1 = 3.5 For Si N 11 =1.46581 for BaF 2 1.000 90.00 0.1154 0.4055 0.831 1.000 90.00 0.1256 0.4083 0.831 Proc. of SPIE Vol. 6469 64690Z-4
Table 4. Summary of the device characteristics for silver mirrors using GaAs and BaF 2 thin film coating on M1 and M2 respectively for C-band and SiO and NaF thin film coating on M1 and M2 respectively for L-band. Substrate index of refraction for M1 and M2 N 2 =0.37-j10.54 for Au N 1 =3.377 For GaAs N 11 =1.46615 for BaF 2 N 2 =0.41-j11.24 for Au N 1 =1.848 SiO N 11 =1.31899 for NaF 1.000 90.00 0.1302 0.4102 0.839 1.000 90.00 0.1177 0.4087 0.839 4. ERROR ANALYSIS Error analysis for the quarter wave device was conducted. Table 5, shows the error analysis s results for the device shown in Table 1 for the C-band. The first row in Table 5 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 105.82 o. The third row shows a 5% change on the actual thin film thickness d 1 of the M1 layer. The actual thin film thickness d is found from the normalized thin film thickness, ζ [11]. Such an error has changed the phase shift slightly to 90.92 o. The last row in the table shows the results for 5% change on d1 & d 11 the actual thin film thicknesses of the of M1 and M2 layers, respectively. This modification changed the phase shift to 81.42 o. Table 5 rt r ( o ) ζ 1 ζ 11 R T No error 1.000 90.00 0.0993 0.4023 0.835 φ =84 o 1.000 105.82 0.0993 0.4023 0.781 5% on d 1 1.000 90.92 0.094335 0.4023 0.833 5% on d 1 & d 11 0.994 81.42 0.094335 0.382185 0.866 Proc. of SPIE Vol. 6469 64690Z-5
5. CONCLUSIONS The design of quarter wave retarders using two parallel mirrors coated with single layer that can operate on C-band and L-band is presented. Two kinds of substrates for the mirrors are considered in this paper, which are silver (Ag) and Gold (Au). The designed devices have an overall reflection of 83%. The output light from the device is parallel to the input light and it is displaced by a distance d. The displacement distance d can be changed to any desire displacement by changing the distance between the two parallel mirrors. An error analysis for the device design was conducted. The error analysis shows that a one degree change in the angle of incident will cause a phase shift of 105.82 o. It also shows that a 5% change on the actual thin film thicknesses of the M1 and M2 layers will cause a phase shift of 81.42 o. 6. REFERENCES 1. Chalraborty, B., Optik 116 (1), p.p. 10-14, 2005. 2. Hariharan, P., Ciddor, P.E., J. of Modern Optics, 51 (15), p.p. 2315-2322, 2004. 3. Azzam, RMA, Spinu, C.L., J. Of the optical society of America, A: Optics & image science and vision, 21 (10) p.p. 2019-2022, 2004. 4. Azzam, RMA, Mahmoud, FA, Applied Optics, 41 (1) p.p. 235-238, 2002. 5. J. Lee, P. Rovira, I An, and R Collins, JOSA, Vol. 21, Issue 8 Page 1980, 2001. 6. N Nagib, Applied Optics, Vol. 39, Issue 13 Page 2078, 2000 7. I Hodgkinson and Q Wu, Applied Optics, Vol. 39, Issue 16 Page 3621, 1999. 8. M. A. Ordal, L. L. et al, Appl. Opt., Vol. 22, No. 7, 1 April 1983, pp. 1099-1119. 9. E. D. Palik, Academic Press, 1985. 10. W. J. Tropf, Opt. Eng., Vol. 34, No. 5, May 1995, pp. 1369-1373. 11. R.M.A. Azzam and M.A. Habli, Optics communications, Vol. 78, number 5,6, page 315, Proc. of SPIE Vol. 6469 64690Z-6