Quantum limits to amplitude noise reduction in semiconductor lasers using weak optical feedback with dispersive loss

We calculate the field power spectrum of a Semiconductor Laser in a finite time window in presence of weak feedback and compare it with numerical simulations. The asymmetry of the side peaks, their frequency shift and the linewidth reduction are characterized. We consider the limit of very weak feedback, in which only side peaks associated with relaxation oscillations modified by the feedback appear in the spectrum.

The linewidth narrowing of a semiconductor laser due to weak optical feedback is analysed, taking into account both phase condition and threshold change for the feedback-induced modes. The achievable linewidth reduction lies in between two limiting cases, 1/(1 + X √(1 + α2))2 and 1/(1 + X)2, where α and X are the linewidth enhancement factor and the feedback parameter, respectively.

It is shown theoretically that semiconductor lasers become bistable with weak optical feedback and that the intensity noise is increased by transitions between the bistable states due to steady-state fluctuations. The bistability occurs in a narrow range of the feedback magnitude, depending on the phase of feedback light at the semiconductor facet. This is in good agreement with observed noise increase at low frequencies caused by external feedback.

Semiconductor lasers are very different from other lasers because refraction variation can't be avoided when the gain is changed. Refraction variation can be introduced the theory of semiconductor laser by a dimensional parameter. This parameter is called linewidth enhancement factor (LEF). The value of LEF is very important for many aspects of laser behavior. The LEF characterizes the linewidth broadening and chirp due to fluctuation in the carrier density. A simple method to measure the linewidth enhancement factor of laser diodes is presented in this paper. The method uses the self-mixing effect at a weak feedback level. An optical beam is reflected and injected into the laser diode cavity by an external target, and is then mixed with the light inside the cavity, causing variations of the optical output power. The waveform of the optical power is determined by the feedback factor C and the LEF. A theoretical formula to compute LEF is proposed for the case when the feedback level C is smaller than 1. The experimental results show this method is feasible and simple when a laser diode operates at single longitudinal mode.

On the theory of a single-mode laser with weak optical feedback

Characterization procedures of different types of semiconductor lasers in a typical transmission line are investigated, with particular attention paid to unavoidable low-level optical feedback. The asymmetric response between front and rear facets is compared with the symmetric response of the solitary device.

We present a simple method for narrowing the intrinsic Lorentzian linewidth of a commercial ultraviolet grating extended-cavity diode laser (TOPTICA DL Pro) using weak optical feedback from a long external cavity. We achieve a suppression in frequency noise spectral density of 20 dB measured at frequencies around 1 MHz, corresponding to the narrowing of the intrinsic Lorentzian linewidth from 200 kHz to 2 kHz. Provided additional active low-frequency noise suppression and long-term drift compensation, the system is suitable for experiments requiring a tunable ultraviolet laser with narrow linewidth and low high-frequency noise, such as precision spectroscopy, optical clocks, and quantum information science experiments.

We analyse the stability of the steady-state solutions of the compound system formed by a single-longitudinal-mode semiconductor laser and an external reflector. Of the large number of these external cavity modes (ECMs) created in pairs of modes and antimodes by moderate feedback, the antimodes are always unstable, while the modes may be stable or unstable when created. The ECMs that have a large positive frequency shift with respect to the emission frequency of the solitary laser are unstable when created. In contrast, the ECMs that have a large, negative frequency shift are stable on creation and remain stable over a relatively large feedback range. For sufficiently large feedback an ECM that is created stable gives way to a time-dependent solution (limit cycle or torus) that is localized in phase space around the ECM; several time-dependent attractors may coexist. Approximating the dynamical equations, taking into account terms up to second order, we obtain relations for the amplitudes of the oscillations of the laser variables for these attractors. The external cavity length and the injection current are key parameters which determine these amplitudes. Our approximations are in good agreement with numerical simulations, and hold even far from the bifurcation points where these attractors originate.

Compact, efficient, diode-laser-based blue light sources are useful for many applications including optical storage and laser printing. Blue light can be generated by frequency doubling the output of reliable, high-power 860-nm lasers in potassium niobate. The Second Harmonic Generation (SHG) conversion efficiency can be substantially increased by placing the nonlinear crystal inside of a resonator in order to increase the infrared intensity in the crystal.1,2,3,4 The build-up of a high infrared intensity and efficient generation of blue output requires precise frequency matching of the diode laser and the SHG resonator. Previously, electronic locking1 and weak optical feedback techniques2,3,4 have been used to maintain this frequency matching. Electronic locking has the disadvantage of requiring an optical isolator to prevent destabilization of the laser frequency by light scattered from the resonator. Weak optical feedback has the disadvantage of requiring electronic control of the phase of the optical feedback as well as precise control of the feedback amplitude.3,4 We describe the operation of an antireflection-coated GaAlAs diode laser in an extended laser cavity that contains the SHG resonator as an intracavity element. The use of an antireflection coating on the laser and strong optical feedback is intended to suppress coupled-cavity effects and produce stable operation of the laser at a single frequency that is resonant with the SHG resonator. With the extended cavity we have obtained blue output powers of up to 12.5 milliwatts.

Numerical analysis of weak optical positive feedback (OPF)controlling chaos is studied in a semiconductor laser. The physical model ofcontrolling chaos produced via modulating the current of semiconductor laseris presented under the condition of OPF. We find the physical mechanism thatthe nonlinear gain coefficient and linewidth enhancement factor of the laserare affected by OPF so that the dynamical behaviour of the system can beefficiently controlled. Chaos is controlled into a single-periodic state, adual-periodic state, a tri-periodic state, a quadr-periodic state, apenta-periodic state, and the laser emitting powers are increased by OPF insimulations. Lastly, another chaos-control method with modulating theamplitude of the feedback light is presented and numerically simulated tocontrol chaotic laser into multi-periodic states.

We report the first experimental observation of the route to chaos for semiconductor lasers with weak optical feedback. For increasing feedback level, the laser undergoes a quasiperiodic route interrupted by frequency locking, which is also predicted by a comprehensive numerical analysis. Experiments further demonstrate the occurrence of quantum-noise-induced transitions between two attractors with different relaxation oscillation frequencies. The attractors are created by two subsequent Hopf bifurcations of the same external cavity mode.

The transient dynamics of a single-mode semiconductor laser subjected to both weak optical feedback and light injection is studied. Even at detuning values for which injection locking is not effective, turn-on jitter and frequency jitter can still be strongly reduced by adjusting either the length of the external cavity or the detuning.

The authors have studied the numerical response of a singlemode semiconductor laser under modulation of the injection current in the presence of optical feedback for different external cavity lengths. They have restricted the experiment to the nonreturn-to-zero modulation scheme and a modulation frequency of 10 Gbit/s. Observations are made that for short cavities (a few millimetres) the eye diagram aperture and the frequency chirp depend strongly on the phase of the reinjected field. Conversely, for cavity lengths of a few centimetres (pig-tail sizes) neither the eye aperture nor the frequency chirp are appreciably affected by the feedback.

We present an experimental observation of the output responses of a Nd:YAG microchip laser with an anisotropic external cavity under weak optical feedback. The feedback mirror is stationary during the experiments. A pair of acousto-optic modulators is used to produce a frequency shift in the feedback light with respect to the initial light. The laser output is a beat signal with 40 kHz modulation frequency and is separated into two orthogonal directions by a Wollaston prism. Phase differences between the two intensity curves are observed as the laser works in two orthogonal modes, and vary with the external birefringence element and the pump power. Theoretical analyses are given, and the simulated results are consistent with the experimental phenomena.

On-chip integration of semiconductor lasers have shown a growing interest in recent years, especially for the development of photonic integrated circuits (PICs) which are of paramount importance for high-speed communication within and between data centers, and fast on-board data exchanges. For all these applications, a key challenge remains the stability of the laser sources integrated on a PIC in presence of external optical feedback with the view to avoid integrated bulky and costly optical isolation. In this study, the effects of external optical feedback are investigated in hybrid InAs/InP quantum dot comb lasers on silicon. The design of the cavity includes a semiconductor optical amplifier section, a saturable absorber and an on-chip external cavity incorporating a vertical coupler. We measured the resulting feedback properties with respect to the operation conditions (bias current and voltage) and to the length of the saturable absorber. We show that under most operating conditions, the laser remains stable against optical feedback, only few regimes of operation occur, which either improve or degrade the frequency comb and/or the radio-frequency beatnote power of the laser.