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As laser technology is making rapid progress, novel protecting devices (optical limiters) are needed to protect optical sensors and human tissues from high power laser damages. An ideal passive optical limiter should have the following characteristics: (1) unity transmittance at low power input; (2) transmittance of the limiter decreases with increasing input power above the saturation level to maintain the maximum transmitted power level constant. It's also preferred that the saturation power of the limiter could easily be adjusted for different applications.
We propose a novel way of building optical limiter based on commercially available all-fiber devices. The proposed device is a double-loop Sagnac interferometer consisting of polarization maintaining (PM) fibers, fiber couplers, and polarization rotators (or waveplates) (Figure 1). This double-loop Sagnac interferometer can be considered as a nonlinear optical loop mirror (NOLM) embedded in another NOLM.
Figure1. Device setup
Optical limiting or switching property of the proposed device originates from self and cross phase modulations (SPM and XPM) due to the Kerr nonlinearity in the PM fibers, which induces nonlinear polarization rotation. We assume that only the PM fibers introduce nonlinear effects while fiber couplers and polarization rotators are linear devices at all input power levels. A direct way to describe the relationship between input and output light is using Jones matrix. The effect of a PM fiber on the incident light field can be expressed by a 2x2 matrix [ PM ],
where Ø is the orientation of the fiber, which is the angle between x-axis and the fast optical axis of the PM fiber, and
 ,
 ,
where ns and nf are refractive indexes along the slow axis and the fast axis of the fiber, and n2 is the nonlinear-index coefficient related to x(3) and Ix and Iy is the instantaneous intensities along x- and y-axis of the fibers. The four wave mixing or the polarization coupling term is ignored due to the large phase mismatching between the two polarization modes. A polarization rotator with rotation angle θ can also be expressed as a 2x2 matrix,
 .
The matrix of a 2x2 fiber coupler with cross power coupling ratio k is written as
 ,
where [ I ] is identity matrix, i is the unit of imaginary number. The fiber couplers used are 50/50 couplers, i.e., k= 0.5 in the following simulations.
The relationship between the output and input electric fields can thus be written as:
where [ E1IN ], [ E2IN ], [ E1OUT ] and [ E2OUT ] are 2-D column vectors which describe the input and output fields of port 1 and port 2 of the first fiber coupler, and [ E2IN ]=[0;0] if light is inputted only from port 1 of the first fiber coupler. Covert matrix [R] is defined as
since the folded fiber (PM fiber 3) flips x-axis component of the electric field.
The output of the device is defined as Iout = |E2OUT| 2 and the transmittance of the device can also be obtained as T=Iout /I in . We use the nonlinear refractive index of n 2 = 2.6x10 -16 cm 2 /W, which is typical for standard silicon fibers. The effective core area of the fiber is chosen to be 50 μm2.
When operated as an optical limiter at the wavelength of 1550 nm, the transmittance and output power as function of input power is shown in Figure 2. The onset of the optical limiting starts from the point of input power being about 1.8W, corresponding to an input intensity of about 3.6x10 6 W/cm 2 . When the input power changes from 1.8W to 3.6W, the output power is clamped to about 1.1W with small variation less than 0.1dB.
Figure 2. Transmission and output power vs. input power when operated as optical limiter
Saturation power can be easily adjusted by changing the lengths of the PM fibers and tuning the angles of the four rotators. Figure 3 shows the relationship between the total fiber length and the saturation power.
Figure 3. Saturation power vs. total fiber length
Properly chosen polarization conditions could make this device a good switch. As shown n in Figure 4, the transmittance of the device would go from nearly zero at low input power level (switch off) to nearly unity at an input power of about 60W (switch on). We can see that the switching contrast is almost 100%.
Figure 5. Filtering responses when operated as a switch
Reference:
Gang Chen and Jin U. Kang, “Nonlinear switching and optical limiting in a double-loop fibre Sagnac filter,” JOURNAL OF OPTICS A-PURE AND APPLIED OPTICS 6 (4): 361-371 APR 2004 |
