Unidirectional Ring Resonator Research Articles

Rate equation analysis for deterministic and unidirectional lasing in ring resonators with an S-shaped coupler

Ring resonators are traditionally popular optical devices that apply to various components in photonic ICs. They also play an important role in the on-chip generation of many novel optical states in topological systems and non-Hermitian systems. Unidirectional lasing of ring resonators is used in many such systems to create exotic states of light including optical vortexes and optical skyrmions, but the unidirectional behavior has not been fully understood. Previous research has constructed a simplified model to explain the steady state behaviors of unidirectional ring resonators, but the carrier dynamics and spontaneous emission were omitted. In this work, we give a numerical analysis of unidirectional ring resonators with an S-shaped coupler. We identified the importance of the gain saturation to robustness against backscattering and high unidirectionality by comparing to the model without saturation. We also discuss the effect of asymmetrical coupling on the deterministic realization of unidirectionality.

A 210-GHz Magnetless Nonreciprocal Isolator in 130-nm SiGe BiCMOS Based on Resistor-Free Unidirectional Ring Resonators

Nonreciprocal components such as circulators, isolators, and gyrators play vital roles in modern communication systems. However, all of them are limited to 0.1 terahertz (THz) due to their poor performances in terms of linearity, loss, and noise at high frequency, making them not amenable for the potential sub-THz/THz operation. In this letter, a 210-GHz nonreciprocal isolator based on the resistor-free unidirectional ring resonators is implemented in a 130-nm SiGe BiCMOS process ( $f_{T}/f_{\mathrm {max}} = 300$ /500 GHz). Thanks to the proposed resistor-free ring resonators, the isolator achieves 1.40-dB loss, 6.7-dB noise figure (NF)/unit, 21.2-dB isolation, and superior linearity. Even compared with the nonreciprocal components operating at a much lower frequency, this structure also exhibits a good performance.

A 1350W Nd: YAG Unstable Ring Laser With Efficient Reverse Wave Suppression

A breakthrough result of a kW-level Nd: YAG slab laser with a unidirectional unstable ring resonator is presented. The reverse wave is efficiently suppressed by a diaphragm placed at the focal point of the negative-branch unstable ring resonator. With specifically developed multi-function sensor and precision placement of the diaphragm, we have achieved the maximum output power of 1350 W with reverse suppression ratio of 54:1 corresponding to an optical-optical efficiency of 21.6% and a slope efficiency of 33.7%. The output power is currently limited by the available pump power. To the best of our knowledge, this is the highest power demonstrated from an Nd: YAG slab laser based on an unstable ring resonator with efficient reverse wave suppression, which is a paramount step to the further development of high power solid-state unidirectional ring lasers.

Study of oscillation performance characteristics of unidirectional photorefractive ring resonators: Cavity detuning dependence

Single unidirectional photorefractive ring resonator (SUPRR) and coupled unidirectional photorefractive ring resonator (CUPRR) were considered with BaTiO3 and LiNbO3 crystals as inter-cavity photorefractive media. The relative oscillation intensity and oscillation frequency shift of two SUPRRs with BaTiO3 and LiNbO3 crystals in their cavities, and four CUPRRs with BaTiO3-BaTiO3, LiNbO3-LiNbO3, BaTiO3-LiNbO3 and LiNbO3-BaTiO3 combinations were analysed relative to cavity detuning parameters and compared the oscillation performance of SUPRR with that of CUPRR. In SUPRR, maximum value of relative oscillation intensity is found for BaTiO3 as compared to that of LiNbO3 for zero cavity detuning. In CUPRR, the oscillation intensity in secondary cavity increases with increasing cavities detuning whereas in primary cavity it decreases with increasing cavities detuning. Major finding of this study is that the BaTiO3-LiNbO3 combination of the coupled system provides the highest relative oscillation intensity.

High-power Ti:sapphire laser at 820 nm for scanning ground-based water–vapor differential absorption lidar

The Ti:sapphire (TISA) laser transmitter of the mobile, three-dimensional-scanning water-vapor differential absorption lidar (DIAL) of the University of Hohenheim is described in detail. The dynamically-stable, unidirectional ring resonator contains a single Brewster-cut TISA crystal, which is pumped from both sides with 250 Hz using a diode-pumped frequency-doubled Nd:YAG laser. The resonator is injection seeded and actively frequency-stabilized using a phase-sensitive technique. The TISA laser is operating near 820 nm, which is optimum for ground-based water-vapor DIAL measurements. An average output power of up to 6.75 W with a beam quality factor of M2<2 is reached. The pointing stability is <13 μrad (rms), the depolarization <1%. The overall optical-optical conversion efficiency is up to 19%. The pulse length is 40 ns with a pulse linewidth of <157 MHz. The short- and long-term frequency stabilities are 10 MHz (rms). A spectral purity of 99.9% was determined by pointing to a stratus cloud in low-elevation scanning mode with a cloud bottom height of ≈2.4 km.

Theoretical analysis of the effects of frequency detuning dependence of photorefractive two- beam coupling coefficient on gain and phase-shifts of the signal beam for a coupled unidirectional photorefractive ring resonators

Dependence of two-beam coupling gain and phase-shift of the signal beams on the frequency detuning for a coupled unidirectional ring resonators based on non-degenerate two-wave mixing in the photorefractive crystals have been investigated in details. The effects of various parameters characterizing the photorefractive medium such as frequency detuning, absorption strength, two-beam energy coupling strength and pump intensity of the external laser beams, on the two-beam coupling gain and phase-shift of the signal beams for a coupled UPRR have also been studied in details. It has been found that the photorefractive gain of the signal beam in the primary cavity of the coupled UPRR can be enhanced to the higher order by taking the lower value of the frequency detuning of the primary cavity which could exist at much lower value of the absorption strength of the crystal B. This higher value of photorefractive gains in the cavities are responsible for the strong coupling between the modes of the oscillations of the coupled UPRR.

Two wave mixing in nonlinear Kerr medium and its dependence on photoconductivity and dielectric properties of the medium

Two-wave mixing spectroscopy in Kerr media is shown to be a powerful technique to quantify the strong enhancement of the phase shift and gain in signal beam. The phase shift and gain in signal beam are important parameters for unidirectional ring resonator, an analytical solution for the two wave mixing gain and phase shift in signal in a nonlinear Kerr medium is presented. We have considered only non-degenerate two wave mixing by introducing the grating decay time in terms of photoconductivity and dielectric constant of the Kerr media. Effect of the oscillation frequency shift and angle between the two interfering beams on phase shift and gain of the signal beam has been studied. We have also studied the influence of photoconductivity and dielectric constant of the Kerr media on phase shift and gain of the signal beam in details.

Study of photoconductive and dielectric dependence of gain and phase-shift in the coupled unidirectional ring resonators based on non-degenerate wave-mixing in photorefractive materials

Photoconductive and dielectric dependence of gain and phase-shift in the coupled unidirectional photorefractive ring resonators (UPRR) have been analyzed for the case of non-degenerate two-wave mixing in photorefractive materials by employing the plane-wave approximation method. The effect of photoconductivity and dielectric constant of the coupled photorefractive crystals (A and B) on the gain and phase-shift in the coupled UPRR have also been studied in details. It has been found that for a given value of the photoconductivity of crystal B, the gain in the primary resonator can be enhanced by selecting lower value of frequency detuning of the same resonator and PR crystal A of higher photoconductivity in the coupled UPRR. But reverse of the case is found for the enhancement of phase-shift. Such enhancement of the gain and phase-shift in the primary resonator are responsible for build-up and non-reciprocal energy transfer between the modes of the internal oscillations, which greatly improves the performance of the coupled UPRR.

Oscillation characteristics of a coupled unidirectional ring resonators with photorefractive crystals

For a coupled unidirectional photorefractive ring resonator (UPRR), the oscillation characteristics have been studied in details in terms of the photoconductive and dielectric constant of the photorefractive (PR) crystals under the assumption of the plane-wave approximation based on non-degenerate two-wave mixing in the photorefractive materials. It has been found that the steady oscillations are possible when the two resonators oscillate independently. Using the plane-wave approximation and steady state oscillation conditions, the effect of the frequency detuning, photoconductivity and dielectric constant of the PR crystals on the relative intensity and frequency of oscillation of the secondary resonator in the coupled UPRR have been studied. It has been found that the relative oscillation frequency of the secondary resonator could be enhanced by selecting PR crystal A of higher absorption strength relative to PR crystal B and the higher photoconductivity of the crystals B as compared to that of the crystal A. Due to the non-reciprocal energy transfer between the oscillating beams and the additional PR phase-shift in the PR crystals A and B, the magnitude of the relative oscillation frequency of the secondary resonator could be controlled by the absorption strength, dielectric constant and photoconductivity of the two crystals.

&gt;400 kHz repetition rate wavelength-swept laser and application to high-speed optical frequency domain imaging

We demonstrate a high-speed wavelength-swept laser with a tuning range of 104 nm (1228-1332 nm) and a repetition rate of 403 kHz. The design of the laser utilizes a high-finesse polygon-based wavelength-scanning filter and a short-length unidirectional ring resonator. Optical frequency domain imaging of the human skin in vivo is presented using this laser, and the system shows sensitivity of higher than 98 dB with single-side ranging depth of 1.7 mm over 4 dB sensitivity roll-off.

High power high beam quality diode-pumped 1319-nm Nd:YAG oscillator-amplifier laser system

This paper demonstrated a high power and high beam quality diode-pumped 1319-nm Nd:YAG master oscillator-power amplifier laser system. A thermally near-unstable resonator with four-rod birefringence compensation flat-flat cavity was adopted as the master oscillator. A solid etalon was inserted in the unidirectional ring resonator to compress the laser linewidth. Under a repetition rate of 500 Hz and pulse width of 160 μs, the master oscillator delivers an average output power of 16.8 W at 1319 nm with linear polarisation, beam quality factor M2 = 1.16 and linewidth of 3.2 GHz. A double-pass power amplifier with two amplifier stages was employed for higher power scaling and the output power was amplified to be 25.9 W with M2 = 1.43.

Effect of photoconductivity and dielectric constant of the photorefractive materials on two-beam coupling gain and phase-shifts for a single unidirectional photorefractive ring resonator

Photoconductive dependence of two-beam coupling between the pump beam and the signal beam in photorefractive materials have been analyzed in case of non-degenerate wave mixing under the undepleted pump approximation method. During the two-wave mixing in photorefractive materials, steady state amplification of the signal beam and oscillation characteristics of a single unidirectional ring resonator has been studied. The domination of the two-beam coupling gain over the combined absorption and resonator losses such as Fresnel reflections from the crystal and imperfect mirrors builds up unidirectional oscillation. The buildup of such an oscillation leads to a saturation of the gain, which can be explained in terms of the photorefractive phase-shift. The existence of this phase-shift between the photorefractive index grating and the illumination intensity pattern, which is of characteristic of the photorefractive effect, leads to an energy transfer between the two beams. For a single unidirectional ring resonators, the effects of photoconductivity of the materials, two-beam energy coupling coefficient, dielectric constant, crystal thickness, and material's absorption coefficient on amplification of the two-beam coupling gain and photorefractive phase-shifts of the signal beam have also been studied in detail. It has been found that amplification of the signal beam and phase-shift can be enhanced by taking the photorefractive crystal having higher photoconductivity and lower dielectric constant, which improves performance of the resonators.

Oscillation dependence of two-wave mixing gain for unidirectional ring resonator in photorefractive materials

Dependence of the coupling strength of two-wave mixing gain in photorefractive materials for the single unidirectional ring resonator on oscillation conditions has been analyzed in the strong nonlinear regime. In this regime, difference between the frequency of the pump beam and oscillating beam is proportional to the cavity-length detuning, which can be explained in terms of the photorefractive phase-shift. This phase-shift results due to slightly non-degenerate two-wave mixing that compensates for cavity detuning and satisfies the round-trip phase condition for the steady-state oscillation. The presence of such a phase-shift allows the possibility of the nonreciprocal steady-state energy transfer between the pump and oscillating beams. If the gain due to the beam coupling is large enough to overcome the cavity losses then the signal beam is amplified in the presence of material absorption. Such amplification is responsible for the oscillations. For the single unidirectional ring resonator, the effects of cavity-length detuning, energy coupling coefficient, crystal thickness of the material, reflectivity of the cavity mirrors and material's absorption coefficient on the frequency and intensity of oscillations have also been studied in detail. It has been found that for the smaller value of absorption coefficient ( α) of the photorefractive crystal, the unidirectional ring resonator can oscillate at almost any cavity-length detuning (Δ Γ) whereas for the larger value of α oscillation occurs only when the cavity-length detuning is limited to small region (around Δ Γ=0). But reverse of the case is found for energy coupling coefficient ( γ 0).

Dependence of gain and phase-shift on crystal parameters and pump intensity in unidirectional photorefractive ring resonators

The steady-state amplification of light beam during two-wave mixing in photorefractive materials has been analysed in the strong nonlinear regime. The oscillation conditions for unidirectional ring resonator have been studied. The signal beam can be amplified in the presence of material absorption, provided the gain due to the beam coupling is large enough to overcome the cavity losses. Such amplification is responsible for the oscillations. The gain bandwidth is only a few Hz. In spite of such an extremely narrow bandwidth, unidirectional oscillation can be observed easily at any cavity length in ring resonators by using photorefractive crystals as the medium and this can be explained in terms of the photorefractive phase-shift. The presence of such a phase-shift allows the possibility of the non-reciprocal steady-state transfer of energy between the two light beams. Dependence of gain bandwidth on coupling constant, absorption coefficient of the material’s cavity length (crystal length) and modulation ratio have also been studied.

Nonlinear frequency conversion in coupled ring cavities

The steady-state distribution of circulating power in coupled, unidirectional ring resonators containing a diode-pumped laser crystal and nonlinear optical elements is computed. The full set of transcendental nonlinear equations describing the interactions between the circulating power and the optical elements is solved by a numerical root find function of a commercial mathematics software. The method allows computation of the output of sequential nonlinear processes such as laser gain, second harmonic generation and optical parametric amplification as a function of the input diode pump power. It is also possible to optimize the nonlinear interaction by selecting the optimum interaction cross-section or crystal length. The circulating power may thereby be re-distributed to obtain the lowest possible passive loss.

A unidirectional photorefractive ring resonator oscillating at 633 nm

We have constructed an optical resonator using a photorefractive crystal as the gain medium. The orientation of the crystal and the angle between the signal and the pump beam are chosen to obtain optimal two-wave coupling. The average output power of the resonator is proportional to the power of the pump beam for a small cavity loss, but this linear relation is broken when the cavity loss is increased. The transverse beam pattern of the signal can be controlled by intracavity apertures.

Transverse effects in photorefractive ring resonators

Transverse effects in unidirectional and bidirectional photorefractive ring resonators with high Fresnel numbers are investigated numerically. The onset of transverse-mode competition, as well as symmetry-breaking intermittent instabilities, is observed as the cavity detuning is varied. Phase relations and frequency shifts in the intracavity field, in particular, antisymmetric response with respect to the frequency shift and cavity detuning, are considered. The buildup of ordered transverse patterns whose temporal dynamics are either periodic or chaotic is followed. The temporal evolution of chaotic mode oscillation is identified as a crisis-induced intermittency at a heteroclinic tangency.

Instability of a multimode oscillation in a photorefractive ring oscillator.

A theory of multimode oscillation in an optical unidirectional ring resonator with photorefractive gain was given in the weak-field limit, in which the mode coupling is considered carefully. The characteristics of single-mode oscillation in steady state were analyzed in detail, especially when the externally applied dc electric field is not zero. By numerical simulation, we investigated a three-mode oscillation and observed instability phenomena which are similar to the periodic oscillation of several transverse family modes observed in experiment. \textcopyright{} 1996 The American Physical Society.

Signal-to-noise ratio improvement by stochastic resonance in a unidirectional photorefractive ring resonator

All-optical signal-to-noise ratio improvements by stochastic resonance have been obtained by use of the intensity bistability of a unidirectional photorefractive ring resonator. A signal-to-noise ratio gain of 10.5 dB has been obtained with a near-unity signal-to-noise ratio input signal at 6 mHz.

MODE ITINERANCY IN A PHOTOREFRACTIVE RING OSCILLATOR

A theory of multimode oscillation in an optical unidirectional ring resonator with photorefractive gain was given in the weak-field limit. In nondegenerate state, the system is stable and can be described by Lotka-Voterra equation. While the system will becomes unstable in certain circumstance owing to the mode-mode interaction in the degenerate or quasi-degenerate condition, such as the periodic alternation behavior.