下载文档原格式
Dear Sir or Madam,I am writing to express my dissatisfaction regarding the quality of the English course I have recently enrolled in at our university.I believe it is imperative that the issues I have encountered are addressed promptly to ensure the educational experience for all students is of the highest standard.Firstly,I have noticed that the course materials provided are outdated and do not align with the current syllabus.This has led to confusion and a lack of clarity in understanding the course objectives.The outdated textbooks do not cover the latest trends and methodologies in the field of English language teaching,which is a significant drawback for students aiming to excel in their studies.Secondly,the teaching methods employed by the course instructor are not conducive to an interactive and engaging learning environment.The lectures are monotonous and lack the necessary stimulation to maintain student interest.The absence of group discussions, practical exercises,and reallife examples makes it difficult for students to apply the concepts learned in class to realworld scenarios.Moreover,the assessment criteria for the course are unclear and inconsistent.The grading system seems arbitrary,and there is a lack of transparency in how the final grades are determined.This has caused anxiety among students,as they are unsure of what is expected of them to succeed in the course.Additionally,the lack of timely feedback on assignments and exams is another area of concern.Students are left in the dark about their performance and areas of improvement, which hinders their ability to learn and grow academically.Constructive criticism and prompt feedback are essential for students to understand their strengths and weaknesses and to work on improving their skills.Lastly,the course schedule is not flexible and does not accommodate the diverse needs of students.Many students have parttime jobs or other commitments,and the rigid timetable makes it challenging for them to balance their academic and personal lives.A more flexible approach to scheduling would greatly benefit the students and enhance their overall learning experience.In light of these concerns,I kindly request that the university administration takes immediate action to address these issues.I suggest the following steps be taken:1.Update the course materials to reflect the current syllabus and incorporate the latesttrends in English language teaching.2.Encourage the course instructor to adopt more interactive and engaging teaching methods,such as group discussions,practical exercises,and reallife examples.3.Clarify the assessment criteria and ensure transparency in the grading system.4.Provide timely and constructive feedback on assignments and exams to help students understand their performance and areas for improvement.5.Review the course schedule and consider implementing a more flexible timetable to accommodate the diverse needs of students.I am confident that by addressing these concerns,the university can enhance the quality of the English course and provide a more fulfilling educational experience for all students.Thank you for your attention to this matter.I look forward to a prompt and positive response.Yours sincerely,Your Name。
Writing an essay in English without plagiarizing requires a combination of creativity, critical thinking,and a thorough understanding of the topic.Here are some steps to ensure your essay is original and wellcrafted:1.Understand the Topic:Begin by thoroughly understanding the topic you are given. This will help you form your own thoughts and arguments,which are essential for original writing.2.Research:Conduct extensive research using various sources such as books,academic journals,and reputable websites.Make sure to take detailed notes and always cite your sources to avoid accidental plagiarism.3.Develop a Thesis Statement:Your thesis statement is the central argument of your essay.It should be clear,concise,and unique to your perspective on the topic.4.Outline Your Essay:Before you start writing,create an outline to organize your thoughts and structure your essay logically.This will help you ensure that your essay flows well and that each paragraph supports your thesis.5.Write in Your Own Words:When writing your essay,always express your ideas in your own words.If you need to quote or paraphrase from a source,make sure to properly cite it to give credit to the original author.e Paraphrasing Techniques:If you need to include information from a source that is not easily rephrased,use paraphrasing techniques to put the information into your own words while maintaining the original meaning.7.Cite All Sources:Proper citation is crucial in avoiding plagiarism.Whether you are quoting,paraphrasing,or summarizing,always provide a citation to the original source.8.Revise and Edit:After writing your first draft,revise your essay to check for clarity, coherence,and consistency.Edit for grammar,punctuation,and spelling errors.e Plagiarism Detection Tools:Before submitting your essay,use plagiarism detection software to ensure that your work is original.These tools can help you identify any unintentional plagiarism.10.Get Feedback:Share your essay with peers,teachers,or mentors to get feedback on its originality and quality.They can provide valuable insights and suggestions for improvement.Remember,the goal is not only to avoid plagiarism but to produce a wellresearched, thoughtful,and original piece of writing that demonstrates your understanding and analysis of the topic.。
Selfimprovement is the key to embarking on a new journey.It is a continuous process that involves setting goals,acquiring knowledge,and developing skills to enhance ones capabilities and adaptability in various aspects of life.Firstly,setting clear and achievable goals is the starting point of selfimprovement.Goals provide direction and motivation,helping individuals to focus their efforts and measure their progress.It is essential to break down longterm goals into smaller,manageable tasks to make the journey less overwhelming.Secondly,acquiring knowledge is crucial for personal growth.Reading books,attending workshops,and taking online courses are some of the ways to expand ones knowledge base.Continuous learning helps individuals stay updated with the latest trends and developments in their field,making them more competitive and valuable in the job market.Thirdly,developing skills is an integral part of selfimprovement.Skills can be categorized into hard skills,such as technical expertise,and soft skills,such as communication and leadership.Identifying areas of improvement and actively working on them can significantly enhance ones performance and increase the chances of success. Moreover,embracing change and being adaptable are essential for personal growth.The world is constantly evolving,and individuals who can adapt to new situations and learn from their experiences are more likely to thrive in their personal and professional lives. Furthermore,maintaining a positive attitude and having a growth mindset contribute to selfimprovement.Believing in ones ability to learn and grow can help individuals overcome challenges and setbacks,fostering resilience and determination.Lastly,seeking feedback and being open to constructive criticism are vital for selfimprovement.Feedback provides valuable insights into ones strengths and weaknesses,allowing for targeted development and growth.In conclusion,selfimprovement is a journey that requires setting goals,acquiring knowledge,developing skills,embracing change,maintaining a positive attitude,and seeking feedback.By committing to this process,individuals can unlock their full potential and achieve success in various aspects of life.。
When reflecting on past mistakes,its important to approach the topic with honesty and introspection.Heres how you might structure an essay about the mistakes youve made in English:Title:Learning from My MistakesIntroduction:Begin by setting the context for why mistakes are an inevitable part of life and how they can be valuable learning experiences.Mention that everyone makes mistakes,and its the lessons learned from them that truly matter.Paragraph1:The First MistakeDescribe a specific mistake you made in the past.For example,you might have made a grammatical error in a written assignment or spoken English test.Provide details about the situation,such as the context,your feelings at the time,and the consequences of the mistake.Paragraph2:The RealizationExplain how you came to realize your mistake.This could involve feedback from a teacher,a peer,or your own selfreflection.Discuss the emotions you felt upon realizing your error,such as embarrassment,disappointment,or even relief that you could correct it.Paragraph3:The ConsequencesDiscuss the impact of the mistake.Did it affect your grade?Did it lead to a misunderstanding or miscommunication?Reflect on how the mistake affected you and others involved.Paragraph4:The Lessons LearnedDetail the lessons you learned from the mistake.This could include understanding the importance of proofreading,practicing more,or seeking help when needed.Explain how you applied these lessons to improve your English skills.Paragraph5:The ImprovementDescribe the steps you took to correct the mistake and prevent similar errors in the future. This might involve creating a study plan,using new learning resources,or developing better habits for language practice.Paragraph6:The GrowthReflect on how the experience of making and learning from the mistake has contributedto your personal growth.Discuss any changes in your attitude towards learning,your approach to challenges,or your resilience in the face of setbacks.Conclusion:Conclude by summarizing the key points of your essay.Reiterate the importance of learning from mistakes and how it has helped you become a better English learner.End on a positive note,expressing gratitude for the opportunities that mistakes provide for growth and learning.Sample Sentences:The moment I realized my mistake,I felt a rush of embarrassment,but it was quickly replaced by a determination to learn from it.Understanding the root of my error helped me to develop a more systematic approach to English grammar.I now make a conscious effort to review my work and seek feedback,ensuring that I dont repeat the same mistakes.Through this experience,Ive learned that mistakes are not just inevitable they are opportunities for growth and selfimprovement.Remember,the purpose of this essay is not only to recount a mistake but also to demonstrate personal growth and the positive changes that resulted from the experience.。
In the modern era of digital technology,the practice of sending red envelopes, traditionally a Chinese New Year custom,has been adapted to the digital realm and is now a common occurrence,even during class time.While this can be seen as a fun and engaging way to interact with students,there are several pros and cons to consider when discussing the practice of sending red envelopes during class.Advantages of Sending Red Envelopes During Class:1.Enhanced Engagement:Red envelopes can serve as a motivational tool to increase student participation and engagement in the classroom.The excitement of receiving a digital reward can make students more attentive and eager to participate in class activities.2.Cultural Integration:For students learning about Chinese culture,sending red envelopes can be an immersive way to experience a traditional custom firsthand.It can also foster a sense of community and inclusivity among students of different cultural backgrounds.3.Instant Gratification:In an age where immediate feedback is valued,digital red envelopes provide instant gratification,which can be a positive reinforcement for good behavior or performance.4.Incentive for Learning:They can be used as a reward for academic achievements or asa means to encourage students to complete tasks or assignments,thereby promoting a culture of learning and achievement.5.Technological Integration:Incorporating digital red envelopes into the classroom can help students become more comfortable with technology and its applications in various aspects of life,including education.Disadvantages of Sending Red Envelopes During Class:1.Distraction:The process of sending and receiving red envelopes can be distracting, taking students focus away from the lesson at hand.The noise and visual distraction can disrupt the learning environment.2.Inequality:Not all students may have access to the necessary technology or financial means to participate in this practice,leading to a sense of exclusion or inequality among students.3.Misuse of Funds:There is a risk that funds meant for educational purposes could bemisused or lead to unhealthy competition among students,focusing more on the monetary reward than on learning.4.Dependency on Technology:Relying on digital methods for rewards can create a dependency on technology for motivation,which may not be sustainable or effective in the long run.5.Potential for Cheating:The digital nature of red envelopes could potentially be exploited by students who might find ways to manipulate the system to gain an unfair advantage.6.Diminishing the Value of Learning:If students come to expect monetary rewards for their efforts,they may begin to view learning as a transactional process rather than an intrinsic pursuit of knowledge and personal growth.In conclusion,while the use of digital red envelopes in the classroom can offer some innovative ways to engage students,it is essential to weigh the potential benefits against the possible cators must consider the broader implications of integrating such practices into the learning environment and ensure that they align with the educational goals and values of the institution.。
Instant gratification is a concept that has gained significant attention in modern society,particularly with the rise of technology and the internet.This phenomenon refers to the desire for immediate results or rewards without any delay or effort.It has become a prevalent aspect of our culture,influencing various aspects of our lives,from our work habits to our personal relationships.The digital age has made it easier than ever to access information and entertainment at our fingertips.With smartphones,social media,and instant messaging,we are constantly bombarded with notifications and updates that demand our attention.This constant stream of information can lead to a sense of impatience and an expectation that everything should be available to us instantly.One of the most significant impacts of instant gratification is on our ability to focus and maintain concentration.When we are used to receiving immediate feedback and rewards, it becomes challenging to engage in tasks that require sustained effort and delayed gratification.This can lead to a decrease in productivity and a lack of satisfaction in our work and personal lives.Moreover,instant gratification can also affect our emotional wellbeing.The constant need for immediate rewards can lead to a sense of dissatisfaction and unhappiness when we are unable to meet these expectations.This can result in feelings of frustration, anxiety,and even depression.However,it is essential to recognize that instant gratification is not inherently negative. In some cases,it can lead to increased motivation and a sense of accomplishment.For example,the ability to quickly access information and resources can help us make informed decisions and solve problems more efficiently.To strike a balance between instant gratification and longterm goals,it is crucial to develop selfdiscipline and patience.This can be achieved by setting realistic expectations, breaking down larger tasks into smaller,manageable steps,and rewarding ourselves for our progress along the way.In conclusion,while instant gratification has become a prominent feature of our modern lives,it is essential to recognize its potential drawbacks and develop strategies to maintain a healthy balance.By cultivating patience and selfdiscipline,we can harness the benefits of instant gratification while also working towards our longterm goals and aspirations.。
In the modern era,the prevalence of smartphones has transformed the way we communicate,access information,and entertain ourselves.However,this technological advancement has also given rise to a new phenomenon known as smartphone addiction. This essay will explore the reasons behind this addiction,its consequences,and potential solutions to mitigate its impact on individuals and society.Reasons for Smartphone Addiction1.Convenience:Smartphones offer a myriad of functions in a single device,from social media to gaming,shopping,and more.This convenience makes it easy for users to become reliant on their devices for daily activities.2.Instant Gratification:The instant feedback provided by notifications and the ability to access information quickly can create a sense of satisfaction and reward,reinforcing the habit of using smartphones excessively.3.Fear of Missing Out FOMO:Social media platforms on smartphones can create a fear of missing out on the latest trends,news,or social interactions,compelling users to constantly check their phones.4.Multitasking Illusion:Many people believe they can multitask effectively with their smartphones,but this often leads to a decrease in productivity and an increase in screen time.Consequences of Smartphone Addiction1.Physical Health Issues:Prolonged use of smartphones can lead to physical health problems such as eye strain,poor posture,and even conditions like texting thumb.2.Mental Health Impact:Excessive use of smartphones has been linked to increased levels of anxiety,depression,and sleep disturbances due to the constant exposure to digital stimuli.3.Social Isolation:While smartphones connect us with the world,they can also lead to social isolation as people spend more time interacting with their devices than with real people.4.Impaired Cognitive Function:Overreliance on smartphones for information and communication can diminish our ability to remember information and engage in deep, critical thinking.Solutions to Mitigate Smartphone Addiction1.Digital Detox:Encouraging periods of time without using smartphones can help individuals regain control over their digital habits.2.App Usage Monitoring:Utilizing features that track and limit app usage can help users become more aware of their screen time and make conscious efforts to reduce it.3.Mindful Use:Being mindful of when and why we use our smartphones can help us make more intentional decisions about our digital interactions.cation and Awareness:Raising awareness about the potential harms of smartphone addiction through education campaigns can help individuals recognize and address their habits.5.Support Systems:Encouraging the development of support systems,such as family or community groups,can provide a network for individuals to share their experiences and seek help in managing their smartphone use.In conclusion,while smartphones are an integral part of modern life,it is crucial to recognize the potential for addiction and its negative effects.By understanding the reasons behind this addiction and implementing strategies to manage our use,we can enjoy the benefits of technology while mitigating its potential harms.。
雅思小作文意见反馈英文回答：In my opinion, feedback is essential for personal growth and improvement. It provides valuable insights and perspectives that can help us identify our strengths and weaknesses. Feedback can come in various forms, such as constructive criticism, praise, or suggestions for improvement. It is important to be open-minded and receptive to feedback, as it can help us develop our skills and reach our full potential.Receiving feedback can sometimes be challenging, especially if it is negative or critical. However, it is important to remember that feedback is not a personal attack, but rather an opportunity for growth. It is crucial to approach feedback with a positive mindset and view it as a chance to learn and improve.One example of the importance of feedback is in theworkplace. When I was working on a team project, my colleague provided me with feedback on my presentation skills. Initially, I felt defensive and took the feedback personally. However, after reflecting on it, I realizedthat the feedback was valid and could help me become a better presenter. I took the feedback into consideration and made changes to my presentation style. As a result, my subsequent presentations were more engaging and effective.Another example is receiving feedback on my writing. When I shared my essay with a friend, they pointed out areas where my arguments were weak and needed further development. Although it was disheartening to hear, I appreciated their honesty and took their feedback on board.I revised my essay and strengthened my arguments, resulting in a higher quality piece of writing.Overall, feedback plays a crucial role in personal growth and improvement. It provides us with valuable insights and perspectives that we may not have considered. By being open-minded and receptive to feedback, we can learn from our mistakes, develop our skills, and reach ourfull potential.中文回答：在我看来，反馈对于个人的成长和进步至关重要。
Improving ones abilities on a daily basis is a crucial aspect of personal development. Here are some strategies and insights that can be incorporated into an English essay on this topic:1.Setting Clear Goals:Start by defining what abilities you want to improve.Be specific about the skills you wish to develop,whether its language proficiency,technical skills,or soft skills like leadership and communication.2.Creating a Daily Routine:Establish a routine that includes time for learning and practicing new skills.Consistency is key to making progress and forming habits that lead to improvement.3.Learning from Various Sources:Diversify your learning resources.Read books,watch educational videos,attend workshops,and engage in online courses to broaden your knowledge base.4.Practical Application:Apply the skills you learn in reallife situations.Theoretical knowledge is valuable,but practical experience solidifies understanding and enhances proficiency.5.Seeking Feedback:Constructive feedback is essential for growth.Dont hesitate to ask for opinions from mentors,peers,or even clients to understand your strengths and areas for improvement.6.Embracing Challenges:Step out of your comfort zone and take on tasks that challenge your current abilities.This will push you to learn and adapt quickly.7.Reflecting on Progress:Regularly assess your progress.Reflect on what youve learned, how youve applied it,and what the outcomes have been.This selfassessment can guide your future learning strategies.8.Staying Updated:In a rapidly changing world,its important to stay current with new developments in your field.Subscribe to relevant newsletters,follow industry leaders on social media,and participate in webinars.working:Build relationships with people who share your interests or work in your working can open doors to new opportunities and provide a support system for learning.10.Maintaining a Growth Mindset:Cultivate an attitude that embraces learning andviews challenges as opportunities for growth rather than setbacks.11.Taking Care of Your Health:A healthy body supports a healthy mind.Ensure you get enough sleep,eat a balanced diet,and engage in regular physical activity to keep your mind sharp and focused.ing Technology:Leverage technology to enhance your learning.There are numerous apps and tools designed to help with learning languages,managing time,and organizing information.13.Teaching Others:One of the best ways to solidify your own understanding is to teach what youve learned to others.It forces you to organize your thoughts and can provide new perspectives on the material.14.Celebrating Small Wins:Recognize and celebrate small victories along the way.This helps to maintain motivation and a positive attitude towards the learning process.15.Continual Learning:Adopt a lifelong learning mindset.The pursuit of knowledge and skill development should not be limited to formal education but should continue throughout ones life.By integrating these strategies into your daily life,you can effectively work towards enhancing your capabilities and achieving personal and professional growth.Remember, the journey of selfimprovement is a marathon,not a sprint,and it requires patience, dedication,and a commitment to continuous learning.。
Giving Constructive Feedback: The Art ofHelping Others GrowIn the realm of interpersonal communication, offering constructive feedback is a crucial skill that can significantly enhance the growth and development of individuals. It involves providing opinions or suggestionsin a manner that is both respectful and beneficial, aimingto foster positive change rather than criticize or belittle. As we navigate through the complexities of social interactions, particularly in an academic setting like the eighth grade, understanding how to deliver constructive feedback effectively becomes paramount.The foundation of giving constructive feedback lies in the establishment of a positive and open dialogue. Itbegins with active listening, a skill that allows us tofully comprehend the perspective and needs of theindividual we are offering feedback to. By listening attentively, we demonstrate respect and create a safe space for honest and candid conversations. This, in turn, fosters a sense of trust and openness, laying the groundwork for effective feedback exchange.Once a positive dialogue is established, it isessential to frame the feedback in a positive and encouraging manner. Instead of focusing on the negatives or pointing out flaws, we should highlight the strengths and achievements of the individual. This approach serves to boost their confidence and motivate them to continuestriving for improvement. For instance, rather than saying, "You made a lot of mistakes in your essay," we can say, "I noticed that you have a unique perspective in your writing. If you could work on your grammar and punctuation, your essays would be even more impressive."Furthermore, specificity is key when providing feedback. Vague or general comments tend to lack impact and may notbe as effective as specific and targeted suggestions. It is helpful to identify specific areas that require improvement and provide clear examples to illustrate the point. This allows the recipient to understand exactly what needs to be addressed and how they can go about making the necessary changes.However, it is also crucial to strike a balance between being constructive and respectful. Feedback should never bedelivered in a manner that is insulting or demeaning. We must remember that the goal is to help the individual grow and improve, not to belittle or humiliate them. It is important to phrase our suggestions in a way that is both honest and encouraging, focusing on the potential for growth rather than dwelling on past mistakes.Moreover, the timing and delivery of feedback are equally important. Providing feedback promptly, while the issue is still fresh in the mind, can be more effective than waiting for a later time. Additionally, delivering feedback in a private and confidential manner can ensure that the recipient feels comfortable and secure, allowing them to fully absorb and process the information.In conclusion, giving constructive feedback is an art that requires sensitivity, honesty, and a genuine desire to help others grow. By establishing a positive dialogue, framing feedback positively, being specific, respectful, and timely, we can provide valuable insights that foster positive change and personal development. As we continue to navigate the complexities of social interactions in the eighth grade and beyond, mastering this skill will serve uswell in building strong relationships and fostering mutual growth.**给别人意见的艺术：助力他人成长**在人际交往中，提供建设性反馈是一项至关重要的技能，它可以极大地促进个人的成长和发展。
Instabilities in a grating feedback external cavitysemiconductor laserDijun Chen, Zujie Fang, Haiwen Cai, Jianxin Geng, and Ronghui QuShanghai Institute of Optics and Fine Mechanics,Chinese Academy of Sciences, Shanghai 201800, Chinadjchen@Abstract: Output power fluctuations in a grating external cavity diode laserwith Littman configuration are described, showing peculiar chaoticbehaviors of self-pulsation at the L-I curve kink points. Different spectralcharacteristics with multiple peaks are observed at upper and lower state ofthe self-pulsation. It is found also that P-N junction voltage jumps in a samepace with the pulsation. The observed phenomena reflect competitionbetween different longitudinal modes, and transient variation of transversemodes in addition. These experimental results may contain informationabout the mechanisms of the chaotic instability in strong filtered feedbacksemiconductor lasers.©2008 Optical Society of AmericaOCIS codes:(140.2020) Diode lasers, (270.3100) Instabilities and chaos, (270.2500)Fluctuations, relaxations, and noise.References and links1.R. Lang and K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection LaserProperties,” IEEE J. Quantum Electron. 16, 347-355 (1980).2. D. Lenstra, B. Verbeek, and A. den Boef, “Coherence collapse in single-mode semiconductor lasers due tooptical feedback,” IEEE J. Quantum Electron. 21, 674-679 (1985).3.R. Tkach and A. Chraplyvy, “Regimes of feedback effects in 1.5-um distributed feedback lasers,” J.Lightwave Technol. 4, 1655-1661 (1986).4.J. Mørk, B. Tromborg, J. Mark, and V. Velichansky, “Instabilities in a laser diode with strong opticalfeedback,” Proc.SPIE 1837, 90-104 (1992).5.J. Mørk, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: Theory andexperiment,” IEEE J. Quantum Electron. 28, 93-108 (1992).6. A. Hohl, H. van der Linden, and R. Roy, “Determinism and stochasticity of power-dropout events insemiconductor lasers with optical feedback,” Opt. Lett. 20, 2396-2398 (1995).7. A. Hohl and A. Gavrielides, “Bifurcation Cascade in a Semiconductor Laser Subject to Optical Feedback,”Phys. Rev. Lett. 82, 1148-1151 (1999).8. E. Detoma, B. Tromborg, and I. Montrosset, “Frequency and time domain analysis of an external cavitylaser with strong filtered optical feedback,” Proc. SPIE 5452, 283-290 (2004).9.T. Führer and T. Walther, “Extension of the mode-hop-free tuning range of an external cavity diode laserbased on a model of the mode-hop dynamics,” Opt. Lett. 33, 372-374 (2008).10.K. Green and B. Krauskopf, “Bifurcation analysis of a multi-transverse-mode VCSEL,” Proc. SPIE 6997,69970O1-9 (2008).11.T. Paoli, “Nonlinearities in the emission characteristics of stripe-geometry (AlGa)As double-heterostructure junction lasers,” IEEE J. Quantum Electron. 12, 770-776 (1976).12.N. Chinone, “Nonlinearity in power-output-current characteristics of stripe-geometry injection lasers,” J.Appl. Phys. 48, 3237-3243 (1977).13.T. Zachos and J. Ripper, “Resonant Modes of GaAs Junction Lasers,” IEEE J. Quantum Electron. 5, 29-37(1969).14.H. Kressel and J. Butler, Semiconductor lasers and hetero-junction LEDs (Academic Press, 1977), Chapter5, p. 172.15.Y. Mitsuhashi, J. Shimada, and S. Mitsutsuka, “Voltage change across the self-coupled semiconductorlaser,” IEEE J. Quantum Electron. 17, 1216-1225 (1981).#99093 - $15.00 USD Received 18 Jul 2008; revised 5 Sep 2008; accepted 15 Sep 2008; published 10 Oct 2008 (C) 2008 OSA13 October 2008 / Vol. 16, No. 21 / OPTICS EXPRESS 170141. IntroductionLasers with a single optical frequency and narrow line-width are used and to be used widely in various important applications such as high precision measurement, laser cooling, and atomic physics researches. For this purpose a lot of efforts have been spent on researches of external cavity semiconductor lasers. The stability of such single frequency laser is of particular importance in order to meet application requirements. Instabilities of semiconductor lasers have long been one of the interesting research topics, especially for the lasers with external feedback. ng and K.Kobayashi[1] presented a systematic study on the effects of external optical feedback; since then much work[2-4] were published on theoretical and experimental studies of laser diodes with various feedback levels. The laser with external feedback is also considered as a typical example of optical chaos, and has attracted many researchers. J. Mørk et al.[5] summarized researches on chaos of semiconductor laser with optical feedback. A.Hohl et al.[6,7]described power-dropout phenomena and bifurcation cascade in semiconductor lasers. E. Detoma et al. [8] presented studies on laser diode with strong filtered optical feedback.In this letter we present experimental studies on instability and chaotic phenomena of an external cavity semiconductor laser with a Littman configuration. We observed that there are several dips in the L-I curve, and the output power at the dips jumped between three levels, resulting in self-pulsation with periods changing between millisecond and microsecond. By using a scanning Fabry-Perot etalon, we observed multi-peaks at the kinks, the numbers and intervals of the peaks were different between upper level and lower level of the self-pulsation, while a good single mode was always measured outside the kinks. A CCD camera was used to record the far field patterns. It is shown that the transverse distribution of the laser beam intensity changed at the kinks. We also measured jumps of the P-N junction voltage under a well stabilized current on the laser diode. A qualitative explanation and discussion on these phenomena will be given in the letter. We believe that these observations will be helpful not only in improving the device performances, but also for understanding optical chaos in the laser.2. Experimental setup and resultsThe semiconductor laser being investigated in this work is a grating feedback external cavity laser with a typical Littman configuration, working at wavelength of 780nm, as shown in Fig.1 schematically. The laser (Toptica LD-0780-0100-AR-1) is AR-coated with facet reflectivity down to 10-4; the grating with line constant of 1800mm-1 (Newport 05HG1800-500-1) is placed and fixed at an incident angle of 70o to the laser beam, which was collimated by a lens (Thorlabs C230TM-B, f=4.51mm, NA=0.55) with output beam width of about 3mm. The total cavity length is about 40mm, which sets the longitudinal mode spacing to be around 3.75 GHz; a piezo transducer-driven high reflectivity mirror is used to tune the cavity length.Fig. 1. A schematic diagram of the external cavity Fig. 2. A typical L-I curve of the ECDL with three dips.laser with Littman configuration.#99093 - $15.00 USD Received 18 Jul 2008; revised 5 Sep 2008; accepted 15 Sep 2008; published 10 Oct 2008 (C) 2008 OSA13 October 2008 / Vol. 16, No. 21 / OPTICS EXPRESS 17015The laser is packaged in a copper block, and cooled and stabilized by a TE cooler at 22o C with stability of 1mK. The injection DC current can be well-stabilized with stability of better than 1μΑ/hour. Fig. 2 shows a typical L-I curve of the ECDL, showing that its threshold is about 35mA and the output power is around 55mW at 180mA. The laser works in a single longitudinal mode for most range of the pumping current, and can be tuned over 20GHz without mode-hopping, which is limited by the piezo driving voltage. The optical frequency can be stabilized by using a rubidium cell and feedback circuits, resulting in a stability of below 1MHz.The L-I curve in Fig. 2 shows a wavelike feature, which is typical for an external cavity laser just as described in Ref. 1. It is noticed, however, that there are sharp dips near I=130, 145 and 180mA; and the laser shows abnormal behaviors at these dips.Firstly the output power fluctuates periodically as shown in Fig. 3 at I ~130mA. Among them Fig. 3(b, c, d, e, f) are from the same oscilloscopic waveform of Fig. 3(a), but with time scales successively reduced as (a) 100ms/div, (b) 20ms/div, (c) 2ms/div, (d) 500μs/div, (e) 50μs/div, and (f) 10ms/div, among which (f) is the enlarged waveform at the falling edge of the pulse. The power fluctuation shows self-pulsation behaviors with some obvious features.(1) The output power fluctuates in stepwise with rather sharp and clear edges. (2) The power fluctuation appears with different temporal features. The lowest is in tens-millisecond range, and with basically equal period, while the highest is in several-microsecond range. (3) The power jumps between three discrete levels in a range of between ~35 and ~40mW, showing a feature of bifurcation. (4) In the middle level, the power fluctuates with basically equal amplitude and varied period, which decreases monotonically and then increases inversely, and repeat a few times, i.e. 6 times in Fig. 3(b).(a) (b)(c) (d)(e) (f)Fig. 3. Self-pulsation waveforms with different time scales: (a) 100ms/div, (b) 20ms/div, (c)2ms/div, (d) 500μs/div, (e) 50μs/div, (f) 10ms/div .The output fluctuation at L-I dips of I ~145 and 180mA show a little bit different behaviors as shown in Fig. 4, where the output jumps periodically, and basically between two levels, whereas rarely to the third level. The ratio of durations at upper level and lower level (C) 2008 OSA 13 October 2008 / Vol. 16, No. 21 / OPTICS EXPRESS 17016#99093 - $15.00 USD Received 18 Jul 2008; revised 5 Sep 2008; accepted 15 Sep 2008; published 10 Oct 2008varies with the injection current as shown in Fig. 4(a) and (b) for two typical examples. These behaviors show typical chaos characteristics, but with different feature from that reported in previous Ref.s.(a) (b)Fig. 4. Self-pulsation waveforms at the second kink: (a) and (b) for two injection currentswith difference around 1mA. Time scale: 100ms/div.To understand the mechanism in detail, we measured the spectrum at the self-pulsations by using a scanning Fabry-Perot etalon (Toptica FPI-100, FSR=1GHz, F>300). Fig. 5(a) shows the spectra together with the power level; Fig. 5(b) is another spectrum together with the voltage on the PZT. It is noticed that there are fewer peaks with higher amplitude at upper output level than at lower level, and the intervals between the peaks are measured to be around 170MHz for upper output level and ~40MHz for lower level. In addition, the peaks in spectrum for lower level appear in groups, and the interval between groups is near the interval for upper level. As a comparison, Fig. 5(c) shows a single mode spectrum in stabilized output case. Taking different orders of scanning F-P etalon into account, the peaks for the upper level could be attributed to different longitudinal modes; while the minor peaks in groups for lower level might be attributed to transverse modes.(a)(b)(c)Fig. 5.(a), (b) Spectrum at upper and lower output levels measured by a scanning F-P etalon (c)Spectrum at injection current region out-of the kinks, with an inclined line of scanning voltage.#99093 - $15.00 USD Received 18 Jul 2008; revised 5 Sep 2008; accepted 15 Sep 2008; published 10 Oct 2008 (C) 2008 OSA13 October 2008 / Vol. 16, No. 21 / OPTICS EXPRESS 17017To make sure if there is any change of the transverse mode at kinks, a CCD camera was used to record far field patterns. Figure 6(a) and (b) are the patterns for upper and lower power levels respectively. Figure 6(c) gives their difference which is simply calculated by a Matlab program, where red and blue regions stand for positive and negative values, and yellow for near zero values. In comparison, the far-field patterns outside the kink were also measured. Figure 6(d) is the difference between patterns for two different current outside the kinks, where blue stands for near zero value, indicating that the patterns have different amplitudes but same distribution. It is shown that the transverse distribution of the laser beam intensity changes at the kinks indeed.(a) (b)(c) (d)Fig. 6. Far-field patterns for upper(a) and lower(b) output level at kinks. (c) Differencebetween patterns (a) and (b). (d) Difference between far-field patterns outside the kinks.Furthermore we measured the P-N junction voltage of the LD chip during the fluctuation, as shown in Fig. 7, where the output power curve was recorded simultaneously.It is shown that the voltage jumps in the same pace with the output power, that is, the voltage jumps to a higher level when the output jumps upper, and with an almost same speed. The voltage step was measured to be ~2mV, where the amplification of electronic circuit had been calibrated. Fig. 8 gives magnified curves of the output and junction voltage variation with the injection current near one of the kinks at ~180mA. It is shown that output and voltage jump simultaneously at the kink. Normally the voltage goes up with the current, whereas jumps down at the kink; meanwhile, the output power goes down slowly with the current near the kink, but goes down much faster at the kink.3. DiscussionsThe above measured and observed results indicate that the grating feedback external cavity laser operates in chaotic instability at the injection current of kinks. It is necessary to point out that the kink positions may move around and the chaotic behaviors may change a lot, when the temperature of ECDL module is changed. It is widely recognized that there are five #99093 - $15.00 USD Received 18 Jul 2008; revised 5 Sep 2008; accepted 15 Sep 2008; published 10 Oct 2008 (C) 2008 OSA13 October 2008 / Vol. 16, No. 21 / OPTICS EXPRESS 17018Fig. 7. Junction voltage (upper blue) and power (lower pink) fluctuations.p o w e r (a r b . u n i t )current (mA)Fig. 8. Junction voltage (red triangle) and power (black square) varied with injection current.states for semiconductor lasers with external feedback, corresponding to five regions in space of feedback level vs. injection current[3,5]. Our external cavity semiconductor laser is believed to work in the fifth state with strong feedback and large injection current, which should be a well stabilized single mode state; but may fall in chaos at the boarder with the fourth region. The theory presented by R. Lang[1] has been widely referred for cases of weak feedback; but it has to be revised for strong feedback case.Many Ref.s on diode lasers with external feedback have studied chaotic instabilities for weak feedback and low injection current[1,2,5], that may be of practical importance in applications such as optical communications. In our external cavity laser the reflectivity of the AR-coated LD chip facet,222r R =, is in the order of 10-4, while the reflectivity of the grating for the first order diffraction is measured to be %40≈g R ; thus the condition 1/)1(22<<−RR R ext for Lang’s formulas is not valid. Ref. 8 analyzed chaos in external cavity lasers with strong filtered optical feedback. The external feedback grating and the AR-coated facet are now composed to be a complex mirror with an effective reflectivity as[8]: 22()(())/(1())i i e g g r r r e r r e ωτωτωωω−−=++,where the reflectivity of the grating has a Lorentzian form of 10()(1()/)g g g r r i ωωωω−=+−Δ;g ωis the peak feedback frequency of the grating; the band width Δω is inversely proportional to the beam width at the grating; and c l e /2=τis the round trip time in the external cavity section. The lasing condition should now be expressed as: 1]2)exp[(1=−−nkl i l g r r e α, where r 1 is the reflectivity of LD chip rear facet; l is the length of chip. Both of gain g and index n are functions of frequency ω, carrier density N , and photon number P , and of junction temperature as well. In the laser with a cavity composed of grating feedback external cavity and internal semiconductor F-P cavity, the grating not only modifies gain spectrum, but also induces frequency-related phase shift at reflection. Offset between gain peak g ωand cavity resonance 0ωdecides the operating mode; and causes also mode hopping, as analyzed in [9].(C) 2008 OSA 13 October 2008 / Vol. 16, No. 21 / OPTICS EXPRESS 17019#99093 - $15.00 USD Received 18 Jul 2008; revised 5 Sep 2008; accepted 15 Sep 2008; published 10 Oct 2008Very few papers on instability analysis have involved the influence of transverse modes. Ref. 10 analyzed bifurcation in VCSELs due to multi-transverse-mode subject to weak external feedback. Although most diode laser chips are designed and fabricated for the fundamental transverse mode, they may get into multiple transverse mode states transiently. It is conjectured that the carrier distribution might be disturbed to deviate from its stable state at L-I kinks. L-I curve kink phenomena were observed earlier [11], and were explained to originate from transverse gain depletion or gain profile deformation [11,12], which may result in higher order transverse modes, and in mode competition as well. Ref. 13 described spectra of a multi-transverse mode diode laser, showing a typical mode spacing of 0.018nm between the first order and fundamental transverse modes, which is about one tenth of the longitudinal mode spacing; and a theory based on a model of Hermite-Gaussian transverse mode was given. A detailed analysis is given in Ref. 14. Since index in semiconductor is a function of carrier density, the carrier distribution variation will lead to a change of effective index and the resonance frequencyωtoo. The experimental results of this paper indicate that the effectof transverse modes should be taken into consideration in understanding the chaotic instability.The junction voltage jump may be a new observed phenomenon. Ref. 15 described voltage change in self-coupled diode lasers, which was induced by external feedback but in stable output state. As well known, junction voltage is a function of temperature, but the transition observed in this work is so fast that it can hardly be explained by temperature change in the active region. The injection current was monitored to be stable with variation below 1μA, so the voltage jump can not be attributed to the current. A constant current means a stable injected rate of electron number, whereas increasing of output photons should imply decreasing of total electron number in the active volume due to stimulated recombination. On the other hand, junction voltage is usually an ascending function of carrier density. So usually a higher output power means a lower junction voltage when the injection current is fixed. Therefore the observed phenomena shown in Fig. 7 and 8 seem contradictory with what is mentioned above.Ref. 15 proposed mechanisms to explain the voltage change with the feedback. One of them is the photoconduction effects by the return beam irradiating the active region and its vicinity, which would lower the series resistance, and thus the voltage. In our ECDL, transiently varied transverse mode distribution induces an expanded near field distribution, and a larger irradiated area surrounding the active region, which will lower the voltage due to the photoconduction, and perhaps the photovoltaic effect as well. On the other hand it causes a lower feedback coupling coefficient and a lower output power. The accompanied voltage jump found at self pulsation state may provide internal information on mechanism of the chaotic instability. More work is surely needed to get an exact and detailed explanation for the phenomena.4. ConclusionIn conclusion, results of experimental study on chaotic instabilities in a grating external cavity diode laser with Littman configuration are presented in the letter. Peculiar behaviors of self-pulsation are described, showing complicated chaotic features at the L-I kinks. Spectral characteristics and far-field patterns are recorded for different output level, which can be attributed to competitions of longitudinal modes and variations of transverse mode distribution. It is observed that junction voltage jumps in the same pace with the output power, which may provide more information to explain observed chaotic instabilities.It is required in practical applications that the ECDL can work stably in a large output range and a large tunable frequency range; and the instabilities should be avoided as far as possible. The observed phenomena presented in this letter may provide information not only for understanding internal mechanisms of the chaos, but also for improving ECDL performances practically. Further work should be done both on theoretical simulation and more experimental observations.#99093 - $15.00 USD Received 18 Jul 2008; revised 5 Sep 2008; accepted 15 Sep 2008; published 10 Oct 2008 (C) 2008 OSA13 October 2008 / Vol. 16, No. 21 / OPTICS EXPRESS 17020。
