In a SinglyResonantOpticalParametricOscillator, the cavity mirrors are highly reﬂecting for only one of the generated waves, most commonly the signal. The ﬁrst experimental report of an SROPO was by Bjorkholm , and in a subsequent paper  the superior stability of SROs as opposed to DROs was demonstrated. This eﬀect is explained in terms of the axial mode spacings of the two diﬀerent ﬁelds. The signal and idler modes in general, have unequal axial mode spacings and hence simultaneous resonance can only be achieved on certain axial modes which are clustered in groups, separated by a spacing period which is large compared with the axial mode spacing. This cluster eﬀect gives rise to the tuning discontinuities and instability with respect to ﬂuctuations in the oscillator parameters, which are observed in DROs. SROs do not experience the cluster eﬀect and the various problems associated with it. Continuous tunability and stability are an issue in the design of an OPO as a light source for resonant infrared pulsed laser deposition, and hence the current project will involve the design of an SRO for this particular application. The following subsections will examine the theory of SROs, speciﬁcally that regarding the threshold power and conversion eﬃciency. The theory of DROs will be omitted.
One of the disadvantages of OPOs as sources of tunable radiation is the broad linewidth that is generally emitted. Normally there will be a large number of signal and idler axial modes that fall under this wide gain bandwidth. An early theoretical study by FCreuzer  showed that under steady state conditions, a singlyresonantoscillator pumped at up to ~ 4.8 times threshold will operate on a single axial mode due to the gain saturation which is a result of pump depletion. In pulsed operation these steady state conditions are rarely reached and there fore a line na rrowing element of some description is required to achieve the narrow linewidths that are required for some applicatio ns. Methods of achieving single axial mode operatio n usually consist of insertion of intra-cavity elements such as étalons  or diffraction gratings . The insertion of any additional elements into the cavity increases the threshold due to losses of the line narrowing element itself, and also the increased build-up time losses with the required increase in cavity length. An alternative is to injection seed the OPO which requires an additional tunable source of narrow linewidth. An elegant way to achieve this is to use one laser to pump two OPOs, one of which is a narrow linewidth master oscillator which seeds the other, a high power slave oscillator or amplifier . The spectral properties exhibited in this work suggest a possible way of achieving narrow linewidth without the insertion of additional cavity elements, or the requirement of an additional source for a seeder.
We address this limitation by employing a novel bi-directional pump geometry for a singlyresonant synchronously pumped ultra-short pulsed OPO. Instead of employing a conventional single-pass geometry, by simultaneously synchronizing a „forward‟ pump pulse and a second counter-propagating pulse in the „reverse‟ direction together with the circulating signal pulse, the signal electric field amplitude experiences gain in both directions and hence the resulting average output power scales nonlinearly with the overall input pump power. By ensuring only one pump pulse with an intensity level below the damage threshold intensity is present in the nonlinear crystal at any given time, this technique permits a total pump intensity of up to twice the damage threshold intensity, without incurring damage. As a consequence, the crystal damage threshold intensity conditions can be relaxed and the average and peak output powers of the OPO can be significantly increased
Abstract: In this paper, the new concept of Nonlinear Output Frequency Response Functions (NOFRFs) is extended to the harmonic input case, an input-independent relationship is found between the NOFRFs and the Generalized Frequency Response Functions (GFRFs). This relationship can greatly simplify the application of the NOFRFs. Then, beginning with the demonstration that a bilinear oscillator can be approximated using a polynomial type nonlinear oscillator, the NOFRFs are used to analyze the energy transfer phenomenon of bilinear oscillators in the frequency domain. The analysis provides insight into how new frequency generation can occur using bilinear oscillators and how the sub-resonances occur for the bilinear oscillators, and reveals that it is the resonant frequencies of the NOFRFs that dominate the occurrence of this well-known nonlinear behaviour. The results are of significance for the design and fault diagnosis of mechanical systems and structures which can be described by a bilinear oscillator model. 1 Introduction
A one-mode sub-harmonic generator is one of the most interesting and well-studied quantum optical systems. This system consists of a nonlinear crystal which is pumped by coherent light and placed inside a cavity coupled to a vacuum reservoir. This quantum optical process leads to the generation of squeezed light. A theoretical analysis of the quadrature squeezing and photon statistics of a signal mode produced by a one-mode sub-har- monic generator has been made by a number of authors -. It has been established that the signal mode has a maximum of 50% squeezing below the coherent-state level -.
in the SROPO below threshold and that the maximum noise reduction below the standard quantum limit is the same at the signal and idler frequencies in a similar way to the doubly-resonant case. As the threshold of oscillation is approached, however, the intensity-difference and quadra- ture spectra display a progressive line-narrowing which is absent in the balanced doubly-resonant case. One of the reasons for the lack of squeezing experiments in SROPOs is that they operate with strongly non-degenerate frequen- cies (two-colours). Since the observation of non-classical correlations in the strongly non-degenerate regime of para- metric down-conversion , however, investigations of quan- tum entanglement in SROPO have gained relevance be- cause of possible optimisation of coherent sources with fluctuations below the shot-noise level. Moreover, SRO- POs have clear technical advantages over doubly-resonant configurations such as continuous temperature tuning and suppression of mode-hopping. It is the aim of this work to compare the analytic results of  for the squeezing and entanglement properties of SROPOs with a numeri- cal analysis of both the linear and nonlinear regimes ap- proaching threshold. In the nonlinear case we observe a progressive reduction of squeezing and quantum entangle- ment while the novel feature of SROPO of narrowing of the spectral line survives although it is reduced while ap- proaching the threshold of oscillation.
Parametric oscillation requires a significant electromag- netic response at the wave vectors and frequencies of the signal and idler. Thus the signal and idler must lie near the polariton dispersion. The signal and idler must also satisfy the requirements of wavevector and frequency conservation in the generation process. In the conventional parametric os- cillator, these two requirements are usually met by exploiting birefringence. 5 Thus the polarizations of the fields for which the device operates are prescribed. In the microcavity para- metric oscillator however, the unusual dispersion of cavity polaritons allows them to be met irrespective of the polariza- tions. This is achieved for pump fields near to a particular ‘‘magic’’ wave vector. In this paper we study the effects of these polarization degrees of freedom.
The Arduino Uno is a microcontroller board based on the ATmega328 (datasheet). It has 14 digital input/output pins (of which 6 can be used as PWM outputs), 6 analog inputs, a 16 MHz crystal oscillator, a USB connection, a power jack, an ICSP header, and a reset button. It contains everything needed to support the microcontroller; simply connect it to a computer with a USB cable or power it with a AC-to-DC adapter or battery to get started. The Uno differs from all preceding boards in that it does not use the FTDI USB-to-serial driver chip. Instead, it features the Atmega8U2 programmed as a USB-to-serial converter. "Uno" means one in Italian and is named to mark the upcoming release of Arduino 1.0. The Uno and version 1.0 will be the reference versions of Arduino,
Non-smooth diﬀerential equations when the vector ﬁeld is only piecewise smooth, occur in various situations: in mechanical systems with dry frictions or with impacts, in control theory, electronics, economics, medicine and biology (see [–] for more references). One way of studying non-smooth systems is a regularization process consisting on approxima- tion of the discontinuous vector ﬁeld by a one-parametric family of smooth vector ﬁelds, which is called a regularization of the discontinuous one. The main problem then is to preserve certain dynamical properties of the original one to the regularized system. Ac- cording to our knowledge, the regularization method has been mostly used to diﬀerential equations with non-smooth nonlinearities, like dry friction nonlinearity (see  and a sur- vey paper ). As it is shown in [, ], the regularization process is closely connected to a geometric singular perturbation theory [, ]. On the other hand, it is argued in  that a harmonic oscillator with a jumping non-linearity with the force ﬁeld nearly inﬁnite in one side is a better model for describing the bouncing ball, rather then its limit version for an impact oscillator. This approach is used also in  when an impact oscillator is approximated by a one-parametric family of singularly perturbed diﬀerential equations, but as discussed in , the geometric singular perturbation theory does not apply.
wide applications due to these anti-ferromagnetic semi- conductor with wide gab ≈ 3.6 eV and cubic rock salt- like crystal structure [1,2]. It offers promising candida- ture for many application such as electrocatalysis , positive electrode in batteries , fuel cell , electro- chromic devices , solar thermal absorber , catalyst for oxygen evolution  and photo electrolysis . Sev- eral physical and chemical methods, such as sputtering , pulsed laser deposition , chemical bath deposi- tion [10,12] and sol-gel  have been used to obtain nickel oxide films. All these methods offer different ad- vantages depending on the application of interest and many efforts have been conduced to obtain films with the desirable physical and/or chemical properties. Among the different methods for film deposition, the relative simplicity of the spray pyrolysis method and its potential application for large area deposition make it very attrac- tive, low cost and feasible for mass production processes.
Optical Transmittance, Reflectance and Absorbance were recorded in the wavelength range (200-800)nm using computerized UV-visible spectrophotometer (Shimadzu UV-1601 PC). Optical transmittance, reflectance and absorbance were reported in order to study the effect of doping on the parameters under investigation.
In particular we demonstrated conditions for minimi- zation of stationary as well as cyclostationary noise. Also the jitter noise introduced in the positioning of the pulsed bias is taken into account and its relation with noise pro- jections on the eigenvectors is determined. Minimization conditions were formulated using parameters of the pro- posed model for the pulsed bias class, allowing to di- rectly infer the circuit design. Finally the analytical re- sults are compared with a dedicated simulator, showing that proposed criteria for noise reduction are congruent with observed trend in the simulated PDS.
Finally we note that the theory can immediately be gen- eralized in two ways. First of all, strictly speaking, Eqs. ~ 7 ! and ~ 8 ! which we used to obtain the theoretical results and the computer simulation data shown in Figs. 2–8, do not apply away from range ~ 3 ! ; and the full theory discussed in Appendix A should then be used. However, in the most in- teresting range of T where the dependence of the SHS on noise intensity is nonmonotonic, the amplitudes of vibration of the oscillator at the overtones of the eigenfrequencies v (E) are small for energies E & T, and the simple theory of Sec. II provides a good approximation. Second, the numeri- cal algorithm @ 12 # used to evaluate the spectral density of fluctuations, and thus the linear susceptibility ~ 9 ! , is limited to resonant frequencies where Q (0) ( v ) has a peak. General analysis of the linear susceptibility requires a complete solu- tion of the appropriately modified Fokker-Planck equation. We have developed the necessary algorithm, and details will be given in a later paper.
time scale of the performed experiment. The observed square root scaling with the number of atoms N, see Fig. 4.5, as well as the nearly homogeneous spatial distribu- tion of excited Rydberg atoms strongly suggests that this is the case, see Fig. 4.4 b. The last condition is met because the effective two-photon wave vector is orthogo- nal to the atomic plane, as both excitation beams are counter-propagating along the z-direction. This implies that no phase gradients or spin waves are imprinted during excitation, contrary to the case when the laser excitation is performed transverse to the extent of the atomic sample . As the atoms are in their respective motional ground states in the optical lattice, motional dephasing can also be excluded. Therefore we assume that the phase is stable, up to irrelevant global fluctuations. Furthermore, a dominating phase dynamically accumulating during the Rabi-oscillation dynamics can be excluded on the grounds of the visibility of the Ramsey fringe, which would be strongly damped in such a case. Under these three assumptions, it is clear that following the same arguments as in the introductory paragraph 4.2, the system dy- namics is constrained to the two symmetric states | G i and | W i . All N − 1 other states with maximally a single excitation are not coupled by the light and therefore do not contribute to the oscillation but rather dephase the Rabi oscillations [219, 220]. Con- sequently, the oscillatory dynamics has to occur in the subspace spanned by | G i and | W i , and the prepared state has maximal overlap with the latter at the oscillation max- ima. This holds true even in the case of a possibly present homogeneous detuning in the experiment, which can only reduce the overlap. Thus, the measured oscillation amplitude constitutes a lower bound to the W-state overlap, demonstrating that the observed dynamics in our experiment is incompatible with classical product states. Similarly, the W-state overlap can also be deduced from the contrast of Ramsey fringes, which has been accomplished in the fully blockaded regime in reference .
should be noted that in study , the authors considered the equation of the fractional oscillator with an external stabilizing inertial effects. It would be interesting to con- sider the Equation (1) subject to an external force, ac- cording to this work, and then proceed to the considera- tion of (1) with a random external force.
Nanoscale dielectric structures have recently attracted significant interest for optical waveguiding and enhanced light absorption [1-8] utilizing low loss and geometry- dependent leaky modes [9-14]. This strong Mie-like resonance results from the excitation of large displacement currents inside the dielectric cavity. They are thus ideal candidates for a broad range of applications, such as light-trapping in solar cells [15, 16] and enabling optical antennas for ultra-compact photodetectors [13, 16, 17]. In particular, owing to their small feature sizes, the fundamental resonance property of deep-subwavelength dielectric structures is leaky. This is in contrast to the interface dominated surface plasmon (SP) type effects present in their metallic counterparts [18-23]. The significant extension of the electric near-field into the bulk environment effectively associates the spectral position of the resonance to the surrounding refractive index, opening up the possibility for such structures to be used for sensing applications via time and cost efficient optical signal transduction methods.
than the surface of the crystal, to prevent shorting of the conducting ends of the crystal which would be brought about by the condensed metal. The sens- ing crystal inside the microscope was driven by a small circuit placed just out- side the microscope. The driving circuit was in turn connected to another circuit which comprised a frequency comparator unit which could read the frequency of the quartz crystal oscillator before and after the deposition of the adsorbate and gave a direct digital reading of ∆ f f ( f is the resonance fre- quency of the crystal before the deposition of the adsorbate and ∆ f is the dif- ference in the frequency of the oscillator after and before the deposition of the adsorbate on the crystal). The mass added to either side of the crystal alters its resonant frequency. The frequency shift obtained for a certain thickness of the deposited film depends on the density of the deposited film  .