Analysis of Tilted Grating Etalon for DWDM Demultiplexer

Transcription

1 Analysis of Tilted Grating Etalon for DWDM Demultiplexer 71 Analysis of Tilted Grating Etalon for DWDM Demultiplexer Sommart Sang-Ngern, Non-member and Athikom Roeksabutr, Member ABSTRACT This paper theoretically analyses the characteristic of a Tilted Grating Etalon (TGE) in the first order coupled wave formalism for the consideration of DWDM (Dense Wavelength Division Multiplexing) demultiplexer. This theory could be used to investigate the characteristic of shifting Bragg wavelength on the effect of device structure parameters such as etalon thickness (L), refractive index (n), grating period (Λ), the angle between z axis and z axis (Φ) and the variation of incident angle. The results will be useful for consideration of device design as well as determination of the suitable operating conditions. riod, etalon thickness and the transmission spectral as the angle of incident wave (incident angle). 2. TILTED GRATING ETALON (TGE) In the order to understand the operating principle of the TGE, the characteristic of both tilted grating and FP needs to be reviewed in combination. Keywords: Tilted Grating Etalon, Bragg Grating, Etalon 1. INTRODUCTION In the recent years, the demand of bandwidth in optical network has been significantly increasing because of the growing of high-speed data communications. One system called DWDM has been improved in order to support all the bandwidth expansion. A tunable optical filter is a key device in such DWDM systems. Since the selective filters are one of the key components, many techniques have been researched. For examples they include, a Fiber Bragg Grating (FBG) [1]-[2], Fabry-Perot Ti-diffused LiNbO3 [3] and Tilted grating structure [4]. The latter one was first demonstrated in 1999 and it is one of our interesting topics. Fig. 1 illustrates the structure of the Tilted Grating Etalon (TGE) that is formed by Fabry-Perot etalon (FP) with tilted grating inside. In TGE, the direction is the propagation wave vector of grating inside the etalon. This direction of the period index modulation is not parallel to the -axis normal to the boundaries. The investigation of such a device when the internal angle of reflected light in the etalon is varied was reported in ref. [4]. However, it lacks of the intensive details. In this paper, we report the informative investigation on the characteristic of Tilted Grating Etalon (TGE) on the effect of other parameters such as the average refractive index, grating pe- EL5R4: Manuscript received on August 12, 24 ; revised on February 22, 25. The authors are with Optical Communication Research Lab Department of Telecommunication Engineering, Mahanakorn University of Technology 51 Cheum Sampan Rd., Nong Chok, Bangkok, Thailand 153 Tel: (662) EXT. 271, Fax: (662) , sommart@mut.ac.th. Fig.1: (TGE). The structure of Tilted Grating Etalon Let A, A 1 denote the slowly varying amplitude of incident (forward mode) wave and diffracted wave (backward mode), respectively. β bragg = π Λ is the Bragg wave vector, Λ is the grating period. The total field of the incident wave inside the tilted grating can be expressed as E(z) = E + forward + E backward (1) = A e [ iβz] + A 1 e [ i(β 2β bragg)z] Consider the same notation, the coupled-wave equations can be formed as [5] da dz da 1 dz = ika 1 (2) = 2iξA 1 + i KA K = K cos θ (3)

2 72 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.3, NO.1 FEBRUARY 25 K = πε ( ) si nλ 2nλ λ cos Φ nλ cos θ ( ) πλ(χ 1) nλ ξ = 2nΛ 2 λ cos Φ nλ cos θ (4) (5) χ = 2nΛ cos (Φ θ) (6) λ : ε si is dielectric permittivity of silica. (ε si = 1.5), n is average refractive index, θ is the internal angle, Φ is the angle between z axis and z axis, λ is wavelength, K is coupling coefficient for period grating seen at θ =. It is worth noting that the coupling between A and A 1 is not symmetrical which appears somewhat uncommon for a pure index coupling first order modulation. The transfer function in terms of transmission coefficient for the incident wave (T i ) in TGE can be found as: T i = Ω i exp ( iβ bragg L) Ω i cosh (Ω i L) + iξ i sinh (Ω i L) (7) In the same way, the transmission coefficient for the diffracted wave (T r ) can be found by replacing θ = θ in to equations (2)-(6). Finally, the expression of transmission coefficient for the diffracted wave (T r ) can be obtained as T r = Ω r exp ( iβ bragg L) Ω r cosh (Ω r L) + iξ r sinh (Ω r L) Ω i = Ω r = ( K K ξ 2 ) (8) (9) The TGE is described as a Fabry-Perot etalon modified by the internal tilted grating. The overall intensity transfer function of TGE can be derived by taking into account the transmission coefficient T i and T r. The calculation is therefore similar to that of the usual Airy function for a FP [6] except for the particular form taken here by internal losses. As a result, the intensity transfer function (Transmission spectral) can be written as T = Ψ = T 1 + Ψ sin 2 ( Φ 2 ) (1) 4R ref τ 2 (1 R ref τ 2 ) 2 (11) τ 2 = T i T r 2 (12) T = (1 R ref ) 2 T i 2 (1 R ref τ 2 ) 2 (13) R ref = [(n n )/(n + n )] 2 is the intensity reflection coefficient 3. THE CHARACTERISTICS OF TGE ON THE EFFECT OF DEVICE STRUCTURE To investigate the characteristic of the TGE, Equation (1) will be used with the variation of the physical parameters of the device. The simulation is performed as a function of wavelength to examine the effect of device structures such as etalon thickness (L), refractive index (n) of grating, and grating period (Λ). The initial practical parameter values used in this work are as follows [4]: the angle between z axis and z axis (Φ) is π 6, refractive index outside etalon (n ) is 1, average refractive index of grating (n) is 3.5, grating period (Λ) is 25 nm, internal angle (θ) is degree, and coupling coefficient for period grating K is 3 L 3. 1 Effect of etalon thickness (L).9 Influence of etalon (L) L= 3 um L= 35 um L= 4 um L= 45 um L= 5 um x 1-6 Fig.2: Relationship between the Transmission of TGE and the wavelength on the etalon effect (L). Fig.2 shows the transmission spectral of TGE as a function of wavelength in the range of nm when the etalon thickness is varied from 3 to 5 nm. The difference between peak and valley of transmission light is reduced as increasing etalon length and wavelength. The peak wavelength is finely either up-shifted or down-shifted as the free spectral range (FSR) seems to be reduced as the etalon length is increased. The etalon length does not have much effect on the finesse of the etalon such that the minimum output light cannot easily be suppressed Effect of average refractive index (n) Fig.3 shows the transmission spectral of TGE as average refractive index of grating in the etalon is varied from 3.5 to As can be seen from the figure, when increasing the index, the starting point of the first transmission optical peak is up-shifted. For example, for n = 3.56 the optical peak starts to transmitted at the wavelength of about 1569 nm but

3 Analysis of Tilted Grating Etalon for DWDM Demultiplexer 73 for n = 3.58, the first optical peak appears at the wavelength of about 1577 nm. Besides, the output light at the wavelength below this starting point is totally suppressed, i.e. no output light. This property is very interesting. If the appropriate refraction of grating is chosen, the desired wavelength in DWDM can be selected. It should be noted that the FSR of the etalon tends to be extended as the wavelength increases..9 Grating Period = 257 nm Grating Period = 256 nm Grating Period = 255 nm Grating Period = 254 nm Grating Period = 253 nm Influence of Grating Period.9 Influence of Refractive index (n) n = 3.5 n = 3.52 n = 3.54 n = 3.56 n = 3.58 x 1-6 Fig.4: Relationship between the Transmission of TGE and the wavelength on the grating period effect (Λ). x 1-6 Fig.3: Relationship between the Transmission of TGE and the wavelength on the average refractive index effect (n) Effect of grating period (Λ) Fig.4 shows the transmission spectral of TGE as grating period is varied from 253 to 257 nm. The property comes from the variation of grating period is similar to the previous. When increasing the grating period the starting point of the first transmission optical peak is up-shifted. For example, for Λ = 253 nm the optical peak starts to transmitted at the wavelength of about 1562 nm but for Λ = 257 nm, the first optical peak appears at the wavelength of about 1587 nm. As the grating period changes of 4 nm, the start transmission optical peak is up-shifted for about 25 nm. This implies that the optical signal in DWDM system can be finely selected by the variation of grating period. In comparison with the case of varying refractive index in which small index variation gives large range of start optical peak difference, the change in grating length gives more feasible in practical control of desired wavelength. 3.4 Effect of the angle between z axis and z axis (Φ) Fig.5 shows the transmission spectral of TGE as angle between z axis and z axis (Φ) is varied from 6 rad (26 o ) to 4 rad (31 o ). The property comes from the variation of the angle can be seen from the figure, when increasing the angle, the starting point of the first transmission optical peak is up-shifted. For example, for Φ = 6 rad the optical peak starts to transmitted at the wavelength of about 1585 nm, but for Φ = 7 rad, the optical peak appears at the wavelength of about 1572 nm, 1576 nm and 1586 nm, respectively. It should be noted that the FSR of the TGE tends to be extended as the wavelength is similar to the previous. By choosing appropriate angle of the TGE structure, the desired wavelength as in DWDM system. We also examined the transmission spectral as the angle of incident wave or incident angle. The result is interesting. Additionally, this paper will discuss the transmission spectral as the incident angle in section 4..9 the angle (z,z') = 4 rad. the angle (z,z') = 2 rad. the angle (z,z') = rad. the angle (z,z') = 8 rad. the angle (z,z') = 6 rad. Influnce of the angle (z,z') x 1-6 Fig.5: Relationship between the Transmission of TGE and the wavelength on the angle between z axis z and axis (Φ).

4 74 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.3, NO.1 FEBRUARY TRANSMISSION SPECTRAL AS THE ANGLE OF INCIDENT WAVE (INCI- DENT ANGLE) degree 1 degree x 1 6 x 1 6 (a) (b) 2 degree 3 degree x 1 6 x 1 6 Fig.6: The simulation model of transmission spectral as the incident angle. (c) (d) Fig.6 shows the simulation model for investigating the characteristic of TGE for the variation of the incident angle. The simulation is performed as a function of wavelength in the range of nm when the incident angle is varied from -5 degree. The physical parameter values used in this simulation are the etalon thickness is 25 um, grating period is 25 nm, average refractive index is 3.5, refractive index outside etalon is 1, the angle between z axis and z axis is 45 rad, internal angle is degree and coupling coefficient for period grating is /L. Fig.7 shows the transmission spectral of TGE as a function of wavelength in the range of nm when the incident angle is varied -5 degree. The TGE can act as a variable band stop wavelength as the incident angle varied. In Fig.7(a), the incident angle is degree which leads to the band stop (center bragg wavelength [7]) at the wavelength of about 1399 nm. As can be seen from the Fig.7(b) to Fig.7(f), when increasing the incident angle, the center bragg wavelength is up-shifted. For Fig.7(c) the center bragg wavelength at the wavelength of about 149 nm but for Fig.7(e) the center bragg wavelength at the wavelength of about 1557 nm. Furthermore, the relation between the center bragg wavelength and the incident angle is illustrated in Fig.8. Fig.8 shows the relationship between the center bragg wavelength of transmission of TGE shift and incident angle. In Fig.8, as the incident angle changes of 5 degree, the center bragg wavelength is up-shifted for about 23 nm. These results will be useful for the design and consideration of a wavelength demultiplexer in DWDM system. Fig.9 presents transmission spectral of the Fabry 4 degree x 1 6 (e) 5 degree x 1 6 Fig.7: Relationship between the transmission of TGE and wavelength on the incident angle: (a) degree, (b) 1 degree, (c) 2 degree, (d) 3 degree, (e) 4 degree and (f ) 5 degree Perot etalon without grating (general Fabry Perot) compared to that of TGE. The numerical parameters are the same as in section 3 except etalon thickness is 15 um. It can be seen from the figure that peak-to-valley ratio and FSR of general Fabry Perot transmission spectral are exactly constant. These results are the same as in theory of Fabry Perot etalon [8]. On another hand, peak-to-valley ratio and FSR of TGE transmission spectral are variable. For example, from wavelength of about 135 nm to about 148 nm, peak-to-valley ratio slightly increases. In the same wavelength duration, FSR slightly decreases. From wavelength of 155 nm to 16 nm peak-to-valley ratio trends decrease while FSR slightly increases. The transmission spectral is zero from wavelength of 148 nm to 155 nm. It could be seen from figures 2, 3, 4, 5, and 7 peakto-valley ratio and FSR of TGE transmission spectral are adjustable. These results indicate that it is pos- (f)

5 Analysis of Tilted Grating Etalon for DWDM Demultiplexer 75 Center Bragg Wavelength (nm) (degree) Fig.8: The relation between the center bragg wavelength and the incident angle. 1.9 Fabry Perot etalon without grating Tilted Grating Etalon (TGE) -6 x 1 Fig.9: The transmission spectral of Fabry Perot etalon without grating and TGE. sible to adjust the parameters to build grating etalon components for DWDM demultiplexers. 5. CONCLUSION The investigation of the characteristic of a Tilted Grating Etalon (TGE) on the effect of varying physical structures such as etalon thickness, average refractive index, grating period, the angle between axis and axis (grating angle) and incident angle, has been intensively reported. If the parameters of device structure are appropriately chosen, the device can be used as the DWDM demultiplexer for photonic networks or optical communication systems. The same scheme can also be applied to spectral filtering in Integrated Optoelectronics (IO). This proposed structure can perform narrow channel spacing, which can be a promising candidate for DWDM system. In addition, it is possible to build grating etalon components by placing acoustic waves into the etalon area of Fabry Perot etalon. References [1] L. R. Chen, Design of flat-top bandpass filters based on symmetric multiple phase-shifted longperiod fiber gerating, Opt. Commun., vol.25, pp , May 22. [2] C. S. Goh, S. Y. Set and K. Kikuchi, Widely Tunable Optical Filters Based on Fiber Bragg Grating, IEEE Photon. Technol. Lett., vol.14, pp , Sep. 22. [3] T. Saito, Y. Endo, M. Yamamoto, K. Oyamada, Study on Fabry-Perot Ti-diffused LiNbO 3 optical waveguide filter, Technical Report of IEICE, pp.7-11, July [4] Y. Boucher, T.Fessant, A. V. Uskov, Angular and spectral filtering in tilted-grating structures, IEE Proc. Optoelectronics, vol.146, pp.35-38, Feb [5] T. K. Gaylord, M. G. Moharam, Analysis and application of optical diffraction by grating, Proc. IEEE, vol.73, no.5, pp , [6] Ammon Yariv, Optical Electronics, 3 rd Edition., pp.88-95, CBS College Publishing, [7] K. O. Hill, G. Meltz, Fiber Bragg Grating Technology Fundamentals and Overview, J. Lightwave Technol., vol.15, pp , [8] E. Hecht, Optics, 3 rd Edition., pp , Addison Wesley, Sommart Sang-Ngern received the B.Eng. and M.Eng. degrees in Electrical Engineering (Telecommunication) from Mahanakorn University of Technology, Bangkok, Thailand, in 1997 and 21, respectively. He is currently the lecturer of Department of Telecommunication Engineering at Mahanakorn University of Technology. His research interests cover fiber optic component, fiber bragg grating (FBG), optical ring resonator, and nonlinear optics. Athikom Roeksabutr received the B.Eng. degree from King Mongkut s Institute of Technology, Ladkrabang, Thailand, in 1984, the M.S. (Electrical) degree from the Florida Institute of Technology, Melbourne, FL, USA, in 1989, and the Ph.D. degree from the school of Electrical Engineering, University of New South Wales, Australia, in Currently he is Vice-president and Dean of Faculty of Engineering at Mahanakorn University of Technology. His research interests cover fiber optic component, optical communication system, and acousto-optic fiber devices.