We present an ab initio treatment of the steady-state of lasers with injected signals that describes a regime, valid for microlasers, in which the locking transition is dominated by cross saturation and spatial hole burning. The theory goes beyond standard approaches and treats multimode lasing with injected signals and finds the possibility of partially locked states and as well as repulsion of the free-running frequencies from the injected signal. The theory agrees well with exact integration of the full wave and matter equations for the system. It can also describe accurately complex modern lasers structures and is applied to the example of deformed disk lasers. We show that in the case of a one-dimensional cavity in the locked or regenerative amplifier regime the theory reduces to an improved version of the Adler equations in the appropriate limit.
We present an ab initio treatment of the steady-state of lasers with injected signals that describes a regime, valid for microlasers, in which the locking transition is dominated by cross saturation and spatial hole burning. The theory goes beyond standard approaches and treats multimode lasing with injected signals and finds the possibility of partially locked states and as well as repulsion of the free-running frequencies from the injected signal. The theory agrees well with exact integration of the full wave and matter equations for the system. It can also describe accurately complex modern lasers structures and is applied to the example of deformed disk lasers. We show that in the case of a one-dimensional cavity in the locked or regenerative amplifier regime the theory reduces to an improved version of the Adler equations in the appropriate limit.
In this thesis we generalize and extend the steady-state ab initio laser theory (SALT), first developed by Türeci and Stone, and apply it problems in laser design. SALT as first formulated modeled the gain medium as identical two-level atoms, leading to the well-known Maxwell Bloch laser equations. The result is a set of coupled non-linear wave equations that treats the openness of the cavity exactly and the non-linear modal interactions to infinite order. Most gain media have more than two atomic levels, and in this thesis we generalize the SALT equations to treat realistic and complex gain media, specifically N-level atomic media with a single lasing transition, N-level atomic media with multiple lasing transitions and semiconductor gain media with particle-hole band excitations. The extension to multiple transitions requires fundamentally enlarging the set of SALT equations, by adding a set of population equations that must be solved self-consistently with the non-linear wave equations for the lasing modes in standard SALT. In addition, the population equation can be generalized to treat gain diffusion, an important problem in a number of laser systems, not treated in SALT or in most earlier laser theories. The semiconductor version (Semi-SALT) includes the continuum of particle-hole transitions and the effect of Pauli blocking of transitions, but is only developed and applied in the free-carrier approximation. The resulting theory is termed complex SALT (C-SALT). We also demonstrate how to incorporate amplification and injected signals naturally within the SALT framework, yielding injection SALT (I-SALT). The generalization to I-SALT leads to a larger set of self-consistent coupled non-linear wave equations, a set for the lasing modes and a set for the injected and amplified fields, coupled through cross gain saturation. It clearly distinguishes the lasing modes, which correspond to poles of the scattering matrix, from the injected fields, which do not; in this limit the locking of a lasing mode corresponds to the injected signal forcing the lasing pole off the real axis, reducing its amplitude to zero. I-SALT is shown to reduce to a version of the standard Adler theory of injection-locked lasing in a certain limit (the single pole approximation). We apply SALT to design a highly multimode cavity for use as a spatially incoherent light source for applications to imaging and microscopy. Laser illumination typically leads to coherent artifacts that degrade optical images; this can be alleviated by having a very large number of modes 500) which are spatially independent and average out such artifacts. We used SALT to model a D-shaped laser cavity with chaotic ray dynamics and showed that a certain shape greatly increases the number of lasing modes for the same cavity size and pump strength, due to a flat distribution of Q-values and reduced mode competition. An on-chip electrically-pumped semiconductor laser was realized using this cavity design and showed negligible coherent artifacts in imaging, as well as much better efficiency and power per mode than traditional incoherent light sources such as LEDs. The thesis also goes beyond semiclassical laser theory to treat quantum noise and the laser linewidth in a SALT-based approach. We demonstrate that SALT solutions can be used in conjunction with a temporal coupled mode theory (TCMT) to derive an analytic formula for the quantum limited laser linewidth in terms of integrals over SALT solutions. This linewidth formula is a substantial generalization of the well-known Schawlow-Townes result and includes all previously known corrections: the Petermann factor, Henry alpha factor, incomplete inversion factor and the "bad cavity factor". However, unlike previous theories these corrections are not simply multiplicative and are not separable in general. The predictions of TCMT linewidth theory are tested quantitatively by means of an FDTD algorithm that includes the Langevin noise as a source term.
The master-equation theory for multimode semiconductor lasers [A. Eschmann and C. W. Gardiner, Phys. Rev. A 54, 760 (1996)] is adapted to treat the case of an injection-locked laser. Both the intensity noise and the phase noise of the system are examined. A decrease in the total intensity noise and in the inten- sity noises of the individual modes is found for increasing injection power, provided the injection signal does not dominate the entire system. A regime is found in which a reduction of the intensity noise below the shot noise level is obtained which is not single-mode squeezing, but which is due to anticorrelations between the individual modes, and a further regime in which true single-mode squeezing exists is also found. The phase noise is found to decrease with increasing injection strength, in other words as phase locking occurs. \textcopyright{} 1996 The American Physical Society.
The theory of the laser amplifier is developed for conditions in which the strength of the input signal is increased from small values, where the amplification is linear, to larger values, where the amplification becomes nonlinear. The below-threshold laser amplifier oscillates at a single frequency equal to that of the input signal, and its properties are found by solution of the nonlinear equation of motion for the single excitation amplitude. For the above-threshold laser amplifier, the effects of the nonlinear behavior are to shift the laser frequency from its free-running value and to transfer intensity from the laser line to the signal frequency and to a range of satellite lines, whose frequency detunings are integer multiples of the signal detuning. The intensities of the various emission lines of the laser are calculated by power-series expansions of the field amplitudes up to terms of fourth order in the input signal strength. The onset of injection locking is determined by the conditions for which the intensity at the shifted free-running laser frequency falls to zero. The injection-locked state is characterized by a single excitation frequency equal to that of the input signal, and its properties are found by solution of the same nonlinear equation of motion as for the below-threshold amplifier. The ranges of input signal strength and detuning are determined for which the injection-locked state is stable. The energy conservation properties of the laser amplifier are considered for each of its operating states. \textcopyright{} 1996 The American Physical Society.
We derive and test a generalization of the steady-state ab initio laser theory (SALT) to treat complex gain media. The generalized theory (C-SALT) is able to treat atomic and molecular gain media with diffusion and multiple lasing transitions, and semiconductor gain media in the free carrier approximation including fully the effect of Pauli blocking. The key assumption of the theory is stationarity of the level populations, which leads to coupled self-consistent equations for the populations and the lasing modes that fully include the effects of openness and non-linear spatial hole-burning. These equations can be solved efficiently for the steady-state lasing properties by a similar iteration procedure as in SALT, where a static gain medium with a single transition is assumed. The theory is tested by comparison to much less efficient finite difference time domain (FDTD) methods and excellent agreement is found. Using C-SALT to analyze the effects of varying gain diffusion constant we demonstrate a cross-over between the regime of strong spatial hole burning with multimode lasing to a regime of negligible spatial hole burning, leading to gain-clamping, and single mode lasing. The effect of spatially inhomogeneous pumping combined with diffusion is also studied and a relevant length scale for spatial inhomogeneity to persist under these conditions is determined. For the semiconductor gain model, we demonstrate the frequency shift due to Pauli blocking as the pumping strength changes.
Abstract : A semiclassical analysis of injected lasers with stable and unstable resonators and arbitrary outcoupling fractions was performed. Homogeneously broadened lasers with Fabry-Perot and with positive branch, confocal unstable resonators were modeled. Both time-dependent and steady-state analyses of free-running and injected lasers were performed. Because of deficiencies in the standing wave semiclassical and the simple saturable gain models, a new semiclassical theory of homogeneously broadened lasers were developed. The theory is predicted upon the following assumptions: the atoms are two-level, a single longitudinal mode exists in the cavity, the transverse mode structure can be adequately modeled by the geometric optics mode, and the laser electric fields can be described by a pair of counterpropagating planar, cylindrical, or spherical traveling waves with different amplitudes. A general semiclassical theory was first developed, and then specialized to the Fabry-Perot and positive branch, confocal unstable resonator cases. Both the Maxwell-Bloch and rate equation approximation forms of the theory were derived. The general theory is sufficiently broad to allow the modeling of the geometric optics mode of any standing wave resonator configuration. The theory was shown to reduce to the simple saturable gain and standing wave semiclassical models in the appropriate limits. The analysis of the injected lasers were performed with the new semiclassical theory. Both time-dependent and steady-state analyses were performed.
We improve the steady-state ab initio laser theory (SALT) of T\"ureci et al. by expressing its fundamental self-consistent equation in a basis set of threshold constant flux states that contains the exact threshold lasing mode. For cavities with nonuniform index and/or nonuniform gain, the new basis set allows the steady-state lasing properties to be computed with much greater efficiency. This formulation of the SALT can be solved in the single-pole approximation, which gives the intensities and thresholds, including the effects of nonlinear hole-burning interactions to all orders, with negligible computational effort. The approximation yields a number of analytic predictions, including a ``gain-clamping'' transition at which strong modal interactions suppress all higher modes. We show that the single-pole approximation agrees well with exact SALT calculations, particularly for high-Q cavities. Within this range of validity, it provides an extraordinarily efficient technique for modeling realistic and complex lasers.