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Project Details
Funding Scheme : General Research Fund
Project Number : 528211
Project Title(English) : A New Method for Achieving High-Energy Mode-Locked Lasers 
Project Title(Chinese) : 實現高能量鎖模激光​​器的新方法 實現高能量鎖模激光​​器的新方法 
Principal Investigator(English) : Prof Wai, Alexander Ping-kong 
Principal Investigator(Chinese) :  
Department :
Institution : The Hong Kong Polytechnic University
E-mail Address : alex.wai@polyu.edu.hk 
Tel :  
Co - Investigator(s) :
Prof Kutz, Jose Nathan
Panel : Engineering
Subject Area : Electrical & Electronic Engineering
Exercise Year : 2011 / 12
Fund Approved : 386,900
Project Status : Completed
Completion Date : 14-3-2014
Project Objectives :
Engineering the cavity nonlinear loss to produce high energy pulses: to design and optimize the cavity nonlinear loss using the proposed iterative geometric model to produce high energy pulses in fiber mode-locked lasers using different mode-locking mechanisms,
Master equation: To develop the corresponding modified average master equation which can capture the essential features of pulses dynamics and multi-pulse instability in fiber mode-locked lasers with different mode-locking mechanisms,
Reduced model: To develop the corresponding reduced model which incorporates the essential discrete components to describe the pulses dynamics and multi-pulse instability in fiber mode-locked lasers with different mode-locking mechanisms, and
Connecting it all together – theory, simulation, and experiments: To carry out experiments in fiber mode-locked lasers with different mode-locking mechanisms and compare the results of the corresponding master equations, reduced models, and iterative geometric models with the experimental results.
Abstract as per original application
(English/Chinese):
通過超短高能量激光脈衝的發展，超快科學到目前為止已經產生了兩位諾貝爾學獎：分子過渡態的觀察和頻率計量的研究。隨著脈衝長度的進一步減少和脈衝能量的進一步提高, 預計會有更多的研究成果產生。另外, 高能量超快激光器在精密加工和衛生保健方面也被廣泛應用。 超短高能量的光脈衝源有助於超快科學的進步。因為光被限制在波導中，所以仔細對準光腔並不是必需的。正因為這一點,相對於固態激光器, 光纖激光器具有重大的現實優勢。光纖的發展潛力已經推動了近二十年的研究，但由於光纖激光器產生的脈衝能量和長度的限制,相對於固體激光器,短脈衝光纖激光器只發揮了非常小的作用。近幾年關於脈衝傳播的物理學新見解提供了飛秒光纖激光器的脈衝能量和峰值功率的數量級的增加。因此，設計節能,低成本, 可與現有的固態激光器競爭的短脈衝光纖激光器, 是有重大的現實意義的。然而,在腔內的能量比較大時，用於產生短脈衝的鎖模機制不再適用或單個脈衝分割成多個脈衝。這種所謂的多脈衝不穩定（MPI）的規定是對一個單脈衝鎖模能量的一個根本的限制。理論和實驗還證明了, 在多脈衝不穩定附近的一個窄的參數範圍內可以觀測到週期或混沌的行為。近日，我們提出一個迭代技術(提供了對於整個多脈衝隨著腔內能量增加的過渡行為一個簡單的幾何描述)。該模型可以捕捉實驗中觀察到的所有關鍵功能，包括週期性和混沌鎖模地區，更重要的是它提供了寶貴的見解(可以最大限度地提高光纖激光器的性能，即提高光纖激光器的鎖模脈衝能量)。 雖然對於大多數光纖激光器的配置，由於大多數光纖激光器離散和周期的性質, 要從激光動力學數值模擬中提取十分準確的結果是仍然困難的。所以將激光動態減少為可以由主方程描述的單個變量，是仍然重要的。並且，其理論研究成果可用於描述鎖模動力學特徵。研究激光動態的另一個有價值的方法是使用由主方程簡化而得到的低維方程。在這個項目中，我們建議使用從迭代的幾何描述中獲得的洞察力去聯繫主方程，降階模型和迭代模型，以指導以光纖激光器產生高能量超快脈衝的實驗。我們將調查商業上最成功的光纖激光器配置之一（使用偏振片和波片的被動鎖模實驗）。我們還將研究其他的被動鎖模模式，如使用非線性光纖環鏡的模式。其主要目標是產生能源與固態激光器相媲美，甚至高於固態激光器的超短脈衝光纖激光器。
Realisation of objectives:
Summary of objectives addressed:
Objectives Addressed Percentage achieved
1.Engineering the cavity nonlinear loss to produce high energy pulsesYes100%
2.Master equationYes100%
3.Reduced modelYes100%
4.Connecting it all togetherYes100%
A. Engineering the cavity nonlinear loss to produce high energy pulses: In the project, we used the proposed iterative geometric model to study a laser cavity mode-locked either by nonlinear polarization rotation using a set of waveplates and passive polarizer or nonlinear optical loop mirrors. We engineered the nonlinear loss in the laser cavity by incorporating a second set of waveplates and polarizer or nonlinear loop mirror into the respective laser cavity. The combination of the two transfer functions can form a more sophisticated transfer function which is capable of producing a multi-pulsing instability and chaotic dynamics suppressing behavior in the laser cavity which are responsible for limiting the energy of a single pulse. In both of the mode locking mechanisms investigated, by optimizing a single parameter the pulse energy per round trip can be doubled when compared with the laser cavity using only a single mode-locking mechanism. Global optimization of the laser output energy has been attempted but proven to be rather difficult because of the number of parameters involved. Much effort has been spent to determine if the multipulsing instability can be eliminated completely for example by adding more waveplates and polarizers or nonlinear optical loop mirrors. The computation complexity of the problem grows rapidly with the number of nonlinear loss added. We have managed to show analytically that the multipulsing instability cannot be eliminated in the case of using only two sets of waveplates and polarizer. Nevertheless, the objective to demonstrate that the cavity nonlinear loss can be engineered to produce high energy pulses is 100% achieved B. Master equation: For both mode-locking mechanisms investigated in this project, we had derived the partial differential equation governing the pulse evolution inside the fiber laser by assuming the laser operates near equilibrium such that the change in the laser pulse in each round trip is small and the discrete changes in the pulse shape and energy can be approximated by a derivative. We approximated the nonlinear transfer function of each of the discrete component, i.e. the amplifier, the fiber, and the nonlinear loss mechanism by Taylor expansion. We have also included the effect of birefringence. The resulting partial differential equation is in the form of vector Ginsburg-Landau equation. The equations were studied both analytically and numerically. The simulation results are compared with that obtained from the discrete geometric model. This objective is 100% achieved. C. Reduced model: For both mode-locking mechanisms investigated in this project, we used the projection operator method rather than the Lagrangian method to derive the reduced model, because the projection operator method does not require the use of a Lagrangian function. We have applied the reduced model to both the discrete geometric model and the master equation. In the discrete model, the reduced model is applied to the each individual component, and so it results in a discrete reduced model. The results from the reduced models are then compared with those from the master equation as well as the discrete geometric model. We found that the reduced models work reasonable well and can predict the multi-pulsing instability threshold in most cases. This objective is also 100% achieved. D. Connecting it all together – theory, simulation, and experiments: We have carried out experiments in both mode locking mechanisms. We have observed energy enhancement up to 60% when compared to the case when a single mode-locking mechanism is used. The discrepancy is not unexpected as the geometric models, the master equations, and the reduced models all involved many approximations making them difficult to make quantitative predictions of a real laser cavity. Thus this objective is considered 100% achieved.
Research Outcome
Major findings and research outcome: We have proposed a general design and engineering principle that can potentially realize the goal of making fiber based lasers directly competitive with solid state devices. The technique is feasible and easy to implement without requiring a new cavity design paradigm. We showed that the cavity nonlinear loss can be engineered to produce high energy pulses. Although the results are far from the desired order-or-magnitude increase, it does suggest a clear method by which multi-pusling instability can be suppressed and the pulse energies can be easily increased. By sweeping a single parameter, an increase of 100% was easily in two different modelocking mechanisms when compared to that when only a single nonlinear polarization rotation or nonlinear optical loop mirror is used. Further engineering and optimization of the transmission functions by tuning the various parameters are expected to lead to further significant increases. This is the first major finding of this project. In the last three decades, theoretical study of lasers, fiber lasers in particular, has been dominated by using the so-called master equation which governs the near equilibrium laser dynamics for a laser cavity made up of discrete as well as non-discrete components. We developed an insightful way to consider the effects of dual transmission curves in the cavity through a geometrical model. The geometric model assumes that pulse shaping mechanisms in the cavity have balanced each other and focuses on the energy aspect of the cavity dynamics. Although the geometrical model is a highly idealized, its simplicity allows many of the key features associated with multi-pulse instability and its suppression to be highlighted. The predictions made with the geometric model hold in the full cavity simulation dynamics using the master equation. The success of the geometric model is another key finding of this project. The results of this project have attracted the attention of the laser modeling community. We had made four invited presentations. Of particular mention is the recent invitation of the PI by the Optical Society of America (OSA) to speak in an OSA internal workshop entitled “Incubator on Quantitative Modelling of Frequency-comb Sources” held in the OSA Headquarters in Washington D.C., United States. It is a gathering of the leading lasers scientists and engineers around the world to discuss the feasibility of quantitative modelling of lasers as frequency-comb sources. The PI was invited because of the recognition on the work achieved in this project.
Potential for further development of the research
and the proposed course of action:		 The success of the project opens up a different approach in the qualitative modeling of laser dynamics. An obvious way forward is the optimization of pulse output energy when more than one set of mode locking mechanisms are used to engineer the nonlinear loss of the cavity. First, more sophisticated optimization algorithms can be adopted to cope with the increase in the computation complexity when the number of mode-locker increases. Second, different type of nonlinear loss elements such as nonlinear polarization, nonlinear optical loop mirrors, carbon nanotubes, graphene, etc. can be combined in various ways and numbers in the search for the “ideal” nonlinear transfer function that can eliminate the onset of multi-pulsing stability and onset of chaotic dynamics. It will also be of particular interests, even within the limitation of the geometric model to determine analytically whether the multipulsing instability can be eliminated completely in any given laser configuration. Another direction of investigation, which is gaining popularity in the laser modeling community, is to carry out detail modeling, not just using the highly idealized geometric model, of the laser cavity in the attempt to match quantitatively the results from simulation with experiments.
Layman's Summary of
Completion Report:		 It is the goal of the fiber laser community to surpass the performance of solid state laser performance. Modeling and simulation are powerful tools in helping design next generation fiber lasers. Theoretical studies allow us to suggest concrete techniques for suppressing the ubiquitous multipulsing instabilities limitations. In this project, we studied both theoretically and experimentally a laser cavity mode-locked by a set of waveplates and passive polarizer or by a nonlinear optical loop mirror. We demonstrated that the pulse energy can be increased by incorporating a second set of waveplates and polarizer or a second nonlinear optical loop mirror in the respective laser cavity. The two nonlinear transmission functions acting in combination can be engineered so as to suppress the multi-pulsing instability responsible for limiting the single pulse per round trip energy in a myriad of mode-locked cavities. Theoretically, the sweeping of a single parameter showed that the energy can doubled. Further engineering and optimization of the transmission functions is expected to lead to further increases. Experimentally, about 60% energy increase is observed. The results suggest a general design and engineering principle that can potentially realize the goal of making fiber based lasers directly competitive with solid state devices.
Research Output
Peer-reviewed journal publication(s)
arising directly from this research project :
(* denotes the corresponding author)
Year of
Publication		 Author(s) Title and Journal/Book Accessible from Institution Repository
2011 Feng Li,* Edwin Ding, Nathan Kutz, and P. K. A. Wai  "Dual transmission filters for enhanced energy in mode-locked fiber lasers," Optics Express, Vol. 19, Issue 23, pp. 23408-23419  No 
2014 Feng Li* and P. K. A. Wai  "Energy enhancement in mode-locked fiber lasers by using multiple nonlinear optical fiber loop mirrors," Chin. Opt. Lett. 12, 2–5.  No 
Recognized international conference(s)
in which paper(s) related to this research
project was/were delivered :
Month/Year/City Title Conference Name
July 2012, Korea F. Li, Edwin Ding, J. Nathan Kutz, and P.K.A. Wai, “Pulse Energy Enhancement in Mode Locked Lasers with Cascaded Nonlinear Polarization Rotation”  17th OptoElectronics and Communications Conference (OECC’2012) 
June 2012 Colorado Springs, Colorado USA J.N. Kutz, F. Li, A.P.K.A. Wai, E. Ding, “Multiple transmission filters for enhanced energy in mode-locked fiber lasers,”  Advance Photonics Congress: Signal Processing in Photonics Communications (SPPCom) 
June 2012, Seattle, Washington, USA (invited talk) P. K. Alex Wai and Feng Li, Edwin Ding, and Nathan Kutz, “Engineering the Laser Cavity Transmission for Enhanced Energy in Mode-locked Fiber Lasers,”  2012 SIAM Conference on Nonlinear Waves and Coherent Structures, Mini Minisymposia: Modeling and Dynamics of Mode-Locked Lasers 
September 2012, Shenzhen, China (invited talk) P. K. A. Wai and Feng Li, Edwin Ding, and Nathan Kutz, “Engineering the Laser Cavity Transmission for Enhanced Energy in Mode-locked Fiber Lasers,”  Sino-Danish Photonics Workshop 
August 11-14, 2014, University of Cambridge, UK (Invited talk) Feng Li, J. Nathan Kutz, and P. K. A. Wai, “Pulse Energy Enhancement of Mode Locked Fiber Laser by Cascading Nonlinear Polarization Rotation,”  2014 SIAM Conference on Nonlinear Waves and Coherent Structures, Minisymposia: Modeling of Optical Combs and Low-Noise Opto-Electronic Sources 
November 19-21, 2014, Washington, DC, USA (Invited talk) Alex Wai, Feng Li, and J. Nathan Kutz “Dynamics of mode-locked fiber lasers,”  OSA Incubator on Quantitative Modelling of Frequency-comb Sources 
Other impact
(e.g. award of patents or prizes,
collaboration with other research institutions,
technology transfer, etc.):		 The project facilitates collaboration between Prof. J. Nathan Kutz of the University of Washington in the United States with the PI at The Hong Kong Polytechnic University leading to joint journal and conference publications. The work from this project has led to four invited presentations. Of particular mention is the recent invitation of the PI by the Optical Society of America to speak in an internal workshop entitled “Incubator on Quantitative Modelling of Frequency-comb Sources” held in the OSA Headquarters in Washington D.C., United States. It is a gathering of the leading lasers scientists and engineers around the world to discuss the feasibility of quantitative modelling of lasers as frequency-comb sources. The PI was invited because of the recognition on the work achieved in this project.
  SCREEN ID: SCRRM00542