scholarly journals Successive uptapering and stationary self-trapped propagation of a laser beam in a saturating nonlinear medium

1995 ◽  
Vol 13 (4) ◽  
pp. 559-567 ◽  
Author(s):  
Sarang Medhekar ◽  
Rajkamal ◽  
S. Konar
Keyword(s):  
Steady State ◽  
Laser Beam ◽  
Nonlinear Medium ◽  
Propagation Distance ◽  
Gain Medium ◽  
Gaussian Laser Beam ◽  
Steady State Analysis ◽  
Material Gain ◽  
Nonabsorbing Medium ◽  
State Analysis

A steady-state analysis of Gaussian laser beam in a nonlinear medium has been presented. It is shown that an oscillatory self-guided beam (whose width is oscillating with the propagation distance) in a saturable nonlinear medium can be uptapered by material gain. Moreover, the present investigation suggests that under certain conditions it is possible to obtain a stationary self-guided beam (planar wavefront) in a nonabsorbing medium from an initially oscillatory (nonplanar wavefront) beam in a nonabsorbing medium by uptapering it in a gain medium.

Analysis of Single Buffer Random Polling System With State-Dependent Input Process and Server/Station Breakdowns

2018 ◽  
Vol 9 (1) ◽  
pp. 22-50 ◽  
Author(s):  
Thomas Y.S. Lee
Keyword(s):  
Steady State ◽  
Linear Model ◽  
Repair Process ◽  
Polling System ◽  
Steady State Analysis ◽  
Relaxation System ◽  
Polling Model ◽  
State Dependent ◽  
Non Linear ◽  
State Analysis

Models and analytical techniques are developed to evaluate the performance of two variations of single buffers (conventional and buffer relaxation system) multiple queues system. In the conventional system, each queue can have at most one customer at any time and newly arriving customers find the buffer full are lost. In the buffer relaxation system, the queue being served may have two customers, while each of the other queues may have at most one customer. Thomas Y.S. Lee developed a state-dependent non-linear model of uncertainty for analyzing a random polling system with server breakdown/repair, multi-phase service, correlated input processes, and single buffers. The state-dependent non-linear model of uncertainty introduced in this paper allows us to incorporate correlated arrival processes where the customer arrival rate depends on the location of the server and/or the server's mode of operation into the polling model. The author allows the possibility that the server is unreliable. Specifically, when the server visits a queue, Lee assumes that the system is subject to two types of failures: queue-dependent, and general. General failures are observed upon server arrival at a queue. But there are two possibilities that a queue-dependent breakdown (if occurs) can be observed; (i) is observed immediately when it occurs and (ii) is observed only at the end of the current service. In both cases, a repair process is initiated immediately after the queue-dependent breakdown is observed. The author's model allows the possibility of the server breakdowns/repair process to be non-stationary in the number of breakdowns/repairs to reflect that breakdowns/repairs or customer processing may be progressively easier or harder, or that they follow a more general learning curve. Thomas Y.S. Lee will show that his model encompasses a variety of examples. He was able to perform both transient and steady state analysis. The steady state analysis allows us to compute several performance measures including the average customer waiting time, loss probability, throughput and mean cycle time.

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