On the basis of the input-output intensity relationship of the signal, this paper will evaluate and discuss the role of the position of the signal going into the Nonlinear Michelson Interferometer (NMI) and its influence on the bistable characteristics. From that results, the position of signal going into the NMI will be chosen, so that the interferometer acts as an optical bistability device.
Nghiên cứu khoa học công nghệ INFLUENCE OF THE POSITION OF INPUT SIGNAL on the BISTABILITY CHARACTERISTIC OF NONLINEAR MICHELSON INTERFEROMETER Nguyen Manh An Abstract: On the basis of the input-output intensity relationship of the signal, this paper will evaluate and discuss the role of the position of the signal going into the Nonlinear Michelson Interferometer (NMI) and its influence on the bistable characteristics From that results, the position of signal going into the NMI will be chosen, so that the interferometer acts as an optical bistability device Keywords: Bitstable device, Nonlinear Michelson interferometer INTRODUTION In recent years there have been many research works on the bistability characteristics of NMI [3, 4, 5, 6, 7]; in the work that the authors have confirmed if select the appropriate parameters, the input-output relationship of signal intensity through NMI will have bistability characteristic; same time, the authors also pay much attention to the role of the reflectivity of the mirrors, the transmission coefficient of the splitter, the absorption coefficient and the initial phase was how to influence that relationship; however we found that the position of input signal also play a big role, have much influence on characteristics of the input-output relationship of the signal In this work we will present the input-output relationship of the signal intensity transmitted through the interferometer and discuss the role of position of signal in bistability characteristics of NMI OUTPUT-INPUT RELATION OF INTENSITIES Nonlinear Michelson interferometer is constructed as shown in Figure It consists of four mirrors M1, M2, M3 and M4 are the corresponding reflection coefficients R1, R2, R3, R4 = 100% = 100% placed perpendicular to each other in pairs: M1 M2, M2 M3, M3 M4, M4 M1 Fig.1 Nonlinear Michelson Interferometer Tạp chí Nghiên cứu KH&CN Quân sù, Sè 29, 02-2014 99 VËt lý The splitter P with transmission through coefficient is T=50% divides the space between the mirrors into two equal parts, the space after the split P is a nonlinear medium with absorption coefficient and refractive index obeying optical Kerr effect n=n0+n2Ictr, where n0 is the linear refractivity, n2 is the nonlinear coefficient, directly relating to third-order susceptibility (3) (electrostatic unit) by the relation 4 Re 3 [2]: n and Ictr is the average intensity of light transmitted through cn0 non-linear medium is called control intensity) Assume that the light travels to mirror M1 with field amplitude E0 A0 ei (t ) equivalent to the intensity I 0cE02 after that passes through and go out NMI from two mirrors M1, M2: + The light go out NMI from mirror M2 will be intensity is: (1 R1 )(1 R2 )e L1 2L2 I out e 2e L2 cos 2( ) I (1) 4MS With: MS R1 e L2 cos 2( ) R2 e 2L2 cos 2( ) R1 cos 2( ) R2 e L1 cos 2( ) R1e 2L2 R2 e 4L2 R1 R2 e 2L1 R1 R2 e 3L2 cos 2( ) (2) R1e L2 cos 2( ) R1 R2 e ( L1 L2 ) cos 2( ) R1 R2 e 2L2 cos 2( ) R2 e ( L1 2 L2 ) cos 2( ) R1 R2 e L1 cos 2( ) 1 3 I ctr 2n L 2 n L I ctr , (3) 2 I ctr , (5) 4 R2 I out , (1 R ) 2 L2 , 2 L1 , (4) (6) (7) Here, α is the absorption coefficient of the nonlinear medium, λ is wavelength of light, L1 is the transmission distance from mirror M1 to the split P, L2 is the , transmission distance from the split P to mirror M2 L=L1+L2, is the phase shift of light caused by the device is called the initial phase + The light go out NMI from mirror M1 will be intensity is: (1 R1 ) e L1 2L2 IR e 2e L2 cos 2( ) I (8) 4MS With MS, 1 is calculated according to the formula (2), (3) and (4) 100 N M An, "Influence of the position nonlinear Michelson interferometer " Nghiên cứu khoa học công nghÖ INFLUENCE OF THE POSITION OF INPUT SIGNAL ON BISTABILITY CHARACTERISTICS OF NMI To evaluate the role of the position of the input signal in the input-output relations of NMI, we will examine the equations (1) and (8) with the control parameter, I0 (input intensity), the splitting parameters (R1, R2, α, λ, n2, φ0) is fixed while the position signal input (L1 and L2) will change Also, for simplicity we choose L / and L / is the integer; this it can be easy to because the Li in order of mm, λ in orderr of μm or smaller So δ2 and δ4 as shown in the formula (4) and (6) is an integer times of 2π Then in the formula of MS, Ictr, Iout contains the function cos then values δ2 and δ4 can be ignored Then the formula (1) and (8) is very much simplified In addition, (7) can be rewritten as follows: R2 (9) I ctr e L1 I R (1 R1 ) 3.1 The light go out NMI from mirror M2 -4 With α=1000, λ=1μm, n2=10 (cm /w), R1=0.1, R2=0.5; while L1 changes to the values L1 = 0.4, 0.45, 0.5, 0.55, 0.6 mm the equation (1) for bistability curves as shown in Figure (the blue curve corresponds to the L1 = 0.4mm, the red curve corresponds to the L1 = 0.45mm, the pink curve corresponds to L1 = 0.5mm, the green curve corresponds to the curve L1 = 0.55mm and black corresponds to L1 = 0.6) It shows that NMI acts as a optical bistability device From the Fig.2, we can see that bistability characteristics of the NMI clearly depends on L1: The state transition threshold (Ion, Ioff ) and the distance between them (Ion - Ioff) are increases with L1 This demonstrates that the switching speed of the device is as high as the smaller L1 and when it does not need high intensity, the Fig Bistability characteristics of NMI (when the light comes out from the mirror M2) with device can also be moved -4 φ 0=-0.175π, α=1000, λ=1μm, n2=10 (cm /w), from the closed state to the open state L1 reduction will R1=0.1, R2=0.5; while L1 changes to the values L1 = 0.4, 0.45, 0.5, 0.55, 0.6 mm drag (Ion-Ioff) decreased, while L1=0.3 Ion is almost identical to Ioff (as shown by the purple curve in Figure 3) When L1