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148 JOURNAL OF NETWORKS, VOL. 5, NO. 2, FEBRUARY 2010 Fig. 14. PER dependence on the MMF length for the combined optical and wireless link Fig. 15. The constellation and spectrum of the transmitted MB OFDM signal with a central frequency 6.6GHz may fall into the up-converted UWB signal spectrum and for this reason it cannot be singled out. This bandwidth overlapping limits the possibility of the up-conversion for a wide range of the UWB OFDM signal frequencies. On the contrary, in the case of the third order nonlinearity the distortion terms of the type 2fUWB + fLO and 2fLO + fUWB fall outside the UWB OFDM signal bandwidth. For this reason, it is possible to provide a much better performance of the up-conversion of a wide range of UWB signal frequencies fUWB by means of the third-order intermodulation. We used the UWB signal power of PUWB = −14dBm, the LO power of −5dBm, and the bias current of 3mA. The measured error-free constellation diagrams and undis- © 2010 ACADEMY PUBLISHER Fig. 16. The constellation and spectrum of the transmitted MB OFDM signal with a central frequency 7.128GHz torted spectra of the both up-converted UWB signals for TFC5, TFC6, and TFC7 bands with the central frequencies fUWB =6.6GHz and fUWB =7.128GHz, respectively, are shown in Figs. 15, 16. These results prove the feasibility of the proposed low cost all-optical up-conversion. VII. CONCLUSIONS In conclusion, we proposed two possible architectures for the high spectral efficiency optical transmission of OFDM UWB signals beyond 40Gb/s: the parallel RF/serial optics architecture and parallel RF/parallel optics architecture. We have carried out the numerical simulations for the parallel RF/parallel optics architecture and predicted its highly quality performance. We investigated theoretically and experimentally the optical link consisted of the directly modulated VCSEL, MMF, p-i-n PD and a wireless channel. We presented the detailed theoretical analysis and numerical results for a novel OCMC detecting device based on the SiGe/Si structure. We demonstrated experimentally the highly efficient and low cost all-optical up-conversion of UWB signals. VIII. ACKNOWLEDGEMENTS This work was supported in part by 1) The European Project UROOF-Photonic Components for UWB over Optical Fiber (IST-5-033615); 2) The Joint HIT-ECI DIAMOND Project supported by the Office of the Chief Scientist of the Israel Ministry of Industry. IX.
APPENDIX EVALUATION OF THE OPTICAL INTENSITY IN A THIN LAYER WITH ABSORPTION The boundary conditions for the electric and magnetic fields at the layer surfaces z =0and z = d yield [31]: z =0→ E + 1 + E− 1 = E+ 2 + E− 2 (46) 1 Z1 � E + 1 − E − 1 � = 1 Z2 � E + 2 − E − 2 z = d → E + 2 exp (−γ 2d)+E − 2 exp (γ 2d) 1 Z2 � (47) = E + 3 exp (−ik3d) (48) � E + 2 exp (−γ 2 d) − E − 2 exp (γ 2 d)� = 1 E Z3 + 3 exp (−ik3d) (49) We assume that the incident wave amplitude E + 1 Then, eliminating E − 1 and E+ 3 we obtain 1+ Z1Z3 Z 2 2 E + 2 is known. E = + 1 exp (γ � 2d) 1+ Z3 � Z2 � � � sinh (γ2d) + (Z1+Z3) � (50) cosh (γ Z2 2d) 1+ Z1Z3 Z 2 2 E − 2 E = − + 1 exp (−γ � 2d) 1 − Z3 � Z2 � � � sinh (γ2d) + (Z1+Z3) � (51) cosh (γ Z2 2d) Substituting (50) and (51) into (26) and (27) we obtain the expressions for the electric and magnetic field in the layer. = = − E + 2x E + 1 exp (−γ 2 (z − d)) � sinh (γ 2d) � 1+ Z1Z3 Z 2 2 (z, t) � 1+ Z3 � exp iωt Z2 � + (Z1+Z3) � (52) cosh (γ Z2 2d) E − 2x E + 1 exp (γ 2 (z − d)) � sinh (γ 2d) � 1+ Z1Z3 Z 2 2 (z, t) � 1 − Z3 � exp iωt Z2 � + (Z1+Z3) � (53) cosh (γ Z2 2d) H + 2y (z,t) =E+ 2x (z, t) ; H Z2 − 2y (z, t) =−E− 2x (z, t) (54) Z2 The time averaged total optical intensity Itot opt in the layer consists of the intensities 〈P + 〉 and 〈P − 〉 of the incident wave and reflected wave, respectively. It has the form [31] where JOURNAL OF NETWORKS, VOL. 5, NO. 2, FEBRUARY 2010 149 I tot opt (z) = � P +� + � P −� � + P � � 1 =Re 2 E+ 2x (z, t) � H + 2y (z,t)� � ∗ © 2010 ACADEMY PUBLISHER (55) ⎧ ⎪⎨ =Re ⎪⎩ 2Z ∗ 2 � � � + E � 1 2 exp [−2Re(γ2 )(z − d)] � � � �sinh (γ2d) 1+ Z1Z3 Z 2 2 � � � �1+ Z3 Z2 � � � 2 + (Z1+Z3)cosh(γ 2 d) Z2 � − P � � 1 =Re 2 E− 2x (z, t) � H − 2y (z, t)� ∗ � � � � 2 ⎫ ⎪⎬ ⎪⎭ (56) ⎧ ⎪⎨ =Re ⎪⎩ − � �E + � � 1 2 � � exp (2 Re (γ2 )(z − d)) �1 − Z3 � � � Z2 2 2Z∗ � � � 2 �sinh (γ2d) 1+ Z1Z3 Z2 � + 2 (Z1+Z3)cosh(γ2d) � � � Z2 2 ⎫ ⎪⎬ ⎪⎭ (57) Taking into account that according to (31) 2Re(γ2) = α and substituting (56) and (57) into (55) we finally obtain expression (32). II. APPENDIX EVALUATION OF THE PHOTOINDUCED CARRIER CONCENTRATION Substituting (32) into equation (43) we obtain g0 (z) =I01 sinh (α (z − d)) − I02 cosh (α (z − d)) (58) where I01 = ηα hν I0 2Z3 cos θ ; I02 = |Z2| ηα hν I0 � 1+ Z2 3 |Z2| 2 � (59) Typically, in the photoinduced plasma, the electron and hole relaxation time ∼ 10ns is much smaller than the carrier lifetime, and electroneutrality condition can be applied [22], [23], [34]. n = p (60) At the illuminated surface of the semiconductor the strong injection mode and ambipolar diffusion are realized when n ≫ n0,p0 and the ambipolar mobility µ a vanishes [20], [21] µ a = µ n µ p (p − n) =0 (61) µ pp + µ nn In our case the thin layer is entirely occupied by the strong injection mode region. Under such conditions continuity equations (38), (39) reduce to the ambipolar diffusion equation [34] ∂n ∂ = Da ∂t 2n n − + g (z, t) (62) ∂z2 τ where it is assumed that τ n = τ p = τ. According to expressions (42)-(44) we separate the steady-state and time dependent parts nph0 (z), n1 (z,t) of the photocarrier concentration n. n = nph0 (z)+n1 (z,t) (63) Substituting (63) into equation (62) we obtain two equations for nph0 (z) and n1 (z,t), respectively ∂ Da 2nph0 ∂z2 ∂n1 ∂t = Da nph0 − τ + g0 (z) =0 (64) ∂2n1 n1 − ∂z2 τ + g0 (z) f (t) (65)
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